$1,100 per month for 10 years, if the account earns 2% per year What the student or parent is asking is: If they deposit $1,100 per month in a savings/investment account every month for 10 years, and they earn 2% per year, how much will the account be worth after 10 years? Deposits are monthly. But interest crediting is annual. What we want is to match the two based on interest crediting time, which is annual or yearly. 1100 per month. * 12 months in a year = 13,200 per year in deposit Since we matched interest crediting period with deposits, we now want to know: If they deposit $13,200 per year in a savings/investment account every year for 10 years, and they earn 2% per year, how much will the account be worth after 10 years? This is an annuity, which is a constant stream of payments with interest crediting at a certain period. [SIZE=5][B]Calculate AV given i = 0.02, n = 10[/B] [B]AV = Payment * ((1 + i)^n - 1)/i[/B][/SIZE] [B]AV =[/B]13200 * ((1 + 0.02)^10 - 1)/0.02 [B]AV =[/B]13200 * (1.02^10 - 1)/0.02 [B]AV =[/B]13200 * (1.2189944199948 - 1)/0.02 [B]AV =[/B]13200 * 0.21899441999476/0.02 [B]AV = [/B]2890.7263439308/0.02 [B]AV = 144,536.32[/B]

$1.40 pays for 30 minutes of parking. How long can you park for with $2.80? Immediately, I see that $2.80 is $1.40 * 2 Which means, if $1.40 pays for 30 minutes of parking $1.40 * 2 = $2.80 means $2.80 pays for 30 minutes * 2 = [B]60 minutes or 1 hour [/B] [I]Double the rate means double the time you can park[/I]

$100 fee plus $30 per month. Write an expression that describes the cost of a gym membership after m months. Set up the cost function C(m) where m is the number of months you rent: C(m) = Monthly membership fee * m + initial fee [B]C(m) = 30m + 100[/B]

$100 is invested in a bank account that gives an annual interest rate of 3%, compounded monthly. How much money will be in the account after 7 years? 7 years * 12 months per year = 84 periods. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=100&nval=84&int=3&pl=Monthly']compound interest calculator[/URL], we get an account balance of: [B]123.34[/B]

$1000 is invested with interest at a rate of 15% per year for 9 years. Find the amount you would have, if it’s continuously compounded Using [URL='https://www.mathcelebrity.com/simpint.php?av=&p=1000&int=15&t=9&pl=Continuous+Interest']our balance calculator[/URL], we get: [B]$3,857.43[/B]

$13 in the bank. You write a check for $17. What is your balance? When you write a check, it's a debit against your account, which means we subtract. So we start with $13. We subtract $17 Our balance is $13 - $17 = [B]-$4[/B]

$2,030.00 was invested at 10% per annum compounded annually. What interest has been earned (in dollars correct to the nearest cent) after 5 years? Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=2030&nval=5&int=10&pl=Annually']compound interest calculator[/URL], we get: [B]3,269.34[/B]

$3.75 in quarters and nickels in her car. The number of nickels is fifteen more than the number of quarters. How many of each type of coin does she have? Let the number of nickels be n, and the number of quarters be q. We know nickels are 0.05, and quarters are 0.25. We're given: [LIST=1] [*]n = q + 15 [*]0.05n + 0.25q = 3.75 [/LIST] Substituting (1) into (2), we get: 0.05(q + 15) + 0.25q = 3.75 0.05q + 0.75 + 0.25q = 3.75 Combine like term: 0.3q + 0.75 = 3.75 [URL='https://www.mathcelebrity.com/1unk.php?num=0.3q%2B0.75%3D3.75&pl=Solve']Typing this equation into our calculator[/URL], we get: [B]q = 10[/B] Substituting q = 10 into Equation (1), we get: n = 10 + 15 [B]n = 25[/B]

$45 and you add $2.25 each day Let d be the number of days. Our Cost function C(d) is: [B]C(d) = 2.25d + 45[/B]

$500 is deposited into a savings account. The bank offers a 3.5% interest rate and the money is left in the account for 5 years. How much interest is earned in this situation? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=5000&nval=5&int=3.5&pl=Annually']compound interest calculator[/URL], we get interest earned as: [B]938.43[/B]

The number is $9,285 from our [URL='http://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=6500&pct1=70&pcheck=2&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pof1=40&pof2=20&pl=Calculate']percentage-decimal-fraction calculator[/URL].

$8000 are invested in a bank account at an interest rate of 10 percent per year. Find the amount in the bank after 5 years if interest is compounded annually Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=8000&nval=5&int=10&pl=Annually']compound interest with balance calculator[/URL], we get: [B]12,884.08[/B]

$96 less x dollars The word [I]less[/I] means we subtract, so we have: [B]$96 - $x or $(96 - x)[/B]

60% of the freshman ate pizza [URL='http://www.mathcelebrity.com/community/x-apple-data-detectors://3']at lunch today[/URL]. If 180 freshman ate pizza, how many freshman are enrolled at our school? 60% of x = 180 We write this as 0.6x = 180 Divide each side by 0.6 to isolate x. We get x = 300 freshman

Free π Digits Calculator - Calculates PI (π) to a set number of decimal places using the Gauss-Legendre Algorithm.

Removing the parentheses since there is nothing to distribute, we have: 10 + x - y = 10 + x - y This is true!

(2,3)(4,5)(6,7)(8,9) represents a function Domain is the x-values: x = (2, 4, 6, 8) Range is the y-values: y = (3, 5, 7, 9) The function y, or f(x) is: y = x + 1 where x = (2, 4, 6, 8) Test this function for x = 2: y = 2 + 1 y = 3 Test this function for x = 4: y = 4 + 1 y = 5 Test this function for x = 6: y = 6 + 1 y = 7 Test this function for x = 8: y = 8 + 1 y = 9

(3,-4) lies on the line with equation 3x-2y=k, find k Plug in our values: 3(3) -2(-4) = k 9 + 8 = k k = [B]17[/B]

(3,3) radius of 4 We have a circle with center (3,3) with a radius of 4. [URL='https://www.mathcelebrity.com/eqcircle.php?h=3&k=3&r=4&calc=1&d1=-1&d2=2&d3=3&d4=2&ceq=%28x+%2B+3%29%5E2+%2B+%28y+-+2%29%5E2+%3D+16&pl=Calculate']Use our circle equation calculator to get the general form and standard form.[/URL]

(4x - 20)/8 = 9y for x Cross multiply: 4x - 20 = 8 * 9y 4x - 20 = 72y Add 20 to each side to isolate x: 4x - 20 + 20 = 72y + 20 Cancel the 20 on the left side, we get: 4x = 72y + 20 Divide each side by 4: 4x/4 = (72y + 20)/4 Cancel the 4 on the left side: x = [B](72y + 20)/4[/B]

Round 98 to the nearest 10. This is 100. Call this a. Calculate b which is a - our original number: b = 100 - 98 b = 2 We can use this formula: (a - b)^2 = a(a- 2b) + b^2 Given a = 100 and b = 2, we have: (100 - 2)^2 = 100(100 - 2(2)) + 2^2 98^2 = 100(96) + 4 98^2 = 9600 + 4 98^2 = [B]9,604[/B] [MEDIA=youtube]8lQdxVVo-Ps[/MEDIA]

(A intersection B) U (A intersection B') This is the [B]Universal Set U[/B]. Everything that isn't A and isn't B is everything else.

(A^C)^C we read this as The complement of the Complement of Set A The complement of set A is anything NOT in A. But the complement of the complement is anything NOT NOT IN A. Which is just [B]A [MEDIA=youtube]-eo-Bq6qZVM[/MEDIA][/B]

[SIZE=6][B](Sqrt(24) + sqrt(96))/2[/B] [B][/B] [B]Simplify sqrt(24)[/B] 24 = 6 * 4 where 4 is the perfect square sqrt(24) = 2 * sqrt(6) [B]Simplify sqrt(96)[/B] 96 = 16 * 6 where 16 is the perfect square sqrt(96) = 4 * sqrt(6) Simplified, we have: (2 * sqrt(6) + 4 * sqrt(6))/2 6 * sqrt(6)/2 [B]3 * sqrt(6)[/B][/SIZE] [SIZE=6] [/SIZE] [MEDIA=youtube]h-4eZOFUR4I[/MEDIA]

+÷+(-) Parentheses first( (-) 12 - 6y So we have: +÷+12 - 6y 2y + 5/6y + 12 - 6y Combine like terms: [B]5/6y - 4y + 12[/B]

-10 times the quantity y minus 4 The quantity y minus 4: y - 4 10 times this quantity: [B]10(y - 4) [/B]

-11, -9, -7, -5, -3 What is the next number? What is the 200th term in this sequence? We see that Term 1 is -11, Term 2 is -9, so we do a point slope equation of (1,-11)(2,-9) to get the [URL='https://www.mathcelebrity.com/search.php?q=%281%2C-11%29%282%2C-9%29']nth term of the formula[/URL] f(n) = 2n - 13 The next number is the 6th term: f(6) = 2(6) - 13 f(6) = 12 - 13 f(6) = [B]-1 [/B] The 200th term is: f(200) = 2(200) - 13 f(200) = 400 - 13 f(200) = [B]387[/B]

-2 <= x +4 < 9 Subtract 4 from each piece: -2 - 4 <= x < 5 Simplify: [B]-6 <= x < 5 [/B] To find the interval notation, we set up our notation: [LIST] [*]The left side has a solid bracket, since we have an equal sign: [*]The right side has an open parentheses, since we have no equal sign [*][B][-6, 5)[/B] [/LIST]

-2 times the quantity q minus 3 q minus 3: q - 3 -2 times the quantity: -2(q - 3)

-2 times the quantity t plus 7 The key word here is quantity. In this case, the quantity is t plus 7 t + 7 -2 times the quantity means we multiply -2 times the quantity t + 7 [B]-2(t + 7) [MEDIA=youtube]nUWLUPfX52k[/MEDIA][/B]

-28 is the solution to the sum of a number p and 21 The sum of a number p and 21: p + 21 The phrase [I]is the solution to[/I] means an equation, so we set p + 21 equal to -28: [B]p + 21 = -28 [/B] If the problem asks you to solve for p, then we [URL='https://www.mathcelebrity.com/1unk.php?num=p%2B21%3D-28&pl=Solve']type this into our search engine[/URL] and we get: p = [B]-49[/B]

-3x to the negative one power Raising to a negative power means taking 1 over the same expression to the positive power" (-3x)^-1 = 1/-3x = [B]-1/3x[/B]

-3x<= -9 or 5+x<6 Take each piece: -3x<= -9 Divide each side by -3: x>=3 Now take 5 + x < 6 5 + x < 6 Subtract 5 from each side: x < 1 Joining together the two inequalities, we have: x<1 or x>=3 Use our [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=x%3C1orx%3E%3D3&pl=Show+Interval+Notation']interval notion calculator[/URL] to find the interval notation of this compound inequality

-5n - 5n - 5 = 5 Solve for [I]n[/I] in the equation -5n - 5n - 5 = 5 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (-5 - 5)n = -10n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] -10n - 5 = + 5 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -5 and 5. To do that, we add 5 to both sides -10n - 5 + 5 = 5 + 5 [SIZE=5][B]Step 4: Cancel 5 on the left side:[/B][/SIZE] -10n = 10 [SIZE=5][B]Step 5: Divide each side of the equation by -10[/B][/SIZE] -10n/-10 = 10/-10 n = [B]- 1 [URL='https://www.mathcelebrity.com/1unk.php?num=-5n-5n-5%3D5&pl=Solve']Source[/URL][/B]

-65 times the difference between a number and 79 is equal to the number plus 98 The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. The first expression, [I]the difference between a number and 79[/I] means we subtract 79 from our arbitrary variable of x: x - 79 Next, -65 times the difference between a number and 79 means we multiply our result above by -65: -65(x - 79) The phrase [I]the number[/I] refers to the arbitrary variable x earlier. The number plus 98 means we add 98 to x: x + 98 Now, let's bring it all together. The phrase [I]is equal to[/I] means an equation. So we set -65(x - 79) equal to x + [B]98: -65(x - 79) = x + 98[/B] <-- This is our algebraic expression If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=-65%28x-79%29%3Dx%2B98&pl=Solve']type this equation into our search engine[/URL], and you get: x = [B]76.31818[/B]

-g + 3/4a = y for a Add g to each side: -g + g + 3/4a = y + g Cancel the g terms on the left side: 3/4a = y + g Cross multiply: 3a = 4(y + g) Divide each side by 3 to isolate a: 3a/3 = 4(y + g)/3 a = [B]4(y + g)/3[/B]

-g+F/A=h^3 for A Add g to each side: -g + g+F/A=h^3 + g Cancel the g's on the left side: F/A = h^3 + g Cross multiply: F = A(h^3 + g) Divide each side by (h^3 + g) F/(h^3 + g) = A(h^3 + g)/(h^3 + g) Cancel (h^3 + g) on the right side: A = [B]F/(h^3 + g)[/B]

-n = n Add n to each side: -n + n = n + n Cancel the n's on the left side: 0 = 2n Only number that solves this is [B]n = 0[/B]

-x squared We take -x and raise it to the 2nd power: (-x)^2 = -x * -x = [B]x^2[/B]

0,7,14,21 What is the next number? What is the 1000th term? We're adding 7 to the last term, so we get a next term of: 21 + 7 = [B]28 [/B] For our nth term, we notice a pattern for the nth term of: 7n - 7 [LIST] [*]n = 1 --> 7(1) - 7 = 0 [*]n = 2 --> 7(2) - 7 = 7 [*]n = 3 --> 7(3) - 7 = 14 [/LIST] For n = 1000, we have: 7(1000) - 7 = 7000 - 7 = [B]6993[/B]

1 - n = n - 1 Solve for [I]n[/I] in the equation 1 - n = n - 1 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables -n and n. To do that, we subtract n from both sides -n + 1 - n = n - 1 - n [SIZE=5][B]Step 2: Cancel n on the right side:[/B][/SIZE] -2n + 1 = -1 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 1 and -1. To do that, we subtract 1 from both sides -2n + 1 - 1 = -1 - 1 [SIZE=5][B]Step 4: Cancel 1 on the left side:[/B][/SIZE] -2n = -2 [SIZE=5][B]Step 5: Divide each side of the equation by -2[/B][/SIZE] -2n/-2 = -2/-2 n = [B]1 [URL='https://www.mathcelebrity.com/1unk.php?num=1-n%3Dn-1&pl=Solve']Source[/URL][/B]

1 apartment equals 10 window each window cost $79.30 there are 30 apartments what is the total for replacing all the windows. 30 apartments * 10 windows per apartment * $79.30 per window = [B]$23,790[/B]

1 box is used every 1.5 days. How many are used in 242 days? Set up a proportion of boxes to days where b is the number of boxes used for 242 days: 1/1.5 = b/242 To solve this proportion for b, we [URL='https://www.mathcelebrity.com/prop.php?num1=1&num2=b&den1=1.5&den2=242&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: b = [B]161.3333[/B]

Free 1 Die Roll Calculator - Calculates the probability for the following events in the roll of one fair dice (1 dice roll calculator or 1 die roll calculator):
* Probability of any total from (1-6)
* Probability of the total being less than, less than or equal to, greater than, or greater than or equal to (1-6)
* The total being even
* The total being odd
* The total being a prime number
* The total being a non-prime number
* Rolling a list of numbers i.e. (2,5,6)
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1 die calculator

1 egg is 2 dollars. Then how much 2 eggs? 2 eggs * 2 dollars / 1 egg = [B]$4[/B]

1 hour and 54 minutes after 7:30 Let's take the easy and lazy way to solve this. 1 hour and 54 minutes is 6 minutes short of 2 hours So we add 2 hours to 7:30: 7:30 + 2 hours = 9:30 Then we subtract off the 6 minutes: 9:30 - 6 minutes = [B]9:24[/B]

1 integer is 7 times another. If the product of the 2 integers is 448, then find the integers. Let the first integer be x and the second integer be y. We have the following two equations: [LIST=1] [*]x = 7y [*]xy = 448 [/LIST] Substitute (1) into (2), we have: (7y)y = 448 7y^2 = 448 Divide each side by 7 y^2 = 64 y = -8, 8 We use 8, since 8*7 = 56, and 56*8 =448. So the answer is [B](x, y) = (8, 56)[/B]

1 multiplied by b squared multiplied by c squared b squared means we raise b to the power of 2: b^2 c squared means we raise c to the power of 2: c^2 b squared multiplied by c squared b^2c^2 1 multiplied by b squared multiplied by c squared means we multiply 1 by b^2c^2 1b^2c^2 Multiplying by 1 can be written by [U][I]removing[/I][/U] the 1 since it's an identity multiplication: [B]b^2c^2[/B]

1 over 14 cubed 14 cubed means we raise 14 to the power of 3: 14^3 1 over 14 cubed is written as: 1/14^3 To simplify this, we [URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=14%5E3&pl=Calculate']evaluate 14^3[/URL] = 2744 So we have: [B]1/2744[/B]

1 over 2 times the sum of x and y The sum of x and y x + y 2 times the sum of x and y 2(x + y) 1 over 2 times the sum of x and y [B]1/2(x + y)[/B]

1 person is born every 5 seconds. How many people are born in 1 minute? Set up the chain: 1 person / 5 seconds * 60 seconds / 1 minute Since 60/5 is 12, and the seconds cancel, we have: [B]12 people / minute[/B]

1 rabbit saw 6 elephants while going to the river. Every elephant saw 2 monkeys going towards the river. Every monkey holds 1 parrot in their hands. How many animals are going towards the river? [LIST] [*]1 rabbit = 1 [*]6 elephants per rabbit = 6 [*]2 monkeys per elephant = 12 [*]1 parrot per monkey = 12 parrots [*][B]31 total animals[/B] [/LIST]

1 rabbit saw 9 elephants while going to the river. Every elephant saw 3 monkeys going to the river. Each monkey had 1 tortoise in each hand. How many animals are going to the river? Trick question: The elephants [U]are not[/U] going to the river. So 1 rabbit goes to the river 3 monkeys go to the river, each holding a tortoise in [B]each hand[/B]. 2 hands per money times 3 monkeys = 6 tortoises So we have 1 rabbit + 3 monkeys + 6 tortoises = [B]10 animals[/B]

1 year from now Mike will be 40 years old. The current sum of the ages of Mike and John is 89. How old is John right now? If Mike will be 40 1 year from now, then he is: 40 - 1 = 39 years old today. And if the current sum of Mike and John's age is 89, then we use j for John's age: j + 39 = 89 [URL='https://www.mathcelebrity.com/1unk.php?num=j%2B39%3D89&pl=Solve']Type this equation into our search engine[/URL], and we get: [B]j = 50[/B]

1 year from now Paul will be 49 years old. The current sum of the ages of Paul and Sharon is 85. How old is Sharon right now? If Paul will be 49 years old 1 year from now, this means today, he is 49 - 1 = 48 years old. Let Sharon's age be s. Then from the current sum of Paul and Sharon's ages, we get: s + 49 = 85 [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B49%3D85&pl=Solve']Type this equation into our search engine[/URL], and get: s = [B]36[/B]

1, 1/2, 1/3, 1/4, 1/5 What is the next number? What is the 89th term of the sequence? Formula for nth term is 1/n Next number is n = 5, so we have [B]1/5[/B] With n = 89, we have [B]1/89[/B]

1, 1/2, 1/4, 1/8, 1/16 The next number in the sequence is 1/32. What is the function machine you would use to find the nth term of this sequence? Hint: look at the denominators We notice that 1/2^0 = 1/1 = 1 1/2^1 = 1/2 1/2^2 = 1/4 1/2^3 = 1/8 1/2^4 = 1/32 So we write our explicit formula for term n: f(n) = [B]1/2^(n - 1)[/B]

At first glance, we see powers of 2 in the denominator of every term except the first one. But if we remember 2^0 = 1, we get our breakthrough. 1/2^0 = 1/1 = 1 Therefore, we stagger the powers of 2 by 1 less than the term we are on: a(n) = [B]1/2^(n - 1) [MEDIA=youtube]Ua-arUukOew[/MEDIA][/B]

1, 4, 9, 16, 25 What is the next number? What is the 50th term? We see that 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25 We build a formula for the nth term: f(n) = n^2 The next number means n = 6th term: f(6) = 6^2 = [B]36 [/B] The 50th term means n = 50: f(50) = 50^2 = [B]2500[/B]

1, 8, 27, 64 What is the 10th term? We see the following pattern: 1^3 = 1 2^3 = 8 3^3 = 27 4^3 = 64 We build our sequence function using this pattern: f(n) = n^3 With n = 10, we have: f(10) = 10^3 f(10) = [B]1,000[/B]

1, 9, 25, 49, .......... What is next 1^2 = 1 3^2 = 9 5^2 = 25 7^2 = 49 So this pattern takes odd numbers and squares them. Our next odd number is 9: 9^2 = [B]81[/B]

1.25, 2, 2.75, 3.5 What is the 100th term? The formula of nth term is: f(n) = 0.75n + 0.5 So the 100th term is: f(100) = 0.75(100) + 0.5 f(100) = 75 + 0.5 f(100) = [B]75.5[/B]

1/2 of a number decreased by twice a number [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]1/2 of a number: x/2 [*]Twice a number means we multiply x by 2: 2x [*]The phrase [I]decreased by[/I] means we subtract [/LIST] [B]x/2 - 2x[/B]

1/2 of the product x and y The product x and y: xy 1/2 of the product: [B]xy/2[/B]

1/2 of x and 10 is 30. Find the x. x and 10 means we add: x + 10 1/2 of this: 1/2(x + 10) The phrase is means equal to, so we set 1/2(x + 10) equal to 30 for our algebraic expression [B]1/2(x + 10) = 30[/B]

1/2 the difference of x and 4 The difference of x and 4: x - 4 1/2 of the difference means we divide x -4 by 2: [B](x - 4)/2[/B]

1/2 the quantity of x plus y The quantity of x plus y x + y 1/2 the quantity means we multiply x + y by 1/2: [B](x + y)/2[/B]

1/2, 3, 5&1/2, 8......203 What term is the number 203? We see the following pattern: 1/2 = 2.5*1 - 2 3 = 2.5*2 - 2 5&1/2 = 2.5*3 - 2 8 = 2.5*4 - 2 We build our function f(n) = 2.5n - 2 Set 2.5n - 2 = 203 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2.5n-2%3D203&pl=Solve']equation solver[/URL], we get: n = [B]82[/B]

1/2a-10b=c solve for a Multiply each side of the equation by 2: 2/2a - 2(10)b = 2c Simplify: a - 20b = 2c Add 20b to each side: a - 20b + 20b = 2c + 20b Cancel the 20b on the left side: [B]a = 2c + 20b [/B] You can also factor out a 2 on the left side for another version of this answer: [B]a = 2(c + 10b)[/B]

1/3 a number increased by 10 times by that same number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 1/3 a number 1/3 * x = x/3 That same number means the same arbitrary variable as above: x 10 times that same number: 10x The phrase [I]increased by[/I] means we add: [B]x/3 + 10x [MEDIA=youtube]29TGt3i28jw[/MEDIA][/B]

1/3 of students at a school are boys. If there are 600 students at the school, how many are girls? If 1/3 are boys, then the number of boys is: 600 * 1/3 600/3 We [URL='https://www.mathcelebrity.com/fraction.php?frac1=600%2F3&frac2=3%2F8&pl=Simplify']type this fraction into our search engine to simplify[/URL], and we get: 200 Now we need to find how many girls are at the school: Girls = Total Students - Boys Girls = 600 - 200 Girls = [B]400[/B]

1/3 of the sum of 4 and p The sum of 4 and p: 4 + p 1/3 of this sum [B](4 + p)/3[/B]

1/3 of the sum of a number and 2 plus 5 is -20 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x the sum of a number and 2: x + 2 1/3 of the sum of a number and 2 1/3(x + 2) 1/3 of the sum of a number and 2 plus 5 1/3(x + 2) + 5 The phrase [I]is[/I] means equal to, so we set 1/3(x + 2) + 5 equal to -20: [B]1/3(x + 2) + 5 = -20[/B]

1/3 times q plus 5 equal q minus 4 1/3 times q plus 5: (q + 5)/3 q minus 4: q - 4 The word [I]equal[/I] means we set (q + 5)/3 equal to q - 4: [B](q + 5)/3 = q - 4[/B]

1/3c increased by the square root of d square root of d: sqrt(d) 1/3c increased by the square root of d [B]1/3c + sqrt(d)[/B]

1/4 of the difference of 6 and a number is 200 Take this [B]algebraic expression[/B] in 4 parts: [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x [*]The difference of 6 and a number means we subtract x from 6: 6 - x [*]1/4 of the difference means we divide 6 - x by 4: (6 - x)/4 [*]Finally, the phrase [I]is[/I] means an equation, so we set (6 - x)/4 equal to 200 [/LIST] [B](6 - x)/4 = 200[/B]

[U]The sum of 6 and 3n:[/U] 6 + 3n [U]1/4 of that sum[/U] [B]1/4(6 + 3n)[/B]

1/4 of the sum of n and 40. The sum of n and 40 n + 40 1/4 of this: (n + 40)/4

1/5 of the sum of the number u and 2 The sum of the number u and 2 means we add 2 to u: u + 2 1/5 of the sum: [B](u + 2)/5[/B]

1/6 times the sum k and 5 The sum k and 5 (k + 5) 1/6 times the sum k and 5 (k + 5)/6

1/9 of all sales were for cash. If cash sales were $59,000, what were the total sales? Let sales be s. We're given: s/9 = 59000 To solve this proportion for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=s&num2=59000&den1=9&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: s = [B]531000[/B]

1/a + 1/b = 1/2 for a Subtract 1/b from each side to solve this literal equation: 1/a + 1/b - 1/b = 1/2 - 1/b Cancel the 1/b on the left side, we get: 1/a = 1/2 - 1/b Rewrite the right side, using 2b as a common denominator: 1/a = (b - 2)/2b Cross multiply: a(b - 2) = 2b Divide each side by (b - 2) a = [B]2b/(b - 2)[/B]

1/n^2 = 3/192 Cross multiply: 192 * 1 = 3 * n^2 3n^2 = 192 Divide each side by 3: 3n^2/3 = 192/3 Cancel the 3's on the left side: n^2 = 64 Take the square root of both sides: n = [B]8 or -8[/B]

10 divided by the sum of 4 and u Take this algebraic expression in parts: The sum of 4 and u means we add 4 to u: 4 + u Next, we divide 10 by this sum: [B]10/(4 + u)[/B]

10 is twice the sum of x and 5 The sum of x and 5 means we add: x + 5 Twice the sum means we multiply by 2: 2(x + 5) The word [I]is[/I] means an equation, so we set 2(x + 5) equal to 10 [B]2(x + 5) = 10[/B]

Sum of a and b a + b half the sum of a and b (a + b)/2 10 less than that (a + b)/2 - 10

10 minus z to the 8th z to the 8th z^8 10 minus this: 10 - z^8

Let d be dogs and c be cows. Then d - 10 = c or c + 10 = d

10 more than a number z, divided by k The phrase [I]a number[/I] means an arbitrary variable, lets call it x. 10 more than a number means we add 10 to x: x + 10 We divide this quantity by k: [B](x + 10)/k[/B]

10 students play tennis, 5 students play soccer, and 4 students play both. How many students are in the class? We want Tennis + Soccer - Both 10 + 5 - 4 [B]11[/B] students in the class

10 times a number is 420 A number denotes an arbitrary variable, let's call it x. 10 times a number: 10x The phrase is means equal to, so we set 10x equal to 420 [B]10x = 420 <-- This is our algebraic expression [/B] If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=10x%3D420&pl=Solve']equation calculator[/URL] We get x = 42

10 times the first of 2 consecutive even integers is 8 times the second. Find the integers. Let the first integer be x. Let the second integer be y. We're given: [LIST=1] [*]10x = 8y [*]We also know a consecutive even integer means we add 2 to x to get y. y = x + 2 [/LIST] Substitute (1) into (2): 10x = 8(x + 2) Multiply through: 10x = 8x + 16 To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=10x%3D8x%2B16&pl=Solve']we type this equation into our search engine[/URL] and we get: [B]x = 8[/B] Since y = x + 2, we plug in x = 8 to get: y = 8 + 2 [B]y = 10 [/B] Now, let's check our work. Does x = 8 and y = 10 make equation 1 hold? 10(8) ? 8(10) 80 = 80 <-- Yes!

10 times the square of a number w divided by 12 The square of a number w w^2 10 times this 10w^2 Divided by 12 [B]10w^2/12[/B]

10 x 12 divided by 9 12/9 1.3333333 Then multiply by 10: [B]13.33333333[/B]

10% of the days in June were sunny. How many days in June were sunny? June has 30 days. We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=10&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type in 10% of 30[/URL] in our search engine: [B]3 days[/B]

10, 1,000, 100,000, 10,000,000 What power of 10 is the 80th term? We see the following pattern 10^1 = 10 10^3 = 1000 10^5 = 100,000 10^7 = 10,000,000 f(n) = 10^(2n - 1) We build the 80th term: f(80) = 10^(2(80) - 1) f(80) = 10^(160 - 1) f(80) = 10^[B]159[/B]

100, 75, 50, 25, 0, -25 What is the next number? What is the 100th term? Using point slope, we get (1, 100)(2, 75) Our [URL='https://www.mathcelebrity.com/search.php?q=%281%2C+100%29%282%2C+75%29&x=0&y=0']series function becomes[/URL] f(n) = -25n + 125 The next term is the 7th term: f(7) = -25(7) + 125 f(7) = -175 + 125 f(7) = [B]-50 [/B] The 100th term is found by n = 100: f(100) = -25(100) + 125 f(100) = -2500 + 125 f(100) = [B]-2375[/B]

100n = 100 Solve for [I]n[/I] in the equation 100n = 100 [SIZE=5][B]Step 1: Divide each side of the equation by 100[/B][/SIZE] 100n/100 = 100/100 n = [B]1[/B]

104 subtracted from the quantity 6 times r is the same as r The quantity 6 times r means we multiply 6 by r: 6r 104 subtracted from 6r is written as: 6r - 104 [B]The phrase [I]is the same as[/I] means we have an equation. So we set 6r - 104 equal to r 6r - 104 = r[/B]

108 times a, reduced by 147 is k subtracted from 56 Take this algebraic expression in pieces: Step 1: 108 times a: 108a Step 2: Reduced by means subtract, so we subtract 47 from 108a: 108a - 47 Step 3: ksubtracted from 56: 56 - k Step 4: The phrase [I]is[/I] means equal to, so we set 108a - 47 equal to 56 - k [B]108a - 47 = 56 - k [MEDIA=youtube]KrY6uzKeeB0[/MEDIA][/B]

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10ac-x/11=3 for a Add x/11 to each side of the equation to isolate a: 10ac - x/11 + x/11 = 3 + x/11 Cancelling the x/11 on the left side, we get: 10ac = 3 + x/11 Divide each side by 10c to isolate a: 10ac/10c = 3 + x/11 Cancelling the 10c on the left side, we get: a = [B]3/10c + x/110c[/B]

10n - 9n + 8n - 7n + 6n = 10 - 9 + 8 - 7 + 6 Solve for [I]n[/I] in the equation 10n - 9n + 8n - 7n + 6n = 10 - 9 + 8 - 7 + 6 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (10 - 9 + 8 - 7 + 6)n = 8n [SIZE=5][B]Step 2: Group the constant terms on the right hand side:[/B][/SIZE] 10 - 9 + 8 - 7 + 6 = 8 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 8n = + 8 [SIZE=5][B]Step 4: Divide each side of the equation by 8[/B][/SIZE] 8n/8 = 8/8 n = [B]1[/B]

10n = 0.5 Solve for [I]n[/I] in the equation 10n = .5 [SIZE=5][B]Step 1: Divide each side of the equation by 10[/B][/SIZE] 10n/10 = .5/10 n = [B]0.05 [URL='https://www.mathcelebrity.com/1unk.php?num=10n%3D.5&pl=Solve']Source[/URL][/B]

The Phrase more then means add, so we have: n + 11

11 to the power of 6 multiply 11 to the power of 3 Take this in parts. [U]Step 1: 11 to the power of 6 means we raise 11 to the 6th power using exponents:[/U] 11^6 [U]Step 2: 11 to the power of 3 means we raise 11 to the 3rd power using exponents:[/U] 11^3 [U]Step 3: Multiply each term together:[/U] 11^6 * 11^3 [U]Step 4: Simplify[/U] Because we have 2 numbers that are the same, in this case, 11, we can add the exponents together when multiplying: 11^(6 + 3) [B]11^9 [MEDIA=youtube]gCxVq7LqyHk[/MEDIA][/B]

110 subtracted from the product of 244 and w is the product of r and 177 increased by 266 The product of 244 and w: 244w 110 subtracted from the product of 244 and w 244w - 110 the product of r and 177 177r the product of r and 177 increased by 266 177r + 266 The word [I]is[/I] means equal to, so we set 244w - 110 equal to 177r + 266 [B]244w - 110 = 177r + 266[/B]

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12 is multiplied by some number, that product is reduced by 9, and the total is equal to 37 The phrase [I]some number[/I] means an arbitrary variable, let's call it x. 12 multiplied by this number: 12x The product of 12x is reduced by 9 12x - 9 The phrase [I]the total is equal to[/I] means an equation, so we set 12x - 9 equal to 37: [B]12x - 9 = 37[/B]

12 is subtracted from d and the result is tripled 12 is subtracted from d: d - 12 the result is tripled means we multiply d - 12 by 3 [B]3(d - 12)[/B]

12 is subtracted from d and the result is tripled. 12 is subtracted from d: d - 12 The result is tripled means we multiply d - 12 by 3 [B]3(d - 12) [MEDIA=youtube]1xqWstiIDP0[/MEDIA][/B]

12 laps in 18 minutes . What is the average time per lap? 18/12 = [B]1.5 minutes per lap[/B]

12 plus 6 times a number is 9 times the number The phrase [I]a number [/I]means an arbitrary variable. Let's call it x. 6 times a number is written as: 6x 12 plus 6 times the number means we add 6x to 12: 12 + 6x 9 times a number is written as: 9x The phrase [I]is[/I] means an equation, so we set 12 + 6x equal to 9x [B]12 + 6x = 9x <-- This is our algebraic expression[/B] [B][/B] If the problem asks you to solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B6x%3D9x&pl=Solve']type this expression into our search engine[/URL] and you get: x = [B]4[/B]

A number means an arbitrary variable, let's call it x. The product of 4 and a number is 4x. 12 plus that product is 4x + 12 Is greater than means an inequality, so we set the entire expression greater than 72 4x + 12 > 72

12 students want pancakes and 14 students want waffles. What is the ratio of the number of students who want pancakes to the total number of students? 12/14 is the initial ratio. However, we can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=12%2F14&frac2=3%2F8&pl=Simplify']So we type 12/14 into our search engine and choose simplify.[/URL] We get: 6/7

12.66 g of calcium are heated in air,17.73 g of calcium oxide is formed.The percent oxygen in the compound is? 17.73g Calcium oxide - 12.66g Calcium = 5.07g Oxygen Mass of the element / Mass of the compound * 100% = 5.07g O / 17.73g CaO2 X 100% = 28.6% of Oxygen in the compound [B][U]Check Your Work [/U][/B] Mass of the element / Mass of the compound X 100% = 12.66g Ca ÷ 17.73g CaO2 X 100% = 71.4% Ca 71.4% Ca + 28.6% O = 100% CaO2

1225 people live in a village,329 are men and 404 are women. how many are children We can have either men, women, or children. We have the following equation where children are "c". 239 + 404 + c = 1225 To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=239%2B404%2Bc%3D1225&pl=Solve']type this equation into our search engine[/URL] and we get: c = [B]582[/B]

13 is the product of 5p and 5 the product of 5p and 5 means we multiply 5p by 5: 5p * 5 25p The word [I]is[/I] means equal to, so we set 25p equal to 13 [B]13 = 25p 25p = 13[/B]

13 minutes to answer 4 problems. how many minutes would it take to answer 22 questions? Set up a proportion of time to problems where m is the number of minutes it would take for 22 questions: 13/4 = m/22 [URL='https://www.mathcelebrity.com/prop.php?num1=13&num2=m&den1=4&den2=22&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get: m = [B]71.5[/B]

13 times the sum of x and 9y The sum of x and 9y means we add 9y to x: x + 9y Now multiply this sum by 13: [B]13(x + 9y)[/B]

132 is 393 multiplied by y 393 multiplied by y 393y The word [I]is[/I] means equal to, so we set 393y equal to 132 as our algebraic expression [B]393y = 132 [/B] If you need to solve for y, use our [URL='http://www.mathcelebrity.com/1unk.php?num=393y%3D132&pl=Solve']equation calculator[/URL]

14 increased by twice Carlos’s age. Use the variable c to represent Carlos age Twice means me multiply a by 2: 2a 14 increased by twice Carlos's age means we add 2a to 14: [B]14 + 2a[/B]

14 is the what of 1/14? [B]Denominator[/B]

14 oranges $3.78 Using our [URL='http://www.mathcelebrity.com/unit-cost-calculator.php?num=14orangesfor3.78&pl=Calculate+Unit+Cost']unit cost calculator[/URL], we get: [B]$0.27 per orange[/B]. You could also enter in the search engine: 14 oranges for $3.78

149 cars are waiting to take a ferry across the channel each ferry can only hold 18 cars how many trips will it take to get all the cars across Number of trips = Total Cars / Cars Per ferry trip Number of trips = 149/18 Number of trips = 8.28 trips We round up to the next integer and we have [B]9 trips[/B]

15 added to a number is 16 times the number [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]15 added to a number: 15 + x [*]16 times the number: 16x [*]The phrase [I]is[/I] means equal to. So we set 15 + x equal to 16x [/LIST] [B]15 + x = 16x[/B]

15 added to the quotient of 8 and a number is 7. Take this algebraic expression in pieces: [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. [*]The quotient of 8 and a number: 8/x [*]15 added to this quotient: 8/x + 15 [*]The word [I]is[/I] means an equation, so we set 8/x + 15 equal to 7 [/LIST] [B]8/x + 15 = 7[/B]

15 mins into fraction of an hour [URL='https://www.mathcelebrity.com/timecon.php?quant=1&pl=Calculate&type=hour']An hour is 60 minutes[/URL], so we have the fraction: 15/60 But we can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=15%2F60&frac2=3%2F8&pl=Simplify']type in 15/60 into our search engine[/URL], click Simplify, and we get: [B]1/4[/B]

15 of the 45 students have brown eyes. What fraction of the students have brown eyes? 15/45 can be [URL='https://www.mathcelebrity.com/fraction.php?frac1=15%2F45&frac2=3%2F8&pl=Simplify']simplified using our fraction simplify calculator[/URL]: [B]1/3[/B]

18 - 15 = 3 student disagreed. 3/18 is the fraction of student who disagreed. [URL='http://www.mathcelebrity.com/perc.php?num=3&den=18&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Converting to a percentage using our fraction to decimal calculator, we get:[/URL] 16.67%

15y + 13/c = m for y Subtract 13/c from each side to isolate the y term: 15y + 13/c - 13/c = m - 13/c Cancel the 13/c on the left side and we get 15y = m - 13/c Now, divide each side by 15 to isolate y: 15y/15 = (m - 13/c)/15 Cancel the 15 on the left side, and we get: y = [B](m - 13/c)/15[/B]

16 decreased by 3 times the sum of 3 and a number Take this algebraic expression in parts: [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. [*]The sum of 3 and a number: 3 + x [*]3 times the sum: 3(3 + x) [*]16 decreased by... means we subtract 3(3 + x) from 16 [/LIST] [B]3(3 + x) from 16[/B]

17 decreased by three times d equals c three times d means we multiply d by 3: 3d 17 decreased by three times d means we subtract 3d from 17 17 - 3d The word [I]equals[/I] means an equation, so we set 17 - 3d equal to c: [B]17 - 3d = c[/B]

17 multiplied by the quantity 9 minus 5 The quantity 9 minus 5: 9 - 5 17 multiplied by the quantity means we wrap 9 - 5 in parentheses: [B]17(9 - 5)[/B]

17 people over the maximum capacity Let the maximum capacity be c. We have: [B]c + 17[/B]

175 out of 200 students have a cell phone. What fraction of the students have a cell phone? 175 out of 200 can be written as: 175/200 This can be simplified, so we [URL='https://www.mathcelebrity.com/fraction.php?frac1=175%2F200&frac2=3%2F8&pl=Simplify']type it in our math engine[/URL] and we get: [B]7/8[/B]

175 students separated into n classes is 25 [U]Divide 175 by n[/U] 175/n [U]The word [I]is[/I] means equal to, so set this expression equal to 25[/U] 175/n = 25 [U]Cross multiply[/U] 25n = 175 [U]Divide each side by 25[/U] [B]n = 7[/B]

The difference of t and 9 is: t - 9 Now, we set up a quotient with 18 as the numerator and t - 9 as the denominator 18 ------ t - 9

18 multiplied by the quantity of 11 plus r The quantity of 11 plus r is written as: 11 + r 18 multiplied by the [I]quantity[/I] means we take 18 and multiply it by the term 11 + r [B]18(11 + r) [MEDIA=youtube]2GYjQTjt8qM[/MEDIA][/B]

19 decreased by the absolute value of c Take this algebraic expression in parts: [LIST] [*]Absolute value of c: |c| [*]19 decreased by the absolute value of c is found by subtracting |c| from 19 [/LIST] [B]19 - |c|[/B]

19 increased by twice Greg’s score use the variable g to represent Greg’s score Use g for Greg's score g Twice g means we multiply g by 2: 2g 19 increased by means we add 2g to 19 [B]2g + 19 [MEDIA=youtube]E9a_U7z-fHE[/MEDIA][/B]

19 increased by twice Vanessa's age Let Vanessa's age be a. Twice means we multiply a by 2: 2a The phrase [I]increased by[/I] means we add 2a to 19: [B]19 + 2a[/B]

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2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than twice a number of home runs the second player hit. how many home runs did each player hit? Declare variables: Let the first players home runs be a Let the second players home runs be b We're given two equations: [LIST=1] [*]a = 2b + 3 [*]a + b = 60 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for a: 2b + 3 + b = 60 Using our math engine, we [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B3%2Bb%3D60&pl=Solve']type this equation[/URL] in and get: b = [B]19 [/B] To solve for a, we substitute b = 19 into equation (1): a = 2(19) + 3 a = 38 + 3 a = [B]41[/B]

2 buses leave at 5:30am, 1 comes every 18 minutes and one comes every 15 minutes when will they both come at the same time again We want the Least Common Multiple (LCM) of 15 and 18. LCM(15, 18) Enter this into the [URL='http://www.mathcelebrity.com/gcflcm.php?num1=15&num2=18&num3=&pl=LCM']search engine[/URL], and we get: [B]90 minutes[/B]

2 cards have different expressions written on them.: 5y - 2 and 3y + 10. for what value of y do the 2 cards represent the same number? If they have the same number, we set them equal to each other and solve for y: 5y - 2 = 3y + 10 To solve for y, we [URL='http://5y - 2 = 3y + 10']type this expression in our search engine [/URL]and we get: y = [B]6[/B]

2 coins are tossed. Find the probability of getting 1 head and 1 tail We can either flip HT or TH. Let's review probabilities: [LIST] [*]HT = 1/2 * 1/2 = 1/4 <-- We multiply since each event is independent [*]TH = 1/2 * 1/2 = 1/4 <-- We multiply since each event is independent [/LIST] P(1 H, 1 T) = P(HT) + P(TH) P(1 H, 1 T) = 1/4 + 1/4 P(1 H, 1 T) = 2/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F4&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we can reduce 2/4 to 1/2 P(1 H, 1 T) = [B]1/2[/B]

Let x be the first even integer. That means the next consecutive even integer must be x + 2. Set up our equation: x + (x + 2) = 118 Group x terms 2x + 2 = 118 Subtract 2 from each side 2x = 116 Divide each side by 2 x = 58 Which means the next consecutive even integer is 58 + 2 = 60 So our two consecutive even integers are [B]58, 60[/B] Check our work: 58 + 60 = 118

2 consecutive odd integers such that their product is 15 more than 3 times their sum. Let the first integer be n. The next odd, consecutive integer is n + 2. We are given the product is 15 more than 3 times their sum: n(n + 2) = 3(n + n + 2) + 15 Simplify each side: n^2 + 2n = 6n + 6 + 15 n^2 + 2n = 6n + 21 Subtract 6n from each side: n^2 - 4n - 21 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-4n-21%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get: n = (-3, 7) If we use -3, then the next consecutive odd integer is -3 + 2 = -1. So we have [B](-3, -1)[/B] If we use 7, then the next consecutive odd integer is 7 + 2 = 9. So we have [B](7, 9)[/B]

2 dice are rolled what is the probability that doubles are rolled less than 11 List out the doubles with a sum less than 11: (1, 1) (2, 2) (3, 3) (4, 4) (5, 5) The probability of each double is 1/6 * 1/6 = 1/36. We have 5 of them, so we have 5*1/36 = [B]5/36[/B]

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2 fair sided die are rolled. How many ways can the dice be rolled to sum exactly 6? [URL='https://www.mathcelebrity.com/2dice.php?gl=1&pl=6&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Using our 2 dice calculator[/URL], we get the following options: [LIST] [*]2,4 [*]3,3 [*]4,2 [*]1,5 [*]5,1 [/LIST] The probability of rolling a sum of 6 is [B]5/36[/B]

2 is added to c, then the result is multiplied by 7 2 is added to c: c + 2 The result is multiplied by 7: [B]7(c + 2)[/B]

2 less than 3 times n is 4 more than n 3 times n: 3n 2 less than 3 times n 3n - 2 4 more than n: n + 4 The word [I]is[/I] means equal to, so we set 3n - 2 equal to n + 4: [B]3n - 2 = n + 4[/B]

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2 more than twice the sum of 10 and a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The sum of 10 and a number means we add x to 10: 10 + x Twice the sum means we multiply 10 + x by 2: 2(10 + x) 2 more than twice the sum means we add 2 to 2(10 + x): [B]2(10 + x) + 2[/B]

2 movie tickets and 3 snacks are $24. 3 movie tickets and 4 snacks are $35. How much is a movie ticket and how much is a snack? Let a movie ticket cost be m, and a snack cost be s. We have: 2m + 3s = 24.3 3m + 4s = 35 Using the [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=2m+%2B+3s+%3D+24.3&term2=3m+%2B+4s+%3D+35&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: m = $7.8 s = $2.9

Free 2 number Word Problems Calculator - This calculator handles word problems in the format below:
* Two numbers have a sum of 70 and a product of 1189 What are the numbers?
* Two numbers have a sum of 70. Their difference 32

2 numbers add to 200. The first is 20 less than the second. Let the first number be x and the second number be y. We're given: [LIST=1] [*]x + y = 200 [*]x = y - 20 [/LIST] Plug (2) into (1) (y - 20) + y = 200 Group like terms: 2y - 20 = 200 [URL='https://www.mathcelebrity.com/1unk.php?num=2y-20%3D200&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]y = 110[/B] <-- This is the larger number Plug y = 110 into Equation (2) to get the smaller number: x = 110 - 20 [B]x = 90[/B] <-- This is the smaller number Let's check our work for Equation (1) using x = 90, and y = 110 90 + 110 ? 200 200 = 200 <-- Good, our solutions check out for equation (1) Let's check our work for Equation (2) using x = 90, and y = 110 90 = 110 - 20 90 = 90 <-- Good, our solutions check out for equation (2)

2 numbers that add up makes 5 but multiplied makes -36 Let the first number be x and the second number be y. We're given two equations: [LIST=1] [*]x + y = 5 [*]xy = -36 [/LIST] Rearrange equation (1) by subtracting y from each side: [LIST=1] [*]x = 5 - y [*]xy = -36 [/LIST] Substitute equation (1) for x into equation (2): (5 - y)y = -36 5y - y^2 = -36 Add 36 to each side: -y^2 + 5y + 36 = 0 We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=-y%5E2%2B5y%2B36%3D0&pl=Solve+Quadratic+Equation&hintnum=0']type it in our search engine and solve[/URL] to get: y = ([B]-4, 9[/B]) We check our work for each equation: [LIST=1] [*]-4 + 9 = -5 [*]-4(9) = -36 [/LIST] They both check out

2 numbers that are equal have a sum of 60 Let's choose 2 arbitrary variables for the 2 numbers x, y Were given 2 equations: [LIST=1] [*]x = y <-- Because we have the phrase [I]that are equal[/I] [*]x + y = 60 [/LIST] Because x = y in equation (1), we can substitute equation (1) into equation (2) for x: y + y = 60 Add like terms to get: 2y = 60 Divide each side by 2: 2y/2 = 60/2 Cancel the 2's and we get: y = [B]30 [/B] Since x = y, x = y = 30 x = [B]30[/B]

2 pens and 1 eraser cost $35 and 3 pens and 4 erasers cost $65. X represents the cost of 1 pen and Y represents the cost of 1 eraser. Write the 2 simultaneous equations and solve. Set up our 2 equations where cost = price * quantity: [LIST=1] [*]2x + y = 35 [*]3x + 4y = 65 [/LIST] We can solve this one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]x (cost of 1 pen) = 15[/B] [*][B]y (cost of 1 eraser) = 5[/B] [/LIST]

2 times a number added to another number is 25. 3 times the first number minus the other number is 20. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]2x + y = 25 [*]3x - y = 20 [/LIST] Since we have matching opposite coefficients for y (1 and -1), we can add both equations together and eliminate a variable. (2 + 3)x + (1 - 1)y = 25 + 20 Simplifying, we get: 5x = 45 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D45&pl=Solve']Typing this equation into the search engine[/URL], we get: [B]x = 9[/B] To find y, we plug in x = 9 into equation (1) or (2). Let's choose equation (1): 2(9) + y = 25 y + 18 = 25 [URL='https://www.mathcelebrity.com/1unk.php?num=y%2B18%3D25&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]y = 7[/B] So we have (x, y) = (9, 7) Let's check our work for equation (2) to make sure this system works: 3(9) - 7 ? 20 27 - 7 ? 20 20 = 20 <-- Good, we match!

2 times a number equals that number plus 5 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 2 times a number means we multiply 2 by x: 2x That number plus 5 means we add 5 to the number x x + 5 The phrase [I]equals[/I] means we set both expressions equal to each other [B]2x = x + 5[/B] <-- This is our algebraic expression If you want to take this further and solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3Dx%2B5&pl=Solve']type this expression in the search engine[/URL] and we get: [B]x = 5[/B]

2 times a number minus 4 times another number is 6. The sum of 2 numbers is 8. Find the 2 numbers. Let the first number be x, and the second number be y. We're given two equations: [LIST=1] [*]2x - 4y = 6 [*]x + y = 8 [/LIST] Using our simultaneous equation calculator, there are 3 ways to solve this: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Substitution']Substitution[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Elimination']Elimination[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] They all give the same answers: (x, y) = [B](6.3333333, 1.6666667)[/B]

2 times a number subtracted by x The phrase [I]a number[/I] means an arbitrary variable, let's call it n. n 2 times a number means we multiply n by 2: 2n The phrase [I]subtracted by[/I] means we subtract 2n from x: [B]x - 2n[/B]

2 times as many dimes as quarters and they have a combined value of 180 cents, how many of each coin does he have? Let d be the number of dimes. Let q be the number of quarters. We're given two equations: [LIST=1] [*]d = 2q [*]0.1d + 0.25q = 180 [/LIST] Substitute (1) into (2): 0.1(2q) + 0.25q = 180 0.2q + 0.25q = 180 [URL='https://www.mathcelebrity.com/1unk.php?num=0.2q%2B0.25q%3D180&pl=Solve']Typing this equation into the search engine[/URL], we get: [B]q = 400[/B] Now substitute q = 400 into equation 1: d = 2(400) [B]d = 800[/B]

2 times b squared minus 6 b squared means we raise b to the 2nd power: b^2 2 times b squared 2b^2 Minus 6: [B]2b^2 - 6[/B]

A number means an arbitrary variable, let's call it x. Half of x means we divide x by 2, or multiply by 0.5 x/2 2 times half x is written: [B]2(x/2)[/B] If we simplify by cancelling the 2's, we just get x.

2 times the quantity x minus 1 is 12 The quantity x minus 1 is written as: x - 1 2 times this quantity: 2(x - 1) The word [I]is[/I] means an equation, so we set 2(x - 1) equal to 12: [B]2(x - 1) = 12[/B]

2 times the sum of 1 and some number is 30. What is the number? We let the phrase "some number" equal the variable x. The sum of 1 and some number is: x + 1 2 times the sum: 2(x + 1) The word "is" means equal to, so we set [B]2(x + 1) = 30[/B]

2 times the sum of 3 and 5 divided by 10 The sum of 3 and 5 is written as: 3 + 5 2 times this sum: 2(3 + 5) Then, we divide this by 10: [B]2(3 + 5)/10[/B] [B][/B] If the problem asks you to simplify this, you [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=2%283%2B5%29%2F10&pl=Perform+Order+of+Operations']type this expression into our search engine[/URL] and get: [B]1.6[/B]

2 times the sum of 3x and 5 the sum of 3x and 5 3x + 5 2 times the sum: [B]2(3x + 5)[/B]

2 times the sum of 7 times a number and 4 This is an algebraic expression. Let's take it in 4 parts: [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]7 times a number means we multiply x by 7: 7x [*]The sum of 7 times a number and 4 means we add 4 to 7x: 7x + 4 [*]Finally, we multiply the sum in #3 by 2 [/LIST] Build our final algebraic expression: [B]2(7x + 4)[/B]

2 times the sum of a number and 3 is equal to 3x plus 4 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The sum of a number and 3 means we add 3 to x: x + 3 2 times this sum means we multiply the quantity x + 3 by 2 2(x + 3) 3x plus 4 means 3x + 4 since the word plus means we use a (+) sign 3x + 4 The phrase [I]is equal to[/I] means an equation, where we set 2(x + 3) equal to 3x + 4 [B]2(x + 3) = 3x + 4[/B]

2 times the sum of a number x and 5 The sum of a number x and 5 means we add 5 to x: x + 5 2 times the sum: [B]2(x + 5)[/B]

2 times the sum of x and 7 plus 10 The sum of x and 7 means we add 7 to x x + 7 2 times the sum means we multiply the quantity x + 7 by 2 2(x + 7) Plus 10 means we add 10 to the 2(x + 7): [B]2(x + 7) + 10[/B]

2 tons of dirt cost $280.00. What is the price per pound? We know that 1 ton = 2000 pounds. So 2 tons = 2*2000 = 4,000 pounds We rewrite this as 4,000 pounds of dirt cost $280.00. We set up a proportion where p is the price per one pound: 4000/280 = 1/p [URL='https://www.mathcelebrity.com/prop.php?num1=4000&num2=1&den1=280&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Plugging this in our search engine[/URL], we get: p = [B]0.07 or 7 cents per pound.[/B]

2 traffic lights are turned on at the same time. 1 blinks every 4 seconds and. the other blinks every 6 seconds. In 60 seconds how many times will they blink at the same time? We want the [URL='https://www.mathcelebrity.com/gcflcm.php?num1=4&num2=6&num3=&pl=LCM']least common multiple of 4 and 6[/URL] which is 12. So ever 12 seconds, both lights blink together: [LIST=1] [*]12 [*]24 [*]36 [*]48 [*]60 [/LIST] So our answer is [B]5 times[/B]

2, 4, 6, 8....1000. What term is the number 1000? Formula for nth term is 2n If 2n = 1000, then dividing each side by 2, we see that: 2n/2 = 1000/2 n = [B]500[/B]

2-thirds of the sum of 5 and a plus the product of 3 and z The sum of 5 and a 5 + a 2-thirds of this sum: 2(5 + a)/3 The product of 3 and z: 3z The word [I]plus[/I] means we add the two terms together: [B]2(5 + a)/3 + 3z[/B]

2/3 of a number 17 is at least 29 The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x 2/3 of a number means we multiply x by 2/3: 2x/3 The phrase [I]is at least[/I] also means greater than or equal to, so we set up the inequality: [B]2x/3 >= 29[/B]

2/5 the cube of a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The cube of a number means we raise x to the power of 3: x^3 2/5 of the cube means we multiply x^3 by 2/5: [B](2x^3)/5[/B]

20 percent of my class is boys. There are 30 boys in class. How many girls in my class? Let c be the number of people in class. Since 20% = 0.2, We're given: 0.2c = 30 [URL='https://www.mathcelebrity.com/1unk.php?num=0.2c%3D30&pl=Solve']Type this equation into our search engine[/URL], we get: c = 150 Since the class is made up of boys and girls, we find the number of girls in the class by this equation: Girls = 150 - 30 Girls = [B]120[/B]

20 teachers made a bulk purchase of some textbooks. The teachers received a 24% discount for the bulk purchase, which originally cost $5230. Assuming the cost was divided equally among the teachers, how much did each teacher pay? [U]Calculate Discount Percent:[/U] If the teachers got a 24% discount, that means they paid: 100% - 24% = 76% [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=76&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']76% as a decimal[/URL] = 0.76 (Discount Percent) [U]Calculate discount price:[/U] Discount Price = Full Price * (Discount Percent) Discount Price = 5230 * 0.76 Discount Price = 3974.80 Price per teacher = Discount Price / Number of Teachers Price per teacher = 3974.80 / 20 Price per teacher = [B]$198.74[/B]

20% of a number is x. What is 100% of the number? Assume x>0. Let the number be n. We're given: 0.2n = x <-- Since 20% = 0.2 To find n, we multiply each side of the equation by 5: 5(0.2)n = 5x n = [B]5x[/B]

20% of Kay’s pencils in her pencil case are broken. What is the chance of taking a pencil that is not broken from the case if she picks one at random? This means 100% - 20% = 80% of pencils are not broken So the probability of drawing a pencil which is [I]not broken[/I] is 80%

$69.99 per apple / 200 apples We want the price per apple. Divide top and bottom by 200 $0.35 per apple.

200 feet shorter than the height of a light house Let the height of a light house be h: h 200 fee shorter mean we subtract 200 from h: [B]h - 200[/B]

2000 people attended a baseball game 1300 of the people attending supported the home team while 700 supported the visiting team what percentage of people attending supported the home team We want the percentage of 1300 out of 2000. [URL='https://www.mathcelebrity.com/perc.php?num=1300&den=2000&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']We go to our search engine and type 1300 out of 2300 as a percent[/URL] and we get: [B]65%[/B]

21 apples and 49 pears. What is the largest number of baskets to make and still use up all the fruit We use our [URL='https://www.mathcelebrity.com/gcflcm.php?num1=21&num2=49&num3=&pl=GCF+and+LCM']greatest common factor calculator for GCF(21, 49)[/URL] to get: GCF(21, 49) = 7 This means with [B]7 baskets[/B]: [LIST] [*]We divide 21 apples by 7 to get 3 apples per basket [*]We divide 49 pears by 7 to get 7 pears per basket [/LIST]

21 the total of 21 and? Let the number we want be n. We have: 21 = 21 + n n must be [B]0[/B], since 21 = 21

217 times u, reduced by 180 is the same as q. Take this algebraic expression pieces: Step 1: 217 times u We multiply the variable u by 217 217u Step 2: reduced by 180 Subtract 180 from 217u 217u - 180 The phrase [I]is the same as[/I] means an equation, so we set 217u - 180 equal to q [B]217u - 180 = q[/B]

2200 dollars is placed in an account with an annual interest rate of 7.25%. How much will be in the account after 29 years [URL='https://www.mathcelebrity.com/compoundint.php?bal=2200&nval=29&int=7.25&pl=Annually']Using our compound interest calculator[/URL], with an initial balance of 2,200, 29 years for time, and 7.25% annual interest rate, we get: [B]16,747.28[/B]

223 subtracted from the quantity 350 times a is equal to b Take this algebraic expression in parts: [LIST] [*]the quantity 350 times a: 350a [*]223 subtracted from the quantity: 350a - 223 [*]The phrase [I]is equal to[/I] means an equation, so we set 350a - 223 equal to b [/LIST] [B]350a - 223 = b[/B]

225 lines per second how many per minute There are 60 seconds in 1 minute, so we have: 225 lines 60 seconds ---------- * -------------- 1 second 1 minute Cancel the second from top and bottom, and we have: [B]13,500 lines --------------- 1 minute[/B]

231 is 248 subtracted from the quantity h times 128 Let's take this algebraic expression in parts: [LIST=1] [*]h times 128: 128h [*]24 subtracted from this: 128h - 248 [*]The word [I]is[/I] means an equation, so we set 128h - 248 equal to 231 [/LIST] [B]128h - 248 = 231[/B] <-- This is our algebraic expression If the problem asks you to solve for h, then you [URL='https://www.mathcelebrity.com/1unk.php?num=128h-248%3D231&pl=Solve']type in this equation into our search engine[/URL] and get: h = [B]3.742[/B]

237 what is the place value of 3 Place value for integers with no decimals from right to left is: 7 is the ones digit 3 is the [B]tens digit[/B]

24 coloring books, 60 crayons, and 84 markers can be packaged into at most how many identical packages? How many of each would each package contain? First, determine the greatest common factor (GCF) of 24, 60, and 84 using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=24&num2=60&num3=84&pl=GCF']GCF calculator[/URL]. GCF(24, 60, 84) = 12 So we have 12 identical packages. Now, figure out how many coloring books, crayons, and markers for each package [LIST] [*]24/12 = 2 coloring books [*]60/12 = 5 crayons [*]84/12 = 7 markers [/LIST] [B]So we have 12 identical packages, each containing 2 coloring books, 5 crayons, and 7 markers[/B]

24 students in a class took an algebra test and 19 of them earned a B or better. What percent of students earned a B or better? Using our [URL='http://www.mathcelebrity.com/perc.php?num=19&den=24&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']percentage calculator[/URL], we have: 19/24 = [B]79.1667%[/B]

249 equals 191 times c, decreased by 199 [U]Take this in pieces:[/U] 191 times c: 191c The phrase [I]decreased by[/I] means we subtract 199 from 191c: 191c - 199 We set this expression equal to 249: [B]191c - 199 = 249[/B] <-- This is our algebraic expression If you want to solve for c, type this equation into the search engine and we get: [B]c = 2.346[/B]

25 boxes are loaded on a truck. If each box weighs 22 kg, what is the total weight of the load? Total Weight = Number of boxes * weight per box Total Weight = 25 * 22 kg Total Weight = [B]550 kg[/B]

250 students have iPhones. This is one third of the population. How many students are there in total? Let the population be p. We're given: 1/3p = 250 Cross multiply: p = 250 * 3 p = [B]750[/B]

26 students 15 like vanilla 16 like chocolate. 3 do not like either flavour. How many like both vanilla and chocolate Define our people: [LIST=1] [*]We have Vanilla Only [*]Chocolate Only [*]Both Vanilla and Chocolate [*]Neither Vanilla Nor Chocolate [*]Add up 1-4 to get our total [/LIST] Total = Vanilla Only + Chocolate Only - Vanilla and Chocolate + Neither 26 = 15 + 16 - V&C + 3 26 = 34 - V&C Subtract 34 from each side -V&C = -8 Multiply each side by -1 [B]V&C = 8[/B]

2755 students were surveyed: 896 chose a falcon, 937 chose a ram, and 842 chose a panther. The remaining did not vote. What is the probability that the students choice was a panther? P(Panther) = Panther Choices / Total Students P(Panther) = 842/2,755 P(Panther) = [B]0.3056[/B]

28 students in class and 16 are boys what is percent of girls? Calculate the number of girls: Girls = Total Students - Boys Girls = 28 - 16 Girls = 12 The percent of girls is found by this formula: Percent of Girls = 100 * Number of Girls / Number of Students Percent of Girls = 100 * 12 / 28 Percent of Girls = 1,200 / 28 Percent of Girls = [B]42.86%[/B]

2900 dollars is placed in an account with an annual interest rate of 9%. Hoe much will be in the account after 13 years to the nearest cent Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=2900&nval=13&int=9&pl=Annually']compound interest with balance calculator[/URL], we get: [B]8,890.83[/B]

2900 dollars is placed in an account with annual interest rate of 9%. How much will be in the account after 13 years, round to the nearest cent Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=2090&nval=13&int=9&pl=Annually']compound interest calculato[/URL]r, we get a balance of: [B]6,407.53[/B]

[I]Is the same as[/I] means equal to. 230 more means we add 230. Set up this equation: c + 230 = 298 To solve for c if needed, visit our [URL='http://www.mathcelebrity.com/1unk.php?num=c%2B230%3D298&pl=Solve']calculator[/URL]. c = 68

2ade[IMG]https://fonts.gstatic.com/s/e/notoemoji/14.0/2797/72.png[/IMG](ae) 2ade/ae the ae terms cancel, so we have: [B]2d[/B]

2 consecutive even integers such that the smaller added to 5 times the larger gives a sum of 70. Let the first, smaller integer be x. And the second larger integer be y. Since they are both even, we have: [LIST=1] [*]x = y - 2 <-- Since they're consecutive even integers [*]x + 5y = 70 <-- Smaller added to 5 times the larger gives a sum of 70 [/LIST] Substitute (1) into (2): (y - 2) + 5y = 70 Group like terms: (1 + 5)y - 2 = 70 6y - 2 = 70 [URL='https://www.mathcelebrity.com/1unk.php?num=6y-2%3D70&pl=Solve']Typing 6y - 2 = 70 into our search engine[/URL], we get: [B]y = 12 <-- Larger integer[/B] Plugging this into Equation (1) we get: x = 12 - 2 [B]x = 10 <-- Smaller Integer[/B] So (x, y) = (10, 12)

2d = (a - b)/(b - c) for d Divide each side by 2 to isolate d: 2d/2 = (a - b)/2(b - c) Cancel the 2's on the left side, we get: d = [B](a - b)/2(b - c)[/B]

2m - n/3 = 5m for n Subtract 2m from each side of the equation: 2m-n/3 - 2m = 5m - 2m -n/3 = 3m Multiply each side of the equation by -3 to isolate n: -3 * -n/3 = -3 * 3m n = [B]-9m[/B]

2n + 1 = n + 10 Solve for [I]n[/I] in the equation 2n + 1 = n + 10 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 2n and n. To do that, we subtract n from both sides 2n + 1 - n = n + 10 - n [SIZE=5][B]Step 2: Cancel n on the right side:[/B][/SIZE] n + 1 = 10 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 1 and 10. To do that, we subtract 1 from both sides n + 1 - 1 = 10 - 1 [SIZE=5][B]Step 4: Cancel 1 on the left side:[/B][/SIZE] n = [B]9[/B]

2n + 10 = 3n + 5 Solve for [I]n[/I] in the equation 2n + 10 = 3n + 5 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 2n and 3n. To do that, we subtract 3n from both sides 2n + 10 - 3n = 3n + 5 - 3n [SIZE=5][B]Step 2: Cancel 3n on the right side:[/B][/SIZE] -n + 10 = 5 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 10 and 5. To do that, we subtract 10 from both sides -n + 10 - 10 = 5 - 10 [SIZE=5][B]Step 4: Cancel 10 on the left side:[/B][/SIZE] -n = -5 [SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE] -1n/-1 = -5/-1 n = [B]5[/B]

2n + 8 - n = 20 Solve for [I]n[/I] in the equation 2n + 8 - n = 20 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (2 - 1)n = n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] n + 8 = + 20 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 8 and 20. To do that, we subtract 8 from both sides n + 8 - 8 = 20 - 8 [SIZE=5][B]Step 4: Cancel 8 on the left side:[/B][/SIZE] n = [B]12[/B]

2n + 8 = 24 Solve for [I]n[/I] in the equation 2n + 8 = 24 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 8 and 24. To do that, we subtract 8 from both sides 2n + 8 - 8 = 24 - 8 [SIZE=5][B]Step 2: Cancel 8 on the left side:[/B][/SIZE] 2n = 16 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2n/2 = 16/2 n = [B]8[/B]

2n - 1&1/2n = 59 1&1/2n = 3/2n or 1.5n So we have: 2n - 1.5n = 59 Solve for [I]n[/I] in the equation 2n - 1.5n = 59 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (2 - 1.5)n = 0.5n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 0.5n = + 59 [SIZE=5][B]Step 3: Divide each side of the equation by 0.5[/B][/SIZE] 0.5n/0.5 = 59/0.5 n = [B]118[/B]

2n - 7 = 0 Solve for [I]n[/I] in the equation 2n - 7 = 0 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -7 and 0. To do that, we add 7 to both sides 2n - 7 + 7 = 0 + 7 [SIZE=5][B]Step 2: Cancel 7 on the left side:[/B][/SIZE] 2n = 7 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2n/2 = 7/2 n = [B]3.5[/B]

2n = 4n Solve for [I]n[/I] in the equation 2n = 4n [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 2n and 4n. To do that, we subtract 4n from both sides 2n - 4n = 4n - 4n [SIZE=5][B]Step 2: Cancel 4n on the right side:[/B][/SIZE] -2n = 0 [SIZE=5][B]Step 3: Divide each side of the equation by -2[/B][/SIZE] -2n/-2 = 0/-2 n = [B]0[/B]

2x - b/y = 4c for y Subtract 2x from each side: 2x - 2x - b/y = 4c - 2x Cancel the 2x's on the left side and we get: -b/y = 4c - 2x Cross multiply: -b = y(4c - 2x) Divide each side by (4c - 2x): -b/(4c - 2x) = y(4c - 2x)/(4c - 2x) Cancel the (4c - 2x) on the right side and we get: [B]y = -b/(4c - 2x) [/B]

2x decreased by 15 is equal to -27 The phrase [I]decreased by[/I] 15 means we subtract 15 from 2x: 2x - 15 The phrase [I]is equal to[/I] means an equation, so we set 2x - 15 equal to -27 [B]2x - 15 = -27 [/B] <-- This is our algebraic expression To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D-27&pl=Solve']type 2x - 15 = -27 into the search engine[/URL].

2x increased by 3 times a number The phrase [I]a number[/I] means an arbitary variable, let's call it x. 3 times a number means we multiply x by 3: 3x The phrase [I]increased by[/I] means we add 3x to 2x: 2x + 3x Simplifying, we get: [B]5x[/B]

2x plus 4 increased by 15 is 57 Take this algebraic expression in parts: [LIST] [*]2x plus 4: 2x + 4 [*][I]Increased by[/I] means we add 15 to 2x + 4: 2x + 4 + 15 = 2x + 19 [*]The word [I]is[/I] means an equation, so we set 2x + 19 equal to 57: [/LIST] Our final algebraic expression is: [B]2x + 19 = 57 [/B] To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B19%3D57&pl=Solve']type this equation into our search engine [/URL]and we get x = [B]19[/B]

2x plus 8, quantity squared 2x plus 8 means we add 8 to 2x: 2x + 8 Squaring the quantity means we raise it to the power of 2: [B](2x + 8)^2[/B]

2x/5 - 9y = 6 for x Add 9y to each side to isolate the x term: 2x/5 - 9y + 9y = 9y + 6 Cancel the 9y's on the left side: 2x/5 = 9y + 6 Multiply each side by 5: 2x * 5/5 = 5(9y + 6) Cancel the 5's on the left side and we get: 2x = 5(9y + 6) Divide each side by 2 to isolate x: 2x/2 = 5/2(9y + 6) Cancel the 2's on the left side and we get our final literal equation of: x = [B]5/2(9y + 6)[/B]

2x/5 - 9y = 6 for x Add 9y to each side of the equation: 2x/5 - 9y + 9y = 6 + 9y Cancel the 9y's on the left side to get: 2x/5 = 6 + 9y Multiply each side of the equation by 5: 5(2x/5) = 5(6 + 9y) Cancel the 5's on the left side to get 2x = 5(6 + 9y) Divide each side of the equation by 2: 2x/2 = 5/2(6 + 9y) Cancel the 2's on the left side to get: x = [B]5/2(6 + 9y)[/B]

2x^2+4x < 3x+6 Subtract 3x from both sides: 2x^2 + x < 6 Subtract 6 from both sides 2x^2 + x - 6 < 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=2x%5E2%2Bx-6&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get: x < 1.5 and x < -2 When we take the intersection of these, it's [B]x < 1.5[/B]

2y divided by the sum of 3x and 5 The sum of 3x and 5 means we add 5 to 3x: 3x + 5 2y divided by the sum of 3x and 5: [B]2y/(3x + 5)[/B]

3a + 4c = 136 2a + 3c = 97 [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=3a+%2B+4c+%3D+136&term2=2a+%2B+3c+%3D+97&pl=Cramers+Method']Using any of the 3 methods here[/URL]: [B]a = 20 c = 19[/B]

3 boys share 100 in the ratio 1:2:2. how much each boy will get? Given the ratio 1 : 2 : 2, calculate the expected number of items from a population of 100 A ratio of 1 : 2 : 2 means that for every of item A, we can expect 2 of item B and 2 of item c Therefore, our total group is 1 + 2 + 2 = 5 [SIZE=5][B]Calculate Expected Number of Item A:[/B][/SIZE] Expected Number of Item A = 1 x 100/5 Expected Number of Item A = 100/5 Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=100&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5 Expected Number of Item A = 20/1 Expected Number of Item A = [B]20[/B] [SIZE=5][B]Calculate Expected Number of Item B:[/B][/SIZE] Expected Number of Item B = 2 x 100/5 Expected Number of Item B = 200/5 Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5 Expected Number of Item B = 40/1 Expected Number of Item B = [B]40[/B] [SIZE=5][B]Calculate Expected Number of Item C:[/B][/SIZE] Expected Number of Item C = 2 x 100/5 Expected Number of Item C = 200/5 Using our [URL='http://mathcelebrity.com/gcflcm.php?num1=200&num2=5&pl=GCF']GCF Calculator[/URL], we see this fraction can be reduced by 5 Expected Number of Item C = 40/1 Expected Number of Item C = [B]40[/B] [B]Final Answer:[/B] (A, B, C) =[B] (20, 40, 40)[/B] for 1:2:2 on 100 people

3 cartons of eggs for $5 what if the cost of 8 cartons Set up a proportion of cartons of eggs to price where p is the price of 8 cartons: 3/5 = 8/p [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=8&den1=5&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get: p = [B]13.33[/B]

3 cases of fresh apples that cost $21.95 per case with 20% off and a 7.5% sales tax Figure out the total cost before the discount: Total Cost before discount = Cases * Price per case Total Cost before discount = 3 cases * $21.95 per case Total Cost before discount = $65.85 Now, find the discounted value of the apples: Discounted Apple Price = Total Cost before discount * (1 - discount percent) Discounted ApplesPrice = $65.85 * (1 - 0.2) <-- 20% is the same as 0.2 Discounted ApplesPrice = $65.85 * 0.8 Discounted ApplesPrice = $52.68 Now, apply the sales tax to this discounted value to get the total bill: Total Bill = Discounted Apple Price * (1 + tax rate) Total Bill = $52.68 * (1 + .075) <-- 7.5% = 0.075 Total Bill = $52.68 * 1.075 Total Bill = [B]$56.63[/B]

3 children painted a local park track of 5000m, Alex painted 70m, Dell painted 15m, and Tony painted 35m. This pattern continues to the end of the track. What percentage of the park did each child paint? 70 + 15 + 35 = 120 When we take[URL='https://www.mathcelebrity.com/modulus.php?num=5000mod120&pl=Calculate+Modulus'] 5000 divided by 120[/URL], we get: 41 remainder 80 So we have: [LIST] [*]Alex: 70 * 41 = 2870 [*]Dell: 15 * 41 = 615 [*]Tony: 35 * 41 = 1435 [/LIST] Now Alex goes next, and paints the full 70. So he has: 2870 + 70 = 2940 Dell goes next, and paints the last 10 615 + 10 = 625 Now for percentages: [LIST] [*]Alex: 2940/5000 = [B]58.8%[/B] [*]Dell: 625/5000 = [B]12.5%[/B] [*]Tony: 1435/5000 = [B]28.7%[/B] [/LIST]

3 consecutive odd integers such that thrice the middle is 15 more than the sum of the other 2. [LIST] [*]Let the first integer be n [*]The next odd one (middle) is n + 2. [*]The next odd one is n + 4 [/LIST] We are given 3(n + 2) = n + n + 4 + 15. Simplifying, we get: 3n + 6 = 2n + 19 [URL='http://www.mathcelebrity.com/1unk.php?num=3n%2B6%3D2n%2B19&pl=Solve']Plugging that problem[/URL] into our search engine, we get n = 13. So the next odd integer is 13 + 2 = 15 The next odd integer is 15 + 2 = 17

3 friends went to dinner and their total bill was $19.50. They each brought $8. If a tip is typically between 15% and 20% of the bill do they have enough for dinner and tip? 15% tip: 19.50 * 1.15 = 22.43 20% tip: 19.50 * 1.2 = 23.4 3 friends each brought $8, so they have: 3 * 8 = $24 So the $24 [B]will cover both a 15% tip and a 20% tip[/B]

3 is subtracted from square of a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x Square of a number means we raise x to the 2nd power: x^2 3 is subtracted from square of a number [B]x^2 - 3[/B]

3 is subtracted from the square of x Let's take this algebraic expression in two parts: Part 1: The square of x means we raise x to the power of 2: x^2 Part 2: 3 is subtracted means we subtract 3 from x^2 [B]x^2 - 3[/B]

3 less than a number times itself The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x Itself means the same variable as above. So we have: x * x x^2 3 less than this means we subtract 3 from x^2: [B]x^2 - 3[/B]

The product of 7 and a number x is written as 7x. 3 more than that product is written as 7x + 3. Finally, that entire expression is less than 26, so we have: 7x + 3 < 26 as our algebraic expression.

3 pack of bouncy balls for $0.96 or 9 pack of bouncy balls for $3.15 Item 1, the 3 pack is the better buy shown on our [URL='http://www.mathcelebrity.com/betterbuy.php?p1=0.96&p2=3.15&q1=3&q2=9&pl=Better+Buy']better buy calculator[/URL].

3 people can build a shed in 8 hours, how long would it take 5 people We set up a proportion of people to hours where h is the number of hours for 5 people: 3/8 = 5/h [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=5&den1=8&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']Using our proportion calculator[/URL], we get: 13.3333 hours But what if the problem asks for minutes? Then we say 8 hours = 60 * 8 = 480 minutes. We set up the proportion where m is the number of minutes: 3/480 = 5/m In this case, [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=5&den1=480&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']we use our search engine again[/URL] and get: m = 800

3 per ride r plus $10 to get into the park Cost function C(r) where r is rides: C(r) = Rate per ride * number of rides + admission cost [B]C(r) = 3r + 10[/B]

We need to find the unit cost, which is the cost of one unit of measurement. The measurement unit is in pounds. If it costs $11.25 for a 3 pound bag, how much is it per pound? $11.25/3 = $3.75 per pound.

3 salads, 4 main dishes, and 2 desserts Total meal combinations are found by multiplying each salad, main dish, and dessert using the fundamental rule of counting. The fundamental rule of counting states, if there are a ways of doing one thing, b ways of doing another thing, and c ways of doing another thing, than the total combinations of all the ways are found by a * b * c. With 3 salads, 4 main dishes, and 2 desserts, our total meal combinations are: 3 * 4 * 2 = [B]24 different meal combinations.[/B]

3 subtracted from the cost of the book Let the cost of the book be b. We have: [B]b - 3[/B]

3 times a number increased by 1 is between -8 and 13. Let's take this algebraic expression in [U]4 parts[/U]: Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x Part 2 - 3 times this number means we multiply x by 3: 3x Part 3 - Increased by 1 means we add 1 to 3x: 3x + 1 The phrase [I]between[/I] means we have an inequality: [B]-8 <= 3x + 1 <=13[/B]

3 times a number is 3 more a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 3 times a number: 3x 3 more than a number means we add 3 to x: x + 3 The word [I]is[/I] means and equation, so we set 3x equal to x + 3 [B]3x = x + 3[/B]

The sum of 4 and 9: 4 + 9 3 times larger than this sum [B]3(4 + 9) <-- This is our algebraic expression [/B] Evaluating this amount: 3(13) [B]39[/B]

3 times the difference between t and y Difference between t and y t - y 3 times this difference: [B]3(t - y)[/B]

3 times the difference of a and b is equal to 4 times c [U]The difference of a and b:[/U] a - b [U]3 times the difference of a and b:[/U] 3(a - b) [U]4 times c:[/U] 4c The phrase [I]is equal to[/I] means an equation. So we set 3(a - b) equal to 4c: [B]3(a - b) = 4c[/B]

The difference of x and 5 means we subtract: x - 5 3 times the difference means we multiply (x - 5) by 3 3(x - 5) Is, means equal to, so we set our expression equal to 15 [B]3(x - 5) = 15 [/B] If you need to take it one step further to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3%28x-5%29%3D15&pl=Solve']equation calculator[/URL]

3 times the quantity 2 decreased by x is 9 The quantity 2 decreased by x. The phrase [I]decreased by[/I] means we subtract: 2 - x 3 times the quantity: 3(2 - x) The word [I]is[/I] means equal to, so we set 3(2 - x) equal to 9: [B]3(2 - x) = 9 [MEDIA=youtube]Hzyt_GajZA4[/MEDIA][/B]

3 times the square of a number x minus 12. Build the algebraic expression piece by piece: [LIST] [*]Square of a number x: x^2 [*]3 times this: 3x^2 [*]Minus 12: [B]3x^2 - 12[/B] [/LIST]

3 times the sum of 2 decreased by x is 9 2 decreased by x: 2 - x 3 times the sum means we multiply 2 - x by 3: 3(2 - x) The phrase [I]is 9[/I] means equal to, so we set 3(2 - x) equal to 9: [B]3(2 - x) = 9[/B]

3 times the sum of twice k and 8 Twice k means we multiply k by 2: 2k The sum of twice k and 8: 2k + 8 3 times the sum: [B]3(2k + 8)[/B]

3 times the sum of x and 9y The sum of x and 9y means we add 9y to x: x + 9y Now we take this sum, and multiply by 3 to get our final algebraic expression: 3(x + 9y)

3 times the width plus 2 times the length Let w be the width Let l be the length We have an algebraic expression of: [B]3w + 2l[/B]

3 times x minus y is 5 times the sum of y and 2 times x Take this algebraic expression in pieces: 3 times x: 3x Minus y means we subtract y from 3x 3x - y The sum of y and 2 times x mean we add y to 2 times x y + 2x 5 times the sum of y and 2 times x: 5(y + 2x) The word [I]is[/I] means an equation, so we set 3x - y equal to 5(y + 2x) [B]3x - y = 5(y + 2x)[/B]

3 to the power of 2 times 3 to the power of x equals 3 to the power of 7. Write this out: 3^2 * 3^x = 3^7 When we multiply matching coefficients, we add exponents, so we have: 3^(2 + x) = 3^7 Therefore, 2 + x = 7. To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%2Bx%3D7&pl=Solve']type it into our search engine[/URL] and we get: x = [B]5[/B]

3 tons of compost cost $3,600.00. What is the price per pound? 1 ton = 2000 pounds, so 3 tons is: 3 * 2000 = 6000 pounds Price per pound = Cost / Total pounds Price per pound = 3600 / 6000 Price per pound = [B]$0.60 per pound[/B]

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3, 6, 12, 24, 48 What is the function machine for this sequence? We see the following pattern: 3 * 2^0 = 3 3 * 2^1 = 6 3 * 2^2 = 12 3 * 2^3 = 24 3 * 2^4 = 48 Our function machine for term n is: [B]f(n) = 3 * 2^(n - 1)[/B]

3, 8, 13, 18, .... , 5008 What term is the number 5008? For term n, we have a pattern: f(n) = 5(n - 1) + 3 Set this equal to 5008 5(n - 1) + 3 = 5008 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=5%28n-1%29%2B3%3D5008&pl=Solve']equation solver,[/URL] we get: n = [B]1002[/B]

987 x 9 ------ Break apart 987: 900 + 80 + 7 So we have: 900 * 9 = 8100 80 * 9 = 720 7 * 9 = 63 Add them up and we get [B]8,883[/B] [MEDIA=youtube]4PfdF3co6HI[/MEDIA]

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3.50 per pound. you bought 18.25 worth of strawberries The question asks for unit cost. Unit Cost = Total Cost / Total Quantity Unit Cost = 18.25 / 3.50 Unit Cost = [B]5.21[/B]

3/4 a number b divided by 5 3/4 a number b: 3b/4 Divided by 5: 3b/4/5 We multiply top and bottom by 5 to remove the double fraction: 3b*5/4 [B]15b/4[/B]

3/4 of the students went skiing.there are 24 students in the class. How’s many went? We want 3/4 of 24. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=24&frac2=3/4&pl=Multiply']type 3/4 of 24 into our search engine[/URL] and get: [B]18 students[/B]

3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the program, how many workers are employed at this company? We read this as 3/5 of the total workers employed at the company equals 24. Let w be the number of workers. We have the following equation: 3/5w = 24 Run [URL='http://www.mathcelebrity.com/1unk.php?num=3%2F5w%3D24&pl=Solve']3/5w = 24[/URL] through the search engine, we get [B]w = 40[/B].

3/8 of income is rent. 360 is rent. How much is annual income Let i equal the annual income. We're told the following: 3i/8 = 360 To solve for i, we [URL='https://www.mathcelebrity.com/prop.php?num1=3i&num2=360&den1=8&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type this in our math engine[/URL] and we get: i = [B]960 [MEDIA=youtube]8gue05tlEGQ[/MEDIA][/B]

Let "a number" equal the arbitrary variable x. The square of that is x^2. 3 times the square of that is 3x^2. Now, 30 increased by means we add 3x^2 to 30 30 + 3x^2

30 increased by 3 times the square of a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x x The square of a number means we raise x to the power of 2: x^2 3 times the square: 3x^2 The phrase [I]increased by[/I] means we add 3x^2 to 30: [B]30 + 3x^2[/B]

30 is equal to thrice y decreased by z Thrice y means we multiply y by 3: 3y Decreased by z means we subtract z from 3y 3y - z The phrase [I]is[/I] means an equal to, so we set up an equation where 3y - z is equal to 30 [B]3y - z = 30[/B]

30 people are selected randomly from a certain town. If their mean age is 60.5 and ? = 4.6, find a 95% confidence interval for the true mean age, ?, of everyone in the town.

30% larger then 1/3 of twice q Take this algebraic expression in 3 parts: [LIST=1] [*]Twice q means multiply q by 2: 2q [*]1/3 of twice q means we multiply 2q in Step 1 by 1/3: 2q/3 [*]30% larger means we multiply 2q/3 in step 2 by 1.3, since 30% = 0.3: 1.3(2q/3) [/LIST] [B]1.3(2q/3)[/B]

300 reduced by 5 times my age is 60 Let my age be a. We have: 5 times my age = 5a 300 reduced by 5 times my age means we subtract 5a from 300: 300 - 5a The word [I]is[/I] means an equation, so we set 300 - 5a equal to 60 to get our final algebraic expression: [B]300 - 5a = 60 [/B] If you have to solve for a, you [URL='https://www.mathcelebrity.com/1unk.php?num=300-5a%3D60&pl=Solve']type this equation into our search engine[/URL] and you get: a = [B]48[/B]

309 is the same as 93 subtracted from the quantity f times 123. The quantity f times 123: 123f Subtract 93: 123f - 93 The phrase [I]is the same as[/I] means an equation, so we set 123f - 93 equal to 309 [B]123f - 93 = 309[/B] <-- This is our algebraic expression If you wish to solve for f, [URL='https://www.mathcelebrity.com/1unk.php?num=123f-93%3D309&pl=Solve']type this equation into the search engine[/URL], and we get f = 3.2683.

31,29,24,22,17 what comes next We see that each sequence term alternates between subtracting 2 and subtracting 5. Since the last term, 17, was found by subtracting 5, our next term is found by subtracting 2 from 17: 17 - 2 = [B]15[/B]

32 girls and 52 boys were on an overseas learning trip . They were divided into as many groups as possible where the number of groups of girls and the number of groups of boys is the same .how many boys and how many girls were in each group We want a number such that our total members divided by this number equals our group size. We take the greatest common factor (32,52) = 4 Therefore, we have: [LIST] [*][B]32/4 = 8 girls in each group[/B] [*][B]52/4 = 13 boys in each group[/B] [/LIST]

324 times z, reduced by 12 is z. Take this algebraic expression in pieces: 324 [I]times[/I] z means we multiply 324 by the variable z. 324z [I]Reduced by[/I] 12 means we subtract 12 from 324z 324z - 12 The word [I]is[/I] means we have an equation, so we set 324z - 12 equal to z [B]324z - 12 = z [/B] <-- This is our algebraic expression

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? The number of students who went on the bus is 331 - 7 in the car = 324 324 students on the bus / 6 buses = [B]54 per bus[/B]

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were In bus? Subtract the 7 students in cars, and we're left with: 331 - 7 = 324 students in buses. 324 students / 6 buses = [B]54 students in each bus[/B].

331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? Calculate the students in buses: Students in buses = Total Students - Students in Cars Students in buses = 331 - 7 Students in buses = 324 Calculate the students in each bus Students in each bus = Students in buses / Number of Buses Students in each bus = 324 / 6 Students in each bus = [B]54[/B]

339 equals 303 times w, minus 293 Take this algebraic expression in pieces: 303 times w: 303w Minus 293: 303w - 293 The phrase [I]equals[/I] means we have an equation. We set 303w - 293 = 339 [B]303w - 293 = 339[/B] <-- This is our algebraic expression To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=303w-293%3D339&pl=Solve']we type this equation into our search engine[/URL] to get: [B]w = 2.086[/B]

35 added to n is greater than or equal to the sum of k and 21 Take this algebraic expression in 3 parts: [LIST=1] [*]35 added to n means we have a sum: n + 35 [*]The sum of k and 21 means we add 21 to k: k +21 [*]The phrase [I]greater than or equal to[/I] means an inequality using this sign (>=), so we write this as follows: [/LIST] [B]n + 35 >= k + 21[/B]

35 m/s for 40 s. how far does it travel? This is a distance problem. The formula to relate, distance, rate, and time is: d = rt We are given r = 35 m/s and t = 40s. We want d d = 35 m/s * 40s d = [B]1,400 meters[/B]

35% of the houses are blue. Write the percent that do not live in blue houses as a decimal and a fraction in simplest form The percent that do not live in blue houses is found by: Not in blue = 100% - 35% Not in blue = 65% [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=65&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Typing 65% in our search engine[/URL], we see that the decimal and fraction is: [LIST] [*]65% as a decimal: [B]0.65[/B] [*]65% as a fraction in simplest form: [B]13/20[/B] [/LIST]

36 PAGES AND IT 3/8CM THICK, WHAT IS THE THICKNESS OF 1 PAGE? Set up a proportion in pages to cm: 36 pages /3/8cm = 1 page/x cm Cross multiply: 36x = 3/8 Divide each side by 36 x = 3/(8 * 36) x = 1/(8*12) x = [B]1/96 cm[/B]

36% of the pupils in class 2 are boys the remaining 16 are girls how many pupils are in class 2? This means 100% - 36% = 64% of the class are girls. And if the class size is s, then we have: 64% of s = 16 Or, written as a decimal: 0.64s = 16 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.64s%3D16&pl=Solve']type it into our search engine[/URL] and we get: s = [B]25[/B]

[U]q times 146:[/U] 146q [U]365 subtracted from that:[/U] 146q - 365 [U]Is the same as means equal to, so we have:[/U] [B]146q - 365 = w[/B]

38 books into 8 boxes. 6 left. How many books in each box Let the number of books in each box be b. We have the following relation: 8b + 6 = 38 to solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B6%3D38&pl=Solve']type it in our search engine[/URL] and we get: b = [B]4[/B]

3abc^4/12a^3(b^3c^2)^2 * 8ab^-4c/4a^2b Expand term 1: 3abc^4/12a^3(b^3c^2)^2 3abc^4/12a^3b^6c^4 Now simplify term 1: 3/12 = 1/4 c^4 terms cancel Subtract powers from variables since the denominator powers are higher: b^(6 - 1) = b^5 a^(3 - 1) = a^2 1/4a^2b^5 Now simplify term 2: 8ab^-4c/4a^2b 8/4 = 2 2c/a^(2 - 1)b^(1 - -4) 2c/ab^5 Now multiply simplified term 1 times simplified term 2: 1/4a^2b^5 * 2c/ab^5 (1 * 2c)/(4a^2b^5 * ab^5) 2c/4a^(2 + 1)b^(5 + 5) 2c/4a^3b^10 2/4 = 1/2, so we have: [B]c/2a^3b^10[/B]

3f,subtract g from the result, then divide what you have by h Take this algebraic expression in pieces: 3f subtract g means we subtract the variable g from the expression 3f: 3f - g Divide what we have by h, means we take the result above, 3f - g, and divide it by h: [B](3f - g)/h[/B]

3k^3 = rt for t This is a literal equation. Let's divide each side of the equation by r, to isolate t: 3k^3/r = rt/r Cancel the r's on the right side, and we get: t = [B]3k^3/r[/B]

A necklace chain costs $15. Beads cost $2.50 each. You spend a total of $30 on a necklace and beads before tax. How many beads did you buy in addition to the necklace? Let the number of beads be b. We're given the following equation: 2.5b + 15 = 30 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5b%2B15%3D30&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]6[/B]

3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5 This is an algebraic expression. Let's take this algebraic expression in 5 parts: [LIST=1] [*]The sum of 2x and 1 means we add 1 to 2x: 2x + 1 [*]2 times the sum of 2x and 1: 2(2x + 1) [*]3x less than the sum of 2x and 1 means we subtract 3x from 2(2x + 1): 2(2x + 1) - 3x [*]The sum of 2 and 5 means we add 5 to 2: 2 + 5 [*]Finally, the phrase [I]equal[/I] means an equation, so we set #3 equal to #4 [/LIST] Our algebraic expression is: [B]2(2x + 1) - 3x = 2 + 5[/B] Now, some problems may ask you to simplify. In this case, we multiply through and group like terms: 4x + 2 - 3x = 7 [B]x + 2 = 7 <-- This is our simplified algebraic expression [/B] Now, what if the problem asks you to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B2%3D7&pl=Solve']you type this into our search engine[/URL] and get: x =[B] 5 [MEDIA=youtube]3hzyc2NPCGI[/MEDIA][/B]

3x over 27 equals 2x minus 2 over 15 3x over 27: 3x/27 2x minus 2 over 15: (2x - 2)/15 Set them equal to each other: 3x/27 = (2x - 2)/15

3x to the power 2n We take the expression 3x raise it to the power of 2n [B](3x)^2n[/B]

4 adults and 3 children cost $40. Two adults and 6 children cost $38 Givens and Assumptions: [LIST] [*]Let the number of adults be a [*]Let the number of children be c [*]Cost = Price * Quantity [/LIST] We're given 2 equations: [LIST=1] [*]4a + 3c = 40 [*]2a + 6c = 38 [/LIST] We can solve this system of equations 3 ways [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4a+%2B+3c+%3D+40&term2=2a+%2B+6c+%3D+38&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we use, we get: [LIST] [*][B]a = 7[/B] [*][B]c = 4[/B] [/LIST]

4 consecutive integers such that the sum of the first 3 integers is equal to the 4th Let n be our first consecutive integer. [LIST=1] [*]n [*]n + 1 [*]n + 2 [*]n + 3 [/LIST] The sum of the first 3 integers is equal to the 4th: n + n + 1 + n + 2 = n + 3 Simplify by grouping like terms: (n + n + n) + (1 + 2) = n + 3 3n + 3 = n + 3 3n = n n = 0 n = 0 n + 1 = 1 n + 2 = 2 n + 3 = 3 Check our work: 0 + 1 +2 ? 3 3 = 3 Our final answer is [B](0, 1, 2, 3}[/B]

4 divided by sin60 degrees. We can write as 4/sin(60). [URL='https://www.mathcelebrity.com/anglebasic.php?entry=60&coff=&pl=sin']Using our trigonometry calculator[/URL], we see sin(60) = sqrt(3)/2. So we have 4/sqrt(3)/2. Multiplying by the reciprocal we have: 4*2/sqrt(3) [B]8/sqrt(3)[/B]

4 less than the sum of 7 and 5 Write this out [B](7 + 5) - 4[/B] Simplified 12 - 4 [B]8[/B]

4 machines can complete a job in 6 hours how long will it take 3 machines to complete the same jobs? Set up a proportion of machines to hours where h is the number of hours that 3 machines take: 4/6 = 3/h [URL='https://www.mathcelebrity.com/prop.php?num1=4&num2=3&den1=6&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL] and we get: h = [B]4.5[/B]

4 minus 3p equals 36 4 minus 3p: 4 - 3p The phrase [I]equals[/I] means an equation, so we set 4 - 3p equal to 36: [B]4 - 3p = 36[/B]

4 multiplied by the cube of p is reduced by 5 The cube of p means we raise p to the 3rd power: p^3 4 multiplied by the cube of p 4p^3 reduced by 5: [B]4p^3 - 5[/B]

4 rectangular strips of wood, each 30 cm long and 3 cm wide, are arranged to form the outer section of a picture frame. Determine the area inside the wooden frame. Area inside forms a square, with a length of 30 - 3 - 3 = 24. We subtract 3 twice, because we account for 2 rectangular strips with a width of 3. Area of a square is side * side. So we have 24 * 24 = [B]576cm^2[/B]

4 teaspons of vegetable oil and 6 teaspoons of vinegar. 20 teaspoons of vegetable oil to how many teaspoons of vinegar? Set up a proportion where x is the number of teaspoons of vinegar in the second scenario: 4/6 = 20/x [URL='http://www.mathcelebrity.com/prop.php?num1=4&num2=20&den1=6&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']Plug that expression into the search engine to get[/URL] [B]x = 30[/B]

4 times 8 to the sixth power 8 to the 6th power: 8^6 4 times this amount: 4 * 8^6 To evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=4%2A8%5E6&pl=Perform+Order+of+Operations']type it in our search engine[/URL] and we get: 1,048,576

4 times a number added to 8 times a number equals 36 Let [I]a number[/I] be an arbitrary variable, let us call it x. 4 times a number: 4x 8 times a number: 8x We add these together: 4x + 8x = 12x We set 12x equal to 36 to get our final algebraic expression of: [B]12x = 36 [/B] If the problem asks you to solve for x, you [URL='https://www.mathcelebrity.com/1unk.php?num=12x%3D36&pl=Solve']type this algebraic expression into our search engine[/URL] and get: x = [B]3[/B]

4 times a number cubed decreased by 7 A number is denoted as an arbitrary variable, let's call it x x Cubed means raise x to the third power x^3 Decreased by 7 means subtract 7 x^3 - 7

4 times a number is the same as the number increased by 78. Let's take this algebraic expression in parts: [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]4 times a number is written as 4x [*]The number increased by 78 means we add 78 to x: x + 78 [*]The phrase [I]the same as[/I] mean an equation, so we set #2 equal to #3 [/LIST] [B]4x = x + 78[/B] <-- This is our algebraic expression If the problem asks you to take it a step further, then [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3Dx%2B78&pl=Solve']we type this equation into our search engine [/URL]and get: x = 26

4 times b increased by 9 minus twice y Take this algebraic expression in parts: Step 1: 4 times b means we multiply the variable b by 4: 4b Step 2: Increased by 9 means we add 9 to 4b: 4b + 9 Step 3: Twice y means we multiply the variable y by 2: 2y Step 4: The phrase [I]minus[/I] means we subtract 2y from 4b + 9 [B]4b + 9 - 2y[/B]

4 times of the sum of the cubes of x and y The cube of x means we raise x to the 3rd power: x^3 The cube of y means we raise y to the 3rd power: y^3 The sum of the cubes means we add: x^3 + y^3 4 times the sum of the cubes: [B]4(x^3 + y^3)[/B]

4 times the difference of 6 times a number and 7 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 6 times a number 6x The difference of 6x and 7 means we subtract 7 from 6x: 6x - 7 Now we multiply this difference by 4: [B]4(6x - 7)[/B]

4 times the number of cows plus 2 times the number of ducks Let c be the number of cows. Let d be the number of ducks. We've got an algebraic expression below: [B]4c + 2d[/B]

4 times the quantity of a number plus 6 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The word [I]plus[/I] means we addd 6 to x x + 6 The phrase [I]4 times the quantity [/I]means we multiply x + 6 by 4 [B]4(x + 6)[/B]

4 times the sum of 10 and twice x Twice x means we multiply x by 2: 2x The sum of 10 and twice x: 10 + 2x Now multiply this sum by 4: [B]4(10 + 2x)[/B]

4 times the sum of 3 plus x squared x squared means we raise x to the power of 2: x^2 3 plus x squared: 3 + x^2 4 times the sum of 3 plus x squared 3(3 + x^2)

The sum of q and p is written q + p 4 times the sum of q and p is written as: [B]4(q + p)[/B]

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4/5 of the sum of k and 3 The sum of k and 3 means we add 3 to k: k + 3 4/5 of the sum means we multiply 4/5 times the sum k + 3: [B]4(k + 3)/5[/B]

40% of the days in September were sunny how many days were sunny? September has 30 days. So we [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=40&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type 40% of 30 in our search engine[/URL]. We get: [B]12 days[/B]

400 reduced by 3 times my age is 214 Let my age be a. We have: 3 times my age: 3a 400 reduced by 3 times my age: 400 - 3a The word [I]is[/I] means an equation. So we set 400 - 3a equal to 214 400 - 3a = 214 Now if you want to solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D214&pl=Solve']type it in the search engin[/URL]e and we get; a = [B]62[/B]

41% of the passengers on the plane are men. 36% of them are women and 11% of them are boys. The remaining 30 passengers are girls. How many passengers are on the plane? Add up the percents: 41% + 36% + 11% = 88% This means that (100% - 88% = 12%) are girls. So if the total amount of passengers on the plane is p, we write 12% s 0.12, and we have: 0.12p = 30 [URL='https://www.mathcelebrity.com/1unk.php?num=0.12p%3D30&pl=Solve']Type this equation into our search engine[/URL], and we get: p = [B]250[/B]

414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost was $755.25. How many adults and children used the pool Let the number of children who used the pool be c, and the number of adults who used the pool be a. We're given two equations: [LIST=1] [*]a + c = 414 [*]2a + 1.75c = 755.25 [/LIST] We have a simultaneous equations. You can solve this any of 3 ways below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] Whichever method you choose, you get the same answer: [LIST] [*][B]a = 123[/B] [*][B]c = 291[/B] [/LIST]

45 students, 12 taking spanish, 15 taking chemistry, 5 taking both spanish and chemistry. how many students are not taking either? Let S be the number of students taking spanish and C be the number of students taking chemistry: We have the following equation relating unions and intersections: P(C U S) = P(C) + P(S) - P(C and S) P(C U S) = 15 + 12 - 5 P(C U S) = 22 To get people that aren't taking either are, we have: 45 - P(C U S) 45 - 22 [B]23[/B]

45 water balloons were given to 9 children. If each child received the same number of water balloons, how many water balloons did each child receive? Water Balloons per child = Total Water Balloons / Number of Children Water Balloons per child = 45/9 Water Balloons per child = [B]5[/B]

45.62% of Ricks home is lit at night with fluorescent bulbs and the remaining with LED lights. what is the percentage is lit with LED lights? Since the remaining is lit with LED lights, fluorescent and LED make up 100% of the lighting. So we have: Percentage of LED lights = 100% - 45.62% Percentage of LED lights = [B]54.38%[/B]

450 people attended a concert at the center. the center was 3/4 full. what is the capacity of the music center. Let the capacity be c. We're given: 3c/4 = 450 To solve this equation, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=450&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: c = [B]600[/B]

46 people showed up to the party. There were 8 less men than women present. How many men were there? Let the number of men be m. Let the number of women be w. We're given two equations: [LIST=1] [*]m = w - 8 [I](8 less men than women)[/I] [*]m + w = 46 [I](46 showed up to the party)[/I] [/LIST] Substitute equation (1) into equation (2) for m: w - 8 + w = 46 To solve for w in this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=w-8%2Bw%3D46&pl=Solve']type in the equation into our search engine [/URL]and we get: w = 27 To solve for men (m), we substitute w = 27 into equation (1): m = 27 - 8 m = [B]19[/B]

46% of bullied students report notifying an adult at school about the incident. How much of the percentage did not notify an adult? When it comes to bullying, either a student notified or did not notify. If 46% notified, then: 100% - 46% = [B]54% did not notify[/B]

48 is the difference of Chrissys height and 13 . Let Chrissy's height = h. The difference of the height and 13 is h - 13. We set this expression equal to 48: [B]h - 13 = 48 [/B] Note: To solve this, [URL='http://www.mathcelebrity.com/1unk.php?num=h-13%3D48&pl=Solve']paste this problem into the search engine[/URL].

4800$ salary spent 12% on clothes 20% on house rent how much money is she left with 12% on clothes plus 20% on house rent = 32% total spendings. If she spent 32%, that means she's left with: 100% - 32% = 68% So we want 68% of 4800. We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=68&den1=4800&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type [I]68% of 4800 [/I]into our search engine[/URL] and we get: [B]3,264[/B]

4d/a - 9 = g for a Add 9 to each side: 4d/a - 9 + 9 = g + 9 Cancel the 9's on the left side and we get: 4d/a = g + 9 Cross multiply: 4d = a(g + 9) Divide each side of the equation by (g + 9) to isolate a: 4d/(g + 9) = a(g + 9)/(g + 9) Cancel the (g + 9) on the right side, and we get: a = [B]4d/(g + 9)[/B]

4n - 8 = n + 1 Solve for [I]n[/I] in the equation 4n - 8 = n + 1 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4n and n. To do that, we subtract n from both sides 4n - 8 - n = n + 1 - n [SIZE=5][B]Step 2: Cancel n on the right side:[/B][/SIZE] 3n - 8 = 1 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -8 and 1. To do that, we add 8 to both sides 3n - 8 + 8 = 1 + 8 [SIZE=5][B]Step 4: Cancel 8 on the left side:[/B][/SIZE] 3n = 9 [SIZE=5][B]Step 5: Divide each side of the equation by 3[/B][/SIZE] 3n/3 = 9/3 n = [B]3[/B]

4 subtracted from 6 times a number is 32. Take this algebraic expression in pieces. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 6 times this number means we multiply by x by 6 6x 4 subtracted from this expression means we subtract 4 6x - 4 The phrase [I]is[/I] means an equation, so we set 6x - 4 equal to 32 [B]6x - 4 = 32 [/B] If you need to solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=6x-4%3D32&pl=Solve']type it in the search engine here[/URL].

Subtract 5 from each side: -8|-2n| = -80 Divide each side by -8 |-2n| = 10 Since this is an absolute value equation, we need to setup two equations: -2n = 10 -2n = -10 Solving for the first one by dividing each side by -2, we get: n = -5 Solving for the second one by dividing each side by -2, we get: n = 5

x + 5 = 11 for the algebraic expression. Plug that into the [URL='http://www.mathcelebrity.com/1unk.php?num=x%2B5%3D11&pl=Solve']search engine[/URL], and solve for x. x = 6.

5 added to x means we use the plus sign for a sum. x + 5 "is" means equals, so we set that equal to 11. x + 5 = 11 <-- This is our algebraic expression.

5 books and 5 bags cost $175. What is the cost of 2 books and 2 bags Let the cost of each book be b and the cost of each bag be c. We're given 5b + 5c = 175 We can factor this as: 5(b + c) = 175 Divide each side of the equation by 5, we get: (b + c) = 35 The problem asks for 2b + 2c Factor out 2: 2(b + c) we know from above that (b + c) = 35, so we substitute: 2(35) [B]70[/B]

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5 chocolates cost $25. What will 15 chocolates cost? Set up a proportion of chocolates to cost, where p is the price of 15 chocolates: 5/25 = 15/p Using our [URL='http://www.mathcelebrity.com/prop.php?num1=5&num2=15&den1=25&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]p = 75[/B]

5 diminished by twice the sum of a and b Take this algebraic expression in parts: [LIST] [*]The sum of a and b: a + b [*]Twice the sum means we multiply a + b by 2: 2(a + b) [*]5 diminished by twice the sum means we subtract 2(a + b) from 5 [/LIST] [B]5 - 2(a + b)[/B]

5 girls share 4 sandwiches. What fraction of the sandwich does each girl get? We want to know sandwiches per girls. So we divide: 4 sandwiches per 5 girls [B]4/5[/B]

5 is one-fourth of a number c [LIST] [*]A number c is just written as c [*]one-fourth of c means we multiply c by 1/4: c/4 [*]The phrase [I]is[/I] means equal to, so we set c/4 equal to 5 [/LIST] [B]c/4 = 5[/B]

5 kids are sharing 3 cupcakes. How much will they each get 3 cupcakes / 5 kids = [B]3/5 cupcake per kid or 0.6 cupcake per kid[/B]

5 more than the reciprocal of a number Take this algebraic expression in pieces: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The reciprocal of this number means we divide 1 over x: 1/x 5 more means we add 5 to 1/x [B]1/x + 5[/B]

5 more than twice the cube of a number. Take this algebraic expression in pieces. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The cube of a number means we raise it to a power of 3 x^3 Twice the cube of a number means we multiply x^3 by 2 2x^3 5 more than twice the cube of a number means we multiply 2x^3 by 5 5(2x^3) Simplifying, we get: 10x^3

5 more than twice the cube of a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x The cube of a number means we raise x to the power of 3: x^3 Twice the cube means we multiply x^3 by 2 2x^3 Finally, 5 more than twice the cube means we add 5 to 2x^3: [B]2x^3 + 5[/B]

The sum of x and y is denoted x + y. 5 more then the is denoted x + y + 5.

5 shirts. 3 pants and 8 shoes how many outfits can you wear Using the fundamental rule of counting, we can have: 5 shirts * 3 pants * 8 shoes = [B]120 different outfits[/B]

5 squared minus a number x 5 squared is written as 5^2 Minus a number x means we subtract the variable x [B]5^2 - x[/B]

5 subtracted from 3 times a number is 44. The problem asks for an algebraic expression. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 3 times this number is 3x. 5 subtracted from this is written as 3x - 5. The phrase [I]is[/I] means an equation, so we set 3x - 5 equal to 44 [B]3x - 5 = 44[/B]

5 times a number increased by 4 is divided by 6 times the same number Take this algebraic expression in parts. Part 1: 5 times a number increased by 4 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x [*]5 times the number means multiply x by 5: 5x [*][I]Increased by 4[/I] means we add 4 to 5x: 5x + 4 [/LIST] Part 2: 6 times the same number [LIST] [*]From above, [I]a number[/I] is x: x [*]6 times the number means we multiply x by 6: 6x [/LIST] The phrase [I]is divided by[/I] means we have a quotient, where 5x + 4 is the numerator, and 6x is the denominator. [B](5x + 4)/6x[/B]

5 times a number is 4 more than twice a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 5 times a number: 5x Twice a number means we multiply x by 2: 2x 4 more than twice a number 2x + 4 The word [I]is[/I] means equal to, so we set 5x equal to 2x + 4 [B]5x = 2x + 4[/B]

5 times a number is that number minus 3 The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. [LIST] [*]5 times a number: 5x [*]That number means we use the same number from above which is x [*]That number minus 3: x - 3 [*]The phrase [I]is[/I] means an equation, so we set 5x equal to x - 3 [/LIST] [B]5x = x - 3[/B]

5 times g reduced by the square of h Take this algebraic expression in pieces: [LIST=1] [*]5 times g means we multiply g by 5: 5g [*]The square of h means we raise h to the 2nd power: h^2 [*]5 times g reduced by the square of h means we subtract h^2 from 5g: [/LIST] [B]5g - h^2[/B]

5 times the product of 2 numbers a and b The product of 2 numbers a and be means we multiply the variables together: ab 5 times the product means we multiply ab by 5: [B]5ab[/B]

5 times the sum of 3 times a number and -5 The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x 3 times a number means we multiply x by 3: 3x the sum of 3 times a number and -5 means we add -5 to 3x: 3x - 5 5 times the sum means we multiply 3x - 5 by 5: [B]5(3x - 5)[/B]

5 times the total of 60 and x The total of 60 and x means we add: 60 + x 5 times the total means we multiply the sum by 5 5(60 + x)

5 years ago Kevin was 3 times as old as Tami. Now he is twice as old as she is. How is each now? Let Kevin's age be k. Let Tami's age be t. We're given the following equations: [LIST=1] [*]k - 5 = 3(t - 5) [*]k = 2t [/LIST] Plug equation (2) into equation (1) for k: 2t - 5 = 3(t - 5) We p[URL='https://www.mathcelebrity.com/1unk.php?num=2t-5%3D3%28t-5%29&pl=Solve']lug this equation into our search engine[/URL] and we get: t = [B]10. Tami's age[/B] Now plug t = 10 into equation (2) to solve for k: k = 2(10) k =[B] 20. Kevin's age[/B]

5, 14, 23, 32, 41....1895 What term is the number 1895? Set up a point slope for the first 2 points: (1, 5)(2, 14) Using [URL='https://www.mathcelebrity.com/search.php?q=%281%2C+5%29%282%2C+14%29&x=0&y=0']point slope formula, our series function[/URL] is: f(n) = 9n - 4 To find what term 1895 is, we set 9n - 4 = 1895 and solve for n: 9n - 4 = 1895 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=9n-4%3D1895&pl=Solve']equation solver[/URL], we get: n = [B]211[/B]

5,10,15,20 What is the next number? What is the 100th term? Increment is by 5, so next number is 20 + 5 = [B]25[/B] Formula for nth number is 5 * n With n = 100, we have 5 * 100 = [B]500[/B]

5/8 Of a class are boys. what fraction of the class are girls? The total class equals 1. Since 5/8 are boys, we subtract 5/8 from 1: 1 - 5/8 But we can write 1 as 8/8. So we have 8/8 - 5/8 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F8&frac2=5%2F8&pl=Subtract']Type this fraction operation into our search engine[/URL] and we get: [B]3/8[/B] are girls

50 is more than the product of 4 and w Take this algebraic expression in pieces: The product of 4 and w mean we multiply the variable w by 4: 4w The phrase [I]is more than[/I] means an inequality using the (>) sign, where 50 is greater than 4w: [B]50 > 4w[/B]

5000 union members of a financially troubled company accepted a 17% pay cut. The company announced that this would save them approximately $108 million annually. Based on this information, calculate the average annual pay of a single union member Let the full salary of the union members be s. Since 17% is 0.17, We're given: 0.17s = 108000000 To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.17s%3D108000000&pl=Solve']type it in our search engine[/URL] and we get: s = 635,294,117.65 Calculate the average annual pay of a single union member: Average Pay = Total Pay / Number of Union Members Average Pay = 635,294,117.65 / 5000 Average Pay = [B]127,058.82[/B]

508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $885.50. How many kids and how many adults were there? Assumptions: [LIST] [*]Let the number of adults be a [*]Let the number of kids be k [/LIST] Given with assumptions: [LIST=1] [*]a + k = 508 [*]2a + 1.25k = 885.50 (since cost = price * quantity) [/LIST] Rearrange equation (1) by subtracting c from each side to isolate a: [LIST=1] [*]a = 508 - k [*]2a + 1.25k = 885.50 [/LIST] Substitute equation (1) into equation (2): 2(508 - k) + 1.25k = 885.50 Multiply through: 1016 - 2k + 1.25k = 885.50 1016 - 0.75k = 885.50 To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=1016-0.75k%3D885.50&pl=Solve']type this equation into our search engine[/URL] and we get: k = [B]174[/B] Now, to solve for a, we substitute k = 174 into equation 1 above: a = 508 - 174 a = [B]334[/B]

52 card deck what is the probability of being dealt a two? There are four 2's in a deck, so we have 4/52. 4/52 is reducible to [B]1/13[/B]

52% of a town's households have children and 25% have pets. If 12% have both, what percent have neither Let C represent households with children. Let P represents households with pets. We have the formula to determine households with Children or Pets as C U P (C Union P) or (C or P): C U P = C + P - (C and P) C U P = 52% + 25% - 12% C U P = 65% Now, if we want to find what percent have neither, we use (C U P)': (C U P)' = 100% - (C U P) (C U P)' = 100% - 65% (C U P)' = [B]35%[/B]

54 is the sum of 15 and Vidyas score. Let Vida's score be s. The sum of 15 and s: s + 15 When they say "is", they mean equal to, so we set s + 15 equal to 54. Our algebraic expression is below: [B]s + 15 = 54 [/B] To solve this equation for s, use our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B15%3D54&pl=Solve']equation calculator[/URL]

54 is the sum of 24 and Julies score. Use the variable J to represent Julies score. Sum of 24 and Julie's score: 24 + J The phrase [I]is[/I] means an equation, so we set 24 + J equal to 54 to get an algebraic expression: [B]24 + J = 54[/B]

54% of students got an F, 15% of students got a D, 19% of students got a B and 12% of students got an A. if there were 26 students, how many got an F? First, we check our total percentages: 54% + 15% + 19% + 12% = 100% <-- Good, we have our full sample set F Students = 54% * 26 F Students = 14.04 -->[B] 14[/B]

55 foot tall tree casts a shadow that is 32 feet long, a nearby woman is 5.5 feet tall. What is the length of shadow she will cast? Set up a proportion of height to shadow length where s is the shadow length of the woman: 55/32 = 5.5/s [URL='https://www.mathcelebrity.com/prop.php?num1=55&num2=5.5&den1=32&den2=s&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get: s = [B]3.2[/B]

56 is the sum of 20 and Donnie's savings. Use the variable d to represent Donnie's savings The sum of 20 and Donnie's savings using [I]d[/I] to represent Donnie's savings: 20 + d The word [I]is[/I] means equal to, so we set 20 + d equal to 56: [B]20 + d = 56[/B]

59 is the difference of vanessas height and 20. Let h be Vanessa's height. We have the difference of h and 20: h - 20 The phrase [I]is[/I] means equal to, so we set h - 20 equal to 59 [B]h - 20 = 59[/B]

59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving. The phrase [I]the sum of[/I] means we add Donnie's savings of d to 16: d + 16 The phrase [I]is[/I] means an equation, so we set d + 16 equal to 59 d + 16 = 59 <-- [B]This is our algebraic expression[/B] Now, if the problem asks you to solve for d, then you[URL='https://www.mathcelebrity.com/1unk.php?num=d%2B16%3D59&pl=Solve'] type the algebraic expression into our search engine to get[/URL]: d = [B]43[/B]

5n - 5 = 85 Solve for [I]n[/I] in the equation 5n - 5 = 85 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -5 and 85. To do that, we add 5 to both sides 5n - 5 + 5 = 85 + 5 [SIZE=5][B]Step 2: Cancel 5 on the left side:[/B][/SIZE] 5n = 90 [SIZE=5][B]Step 3: Divide each side of the equation by 5[/B][/SIZE] 5n/5 = 90/5 n = [B]18[/B]

5^(n - 1) = 15,625 We know 5^6 = 15,625, so we have: n - 1 = 6 Add 1 to each side: n - 1 + 1 = 6 + 1 Cancel the 1's on the left side: n = [B]7[/B]

6 books cost 9.24. How much is 1 book Set up a proportion of cost to books where x is the cost for 1 book: 9.24/6 = x/1 To solve this proportion for x, we [URL='https://www.mathcelebrity.com/prop.php?num1=9.24&num2=x&den1=6&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: x = [B]1.54[/B]

6 boys have a mean age of 10 years and 14 girls have a mean age of 5 work out the mean age of the 20 children [U]Calculate Sum of boys ages:[/U] Sum of boys ages/6 = 10 Cross multiply, and we get: Sum of boys ages = 6 * 10 Sum of boys ages = 60 [U]Calculate Sum of girls ages:[/U] Sum of girls ages/14 = 5 Cross multiply, and we get: Sum of girls ages = 14 * 5 Sum of girls ages = 70 Average of 20 children is: Average of 20 children = (Sum of boys ages + sum of girls ages)/20 Average of 20 children = (60 + 70)/20 Average of 20 children = 130/20 Average of 20 children = [B]6.5 years[/B]

6 diminished by twice x is at most 8 Twice x means we multiply x by 2: 2x 6 diminished by twice x means we subtract 2x from 6: 6 - 2x The phrase [I]is at most[/I] is an inequality using the sign <=, so we have: [B]6 - 2x <= 8[/B]

6 is divided by square of a number The phrase [I]a number [/I]means an arbitrary variable, let's call it x. x the square of this means we raise x to the power of 2: x^2 Next, we divide 6 by x^2: [B]6/x^2[/B]

6 is one third of a number s A number s is written as s: s One third of a number s means we multiply s by 1/3 s/3 The word [I]is[/I] means equal to, so we set s/3 equal to 6 [B]s/3 = 6[/B]

6 mph, 2 hours what is the distance Distance = Rate * Time Distance = 6 mph * 2 hours Distance = [B]12 miles [/B] You can also use our [URL='http://www.mathcelebrity.com/drt.php?d=+&r=+6&t=+2&pl=Calculate+the+missing+Item+from+D%3DRT']distance-rate-time calculator[/URL]

6 numbers have a mean of 4. What is the total of the 6 numbers? Mean = Sum of numbers / Count of numbers Plug our Mean of 4 and our count of 6 into this equation: 4 = Sum/Total of Numbers / 6 Cross multiply: Sum/Total of Numbers = 6 * 4 Sum/Total of Numbers = [B]24[/B]

6 plus twice the sum of a number and 7. The phrase [I]a number[/I] mean an arbitrary variable, let's call it x. The sum of a number and 7 means we add 7 to the variable x. x + 7 Twice the sum means we multiply the sum by 2: 2(x + 7) 6 plus means we add 6 to 2(x + 7) [B]6 + 2(x + 7)[/B]

6 red marbles 9 green marbles and 5 blue marbles two marbles are drawn without replacement what is the probability of choosing a green and then a blue marble First draw: there are 6 red + 9 green + 5 blue = 20 marbles We draw 9 possible green out of 20 total marbles = 9/20 Second draw: We don't replace, so we have 6 red + 8 green + 5 blue = 19 marbles We draw 5 possible blue of out 19 total marbles = 5/19 Our total probability, since each event is independent, is: [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F20&frac2=5%2F19&pl=Multiply']9/20 * 5/19[/URL] = [B]9/76[/B]

6 sided die probability to roll a odd number or a number less than 6 First, we'll find the set of rolling an odd number. [URL='https://www.mathcelebrity.com/1dice.php?gl=1&opdice=1&pl=Odds&rolist=+2%2C3%2C4&dby=+2%2C3%2C5&montect=+100']From this dice calculator[/URL], we get: Odd = {1, 3, 5} Next, we'll find the set of rolling less than a 6. [URL='https://www.mathcelebrity.com/1dice.php?gl=4&pl=6&opdice=1&rolist=+2%2C3%2C4&dby=+2%2C3%2C5&montect=+100']From this dice calculator[/URL], we get: Less than a 6 = {1, 2, 3, 4, 5} The question asks for [B]or[/B]. Which means a Union: {1, 3, 5} U {1, 2, 3, 4, 5} = {1, 2, 3, 4, 5} This probability is [B]5/6[/B]

6 subtracted from the product of 5 and a number is 68 Take this algebraic expression in parts. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The product of 5 and this number is: 5x We subtract 6 from 5x: 5x - 6 The phrase [I]is[/I] means an equation, so we set 5x - 6 equal to 68 [B]5x - 6 = 68[/B]

6 times a number multiplied by 3 all divided by 4 Take this algebraic expression in parts: [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x [*]6 times a number: 6x [*]Multiplied by 3: 3(6x) = 18x [*]All divided by 4: 18x/4 [/LIST] We can simplify this: We type 18/4 into our search engine, simplify, and we get 9/2. So our answer is: [B]9x/2[/B]

6 times a number, x, is at least 22. 6 times a number x: 6x The phrase [I]is at least[/I] means greater than or equal to. So we have an inequality: [B]6x >= 22[/B] <-- This is our algebraic expression [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=6x%3E%3D22&pl=Show+Interval+Notation']To solve this for x, paste this into the search engine[/URL] and we get: [B]x >= 3.666667[/B]

6 times j squared minus twice j squared j squared means we raise the variable j to the power of 2: j^2 6 times j squared means we multiply j^2 by 6: 6j^2 Twice j squared means we multiply j^2 by 2: 2j^2 The word [I]minus[/I] means we subtract 2j^2 from 6j^2 6j^2 - 2j^2 So if you must simplify, we group like terms and get: (6 - 2)j^2 [B]4j^2[/B]

6 times the quantity 17b minus 19 the quantity 17b minus 19 17b - 19 6 times the quantity 17b minus 19 6(17b - 19)

6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number We've got two algebraic expressions here. Let's take it in parts: Term 1: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The reciprocal is 1/x Multiply this by 6: 6/x Term 2: Reciprocal of 7: 1/7 2 times this: 2/7 We set these terms equal to each other: 6/x = 2/7 [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=2&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get: [B]x = 21[/B]

6 times the reciprocal of a number equals 3 times the reciprocal of 7 . This is an algebraic expression. Let's take it in parts: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The reciprocal of a number x means we divide 1 over x: 1/x 6 times the reciprocal means we multiply 6 by 1/x: 6/x The reciprocal of 7 means we divide 1/7 1/7 3 times the reciprocal means we multiply 1/7 by 3: 3/7 Now, the phrase [I]equals[/I] mean an equation, so we set 6/x = 3/7 [B]6/x = 3/7[/B] <-- This is our algebraic expression If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=3&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']we type this proportion in our search engine[/URL] and get: x = 14

6 times the sum of a number and 3 is equal to 42. What is this number? The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The sum of a number and 3 means we add 3 to x: x + 3 6 times the sum: 6(x + 3) The word [I]is[/I] means an equation, so we set 6(x + 3) equal to 42 to get our [I]algebraic expression[/I] of: [B]6(x + 3) = 42[/B] [B][/B] If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/1unk.php?num=6%28x%2B3%29%3D42&pl=Solve']you type this equation into our search engine[/URL] and you get: x = [B]4[/B]

6 times the sum of a number and 5 is 16 A number represents an arbitrary variable, let's call it x x The sum of x and 5 x + 5 6 times the sum of x and 5 6(x + 5) Is means equal to, so set 6(x + 5) equal to 16 [B]6(x + 5) = 16 <-- This is our algebraic expression Solve for x[/B] Multiply through: 6x + 30 = 16 Subtract 30 from each side: 6x - 30 + 30 = 16 - 30 6x = -14 Divide each side by 6 6x/6 = -14/6 Simplify this fraction by dividing top and bottom by 2: x = [B]-7/3 [MEDIA=youtube]oEx5dsYK7DY[/MEDIA][/B]

6 times y divided by x squared 6 times y: 6y x squared means we raise x to the power of 2: x^2 The phrase [I]divided by[/I] means we have a fraction: [B]6y/x^2[/B]

6 times y divided by x squared 6 times y: 6y x squared means we raise x to the power of 2: x^2 The phrase [I]divided by[/I] means we divide 6y by x^2: [B]6y/x^2[/B]

6 years from now Cindy will be 25 years old. in 12 years, the sum of the ages of Cindy and Jose will be 91. how old is Jose right now? Let c be Cindy's age and j be Jose's age. We have: c + 6 = 25 This means c = 19 using our [URL='https://www.mathcelebrity.com/1unk.php?num=c%2B6%3D25&pl=Solve']equation calculator[/URL]. We're told in 12 years, c + j = 91. If Cindy's age (c) is 19 right now, then in 12 years, she'll be 19 + 12 = 31. So we have 31 + j = 91. Using our [URL='https://www.mathcelebrity.com/1unk.php?num=31%2Bj%3D91&pl=Solve']equation calculator[/URL], we get [B]j = 60[/B].

60 is the sum of 22 and Helenas height. Use the variable h to represent Helenas height. If height is represented by h, we have: 22 and h 22 + h When they say "is the sum of", we set 22 + h equal to 60 [B]22 + h = 60[/B]

60 percent of a number minus 17 is -65 Using our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=60&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percent to decimal calculator[/URL], we see that 60% is 0.6, so we have: 0.6 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So 60% of a number is: 0.6x Minus 17: 0.6x - 17 The word [I]is[/I] means an equation, so we set 0.6x - 17 equal to -65 to get our algebraic expression of: [B]0.6x - 17 = -65[/B] [B][/B] If you want to solve for x in this equation, you [URL='https://www.mathcelebrity.com/1unk.php?num=0.6x-17%3D-65&pl=Solve']type it in our search engine and you get[/URL]: [B]x = -80[/B]

63 oranges is shared among 3 boys in the ratio of 2:3:4 how many oranges will the second boy receive? Total sharing is 2 + 3 + 4 = 10. [LIST] [*]Boy 2 = 3/10 * 63 = [B]18.9 oranges[/B] [/LIST]

64 divided by the cube of y The cube of y means y raised to the 3rd power: y^3 64 divided by this: [B]64/y^3[/B]

64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44. The phrase [I]difference between[/I] means we subtract 44 from a: a - 44 The phrase [I]64 is[/I] means an equation, so we set a - 44 equal to 64 [B]a - 44 = 64 <-- This is our algebraic expression [/B] If you want to solve for a, then we [URL='https://www.mathcelebrity.com/1unk.php?num=a-44%3D64&pl=Solve']type this expression into our search engine[/URL] and get: [B]a = 108[/B]

64 is 4 times the difference between Sarah’s age a, and 44.Assume Sarah is older than 44 Difference between Sarah's age (a) and 44 (Assuming Sarah is older than 44): a - 44 4 times the difference: 4(a - 44) The word [I]is[/I] means equal to, so we set 4(a - 44) equal to 64 to get our algebraic expression: [B]4(a - 44) = 64[/B] If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=4%28a-44%29%3D64&pl=Solve']type this equation into our search engine[/URL] and we get: a = [B]60[/B]

66 decreased by Janelle's savings is 15 Let Janelle's savings be s. 66 decreased by s is: 66 - s The word [I]is[/I] means equal so we set 66 - s equal to 15 [B]66 - s = 15[/B]

67 less than the quantity 96 times q 96 times q: 96q 67 less than the quantity 96 times q [B]96q - 67[/B]

6700 dollars is placed in an account with an annual interest rate of 8%. How much will be in the account after 24 years, to the nearest cent? [URL='https://www.mathcelebrity.com/intbal.php?startbal=6700&intrate=8&bstart=1%2F1%2F2000&bend=1%2F1%2F2024&pl=Annual+Credit']Using our balance with interest calculator[/URL], we get: [B]$42,485.94[/B]

6700 dollars is placed in an account with an annual interest rate of 8%. show much will be in the account after 24 years, to the nearest cent ? Using our compound interest calculator, we get: [B]42,485.91 [MEDIA=youtube]0C25FB_4004[/MEDIA][/B]

6700 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 28 years, to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=6700&nval=28&int=8.25&pl=Annually']balance with interest calculator[/URL], we get: 61,667.47

69 divided by the sum of 10 and y The sum of 10 and y 10 + y 69 divided by this [B]69/(10 + y)[/B]

7 added to the quotient of 2x and 4 The quotient of 2x and 4: 2x/4 7 added to 2x/4: [B]2x/4 + 7[/B]

7 and 105 are successive terms in a geometric sequence. what is the term following 105? Geometric sequences are set up such that the next term in the sequence equals the prior term multiplied by a constant. Therefore, we express the relationship in the following equation: 7k = 105 where k is the constant [URL='https://www.mathcelebrity.com/1unk.php?num=7k%3D105&pl=Solve']Type this equation into our search engine[/URL] and we get: k = 15 The next term in the geometric sequence after 105 is found as follows: 105*15 = [B]1,575[/B]

7 black shirts 5 white shirts 10 gray shirts one is chosen at random, what is the probability that it is not gray [U]Find the total shirts:[/U] Total shirts = Black Shirts + White Shirts + Gray Shirts Total shirts = 7 + 5 + 10 Total shirts = 22 [U]Calculate the probability of choosing a gray shirt:[/U] P(Gray) = Number of Gray shirts / Total Shirts P(Gray) = 10/22 We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=10%2F22&frac2=3%2F8&pl=Simplify']type in 10/22 into our search engine, choose simplify[/URL], and we get: P(Gray) = [B]5/11[/B]

7 is 1/4 of some number The phrase [I]some number[/I] means an arbitrary variable, let's call it x. 1/4 of this is written as: x/4 The word [I]is[/I] means an equation, so we set x/4 equal to 7: [B]x/4 = 7[/B]

7 minus a number all divided by 4 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 7 minus a number 7 - x All divided by 4: [B](7 - x)/4[/B]

7 multiplied by the quantity 7 take away 6 Take this algebraic expression in pieces: [LIST] [*]7 take away 6: 7 - 6 [*]7 multiplied by the quantity: [B]7(7 - 6)[/B] [/LIST] This is our algebraic expression. If you need to evaluate this expression, we [URL='https://www.mathcelebrity.com/order-of-operations-calculator.php?num=7%287-6%29&pl=Perform+Order+of+Operations']type it in the search engine[/URL] and we get; [B]7[/B]

7 out of every 30 students ride their bikes to school. There are 720 students. How many ride their bikes Set up a proportion of students who ride their bike to total students where r is the number of students who ride their bikes: 7/30 = r/720 To solve this proportion for r, we [URL='https://www.mathcelebrity.com/prop.php?num1=7&num2=r&den1=30&den2=720&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our calculation engine and we get:[/URL] r = [B]168[/B]

7 plus the quantity of 9 increased by a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x 9 increased by a number means we add 9 to x 9 + x 7 plus this quantity means we add (9 + x) to 7 [B]7 + (9 + x)[/B]

7 plus the quotient of 12 and x is 2 The quotient of 12 and x: 12/x 7 plus the quotient of 12 and x: 7 + 12/x The word [I]is[/I] means equal to, so we set 7 + 12/x equal to 2: [B]7 + 12/x = 2[/B]

7 salads, 10 main dish, 6 dessert Using the Fundamental Rule of Counting, we have: 7 * 10 * 6 = 420 possible meals

7 subtracted from x cubed x cubed means x raised to the 3rd power x^3 7 subtracted from this [B]x^3 - 7[/B]

7 times a number and 2 is equal to 4 times a number decreased by 8 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 7 times a number: 7x and 2 means we add 2: 7x + 2 4 times a number 4x decreased by 8 means we subtract 8: 4x - 8 The phrase [I]is equal to[/I] means an equation, so we set 7x + 2 equal to 4x - 8: [B]7x + 2 = 4x - 8[/B]

7 times a number increased by 4 times the number Let [I]a number[/I] and [I]the number[/I] be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces: [LIST] [*]7 times a number: 7x [*]4 times the number: 4x [*]The phrase [I]increased by[/I] means we add 4x to 7x: [*]7x + 4x [*]Simplifying, we get: (7 + 4)x [*][B]11x[/B] [/LIST]

7 times a number is the same as 12 more than 3 times a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [B][U]Algebraic Expression 1:[/U][/B] 7 times a number means we multiply 7 by x: 7x [B][U]Algebraic Expression 2:[/U][/B] 3 times a number means we multiply 3 by x: 3x 12 more than 3 times a number means we add 12 to 3x: 3x + 12 The phrase [I]is the same as[/I] means an equation, so we set 7x equal to 3x + 12 [B]7x = 3x + 12[/B] <-- Algebraic Expression

7 times a positive number n is decreased by 3, it is less than 25 7 times a positive number n: 7n Decreased by 3: 7n - 3 The phrase [I]it is less than [/I]means an inequality. So we relate 7n - 3 less than 25 using the < sign to get our algebraic expression of: [B]7n - 3 < 25[/B]

7 times the cube of the sum of x and 8 Take this algebraic expression in 3 parts: [LIST=1] [*]The sum of x and 8 means we add 8 to x: x + 8 [*]The cube of this sum means we raise the sum to the 3rd power: (x + 8)^3 [*]7 times this cubed sum means we multiply (x + 8)^3 by 7: [/LIST] [B]7(x + 8)^3[/B]

7 times the number of lions plus 4 times the number of tigers Let the number of lions be l Let the number of tigers be t We have an algebraic expression of: [B]7l + 4t[/B]

7 times the quantity of 3 times a number reduced by 10 The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. x 3 times a number: 3x Reduced by 10 means we subtract 10: 3x - 10 7 times this quantity: [B]7(3x - 10)[/B]

7 times the quantity of a plus b The quantity of a plus b: a + b 7 times this quantity: [B]7(a + b)[/B]

7 ½ decimal Convert the mixed fractions 7 & 1/2 to an improper fraction [URL='https://www.mathcelebrity.com/fraction.php?frac1=7%261%2F2&frac2=3%2F8&pl=Simplify']7 1/2[/URL] = 15/2 Convert the improper fraction to a decimal: [URL='https://www.mathcelebrity.com/perc.php?num=15&den=2&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']15/2[/URL] = [B]7.5[/B]

7, 10, 15, 22 What is the next number in the sequence? What is the 500th term? We see that: 1^2 + 6 = 7 2^2 + 6 = 10 3^3 + 6 = 15 4^2 + 6 = 22 We build our function as f(n) = n^2 + 6 Next term in the sequence is f(5) f(5) = 5^2 + 6 f(5) = 25 + 6 f(5) = [B]31 [/B] Calculate the 500th term: f(500) = 500^2 + 6 f(500) = 250,000 + 6 f(500) = [B]250,006[/B]

7.5 degrees C to -5.21 degrees C. Kayla and Jason were discussing the changes in temperature. Kayla said, "Wow, I can't believe the temperature fell 12.71 degrees C." Jason said, "What are you talking about? The temperature only fell 2.29 degrees C." Who is correct [B]Kayla[/B] is correct. The temperature change TC is: TC = High Temp - Low Temp TC = 7.5 - (-5.21) TC = 7.5 + 5.21 ([I]Since a minus negative is positive)[/I] TC = 12.71

7/4 yards represents 4/5 of the full length of rope. Find the length of the entire jump rope. Let the entire jump rope length be l. We're given the proportion: 4l/5 = 7/4 We type this in our search engine and our [URL='https://www.mathcelebrity.com/prop.php?num1=4l&num2=7&den1=5&den2=4&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] solves for l to get: l = [B]2.1875 yards[/B]

7100 dollars is placed in an account with an annual interest rate of 7.75%. How much will be in the account after 30 years, to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7100&nval=30&int=7.75&pl=Annually']balance with compound interest calculator[/URL], we get: 66,646.40

7100 dollars is placed in an account with an interest of 7.75%. How much will be in the account after 30 years to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7100&nval=30&int=7.75&pl=Annually']balance with interest calculator[/URL], we get: [B]$66,646.40[/B]

72 pounds and increases by 3.9 pounds per month Let m be the number of months. We write the algebraic expression below: [B]3.9m + 72[/B]

75% of a ship’s cargo was destroyed by an on-board fire. The captain of the ship sold the remaining cargo, which was slightly damaged, for 25% of its real value and received $1400. What was the value of the cargo before the fire? (Do not include the $ sign or commas in the answer) So 25% of the cargo is left. This was sold at 25% of value. Let the starting value be s: We have 0.25 * 0.25 * s = 1400 0.0625s = 1400 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.0625s%3D1400&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]22400[/B]

756.218 which digit is in the thousands place Starting from the right of the decimal, we have the tenths place, hundreds place, thousands place. So [B]8[/B] is the thousands place

76 decreased by twice a number. Use the variable n to represent the unknown number. Twice a number (n) means we multiply the unknown number n by 2: 2n 76 decreased by twice a number means we subtract 2n from 76 using the (-) operator [B]76 - 2n[/B]

76 subtracted from p is equal to the total of g and 227 We've got two algebraic expressions. Take them in pieces: Part 1: 76 subtracted from p We subtract 76 from the variable p p - 76 Part 2: The total of g and 227 The total means a sum, so we add 227 to g g + 227 Now the last piece, the phrase [I]is equal to[/I] means an equation. So we set both algebraic expressions equal to each other: [B]p - 76 = g + 227[/B]

7700 dollars is placed in an account with an annual interest rate of 5.75%. How much will be in the [URL='https://www.mathcelebrity.com/compoundint.php?bal=7700&nval=5.75&int=24&pl=Annually']Using our compound balance interest calculator[/URL], we get: [B]$26,525.61[/B]

7700 dollars is placed in an account with an annual interest rate of 5.75%. How much will be in the account after 24 years, to the nearest cent? [URL='https://www.mathcelebrity.com/compoundint.php?bal=7700&nval=24&int=5.75&pl=Annually']Using our balance with interest calculator[/URL], we get: [B]$29,459.12[/B]

78 times the quantity p minus 3 The quantity p minus 3: p - 3 78 times this quantity: [B]78(p - 3)[/B]

7900 dollars is placed in an account with an annual interest rate of 5.5%. How much will be in the account after 11 years, to the nearest cent? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7900&nval=11&int=5.5&pl=Annually']compound interest calculator[/URL], we get: [B]14,236.53[/B]

7n + 4 + n - 5 = 63 Solve for [I]n[/I] in the equation 7n + 4 + n - 5 = 63 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (7 + 1)n = 8n [SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE] 4 - 5 = -1 [SIZE=5][B]Step 3: Form modified equation[/B][/SIZE] 8n - 1 = + 63 [SIZE=5][B]Step 4: Group constants:[/B][/SIZE] We need to group our constants -1 and 63. To do that, we add 1 to both sides 8n - 1 + 1 = 63 + 1 [SIZE=5][B]Step 5: Cancel 1 on the left side:[/B][/SIZE] 8n = 64 [SIZE=5][B]Step 6: Divide each side of the equation by 8[/B][/SIZE] 8n/8 = 64/8 n = [B]8[/B]

8 bags weigh 14 pounds. how much do 20 bags weigh Set up a proportion of bags to pounds where p is the number of pounds for 20 bags: 8/14 = 20/p We [URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=20&den1=14&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion in our calculator[/URL] and we get: p = [B]35[/B]

8 bricklayers can build a wall in 10 days. How long would it take 5 bricklayers to build? Set up a proportion of bricklayers to building time where t is the amount of time it takes 5 bricklayers to build a wall: 8/10 = 5/t To solve this proportion for t, we [URL='https://www.mathcelebrity.com/prop.php?num1=8&num2=5&den1=10&den2=t&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: t = [B]6.25 days[/B]

Take this in parts: First, the phrase, "a number" means we pick an arbitrary variable, let's call it x. The product of a number and 7 is 7x. 8 increased by the product of 7x means we add them together. 7x + 8 Finally that entire expression is greater than [U]or equal to[/U] -18 [B]7x + 8 >=-18[/B]

8 is subtracted from the square of x Take this algebraic expression in parts: [LIST] [*]The square of x means we raise x to the power of 2: x^2 [*]8 subtracted from the square of x is found by subtracting 8 from x^2 [/LIST] [B]x^2 - 8[/B]

8 less than X means X - 8. The word is means equal to. So we have: X - 8 = 31

8 less than triple the difference of 2x and 6 The [I]difference[/I] of 2x and 6 means we [B]subtract[/B] 6 from 2x 2x - 6 [I]Triple[/I] this difference means we [B]multiply by 3[/B] 3(2x - 6) 8 [I]less[/I] means we [B]subtract 8 from this expression 3(2x - 6) - 8[/B]

8 more than the product of x and 2 equals 4 The product of x and 2: 2x 8 more than this, means we add 8: 2x + 8 Set this equal to 4: [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B8%3D4&pl=Solve']2x + 8 = 4[/URL] <-- Algebraic expression to solve for x, type this into the search engine and we get [B]x = -2[/B].

8 more than twice a number is less than 6 more than the number. This is an algebraic expression, let's take it in pieces... The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 8 more than twice a number: Twice a number means multiply x by 2: 2x Then add 8: 2x + 8 6 more than the number, means we add 6 to x x + 6 The phrase [I]is less than[/I] means an inequality, where we set 2x + 8 less than x + 6 [B]2x + 8 < x + 6[/B]

8 sweets divided by 4 pupils = 2 sweets per pupil. We can also write this as a proportion: 8 sweets x sweets ---------- = ------------ 4 pupils 1 pupil Express this as 8/4 = x/1. [URL='http://www.mathcelebrity.com/prop.php?num1=8&num2=x&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Enter that into the search engine[/URL] x = 2

8 taken away from y This is an algebraic expression. The phrase [I]taken away[/I] means we subtract 8 from y: [B]y - 8[/B]

8 times 4 plus m squared m squared means we raise m to the power of 2 m^2 4 plus m squared: 4 + m^2 8 times 4 plus m squared [B]8(4 + m^2)[/B]

8 times the difference of 5y and 3 The difference of 5y and 3 means we subtract 3 from 5y: 5y - 3 8 times the difference means we multiply (5y - 3) by 8: [B]8(5y - 3)[/B]

8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is the number? Let the number be n. We're given two expressions: [LIST=1] [*]8(n - 2) [I]difference means we subtract[/I] [*]3(n + 3) [I]sum means we add[/I] [/LIST] The phrase [I]is the same as[/I] mean an equation. So we set the first expression equal to the second expression: 8(n - 2) = 3(n + 3) To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=8%28n-2%29%3D3%28n%2B3%29&pl=Solve']type it in our search engine[/URL] and we see that: n =[B] 5[/B]

8 times the quantity x plus y The quantity x plus y: x + y 8 times the quantity: [B]8(x + y)[/B]

8 times the sum of 5 times a number and 9 Take this algebraic expression in parts: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 5 times a number means: 5x The sum of this and 9 means we add 9 to 5x: 5x + 9 Now we multiply 8 times this sum: [B]8(5x + 9)[/B]

8 to the power of 8 divided by 8 8 to the power of 8 8^8 Divided by 8 [B]8^8/8[/B]

8 to the power of x over 2 to the power of y Step 1: 8 to the power of x means we take 8 and raise it to an exponent of x: 8^x Step 2: 2 to the power of y means we take 2 and raise it to an exponent of y: 2^y Step 3: The word [I]over[/I] means a quotient, also known as divided by, so we have: [B]8^x/2^y [MEDIA=youtube]SPQKOt5EoqA[/MEDIA][/B]

8 years from now a girls age will be 5 times her present age whats is the girls age now. Let the girl's age now be a. We're given: a + 8 = 5a [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B8%3D5a&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]a = 2[/B]

8,11,14,17,20 What is the next number? What is the 150th term? We're adding by 3 to the last number in the sequence, so we have the next number as: 20 + 3 = [B]23 [/B] For the nth term, we have a formula of this: 3n + 5 3(1) + 5 = 8 3(2) + 5 = 11 3(3) + 5 = 14 With n = 150, we have: 3(150) + 5 = 450 + 5 = [B]455[/B]

80 people 40% were women 12 were children. How many men? Calculate the number of women: 40% of 80 is 32. 12 were children, so the women and children = 32 + 12 = 44. Which means the men = 80 - 44 = [B]36[/B]

8300 dollars is placed in an account with an annual interest rate of 6.5%. How much will be in the account after 14 years, to the nearest cent? [URL='https://www.mathcelebrity.com/compoundint.php?bal=8300&nval=14&int=6.5&pl=Annually']Using our balance with interest calculator[/URL], we get: [B]$20,043.46[/B]

85 bags of nuts are to be divided among 18 friends. Each bag contains 15 nuts. How many nuts will each friend get? [B][U]Calculate the total nuts:[/U][/B] Total Nuts = Total Bags * Nuts Per Bag Total Nuts = 85 * 15 Total Nuts = 1,275 [B][U]Figure out how many nuts each person gets:[/U][/B] Nuts per person = Total Nuts / Friends Nuts per person = 1,275 / 18 Nuts per person = [B]70.83[/B]

9 divided by the quantity x plus y The quantity x plus y: x + y 9 divided by this quantity: [B]9/(x + y)[/B]

9 divided by the sum of x and 4 is equal to 6 divided by x minus 4. Build our two algebraic expressions first: 9 divided by the sum of x and 4 9/(x + 4) 6 divided by x minus 4 6/(x - 4) The phrase [I]is equal to[/I] means and equation, so we set the algebraic expressions equal to each other: [B]9/(x + 4) = 6/(x - 4) <-- This is our algebraic expression[/B] [B][/B] If the problem asks you to solve for x, we cross multiply: 9(x - 4) = 6(x + 4) To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%28x-4%29%3D6%28x%2B4%29&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]20[/B]

9 friends brought 178 tickets How many more ticket would they have to buy for all of them could have the same amount? If we take [URL='https://www.mathcelebrity.com/modulus.php?num=178mod9&pl=Calculate+Modulus']178 mod 9[/URL] to find the remainder, we get 7. If we buy the 7 more (remainder) tickets, we have: 9 friends - 7 remainder = 2 tickets To prove our work, we add the 2 tickets + 178 tickets = 180 tickets 180 tickets / 9 friends = 20 tickets per friends So our answer is [B]2 tickets[/B]

9 friends were paid $385 to clean up the local lake. How much does each friend receive Each friend gets: Total Payment / Number of friends $385/9 [B]$42.78[/B]

9 is one-third of a number x A number x can be written as x x one-third of a number x means we multiply x by 1/3: x/3 The phrase [I]is[/I] means an equation, so we set 9 equal to x/3 to get our final algebraic expression of: [B]x/3 = 9[/B] If the problem asks you to solve for x, you [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=9&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type this algebraic expression into our search engine[/URL] and you get: [B]x = 27[/B]

9 is the sum of 7 and twice a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Twice a number means we multiply x by 2: 2x The sum of 7 and twice a number 7 + 2x The word [I]is[/I] mean equal to, so we set 7 + 2x equal to 9: [B]7 + 2x = 9[/B]

9 is the sum of thrice x and y Thrice x means multiply x by 3: 3x Sum of this and y: 3x + y Now we set this expression equal to 9: [B]3x + y = 9[/B]

9 less than 5 times a number is 3 more than 2x The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x 5 times a number means we multiply x by 5: 5x 9 less than 5x means we subtract 9 from 5x: 5x - 9 3 more than 2x means we add 3 to 2x: 2x + 3 The word [I]is[/I] means an equation, so we set 5x - 9 equal to 2x + 3: [B]5x - 9 = 2x + 3 <-- This is our algebraic expression[/B] [B][/B] If you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-9%3D2x%2B3&pl=Solve']type this equation into the search engine[/URL], and we get: x = [B]4[/B]

9 less than the product of the profit, p, and 6 [U]The product of the profit p and 6:[/U] 6p [U]9 less than the product:[/U] [B]6p - 9[/B]

9 less than twice x is twice y Twice x means we multiply x by 2: 2x 9 less than Twice x means we subtract 9 from 2x 2x - 9 Twice y means we multiply y by 2: 2y The word [I]is[/I] means equal to, so we set 2x - 9 equal to 2y: [B]2x - 9 = 2y[/B]

9 rulers cost the same as 11 erasers. One eraser cost 0.09 cents. What is the cost of 1 ruler Let the cost of a ruler be r. We're given: 9r = 11(0.09) 9r = 0.99 Divide each side by 9 and we get: r = [B]0.11[/B]

9 subtracted from the product of 3 and a number is greater than or equal to 16 [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x [*]The product of 3 and a number means we multiply 3 times x: 3x [*]9 subtracted from the product: 3x - 9 [*]The phrase is greater than or equal to means an inequality. So we set up an inequality with >= for the greater than or equal to sign in relation to 3x - 9 and 16 [/LIST] Our algebraic expression (inequality) becomes: [B]3x - 19 >= 16[/B]

9 times a number is that number minus 10 The phrase [I]a number[/I] means we define a random/arbitrary variable, let's call it x: x 9 times a number means we multiply x by 9: 9x The phrase [I]that number[/I] refers back to the original arbitrary variable we defined above, which is x: x That number minus 10 means we subtract 10 from x: x - 10 The word [I]is[/I] means equal to, so we set 9x equal to x - 10 [B]9x = x - 10[/B]

9 times a number is that number minus 3 Let [I]a number[/I] be an arbitrary variable, let's call it x. We're given: 9 times a number is 9x The number minus 3 is x - 3 The word [I]is[/I] means an equation, so we set 9x equal to x - 3 to get our [I]algebraic expression[/I]: [B]9x = x - 3[/B] To solve for x, we type this equation into our search engine and we get: x = [B]-0.375 or -3/8[/B]

9 times x is twice the sum of x and 5 9 times x: 9x the sum of x and 5 x + 5 twice the sum of x and 5 2(x + 5) The phrase [I]is[/I] means equal to, so we set 9x equal to 2(x + 5) [B]9x = 2(x + 5)[/B]

9 workers were hired to harvest potatoes from a field. each is given a plot which is 11*7 feet in size. what is the total area of the field The area of each plot is 11*7 = 77 With 9 workers, the total area of the field is: 9 * 77 = [B]693 sq feet[/B]

9, 3, 1, 1/3, 1/9 What is the next number in this sequence? What is the function machine for this sequence? We see the following pattern in this sequence: 9 = 9/3^0 3 = 9/3^1 1 = 9/3^2 1/3 = 9/3^3 1/9 = 9/3^4 Our function machine formula is: [B]f(n) = 9/3^(n - 1) [/B] Next term is the 6th term: f(6) = 9/3^(6 - 1) f(6) = 9/3^5 f(6) = 9/243 f(6) = [B]1/27[/B]

90% of the day in September were sunny. How many day were sunny? September has 30 days, so we have: Sunny Days = 90% * 30 [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=90&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Sunny Days[/URL] = [B]27[/B]

9000 dollars is placed in an account with an annual interest rate of 8%. How much will be in the account after 17 years, to the nearest cent? Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=9000&nval=17&int=8&pl=Annually']compound interest accumulated balance calculator[/URL], we get: [B]$33,300.16[/B]

963 animals on a farm, 159 sheep and 406 cows and pigs. How many are pigs? Set up equation to represent the total animals on the farm Total Animals = Cows + Pigs + Sheep Now plug in what is given 963 = 406 + Pigs + 159 Simplify: Pigs + 565 = 963 Subtract 565 from each side [B]Pigs = 398[/B]

993 cold drinks bottles are to be placed in crates. Each crate can hold 9 bottles. How many crates would be needed and how many bottles will remain? Let c equal the number of crates 9 bottles per crate * c = 993 9c = 993 Solve for [I]c[/I] in the equation 9c = 993 [SIZE=5][B]Step 1: Divide each side of the equation by 9[/B][/SIZE] 9c /9 = 993/9 c = 110.33333333333 Since we can't have fractional crates, we round up 1 to the next full crate c = [B]111[/B]

9x is subtracted from the sum of 3y and 4 The sum of 3y and 4 3y + 4 9x is subtracted from the sum of 3y and 4 [B]3y + 4 - 9x[/B]

A $1,000 deposit is made at a bank that pays 12% compounded monthly. How much will you have in your account at the end of 10 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=10000&nval=120&int=12&pl=Monthly']compound interest calculator[/URL] with time = 10 years * 12 months per year = 120, we get: [B]33,003.87[/B]

A $1,000 investment takes a 10% loss each year. What will be the value 3 years? 10% is 0.1. Our Balance function B(y) where y is the number of years since the start is: B(y) = 1000(1 - 0.1)^y B(y) = 1000(0.9)^y We want to know B(3): B(3) = 1000(0.9)^3 B(3) = 1000(0.729) B(3) = [B]729[/B]

A $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percent off the sale price, making the new sale price $285.60. What was the second percent discount that was given? Let the second discount be d. We're given: 480 * (1 - 0.3)(1 - d) = 285.60 480(0.7)(1 - d) = 285.60 336(1 - d) = 285.60 336 - 336d = 285.60 [URL='https://www.mathcelebrity.com/1unk.php?num=336-336d%3D285.60&pl=Solve']Type this equation into our search engine[/URL] to solve for d and we get: d = [B]0.15 or 15%[/B]

A $650 television costs $702 after sales tax is figured in. What is the sales tax percentage? [U]Calculate Sales Tax Amount:[/U] Sales Tax Amount = Total Bill - Original Cost Sales Tax Amount = 702 - 650 Sales Tax Amount = 52 [U]Calculate Sales Tax Percentage:[/U] Sales Tax Percentage = 100% * Sales Tax Amount / Original Cost Sales Tax Percentage = 100% * 52 / 650 Sales Tax Percentage = 100% * 0.08 Sales Tax Percentage = [B]8%[/B]

A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by y = 654,000 ? 1800x dollars. After how many months will the value of the building be $409,200? We want to know x for the equation: 654000 - 1800x = 409200 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=654000-1800x%3D409200&pl=Solve']type it in our math engine[/URL] and we get: x = [B]136 months[/B]

A $675 stereo receiver loses value at a rate of about $18 per month The equation y = 675 - 18x represents the value of the receiver after x months. Identify and interpret the x- and y-intercepts. Explain how you can use the intercepts to help you graph the equation y = 675 - 18x The y-intercept is found when x is 0: y = 675 - 18(0) y = 675 - 0 y = 675 The x-intercept is found when y is 0: 0 = 675 - 18x [URL='https://www.mathcelebrity.com/1unk.php?num=675-18x%3D0&pl=Solve']Typing this equation into our search engine[/URL], we get: x = 37.5

A $750 television is on sale for 30% off. There is a 7% sales tax on the television. How much do you pay? 30% off: 750(1 - 0.3) 750(0.7) = 525 Now, add 7% sales tax 525 * (1.07) = [B]561.75[/B]

a +?b +?c =?180 for b We have a literal equation. Subtract (a + c) from each side of the equation to isolate b: a + b + c - (a + c) = 180 - (a + c) The (a + c) cancels on the left side, so we have: [B]b = 180 - (a + c)[/B] or, distributing the negative sign: [B]b = 180 - a - c[/B]

A 1.5 inch tall preying mantis will sometimes hold its ground and attempt to fight a person who is 6 feet tall. If a person who is 6 feet tall is engaged in a battle with an animal that was proportionally as tall as the person is to the preying mantis, how tall would the animal be? In terms of inches, [URL='https://www.mathcelebrity.com/linearcon.php?quant=6&pl=Calculate&type=foot']6 feet = 72 inches[/URL] Set up a proportion of height of smaller creature to larger creature where h is the heigh of the animal 1.5/72 = 72/h Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=1.5&num2=72&den1=72&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: h = 3456 inches In terms of feet, we have [URL='https://www.mathcelebrity.com/linearcon.php?quant=3456&pl=Calculate&type=inch']3456 inches[/URL] = [B]288 feet[/B]

A 10 ounce serving of energy drink contains about 190 mg of caffeine approximately how much caffeine is in a 25 ounce of energy drink? Set up a proportion of caffeine to ounces where c is the amount of caffeine in a 25 ounce drink: 190/10 = c/25 [URL='https://www.mathcelebrity.com/prop.php?num1=190&num2=c&den1=10&den2=25&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL] and we get: c = [B]475[/B]

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and short response questions are worth 8 points each. Write a system of linear equations that represents this situation Assumptions: [LIST] [*]Let m be the number of multiple choice questions [*]Let s be the number of short response questions [/LIST] Since total points = points per problem * number of problems, we're given 2 equations: [LIST=1] [*][B]m + s = 20[/B] [*][B]3m + 8s = 100[/B] [/LIST] We can solve this system of equations 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get: [B]m = 12, s = 8[/B]

A 12 feet ladder leans against the side of a house. The bottom of the ladder is 9 feet from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth. We have a right triangle, where 12 is the hypotenuse. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=9&hypinput=12&pl=Solve+Missing+Side']Using our right triangle calculator[/URL], we get: side = [B]7.9[/B]

a 12 sided die is rolled find the probability of rolling a number greater than 7 We assume this is a fair die, not loaded. This means each side 1-12 has an equal probability of 1/12 of being rolled. The problem asks, P(Roll > 7) Greater than 7 means our sample space is {8, 9, 10, 11, 12} If each of these 5 faces have an equal probability of being rolled, then we have: P(Roll > 7) = P(Roll = 8) + P(Roll = 9) + P(Roll = 10) + P(Roll = 11) + P(Roll = 12) P(Roll > 7) = 1/12 + 1/12 + 1/12 + 1/12 + 1/12 P(Roll > 7) =[B] 5/12[/B]

A 12% acid solution is made by mixing 8% and 20% solutions. If the 450 ml of the 12% solution is required, how much of each solution is required? Component Unit Amount 8% Solution: 0.08 * x = 0.08x 20% Solution: 0.2 * y = 0.2y 12% Solution: 0.12 * 450 = 54 We add up the 8% solution and 20% solution to get two equations: [LIST=1] [*]0.08x + 0.2y = 54 [*]x + y = 450 [/LIST] We have a simultaneous set of equations. We can solve it using three methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]x = 300 ml[/B] [*][B]y = 150 ml[/B] [/LIST]

A 12-ounce bottle of shampoo lasts Enrique 16 weeks. How long would you expect an 18-ounce bottle of the same brand to last him? Set up a proportion of ounces to weeks were w is the amount of weeks an 18-ounce bottle will last: 12/16 = 18/w We [URL='https://www.mathcelebrity.com/prop.php?num1=12&num2=18&den1=16&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion in our search engine to solve for w[/URL] and we get: w = [B]24[/B]

A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,,8,9,10,11,12}. Find the probability of rolling a number less than 6. We want a {1, 2, 3, 4, 5} P(X < 6) =[B] 5/12[/B]

A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12}. Find the probability of rolling a number less than 6. We have 12 outcomes. Less than 6 means 1, 2, 3, 4, 5. Our probability P(x < 6) is: P(x < 6) = [B]5/12[/B]

A 124-inch length of ribbon is to be cut into three pieces. The longest piece is to be 36 inches longer than the shortest piece, and the third piece is to be half the length of the longest piece. Find the length of each piece of ribbon. [LIST] [*]Let the longest piece be l. [*]The shortest piece is s = l - 36 [*]The third medium piece m = 0.5l [/LIST] We know s + m + l = 124. Now substitute for s and m (l - 36) + 0.5l + l = 124 Combine like terms: 2.5l - 36 = 124 Type [URL='http://www.mathcelebrity.com/1unk.php?num=2.5l-36%3D124&pl=Solve']2.5l - 36 = 124 into our search engine[/URL], we get l = [B]64[/B] Shortest piece s = 64 - 36 = [B]28[/B] Medium piece m = 0.5(64) = [B]32[/B]

A 128 ounce carton of milk states that there are 20 servings. How many ounces are in a serving? We divide 128 ounces by 20 servings to get ounces per serving: 128 ounces / 20 servings [B]6.4 ounces / serving[/B]

A 13 ft. ladder is leaning against a building 12 ft. up from the ground. How far is the base of the ladder from the building? This is a classic 5-12-13 pythagorean triple, where the hypotenuse is 13, and the 2 sides are 5 and 12. The building and the ground form a right triangle. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=12&hypinput=13&pl=Solve+Missing+Side']You can see the proof here[/URL]...

A 13ft ladder leans against the side of a house. The bottom of the ladder is 10ft from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth. We have a right triangle. Hypotenuse = 13, one leg = 10. We use our [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=10&hypinput=13&pl=Solve+Missing+Side']Pythagorean theorem Calculator to solve for the other leg[/URL]: s = [B]8.3066[/B]

A 15 feet piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces. If the shorter piece is x, the longer piece is 20 - x We also are given 15 - x = 2x + 3 Add x to each side: 3x + 3 = 15 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B3%3D15&pl=Solve']equation calculator[/URL], we get a shorter piece of: [B]x = 4[/B] The longer piece is: 15 - x 15 - 4 [B]11[/B]

A 16 pound roast will feed 24 people. If the largest roast you can buy is 12 pounds. How many people can you feed? Set up a proportion of roast pounds to people fed, where p is the number of people fed on a 12 pound roast: 16/24 = 12/p [URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=12&den1=24&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Run this through our proportion calculator[/URL] by typing 16/24 = 12/p into our search engine. We get [B]p = 18[/B]. A 12 pound roast will feed 18 people.

A 1975 comic book has appreciated 8% per year and originally sold for $0.26. What will the comic book be worth in 2020 Calculate the number of years: 2020 - 1975 = 45 Set up the accumulation function A(t) where t is the number of years since 1975: A(t) = 0.26(1.08)^t We want A(45) A(45) = 0.26(1.08)^45 A(45) = 0.26 * 32.9045 A(45) = [B]8.30[/B]

A 2-quart carton of sour cream costs $7.96. What is the price per pint? Using our [URL='https://www.mathcelebrity.com/liqm.php?quant=2&pl=Calculate&type=quart']conversion calculator[/URL]: 2 quarts = 4 pints $7.96/4 pints = [B]$1.99 per pint[/B]

A 20 feet piece of string is cut into two pieces so that the longer piece is 5 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces. If the shorter piece is x, the longer piece is 20 - x We also are given 20 - x = 2x + 5 Add x to each side: 3x + 5 = 20 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B5%3D20&pl=Solve']equation calculator[/URL], we get a shorter piece of: [B]x = 5 [/B] The longer piece is: 20 - x 20 - 5 [B]15[/B]

A 20 oz. bottle of Pepsi costs $1.60 in 2010 and $1.85 in 2014. What is the percent of increase? Round to the nearest percent if necessary. We [URL='https://www.mathcelebrity.com/markup.php?p1=1.60&m=&p2=1.85&pl=Calculate']type 1.60 to 1.85 percent increase in our search engine[/URL] and we get: [B]15.63% percent increase[/B]

a 24 sheet of aluminum is to be cut into 2.5 strips. how wide is the remaining wasted piece of aluminum Divide 24 by 2.5 to get number of sheets: 24/2.5 = 9.6 So we have 9 full sheets. Which means each strip is [B]0.6 wide[/B]

A 3 gallon bottle of bleach cost $16.32. What is the price per cup? We're given 16.32 / 3 gallons Divide the top and bottom of the fraction by 3 to get the cost per gallon: 16.32/3 = 5.44 gallon Using our [URL='https://www.mathcelebrity.com/liqm.php?quant=1&pl=Calculate&type=gallon']measurement converter[/URL], we see that: 1 gallon = 16 cups So 5.44 /16 cups=[B]$0.34 per cup[/B]

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey? [U]Set up the relationship of still water speed and downstream speed[/U] Speed down stream = Speed in still water + speed of the current Speed down stream = x+2 Therefore: Speed upstream =x - 2 Since distance = rate * time, we rearrange to get time = Distance/rate: 15/(x+ 2) + 15 /(x- 2) = 3 Multiply each side by 1/3 and we get: 5/(x + 2) + 5/(x - 2) = 1 Using a common denominator of (x + 2)(x - 2), we get: 5(x - 2)/(x + 2)(x - 2) + 5(x + 2)/(x + 2)(x - 2) (5x - 10 + 5x + 10)/5(x - 2)/(x + 2)(x - 2) 10x = (x+2)(x-2) We multiply through on the right side to get: 10x = x^2 - 4 Subtract 10x from each side: x^2 - 10x - 4 = 0 This is a quadratic equation. To solve it, [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2-10x-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine[/URL] and we get: Speed of the boat in still water =X=5 +- sq. Root of 29 kmph We only want the positive solution: x = 5 + sqrt(29) x = 10.38 [U]Calculate time for upstream journey:[/U] Time for upstream journey = 15/(10.38 - 2) Time for upstream journey = 15/(8.38) Time for upstream journey = [B]1.79[/B] [U]Calculate time for downstream journey:[/U] Time for downstream journey = 15/(10.38 + 2) Time for downstream journey = 15/(12.38) Time for downstream journey = [B]1.21[/B]

A 3-digit security code can use the numbers 0-9. How many possible combinations are there if the numbers can be repeated [0-9] * [0-9] * [0-9] 10 * 10 * 10 = [B]1,000 combinations[/B]

A 3-foot stick casts a shadow of 8 feet. If at the same time a tree casts a shadow of 15 feet, how tall is the tree? Set up a proportion of height to shadow length where t is the height of a tree: 3/8 = t/15 Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3&num2=t&den1=8&den2=15&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get: t = [B]5.625[/B]

A 3-gallon bucket of paint costs $87.12. What is the price per quart? 3 gallons equals 12 quarts with our [URL='https://www.mathcelebrity.com/liqm.php?quant=3&pl=Calculate&type=gallon#quart']conversion calculator[/URL]. We divide 87.12 for 12 quarts by 12: [URL='https://www.mathcelebrity.com/perc.php?num=87.12&den=12&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']87.12 / 12[/URL] = [B]$7.26 per quart[/B]

A 5 foot ladder is leaning against a wall. If the bottom of the ladder is 3 feet from the base of the wall, how high up the wall is the top of the ladder? The answer is [B]4[/B]. Since we have a right triangle, with special ratio 3-4-5. The ladder represents the hypotenuse.

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of the two poles, what is the minimum length of cord you would need? The difference between the 70 foot and 50 foot pole is: 70 - 50 = 20 foot height difference. So we have a right triangle, with a height of 20, base of 30. We want to know the hypotenuse. Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=20&side2input=30&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator to solve for hypotenuse[/URL], we get: hypotenuse = [B]36.06 feet[/B]

A 50-pound bowling ball and an 8-pound bowling ball are dropped from a tall building. Which ball will hit first? [B]They will land at the same time[/B] [B]How fast something falls due to gravity is determined by a number known as the "acceleration of gravity", which is 9.81 m/s^2 at the surface of our Earth. In one second, [I]any object[/I]’s downward velocity will increase by 9.81 m/s because of gravity. This is just the way gravity works - it accelerates everything at exactly the same rate.[/B]

A 5L juice container has 3.6L of juice left. What percentage has been used? What has been used? 5L - 3.6L = 1.4L Now, the [URL='http://www.mathcelebrity.com/perc.php?num=1.4&den=5.4&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']percentage used[/URL] is 1.4L/5.4L = [B]25.93%[/B]

A 6-sided die is rolled once. What is the probability of rolling a number less than 4? Using our [URL='https://www.mathcelebrity.com/1dice.php?gl=4&pl=4&opdice=1&rolist=+2%2C3%2C4&dby=+2%2C3%2C5&montect=+100']one dice calculator[/URL], we get: P(N < 4) = [B]1/2[/B]

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $188,800? Let x be the number of $24 tickets, and y be the number of $40 tickets. We have: [LIST=1] [*]24x + 40y = 188,800 [*]x + y = 6,000 [*]Rearrange (2) to solve for x: x = 6000 - y [*]Plug in (3) to (1): [/LIST] 24(6000 - y) + 40y = 188800 144,000 - 24y + 40y = 188,800 16y + 144,000 = 188,800 Subtract 144,000 from each side: 16y = 44,800 Divide each side by 16 y = 2,800 ($40 tickets) Plug this into (2) x + 2,800 = 6000 Subtract 2,800 from each side: x = 3,200 ($24 tickets)

A 7 by 5 photo was enlarged. The length and width were enlarged 125%. Find the perimeter of the photo. Enlarge length 125%: 7 * 1.25 = 8.75 Enlarge width 125%: 5 * 1.25 = 6.25 Perimeter of the enlarged photo is 2l + 2w, so we have: P = 2(8.75) + 2(6.25) P = 17.5 + 12.5 P = [B]30[/B]

A 7-foot piece of cotton cloth costs $3.36. What is the price per inch? Using [URL='https://www.mathcelebrity.com/linearcon.php?quant=7&pl=Calculate&type=foot']our length converter[/URL], we see that: 7 feet = 84 inches So $3.36 for 84 inches. We [URL='https://www.mathcelebrity.com/perc.php?num=3.36&den=84&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']divide $3.36 by 84[/URL] to get the cost per inch: $3.36/84 = [B]0.04 per inch[/B]

A 74 inch rake is Leaning against a wall. The top of the rake hits the wall 70 inches above the ground. How far is the bottom of the rake from the base of the wall? We have a right triangle. Hypotenuse is the rake length fo 74 inches. One of the legs is 70. We [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=70&hypinput=74&pl=Solve+Missing+Side']use our right triangle calculator to solve for the other leg[/URL]: [B]24 inches[/B]

a 9-foot rope is cut into two pieces one piece is x feet express the length of the other piece in terms of x Piece 1 + Piece 2 = 9 Piece 1 = x x + Piece 2 = 9 Subtracting x from each side, we get: x - x + Piece 2 = 9 - x Cancel the x's on the left side, we get: Piece 2 = [B]9 - x [/B] Check our work: x + 9 - x ? 9 9 = 9

A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the other. How long should the pieces be? The key phrase in this problem is [B]two pieces[/B]. Declare Variables: [LIST] [*]Let the short piece length be s [*]Let the long piece length be l [/LIST] We're given the following [LIST=1] [*]s = l - 10 [*]s + l = 98 (Because the two pieces add up to 98) [/LIST] Substitute equation (1) into equation (2) for s: l - 10+ l = 98 Group like terms: 2l - 10 = 98 Solve for [I]l[/I] in the equation 2l - 10 = 98 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -10 and 98. To do that, we add 10 to both sides 2l - 10 + 10 = 98 + 10 [SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE] 2l = 108 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2l/2 = 108/2 l = [B]54[/B] To solve for s, we substitute l = 54 into equation (1): s = 54 - 10 s = [B]44[/B] Check our work: The shorter piece is 10 inches shorter than the longer piece since 54 - 44 = 10 Second check: Do both pieces add up to 98 54 + 44 ? 98 98 = 98

a = v^2/r for r Start by cross multiplying to get r out of the denominator: ar = v^2 Divide each side of the equation by a to isolate r: ar/a = v^2/a Cancel the a's on the left side, and we get: r = [B]v^2/a[/B]

A = {1, 3, 5, 7, 9} B = {2, 4, 6, 8, 10} C = {1, 5, 6, 7, 9} A ? (B ? C) = B ? C = {6} A ? (B ? C) = [B]{} or the empty set[/B]

A b = b a is an example of the property called the [B]commutative property of multiplication[/B].

A bacteria population increases every hour. At 12pm there are 5 cells. At 1pm there are 10 cells. At 2pm there are 20 cells. At 3pm there are 40 cells. If this pattern continues, how many cells will there be at 7pm? The bacteria cells double each hour in the example above. From 3pm to 7pm, we have 4 hours, meaning 4 doubling periods. Which is 2 * 2 * 2 * 2 or 2^4. So we have: 40 * 2^4 40 * 16 = [B]640 cells[/B]

A bag contains 10 red balls, 10 green balls and 6 white balls. Two balls are drawn at random from the bag without replacement. What is the probability that they are of different colours? [LIST] [*]The key phrase here is [I]without replacement[/I]. [*]First, it's easier to find the probability of both colors matching, and then subtracting that from 1. [/LIST] We want 1 - (P(Red-Red) + P(Green-Green) + P(White-White)). So we have the following: [U]Find the probability of both colors matching[/U] P(Red-Red) = 10/26 * 9/25 = 0.138462 P(Green-Green) = 10/26 * 9/25 = 0.138462 P(White-White) = 6/26 * 5/25 = 0.046154 P(Red-Red) + P(Green-Green) + P(White-White) = 0.13846 + 0.13846 + 0.046154 = 0.3231 Now, we want to take the complement of this probability which is no colors matching, so we have: P(Both Different Colors) = 1 - P(Same Colors) P(Both Different Colors) = 1 - 0.3231 P(Both Different Colors) = [B]0.6769[/B]

A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag? Let the red marbles be r Let the black marbles be b. A 19 to 1 red to black is written as: r = 19b We're also given: b + r = 120 Substitute r = 19b into this equation and we get: b + 19b = 120 Combine like terms: 20b = 120 To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=20b%3D120&pl=Solve']we type it in our search engine [/URL]and we get: b = 6 Since r = 19b, we substitute b = 6 into this equation to solve for r: r = 19(6) r = [B]114[/B]

A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag? Using our [URL='https://www.mathcelebrity.com/ratio.php?simpratio=100%3A350&rs=19%3A1&rtot=120&pl=Calculate+Ratio']ratio calculator[/URL], we get: [LIST] [*]Red = 114 [*]Black = 6 [/LIST]

A bag contains 19 balls numbered 1 through 19. What is the probability that a randomly selected ball has an even number? Even numbers in the bag are {2,4,6,8,10,12,14,16,18} So we have 9 total even numbers. Therefore, the probability of drawing an even number is [B]9/19[/B]

A bag contains 2 red marbles, 3 blue marbles, and 4 green marbles. What is the probability of choosing a blue marble, replacing it, drawing a green marble, replacing it, and then drawing a red marble? Calculate total marbles in the bag: Total marbles in the bag = Red Marbles + Blue Marbles + Green Marbles Total marbles in the bag = 2 + 3 + 4 Total marbles in the bag = 9 [U]First choice, blue marble[/U] P(blue) = Total Blue Marbles / Total Marbles in the bag P(blue) = 3/9 [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F9&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we see: P(blue) = 1/3 [U]Second choice, green marble with all the marbles back in the bag after replacement[/U] P(green) = Total Green Marbles / Total Marbles in the bag P(green) = 4/9 [U]Third choice, red marble with all the marbles back in the bag after replacement[/U] P(red) = Total Red Marbles / Total Marbles in the bag P(red) = 2/9 Since each event is independent, we multiply each probability: P(blue, green, red) = P(blue) * P(green) * P(red) P(blue, green, red) = 1/3 * 4/9 * 2/9 P(blue, green, red) = [B]8/243[/B]

A bag contains 3 black, 4 red, 3 yellow, and 2 green marbles. What is the probability of drawing a black and then a red marble out of the bag without replacing the black marble before drawing the red marble? The phrase [U][B]without replacement[/B][/U] is a huge clue on this problem. Take each draw and calculate the probability. Draw 1: P(Drawing a red) P(Drawing a red) = Total Red marbles n the jar / Total marbles in the jar P(Drawing a red) = 4/12 4/12 simplifies to 1/3 using a common factor of 4: P(Drawing a red) = 1/3 Draw 2: P(Drawing a black) P(Drawing a black) = Total Black marbles in the jar / Total marbles in the jar [I]We drew one red marble already. Without replacement means we do not put it back. Therefore, we have 12 - 1 = 11 marbles left in the jar.[/I] P(Drawing a black) = 3/11 The question asks, what is the the following probability: P(Drawing a Red, Drawing a Black) Because each draw is [I][U]independent[/U], [/I]we multiply each draw probability together: P(Drawing a Red, Black) = P(Drawing a Red) * P(Drawing a Black) P(Drawing a Red, Black) = 1/3 * 3/11 P(Drawing a Red, Black) = [B]1/11[/B]

A bag contains 3 red marbles and 4 blue marbles. a marble is taken at random and replaced. Another marble is taken from the bag. Work out the probability that the two marbles taken from the bag are the same color. [LIST] [*]Total number of marbles in the bag is 3 + 4 = 7. [*]The problem asks for the probability of (RR) [I]or[/I] (BB). [*]It's worthy to note we are replacing the balls after each draw, which means we always have 7 to draw from [/LIST] Since each draw is independent, we take the product of each event for the total event probability. P(RR) = 3/7 * 3/7 = 9/49 P(BB) = 4/7 * 4/7 = 16/49 We want to know P(RR) + P(BB) P(RR) + P(BB) = 9/49 + 16/49 = 25/49 [MEDIA=youtube]26F9vjsgNGs[/MEDIA]

A bag contains 3 white balls and 2 black balls. Another bag contains 2 white and 4 black balls. A bag and a ball are picked random. Then probability of that the ball will be white is: Probability that you pick any bag is 0.5. Bag 1 White Ball = 0.5(3/5) = 3/10 = 0.3 Bag 2 White Ball = 0.5(2/6) = 1/6 = 0.16667 Add them both: 0.3 + 0.16667 = [B]0.46667[/B]

A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles. You select one marble at random from the bag. What is P(blue) P(blue) = Number of blue marbles / Total Marbles P(blue) = 5 / (5 + 6 + 4) P(blue) = 5/15 We can reduce this. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F15&frac2=3%2F8&pl=Simplify']type in 5/15 into our search engine, choose simplify[/URL], and we get: P(blue) = [B]1/3[/B]

A bag contains 6 red balls and 7 green balls. You plan to select 4 balls at random. Determine the probability of selecting 4 green balls. Assuming draw without replacement of the balls, we have: [LIST=1] [*]Selection 1: 7 green out of 13 balls [*]Selection 2: 6 green out of 12 balls [*]Selection 3: 5 green out of 11 balls [*]Selection 4: 4 green out of 10 balls [/LIST] Since each draw is independent, we multiply each probability of green: P(GGGG) = 7/13 * 6/12 * 5/11 * 4/10 P(GGGG) = 840/17,160 P(GGGG) = [B]0.05[/B]

A bag contains 666 red balls, 444 green balls, and 333 blue balls. If we choose a ball, then another ball without putting the first one back in the bag, what is the probability that the first ball will be green and the second will be red? [U]Calculate total number of balls to start:[/U] Total Balls = Red Balls + Green Balls + Blue Balls Total Balls = 666 + 444 + 333 Total Balls = 1,443 [U]Calculate the probability of drawing a green ball on the first pick:[/U] P(Green) = Green Balls / Total Balls P(Green) = 444/1443 P(Green) = 0.30769 [U]Calculate the probability of drawing a red ball on the second pick (without replacement):[/U] Total Balls decrease by 1, since we do not replace. So Total Balls = 1,443 - 1 = 1,442 P(Red) = Red Balls / Total Balls P(Red) = 666/1442 P(Red) = 0.46186 Now, we want the probability of Green, Red in that order. Since each event is independent, we multiply the event probabilities P(Green, Red) = P(Green) * P(Red) P(Green, Red) = 0.30769 * 0.46186 P(Green, Red) = [B]0.14211[/B]

A bag contains 7 red, 9 white, and 4 blue marbles. Find the probability of picking 3 blue marbles if each marble is NOT returned to the bag before the next marble is picked. The problem states we will have no replacement. [LIST] [*]First draw probability is 4 blue marbles out of (7 red + 9 white + 4 blue) = 20 marbles (4/20) [*]Second draw probability is 3 blue marbles out of (7 red + 9 white + 3 blue) = 19 marbles (3/19) [*]Third draw probability is 2 blue marbles out of (7 red + 9 white + 2 blue) = 18 marbles (2/18) [/LIST] Each draw is independent, so we multiply the three draws together: 4/20 * 3/19 * 2/18 24/6840 [B]0.0035[/B]

A bag contains 8 marbles of different colors. How many ways unique ways or orders can you select 3 marbles? We want the combinations formula, 8 choose 3, or 8C3. [URL='https://www.mathcelebrity.com/permutation.php?num=8&den=3&pl=Combinations']Type 8 C 3 into our search engine and we get:[/URL] [B]56 unique ways[/B]

A bag contains tiles, 3 tiles are red. 6 tiles are green, and 3 tiles are blue. A tile will be randomly selected from the bag . What is the probability that the tile selected will be green P(green) = Number of green tiles / Total Tiles P(green) = 6 / (3 + 6 + 3) P(green) = 6 / 12 We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F12&frac2=3%2F8&pl=Simplify']type in 6/12 into our search engine, pick simplify[/URL], and we get: P(green) = [B]1/2 or 0.5[/B]

A bag has 3 red, 5 blue, and 2 yellow pieces of candy. What is the theoretical probability of drawing a blue piece of candy P(Blue) = Blue Candies / Total Candies P(Blue) = 5 / (3 + 5 + 2) P(Blue) = 5 / 10 We can [URL='https://www.mathcelebrity.com/search.php?q=5%2F10&x=0&y=0']simplify this using our GCF calculator[/URL] and we get: P(Blue) = [B]1/2[/B]

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 290 feet by 150 feet. The area of a rectangle is length * width, so we have: A = 290 * 150 A = 43,500 sq ft. Now, to find the number of bags needed for a 300 square feet per bag of fertilizer, we have: Bags Needed = Total Square Feet of Lawn / Square Feet covered per bag Bags Needed = 43,500 / 300 Bags Needed = [B]145[/B]

A bag of marbles is said to contain 50 marbles to the nearest ten. What is the greatest number of marbles that could be in the bag and what is the least number of marbles that could be in the bag The key word in this problem is [I][B]nearest ten[/B][/I]. The nearest ten below 50 starts at 45. Why? Because the last digit is 5. At 5, we round up to the nearest ten. Therefore, the least number of marbles in the bag is 45 since it rounds up to 50 for the nearest ten The greatest number above 50 rounded to the nearest ten is 54, because less than 5 on the last digit means we round down. Therefore, the greatest number of marbles in the bag is 54 since it rounds down to 50 when the last digit is less than 5 Answer: {[B]45, 54} [MEDIA=youtube]-cl_OHA8-yc[/MEDIA][/B]

A bag of quarters and nickels is worth $8.30. There are two less than three times as many quarters as nickels. How many of the coins must be quarters? Assumptions and givens: [LIST] [*]Let the number of quarters be q [*]Let the number of nickels be n [/LIST] We have two equations: [LIST=1] [*]0.05n + 0.25q = 8.30 [*]n = 3q - 2 [I](Two less than Three times)[/I] [/LIST] Plug in equation (2) into equation (1) for q to solve this system of equations: 0.05(3q - 2) + 0.25q = 8.30 To solve this equation for q, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.05%283q-2%29%2B0.25q%3D8.30&pl=Solve']type it in our search engine[/URL] and we get: q = [B]21[/B]

A bag of rice says to mix 3 cups of rice with 2 cups of water. How much water would be needed to mix with 2 cups of rice? Set up a proportion of cups of rice to water where w is the amount of water needed for 2 cups of rice: 3/2 = 2/w To solve this proportion for w, we [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=2&den1=2&den2=w&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: w = [B]1.33333[/B]

A baker determined the annual profit in dollars from selling pies using p(n ) = 52n - 0.05n^2, where n is the number of pies sold. What is the annual profit if the baker sells 700 pies? p(700) = 52(700) - 0.05(700)^2 p(700) = 36400 - 0.05 * 490000 p(700) = 36400 - 24500 p(700) = [B]11900[/B]

A baker determined the annual profit in dollars from selling pies using p(n) = 52n - 0.05n^2 , where n is the number of pies sold. What is the annual profit if the baker sells 400 pies? p(400) = 52(400) - 0.05(400)^2 p(400) = 20800 - 0.05(160000) p(400) = 20800 - 8000 p(400) = [B]12800[/B]

A baker makes 387 cupcakes. They are sold in packs of six. How many full packs can be made? How many cupcakes are leftover? Full packs = Lowest Rounded Integer of (Total cupcakes / packs) Full packs = Lowest Rounded Integer of 387/6 Full Packs = Lowest Rounded Integer of 64.5 Full Packs = [B]64[/B] Leftover = [URL='https://www.mathcelebrity.com/modulus.php?num=387mod6&pl=Calculate+Modulus']387 mod 6[/URL] Leftover = [B]3[/B]

A baker needs 25 kilograms of flour for his bakeshop that is good for a week. If a bag of flour weighs 6 kilograms and is sold only per bag, how many bags of flour should he buy? 25 kilograms of flour /6 kilograms per bag = 4.1667 bags If they only sell full bags, then we round up to [B]5 bags[/B]

A bakery has a fixed cost of $119.75 per a day plus $2.25 for each pastry. The bakery would like to keep its daily costs at or below $500 per day. Which inequality shows the maximum number of pastries, p, that can be baked each day. Set up the cost function C(p), where p is the number of pastries: C(p) = Variable Cost + Fixed Cost C(p) = 2.25p + 119.75 The problem asks for C(p) at or below $500 per day. The phrase [I]at or below[/I] means less than or equal to (<=). [B]2.25p + 119.75 <= 500[/B]

A bakery offers a sale price of $3.50 for 4 muffins. What is the price per dozen? 1 dozen = 12 muffins What this problem is really asking, $3.50 for 4 muffins. Let p be the price for 12 muffins (1 dozen). Set up a proportion of cost to muffins. 3.50/4 = p/12 Using our math engine, we [URL='https://www.mathcelebrity.com/prop.php?num1=3.50&num2=p&den1=4&den2=12&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search box[/URL] and get: p = [B]10.5 muffins [MEDIA=youtube]ccY7yDkKvzs[/MEDIA][/B]

A bakery received a shipment of 4,554 peaches. If it takes 9 peaches to bake a peach pie, how many peach pies can the bakery make? Total Pies = Total Peaches / 9 Total Pies = 4,554 / 9 Total Pies = [B]506[/B]

A bakery sells 5800 muffins in 2010. The bakery sells 7420 muffins in 2015. Write a linear model that represents the number y of muffins that the bakery sells x years after 2010. Find the number of muffins sold after 2010 through 2015: 7,420 - 5,800 = 1,620 Now, since the problem states a linear sales model, we need to determine the sales per year: 1,620 muffins sold since 2010 / 5 years = 324 muffins per year. Build our linear model: [B]y = 5,800 + 324x [/B] Reading this out loud, we start with 5,800 muffins at the end of 2010, and we add 324 more muffins for each year after 2010.

A ball is dropped from a height of 12 feet and returns to a height that is one-half of the height from which it fell. The ball continues to bounce half the height of the previous bounce each time. How far will the ball have traveled when it hits the ground for the fifth time? Take the top of the bounces one at a time: [LIST=1] [*]Ball is dropped 12 feet and it bounces up to 6 feet [*]Ball drops 6 feet back down and bounces up to 3 feet up [*]Ball drops 3 feet back down and bounces up to 1.5 feet up [*]Ball drops 1.5 feet down and bounces up to 0.75 feet up [*]Return down after Bounce 5 is 0.75 feet down [/LIST] [U]Total distance travelled:[/U] 12 + 6 + 6 + 3 + 3 + 1.5 + 1.5 + 0.75 + 0.75 [B]34.5 feet [MEDIA=youtube]OvDp4Y3vOPY[/MEDIA][/B]

A ball was dropped from a height of 6 feet and began bouncing. The height of each bounce was three-fourths the height of the previous bounce. Find the total vertical distance travelled by the all in ten bounces. The height of each number bounce (n) is shown as: h(n) = 6(0.75)^n We want to find h(10) h(n) = 6(0.75)^n Time Height 0 6 1 4.5 2 3.375 3 2.53125 4 1.8984375 5 1.423828125 6 1.067871094 7 0.8009033203 8 0.6006774902 9 0.4505081177 10 0.3378810883 Adding up each bounce from 1-10, we get: 16.98635674 Since vertical distance means both [B]up and down[/B], we multiply this number by 2 to get: 16.98635674 * 2 = 33.97271347 Then we add in the initial bounce of 6 to get: 33.97271347 + 6 = [B]39.97271347 feet[/B]

A bamboo tree grew 3 inches per day. How many days will it take the tree to grow 144 inches? Choose the correct equation to represent this situation. Let the number of days be d. We have the equation: 3d = 144 To solve this equation for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=3d%3D144&pl=Solve']type it in our search engine[/URL] and we get: d = [B]48[/B]

A band came on stage at 9:55 and preformed for 2hours and 27 minutes what time did there performance end? 2 hours from 9:55 means we add 2 hours to the hour of 9: 9 + 2 = 11 11:55 Now we add 27 minutes to this time: 5 more minutes gets us to 12:00 PM 27 -5 = 22 minutes So we add 22 more minutes to get [B]12:22 PM[/B]

A bank charges a service fee of $7.50 per month for a checking account. A bank account has $85.00. If no money is deposited or withdrawn except the service charge, how many months until the account balance is negative? Let m be the number of months. Our balance is denoted by B(m): B(m) = 85 - 7.5m The question asks when B(m) is less than 0. So we set up an inequality: 85 - 7.5m < 0 To solve this inequality for m, [URL='https://www.mathcelebrity.com/1unk.php?num=85-7.5m%3C0&pl=Solve']we type it in our search engine[/URL] and we get: m > 11.3333 We round up to the next whole integer and get [B]m = 12[/B]

A barn contains cows, ducks, and a 3-legged dog named Tripod. There are twice as many cows as ducks in the barn and a total of 313 legs. How many ducks are there in the barn? [LIST] [*]Let the number of ducks be d. Duck legs = 2 * d = 2d [*]Number of cows = 2d. Cow legs = 4 * 2d = 8d [*]1 dog Tripod has 3 legs [/LIST] Total legs: 2d + 8d + 3 = 313 Solve for [I]d[/I] in the equation 2d + 8d + 3 = 313 [SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE] (2 + 8)d = 10d [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 10d + 3 = + 313 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 3 and 313. To do that, we subtract 3 from both sides 10d + 3 - 3 = 313 - 3 [SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE] 10d = 310 [SIZE=5][B]Step 5: Divide each side of the equation by 10[/B][/SIZE] 10d/10 = 310/10 d = [B]31[/B] [URL='https://www.mathcelebrity.com/1unk.php?num=2d%2B8d%2B3%3D313&pl=Solve']Source[/URL]

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a function to model the situation the value of the card in 2020.Let x be number of years since 1970 The formula for accumulated value of something with a percentage growth p and years x is: V(x) = Initial Value * (1 + p/100)^x Set up our growth equation where 8% = 0.08 and V(y) for the value at time x and x = 2020 - 1970 = 50, we have: V(x) = 100 * (1 + 8/100)^50 V(x) = 100 * (1.08)^50 V(x) = 100 * 46.9016125132 V(x) = [B]4690.16[/B]

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many more tickets would they need to sell to earn at least $441? Let the number of tickets above 42 be t. A few things to note on this question: [LIST] [*]The phrase [I]at least[/I] means greater than or equal to, so we have an inequality. [*]Earnings = Price * Quantity [/LIST] We're given: Earnings = 4.50 * 42 + 4.5t >= 441 Earnings = 189 + 4.5t >= 441 We want to solve this inequality for t: Solve for [I]t[/I] in the inequality 189 + 4.5t ? 441 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 189 and 441. To do that, we subtract 189 from both sides 4.5t + 189 - 189 ? 441 - 189 [SIZE=5][B]Step 2: Cancel 189 on the left side:[/B][/SIZE] 4.5t ? 252 [SIZE=5][B]Step 3: Divide each side of the inequality by 4.5[/B][/SIZE] 4.5t/4.5 ? 252.4.5 [B]t ? 56[/B]

A baseball player gets 12 hits in 40 at bats. What percent are hits, and what percent are not hits? Percent Hits = 12/40 Using our [URL='http://www.mathcelebrity.com/perc.php?num=12&den=40&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']percent calculator[/URL], we get [B]30%[/B] Since you either get a hit or you don't, we subtract 30% from 100% to find the percent of not hits: Percent Not Hits = 100 - 30% = [B]70%[/B]

A baseball player gets 3 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games? We set up a proportion of hits to games where h is the number of hits the player gets in 45 games: 3/15 = h/45 [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=h&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']Enter this into our search engine[/URL], and we get [B]h = 9[/B].

A baseball player gets 7 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games? Let's find the proportion of hits to games. Using h as the number of hits in 45 games, we have: 7/15 = h/45 Using our [URL='http://www.mathcelebrity.com/prop.php?num1=7&num2=h&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get h = 21

a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bring his average up to 0.400? Let the amount of consecutive hits needed be h. We have: hits / at bats = Batting Average Plugging in our numbers, we get: (9 + h)/60 = 0.400 Cross multiply: 9 + h = 60 * 0.4 9 + h = 24 To solve this equation for h, [URL='https://www.mathcelebrity.com/1unk.php?num=9%2Bh%3D24&pl=Solve']we type it in our search engine[/URL] and we get: h = [B]15[/B]

A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many different ways are there to arrange the batting order of 9 starting players if only one pitcher is used at a time and the pitcher always bats last. (This means that 8 players are taken from the position players and one pitcher is then added at the end of the lineup.) First 8 positions: [URL='https://www.mathcelebrity.com/permutation.php?num=15&den=8&pl=Permutations']15P8[/URL] = 259,459,200 For the pitcher, we can have 10 different possibilities for the 9th player: 259,459,200 x 10 = [B]2,594,592,000 ways[/B]

A baseball team won 40% of its first 30 games. The team then won 65% of its next 60 games. Approximately what percent of the games did the team win? Using our percentage calculators, we type the following statements into our search engine and get: [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=45&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']45% of 30[/URL] = 13.5 [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=65&den1=60&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']65% of 60[/URL] = 39 For a total of 52.5 games won The team played 30 + 60 = 90 games. So we want to know the pecent: [URL='https://www.mathcelebrity.com/perc.php?num=52&den=90&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']52/90[/URL] = [B]57.78%[/B]

A basket of goods was valued at $45.40 in January 2011. The inflation rate for the year was 4%. What is the expected cost of the basket of goods in January 2012? Write your answer to the nearest cent. 2012 cost = 2011 cost * (1 + I/100) 2012 cost = 45.40 * (1 + 4/100) 2012 cost = 45.40 * (1 + 0.04) 2012 cost = 45.40 * (1.04) 2012 cost = [B]47.22[/B]

A beach volleyball court is 10 yards wide and 17 yards long. The rope used for the boundary line costs $2.00 per yard. How much would it cost to buy a new boundary line for the court? [U]Approach:[/U] [LIST] [*]A volleyball court is shaped as a rectangle. [*]And the boundary line runs on the perimeter of the rectangle. [*]So we want the perimeter of the rectangle [/LIST] Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=17&w=10&a=&p=&pl=Calculate+Rectangle']rectangle calculator with length = 17 and width = 10[/URL], we have: P = [B]54[/B]

A bedroom set that normally sells for $1100 is on sale for 15% off. If sales tax rate is 2%, what is the total price of the bedroom set if it is bought while on sale? [U]Calculate the sale price:[/U] Sale Price = Normal Price * (1 - Sales Percentage) [U]With our sales percentage of 15% = 0.15, we have:[/U] Sale Price = 1100 * (1 - 0.15) Sale Price = 1100 * (0.85) Sale Price = 935 [U]Calculate post tax amount:[/U] Post tax amount = Sale Price * (1 + Tax Percentage) [U]With our tax percentage of 2% = 0.02, we have:[/U] Post tax amount = 935 * (1 + 0.02) Post tax amount = 935 * (1.02) Post tax amount = [B]$953.70[/B]

a bell ring every 15 seconds another bell ring 30 seconds.at 3:00 pm the 2 bells ring simultaneously.at what time will the bells ring again at the same time The [URL='https://www.mathcelebrity.com/gcflcm.php?num1=15&num2=30&num3=&pl=GCF+and+LCM']Least Common Multiple (LCM)[/URL] of 15 and 30 is 30: Therefore, 30 seconds from now, 3:00, is when the 2 bells will ring simultaneously. We add 30 seconds to 3:00 and get: 3:00 and 30 seconds.

A bell rings every 18 seconds, while another bell rings every 60 seconds. At 5:00 pm the two ring simultaneously. At what time will be the bell ring again at the same time. We want the Least Common Multiple of 18 and 60. Using our [URL='https://www.mathcelebrity.com/gcflcm.php?num1=18&num2=60&num3=&pl=GCF+and+LCM']least common multiple of 18 and 60[/URL] is [B]180 [/B] 180/18 = 10 (18 second periods) 180/60 = 3 (60 second periods) 180 seconds = 3 minutes So the next time the bells ring simultaneously is 5:00 + 3 = [B]5:03 pm[/B]

A bicycle helmet is priced at $18.50. If it is on sale for 10% off and there is 7% sales tax, how much will it cost after tax? [U]Calculate percent off first:[/U] 10% off means 90% off the price $18.50 * (1 - 0.1) $18.50 * (0.9) = 16.65 [U]Now, add 7% sales tax to the discounted price[/U] Price after sales tax = Discounted Price * 1.07 Price after sales tax = 16.65(1.07) [B]Price after sales tax = 17.82[/B]

A bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $80. How many bicycles must the store sell each month to break even? Profit = Revenue - Cost Let the number of bikes be b. Revenue = 80b Cost = 60b + 1500 Break even is when profit equals 0, which means revenue equals cost. Set them equal to each other: 60b + 1500 = 80b We [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B1500%3D80b&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]75[/B]

A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The average selling price of each bicycle is $95. How many bicycles must the store sell each month to break even? Let the number of bikes be b. Set up our cost function, where it costs $45 per bike to produce C(b) = 45b Set up our revenue function, where we earn $95 per sale for each bike: R(b) = 95b Set up our profit function, which is how much we keep after a sale: P(b) = R(b) - C(b) P(b) = 95b - 45b P(b) = 50b The problem wants to know how many bikes we need to sell to break-even. Note: break-even means profit equals operating cost, which in this case, is $2,750. So we set our profit function of 50b equal to $2,750 50b = 2750 [URL='https://www.mathcelebrity.com/1unk.php?num=50b%3D2750&pl=Solve']We type this equation into our search engine[/URL], and we get: b = [B]55[/B]

a bicycle store costs $3600 per month to operate. The store pays an average of $60 per bike. the average selling price of each bicycle is $100. how many bicycles must the store sell each month to break even? Cost function C(b) where b is the number of bikes: C(b) = Variable Cost + Fixed Cost C(b) = Cost per bike * b + operating cost C(b) = 60b + 3600 Revenue function R(b) where b is the number of bikes: R(b) = Sale price * b R(b) = 100b Break Even is when Cost equals Revenue, so we set C(b) = R(b): 60b + 3600 = 100b To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B3600%3D100b&pl=Solve']type it in our math engine[/URL] and we get: b = [B]90[/B]

A bicycle wheel is one meter around. If the spikes are 4 centimeters apart, how many spokes are on the wheel altogether? 1 meter = 100 cm per our [URL='https://www.mathcelebrity.com/linearcon.php?quant=1&pl=Calculate&type=meter']conversions calculator[/URL] 100 cm for the whole circle / 4 cm for each spike = [B]25 spikes[/B]

A bike is purchased for $200 and sold for $150. Determine the percentage of profit or loss. [U]Since sale price is less than purchase price, we have a loss:[/U] Loss = Sale Price - Purchase Price Loss = 150 - 200 Loss = -50 [U]Calculate percent loss:[/U] Percent Loss = 100% * Loss / Purchase Price Percent Loss = 100% * -50/200 Percent Loss = 100% *- 1/4 Percent Loss = [B]-25%[/B]

A bill at a resturant came to $95.75. There is 7.5% sales tax added on. You want to leave a 20% tip to the total bill, after tax. How much money will you need to leave for the bill altogether? Since the tip is [I]after tax[/I], we have: Total Bill = Pre-tax Bill * (1 + Sales Tax Percent) * (1 + Tip Percent) Total Bill = $95.75 * (1 + 0.07) * (1 + 0.2) Total Bill = $95.75 * 1.07 * 1.2 Total Bill = [B]$122.94[/B]

A binomial probability experient is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment. n = 40, p = 0.05, x = 2 P(2) = Answer is [B]0.2777[/B]. Using Excel formula of =BINOMDIST(2,40,0.05,FALSE) or using our [URL='http://www.mathcelebrity.combinomial.php?n=+40&p=0.05&k=2&t=+5&pl=P%28X+%3D+k%29']binomial probability calculator[/URL]

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the tree. How tall is the tree? So we have a [U]right triangle[/U]. Hypotenuse is 15. Base is 12. We want the length of the leg. The formula for a right triangle relation of sides is a^2 + b^2 = c^2 where c is the hypotenuse and a, b are the sides Rearranging this equation to isolate a, we get a^2 = c^2 - b^2 Taking the square root of both sides, we get a = sqrt(c^2 - b^2) a = sqrt(15^2 - 12^2) a = sqrt(225 - 144) a = sqrt(81) a = [B]9 meters[/B]

A blue dice and a red dice are tossed what is the probability that a 6 will appear on both dice Each event is independent. P(Blue dice 6) = 1/6 P(Red Dice 6) = 1/6 P(Blue 6, Red 6) = 1/6 * 1/6 = [B]1/36[/B]

A blue die and a green die are rolled. Find the probability that the blue and green are both less than 6 P(Blue not 6) = 5/6 P(Green not 6) = 5/6 Each one is independent of the other, so the probability that both are less than 6 is: P(Both not 6) = P(Blue not 6) x P(Green not 6) P(Both not 6) = 5/6 * 5/6 P(Both not 6) = [B]25/36 = 0.6944[/B]

A boa constrictor is 18 inches long at birth and grows 8 inches per year. Write an equation that represents the length y (in feet) of a boa constrictor that is x years old. 8 inches per year = 8/12 feet = 2/3 foot [B]y = 18 + 2/3x[/B]

A board must be cut into three pieces that are the same length. If it takes five minutes for each cut, how long will it take to saw the board into three pieces that are the same size? Three equal pieces means only 2 cuts on the board: 2 cuts * 5 minutes per cut = [B]10 minutes[/B]

A boat can carry 582 passengers to the base of a waterfall. A total of 13,105 people ride the boat today. All the rides are full except for the first ride. How many rides are given? 582 passengers on the boat Let r be the number of rides So we want to find r when: 582r = 13105 To solve for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=582r%3D13105&pl=Solve']type this equation into our math engine[/URL] and we get: r = 22.517 If we round this down, setting 0.517 rides as the first ride, we get: r = [B]22 [MEDIA=youtube]0J2YRPzKsoU[/MEDIA][/B]

A boat costs 14950 and decrease in value by 7% per year how much will the boat be worth after 8 years? If a boat decreases in value 7% in value, then our new value each year is 100% - 7% = 93%. So we have a B(y) function where B(y) is the value of the boat after y years: B(y) = 14,950 * (1 - 0.07)^y Simplifying, we get: B(y) = 14,950 * (0.93)^y The problem asks for B(8) B(8) = 14,950 * (0.93)^7 B(8) = 14,950 * 0..6017 B(8) = [B]8,995.43[/B]

A boat is marked up 1/5 of the original price. The original price was $50. What is the new price of the boat 1/5 of 50 equals 10. So we add the markup of 10 to the original price of 50: 50 + 10 = [B]$60[/B]

a boat traveled 336 km downstream with the current. The trip downstream took 12 hours. write an equation to describe this relationship We know the distance (d) equation in terms of rate (r) and time (t) as: d = rt We're given d = 336km and t = 12 hours, so we have: [B]336 km = 12t [/B] <-- this is our equation Divide each side by 12 to solve for t: 12t/12 = 336/12 t = [B]28 km / hour[/B]

A boat traveled at a constant speed for 32 hours, covering a total distance of 597 kilometers. To the nearest hundredth of a kilometer per hour, how fast was it going? Distance = Rate * Time We're given t = 32, and d = 597. Using our [URL='https://www.mathcelebrity.com/drt.php?d=+597&r=+&t=32&pl=Calculate+the+missing+Item+from+D%3DRT']distance, rate, and time calculator[/URL], we get: r = [B]18.656 km/hr[/B]

A book cost $8.50 without tax. If the tax rate is 7%, what is the total cost of the book including tax? 8.50 * 1.07 = [B]$9.10[/B]

A book is discounted 45%. If the original price is $40, what is the new price? 45% discount means we pay 100% - 45% = 55% 40 * 55% = [B]22[/B]

A book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books they make sell for $40 each. [B][U]Set up Cost Function C(b) where b is the number of books:[/U][/B] C(b) = Fixed Cost + Variable Cost x Number of Units C(b) = 180,000 + 25(b) [B]Set up Revenue Function R(b):[/B] R(b) = 40b Set them equal to each other 180,000 + 25b = 40b Subtract 25b from each side: 15b = 180,000 Divide each side by 15 [B]b = 12,000 for break even[/B]

a book which was marked at $84 was sold for $75.60 .calculate the percent discount Using our [URL='https://www.mathcelebrity.com/markup.php?p1=84&m=&p2=+75.60&pl=Calculate']markdown calculator[/URL], we get: [B]10% markdown/percent discount[/B]

A bookstore was selling books for 50% off. A shelf in the store had a sign that said "Books on this shelf take an additional 25% off." Leta picked out books from the discount shelf that had a regular price of $100. How much did Leta pay for the discounted books? 100 with 50% discount is $40 $50 with a 25% discount is $12.50 off $50 - $12.50 = [B]$37.50[/B]

A Bouquet of lillies and tulips has 12 flowers. Lillies cost $3 each, and tulips cost $2 each. The bouquet costs $32. Write and solve a system of linear equations to find the number of lillies and tulips in the bouquet. Let l be the number of lillies and t be the number of tulips. We're given 2 equations: [LIST=1] [*]l + t = 12 [*]3l + 2t = 32 [/LIST] With this system of equations, we can solve it 3 ways. [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter which method we choose, we get: [LIST] [*][B]l = 8[/B] [*][B]t = 4[/B] [/LIST] [B]Now Check Your Work For Equation 1[/B] l + t = 12 8 + 4 ? 12 12 = 12 [B]Now Check Your Work For Equation 2[/B] 3l + 2t = 32 3(8) + 2(4) ? 32 24 + 8 ? 32 32 = 32

A bowl contains 45 oranges. If ? of the oranges are bad; how many are good? Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=2%2F3&pl=Subtract']fraction operator calculator[/URL], we see that: 1 - 2/3 = 1/3 of the oranges are good. We want 1/3 of 45. [URL='https://www.mathcelebrity.com/fraction.php?frac1=45&frac2=1/3&pl=Multiply']Typing this expression into our search engine[/URL], we get: [B]15 good oranges[/B]

A bowler knocks down at least 6 pins 70 percent of the time. Out of 200 rolls, how many times can you predict the bowler will knock down at least 6 pins? Expected Value of (knocking down at least 6 pins) = number of rolls * probability of knocking down at least 6 pins Expected Value of (knocking down at least 6 pins) = 200 * 0.7 Expected Value of (knocking down at least 6 pins) = [B]140[/B]

A box contains 4 plain pencils and 4 pens. A second box contains 5 color pencils and 3 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected? [LIST] [*]First box, P(pen) = 4/8 = 1/2 = 0.5 [*]Second box, P(crayon) = 3/8 [/LIST] Since each event is independent, we have: P(Pen from Box 1) * P(Crayon from Box 2) = 1/2 * 3/8 = [B]3/16 or 0.1875[/B]

A box contains 10 bells. There are 6 red bells and the rest are silver. What is the probability of picking two bells of the same color if the bell is replaced after each pick? If there are 6 red bells, then we have 10 - 6 = 4 silver bells. The problem asks for the probability of picking two bells of the same color. Which mean we have 2 scenarios: [LIST=1] [*]Silver, Silver [*]Red, Red [/LIST] Find the probability of Silver, Silver: Since each draw is independent, and we replace the bells, we have a 4/10 chance of picking silver. [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F10&frac2=3%2F8&pl=Simplify']Simplified, this is 2/5[/URL]. (2/5)(2/5) = 4/25 Find the probability of Red, Red: Since each draw is independent, and we replace the bells, we have a 6/10 chance of picking silver. [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F10&frac2=3%2F8&pl=Simplify']Simplified, this is 3/5[/URL]. (3/5)(3/5) = 9/25 Because we want Silver, Silver [B][U]or[/U][/B] Red, Red, we add the two probabilities. 4/25 + 9/25 = [B]13/25[/B]

A box contains 22 red apples and 3 green apples. Three apples are selected at random, one after the other, without replacement. please show the steps. (a) The first two apples are green. What is the probability that the third apple is red? (b) What is the probability that exactly two of the three apples are red? a) You have 22 red apples left and 1 green left leaving 23 total apples left. Therefore, probability of red is [B]P(R) = 22/23[/B] b) Determine our sample space to select exactly two red apples in three picks. [LIST=1] [*]RRG [*]RGR [*]GRR [/LIST] [U]Now determine the probabilities of each event in the sample space[/U] P(RRG) = 22/25 * 21/24 * 3/23 = 0.1004 P(RGR) = 22/25 * 3/24 * 21/23 = 0.1004 P(GRR) = 3/25 * 22/24 * 21/23 = 0.1004 [U]We want the sum of the three probabilities[/U] P(RRG) + P(RGR) + P(GRR) = 0.1004 + 0.1004 + 0.1004 P(RRG) + P(RGR) + P(GRR) = 3(0.1004) P(RRG) + P(RGR) + P(GRR) = [B]0.3012[/B]

A box contains 4 plain pencils and 4 pens. A second box contains 5 color pencils and 3 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected? [LIST] [*]First box, P(pen) = 4/8 = 1/2 = 0.5 [*]Second box, P(crayon) = 3/8 [/LIST] Since each event is independent, we have: P(Pen from Box 1) * P(Crayon from Box 2) = 1/2 * 3/8 = [B]3/16 or 0.1875[/B]

A box contains 4 red jellies, 6 blue jellies and 5 yellow jellies. What is the probability that a jelly chosen randomly from the box is not red? Calculate Total Jellies: Total Jellies = Red Jellies + Blue Jellies + Yellow Jellies Total Jellies = 4 + 6 + 5 Total Jellies = 15 Not choosing a red jelly means choosing a blue [B]or[/B] yellow jelly P(not red jelly) = P(blue) + P(Yellow) P(not red jelly) = (Blue Jelly + Yellow Jelly) / Total Jellies P(not red jelly) = (6 + 5)/15 P(not red jelly) = [B]11/15[/B]

A box contains 5 black and 2 white balls. 2 balls are drawn without replacement. Find the probability of drawing 2 black balls. First draw probability of black is: Total Balls in box = Black balls + white balls Total Balls in Box = 5 + 2 Total Balls in Box = 7 P(Black) = Black Balls / Total balls in box P(Black) = 5/7 Second draw probability of black (with no replacement) is: Total Balls in box = Black balls + white balls Total Balls in Box = 4 + 2 Total Balls in Box = 6 P(Black) = Black Balls / Total balls in box P(Black) = 4/6 Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F6&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL], we see that 4/6 is: 2/3 Since each event is independent, we can multiply them to find the probability of drawing 2 black balls: P(Black, Black) = 5/7 * 2/3 [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F7&frac2=2%2F3&pl=Multiply']P(Black, Black)[/URL] = 10/21 [MEDIA=youtube]HEa_G3nwgUQ[/MEDIA]

A box contains 5 plain pencils and 3 pens. A second box contains 2 color pencils and 2 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected [U]Calculate the probability of a plain pencil in the first box:[/U] P(plain pencil in the first box) = Total Pencils / Total Objects P(plain pencil in the first box) = 5 pencils / (5 pencils + 3 pens) P(plain pencil in the first box) = 5/8 [U]Calculate the probability of a color pencil in the first box:[/U] P(color in the second box) = Total Pencils / Total Objects P(color in the second box) = 2 pencils / (2 pencils + 2 crayons) P(color in the second box) = 2/4 We can simplify this. [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F4&frac2=3%2F8&pl=Simplify']Type 2/4 into our search engine[/URL] and we get 1/2 Now the problem asks for the probability that a plain pencil from the first box and a color pencil from the second box are selected. Since each event is independent, we multiply them together to get our answer: P(plain pencil in the first box, color in the second box) = P(plain pencil in the first box) * P(color in the second box) P(plain pencil in the first box, color in the second box) = 5/8 * 1/2 P(plain pencil in the first box, color in the second box) = [B]5/16[/B]

A box contains 5 plain pencils and 7 pens. A second box contains 4 color pencils and 4 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected? Probability of plain pencil from first box: 5/(5 + 7) = 5/12 Probability of color pencil from second box: 4/(4 + 4) = 4/8 = 1/2 Probability of both events together: Since each event is independent, we multiply probabilities: 5/12 * 1/2 = [B]5/24[/B]

A box contains 6 yellow, 3 red, 5 green, and 7 blue colored pencils. A pencil is chosen at random, it is not replaced, then another is chosen. What is the probability of choosing a red followed by a green? We have 6 + 3 + 5 + 7 = 21 total pencils P(Red on the first draw) = Total Red / Total pencils P(Red on the first draw) = 3/21 [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F21&frac2=3%2F8&pl=Simplify']P(Red on the first draw)[/URL] = 1/7 We're drawing without replacement, this means on the next draw, we have 21 - 1 = 20 pencils P(Green on the second draw) = Total Green / Total pencils P(Green on the second draw) = 5/20 [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F20&frac2=3%2F8&pl=Simplify']P(Green on the second draw) [/URL]= 1/4 Since each event is independent, we have: P(Red on first, green on second) = P(Red on First) * P(green on second) P(Red on first, green on second) = 1/7 * 1/4 P(Red on first, green on second) = [B]1/28[/B]

A box had x pencils. Then 6 pencils were removed from the box. The box now has 54 pencils. Removed means we subtract from the total. So Our equation is: x - 6 = 54 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-6%3D54&pl=Solve']type it in our search engine [/URL]and we get: x = [B]60[/B]

A box has y oranges. 5 oranges are rotten and removed. The remaining oranges are placed equally into 2 containers . Each container has ______oranges Remove 5 rotten oranges means we subtract 5 from y: y - 5 If each of the two remaining boxes contains an equal amount of the remaining oranges, we have: [B](y - 5)/2[/B] oranges in each box

A box is filled with 10 green cards, 4 blue cards, and 4 brown cards. A card is chosen at random from the box. What is the probability that it is a green or a brown card? Calculate Total Cards: 10 green cards + 4 blue cards + 4 brown cards = 18 cards "Or", means either or, so we want P(Green) + P(Brown) [U]Find P(Green)[/U] P(Green) = Green Cards / Total Cards P(Green) = 10/18 <-- Simplify by dividing top and bottom by 2 P(Green)= 5/9 <-- Simplify by dividing top and bottom by 2 Find P(Brown) P(Brown) = Brown Cards / Total Cards P(Brown) = 4/18 <-- Simplify by dividing top and bottom by 2 P(Brown)= 2/9 <-- Simplify by dividing top and bottom by 2 P(Green) + P(Brown) = 5/9 + 2/9 P(Green) + P(Brown) = [B]7/9[/B]

A box is filled with 5 blue cards,2 red cards, and 5 yellow cards. A card is chosen at random from the box. What is the probability that it is a blue or a yellow card? Write your answer as a fraction in simplest form. We want P(B) + P(Y) P(B) = 5/12 P(Y) = 5/12 P(B) + P(Y) = 5/12 + 5/12 = 10/12 Reduce this fraction using 2 as our common factor: [B]5/6[/B]

A box of goldfish food can feed 3 fish for 4 weeks. How long will the box last if there are 7 goldfish? 4 weeks = 7 * 4 = 28 days One box = 3 fish * 28 days = 84 days 84 days / 7 goldfish = [B]12 days[/B]

A box of pencils weights 3.25 grams. If the teacher orders 14 boxes, how much would the pencils weigh? Total Weight = Number of Boxes * Weight per box Total Weight = 14 * 3.25 Total Weight = [B]45.5 grams[/B]

A boy has 6 toys he loses 3. How many does the boy have? We subtract 3 from 6 since losing means less, and we have: 6 - 3 = [B]3[/B]

A boy has m mangoes. He sells three of them write down an expression to represent how much he now has. When the boy sells the mangos, he has less. So we subtract 3 from m to get: [B]m - 3[/B]

A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find the present age of each? Let the boy's age be b and his brother's age be c. We're given two equations: [LIST=1] [*]b = c + 10 [*]b + 4 = 2(c + 4) [/LIST] Substitute equation (1) into equation (2): (c + 10) + 4 = 2(c + 4) Simplify by multiplying the right side through and grouping like terms: c + 14 = 2c + 8 [URL='https://www.mathcelebrity.com/1unk.php?num=c%2B14%3D2c%2B8&pl=Solve']Type this equation into our search engine[/URL] and we get: c = [B]6[/B] Now plug c = 6 into equation (1): b = 6 + 10 b = [B]16[/B]

A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their present ages? Let b be the boy's age and s be his sister's age. We're given two equations: [LIST=1] [*]b = s + 6 [*]b + 3 = 2(s + 3) [/LIST] Plug in (1) to (2): (s + 6) + 3 = 2(s + 3) s + 9 = 2s + 6 [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B9%3D2s%2B6&pl=Solve']Plugging this equation into our search engine[/URL], we get: [B]s = 3[/B] We plug s = 3 into Equation (1) to get the boy's age (b): b = 3 + 6 [B]b = 9[/B]

A boy is 6 years younger than his sister. If he is (x-9) years old, how long will it take for his sister to be x years old? If the boy is x - 9 years old, and he's 6 years younger than his sister, than the sister is older by 6 years. Sister's Age = x - 9 + 6 Sister's Age = x - 3 In order to be x years old, we must add 3 years: x - 3 + 3 = x So in [B]3 years, [/B]the sister will be x years old.

a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that the middle piece is 6inches longer than the shortest piece and the shortest piece is 9 inches shorter than the longest price. how long should the three pieces be? Let the longest piece be l. The middle piece be m. And the short piece be s. We have 2 equations in terms of the shortest piece: [LIST=1] [*]l = s + 9 (Since the shortest piece is 9 inches shorter, this means the longest piece is 9 inches longer) [*]m = s + 6 [*]s + m + l = 57 [/LIST] We substitute equations (1) and (2) into equation (3): s + (s + 6) + (s + 9) = 57 Group like terms: (1 + 1 + 1)s + (6 + 9) = 57 3s + 15 = 57 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3s%2B15%3D57&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]14 [/B] [U]Plug s = 14 into equation 2 to solve for m:[/U] m = 14 + 6 m = [B]20 [/B] [U]Plug s = 14 into equation 1 to solve for l:[/U] l = 14 + 9 l = [B]23 [/B] Check our work for equation 3: 14 + 20 + 23 ? 57 57 = 57 <-- checks out [B][/B]

A boy spent one-half of his money for a book and one-third of his money for a pen. The remaining $2.25 he saved. How much money did he originally have? Find out what percent of money was spent Using a common denominator of 6, we have 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Therefore, 1/6 of his money is left to save. Let the boy's original money be x. We have: x/6 = 2.25 Cross multiply, we get x = [B]13.50[/B]

A brand new car that is originally valued at $25,000 depreciates by 8% per year. What is the value of the car after 6 years? The Book Value depreciates 8% per year. We set up a depreciation equation: BV(t) = BV(0) * (1 - 0.08)^t The Book Value at time 0 BV(0) = 25,000. We want the book value at time 6. BV(6) = 25,000 * (1 - 0.08)^6 BV(6) = 25,000 * 0.92^6 BV(6) = 25,000 * 0.606355 BV(6) = [B]15,158.88[/B]

A broken clock that loses 12 minutes every hour is set at 12:00 noon at the same time a normal clock has its time set to 12:00 noon. When the broken clock reaches 12:00 midnight, what will the normal clock read? Set up a proportion normal clock to broken clock: 60/48 = n/12 Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=60&num2=n&den1=48&den2=12&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get: n = [B]15 hours [/B] 12:00 AM plus 15 hours = [B]3 pm[/B]

A builder needs 36 nails to finish a projects. If the nails come in packages of 3, how many packages should the builder purchase? Packages needed = Total Nails / Nails per package Packages needed = 36/3 Packages needed = [B]12[/B]

A bunny population is doubling every 2 years. There are currently 45 bunnies. How many will there be in 10 years? Find the number of doubling periods: Number of Doubling periods = Time / Doubling period Number of Doubling periods = 10/2 Number of Doubling periods = 5 Create a function to determine the amount of bunnies after each doubling period: B(n) = 45 * 2^n Since we calculated 5 doubling periods, we want B(5): B(5) = 45 * 2^5 B(5) = 45 * 32 B(5) = [B]1,440[/B]

A bus can at most be filled with 36 passengers. If there are currently 25 passengers there already. How many passengers can be added at most? We have 36 - 25 existing passengers = [B]11 passengers can be added at most[/B]

A bus holds 45 students. How many buses were taken on a field trip if 13 students travels by car and total of 320 students went on a trip? [U]Find the number of students who went on the bus:[/U] Number of students who went on the bus = Total students on field trip - students who traveled by car Number of students who went on the bus = 320 - 13 Number of students who went on the bus = 307 Calculate the number of buses needed: Number of buses needed = Number of students who went on the bus / Bus Capacity Number of buses needed = 307 / 45 Number of buses needed = 6.822 We round up for a full bus to get [B]7 buses[/B]

A bus is carrying 135 passengers, which is 3/4 of the capacity of the bus. What is the capacity of the bus Let the capacity of the bus be c. We're given: 3c/4 = 135 To solve for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=135&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type this equation into our search engine [/URL]and we get: c = [B]180[/B]

A bus ride cost 1.50. A 30 day pass cost $24. Write an inequallity to show that the 30 day pass is the better deal Let the number of days be d. We have the inequality below where we show when the day to day cost is greater than the monthly pass: 1.5d > 24 To solve this inequality for d, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.5d%3E24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get: [B]d > 16[/B]

A bus usually takes 25 minutes. Because of traffic the trip took 7 minutes longer. How long did the trip take? The word [I]longer[/I] means we add, so we have: 25 + 7 = [B]32 minutes[/B]

A business owner spent $4000 for a computer and software. For bookkeeping purposes, he needs to post the price of the computer and software separately. The computer costs 4 times as much as the software. What is the cost of the software? Let c be the cost of the computer and s be the cost of the software. We have two equations: [LIST=1] [*]c + s = 4000 [*]c = 4s [/LIST] Substitute (2) into (1) (4s) + s = 4000 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=4s%2Bs%3D4000&pl=Solve']equation solver[/URL], we get [B]s = 800[/B]. Substitute this into Equation (2), we get: c = 4(800) [B]c = 3,200[/B]

A cab charges $5 for the ride plus $1.25 per mile. How much will a 53 mile trip cost? We set up our cost function C(m) where m is the number of miles: C(m) = 1.25m + 5 The problem asks for C(53): C(53) = 1.25(53) + 5 C(53) = 66.25 + 5 C(53) = [B]$71.25[/B]

A cab company charges $5 per cab ride, plus an additional $1 per mile driven , How long is a cab ride that costs $13? Let the number of miles driven be m. Our cost function C(m) is: C(m) = Cost per mile * m + cab cost C(m) = 1m + 5 The problem asks for m when C(m) = 13: 1m + 5 = 13 To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=1m%2B5%3D13&pl=Solve']we type it in our search engine[/URL] and we get: m = [B]8[/B]

A cab company charges $5 per cab ride, plus an additional $3 per mile driven. How long is a cab ride that costs $17? Let m be the number of miles driven. We setup the cost equation C(m): C(m) = Cost per mile driven * miles driven + ride cost C(m) = 3m + 5 The questions asks for m when C(m) is 17: 3m + 5 = 17 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%2B5%3D17&pl=Solve']type it in our search engine[/URL] and we get: m = [B]4[/B]

A cable company charges $75 for installation plus $20 per month. Another cable company offers free installation but charges $35 per month. For how many months of cable service would the total cost from either company be the same [U]Set ups the cost function for the first cable company C(m) where m is the number of months:[/U] C(m) = cost per month * m + installation fee C(m) = 20m + 75 [U]Set ups the cost function for the second cable company C(m) where m is the number of months:[/U] C(m) = cost per month * m + installation fee C(m) = 35m The problem asks for m when both C(m) functions are equal. So we set both C(m) functions equal and solve for m: 20m + 75 = 35m To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=20m%2B75%3D35m&pl=Solve']type this equation into our search engine[/URL] and we get: m = [B]5[/B]

A cake is to be divided into 8 equal parts. After division, each equal portion is again divided into 2 equal individual parts. How big is each of the new equal parts? 1 cake * 8 parts * 2 parts = 16 parts. So each slice is 1/16 of a cake.

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 8 minutes? Set up a proportion of gallons of water to time where g is the number of gallons of water in 8 minutes. 15/10 = g/8 [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=g&den1=10&den2=8&propsign=%3D&pl=Calculate+missing+proportion+value']Run this problem through our proportion calculator[/URL] to get [B]g = 12.[/B]

A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 14 minutes? Set up a proportion of gallons of water over minutes where g is the number of gallons the camel can drink in 14 minutes: 15/10 = g/14 [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=g&den1=10&den2=14&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get: [B]g = 21[/B]

A camera normally cost for $450 is on sale for $315 what is the discount rate as the percentage on the camera Using our [URL='https://www.mathcelebrity.com/markup.php?p1=450&m=&p2=+315&pl=Calculate']markdown calculator[/URL], we get: [B]-30%[/B]

A candidate for mayor wants to gauge potential voter reaction to an increase recreational services by estimating the proportion of voter who now use city services. If we assume that 50% of the voters require city recreational services, what is the probability that 40% or fewer voters in a sample of 100 actually will use these city services? First, let's do a test on the proportion using our [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=+40&n=+100&ptype=%3D&p=+0.5&alpha=+0.05&pl=Proportion+Hypothesis+Testing']proportion hypothesis calculator[/URL]: We get Z = -2 Now use the [URL='http://www.mathcelebrity.com/zscore.php?z=p%28z%3C-2%29&pl=Calculate+Probability']z-score calculator[/URL] to get P(z<-2) = [B]0.02275[/B]

A candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the candlestick is 13.4 inches tall. Write and solve a linear equation to find the original height of the candle. Let h equal the number of hours the candlestick burns. We have a candlestick height equation of C. C = 13.4 + 0.2(8) <-- We need to add back the 8 hours of candlestick burning C = 13.4 + 1.6 C = [B]15 inches[/B]

A car drives 3 feet the first second, 9 feet in the next second, and 27 feet in the third second. If the pattern stays the same, how far will the car have traveled after 5 seconds, in feet? Our pattern is found by the distance function D(t), where we have 3 to the power of the time (t) in seconds as seen below: D(t) = 3^t The problem asks for D(5): D(5) = 3^5 [URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=3%5E5&pl=Calculate']D(5)[/URL] = [B]243[/B]

A car is bought for $2400 and sold one year later $1440 find the loss as a percentage of the cost price. (2400 - 1440)/2400 960/2400 0.4 As a percentage, we multiply by 100 to get [B]40%[/B]

A car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will the car be worth $7300 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer. Set up the depreciation equation D(t) where t is the number of years in the life of the car: D(t) = 24,000 * (1 - 0.3)^t D(t) = 24000 * (0.7)^t The problem asks for D(t)<=7300 24000 * (0.7)^t = 7300 Divide each side by 24000 (0.7)^t = 7300/24000 (0.7)^t= 0.30416666666 Take the natural log of both sides: LN(0.7^t) = -1.190179482215518 Using the natural log identities, we have: t * LN(0.7) = -1.190179482215518 t * -0.35667494393873245= -1.190179482215518 Divide each side by -0.35667494393873245 t = 3.33687437943 [B]Rounding this up, we have t = 4[/B]

A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the resale value be after 4 years? Set up a book value function B(t) where t is the number of years after purchase date. If an asset decreases by 30%, we subtract it from the original 100% of the starting value at time t: B(t) = 19,000(1-0.3)^t Simplifying this, we get: B(t) = 19,000(0.7)^t <-- I[I]f an asset decreases by 30%, it keeps 70% of it's value from the prior period[/I] The problem asks for B(4): B(4) = 19,000(0.7)^4 B(4) = 19,000(0.2401) B(4) = [B]4,561.90[/B]

A car is purchased for 27,000$. After each year the resale value decreases by 20%. What will the resale value be after 3 years? If it decreases by 20%, it holds 100% - 20% = 80% of the value each year. So we have an equation R(t) where t is the time after purchase: R(t) = 27,000 * (0.8)^t The problem asks for R(3): R(3) = 27,000 * (0.8)^3 R(3) = 27,000 * 0.512 R(3) = [B]13.824[/B]

A car is traveling 60 km per hour. How many hours will it take for the car to reach a point that is 180 km away? Rate * Time = Distance so we have t for time as: 60t = 180 To solve this equation for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=60t%3D180&pl=Solve']type it in the search engine[/URL] and we get: t = [B]3[/B]

a car is traveling 75 kilometers per hour. How many meters does the car travel in one minute convert from Kilometers to meters 1 kilometer = 1000 meters 75 kilometers = 1000 meters * 75 = 75000 meters convert from hours to minutes 1 hour = 60 minutes, the car travels: 75,000 meters / 60 minutes = [B]1,250 meters / minute[/B]

A car is traveling on a freeway at 50 mph with the cruise control set at 50 mph. Another car is traveling at 90 mph with the cruise control set at 90 mph. Which car has a higher acceleration? Acceleration means a change in speed. Neither car has a change in speed, [B]so both cars have the same acceleration which is 0[/B]

a car is worth 24000 and it depreciates 3000 a year how long till it costs 9000 Let y be the number of years. We want to know y when: 24000 - 3000y = 9000 Typing [URL='https://www.mathcelebrity.com/1unk.php?num=24000-3000y%3D9000&pl=Solve']this equation into our search engine[/URL], we get: y = [B]5[/B]

A car rents $35 per day plus 15 cents per mile driven Set up the cost function C(m) where m is the number of miles driven: C(m) = Cost per mile * m + Daily Fee [B]C(m) = 0.15m + 35[/B]

A car repair bill was $441. This included $153 for parts and four hours of labor . Find the hourly rate I was charge for labor Subtract the cost of parts from the total repair bill to get the labor cost: Labor Cost = Total Bill - Parts Cost Labor Cost = 441 - 153 Labor Cost = 288 Labor Cost can be broken down into Labor divided by hours Hourly Labor Rate = Labor Cost / Labor Hours Hourly Labor Rate = = 288 / 4 Hourly Labor Rate = [B]72[/B]

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the month. If he is aiming to earn a minimum of $3200 a month, what is the possible value of sales that will enable this? to start, we have: [LIST] [*]Let the salesman's monthly sales be s. [*]With a 10% discount as a decimal of 0.1 [*]The phrase [I]a minimum[/I] also means [I]at least[/I] or [I]greater than or equal to[/I]. This tells us we want an inequality [*]We want 10% times s + 800 per month is greater than or equal to 3200 [/LIST] We want the inequality: 0.1s + 800 >= 3200 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.1s%2B800%3E%3D3200&pl=Solve']type this inequality into our search engine[/URL] and we get: [B]s >= 24000[/B]

A car travels 16 m/s and travels 824 m. How long was the car moving? Distance = Rate * Time, so we have: 824m = 16m/s * t Using our [URL='https://www.mathcelebrity.com/drt.php?d=+824&r=16&t=&pl=Calculate+the+missing+Item+from+D%3DRT']distance calculator[/URL], we get: [B]51.5 seconds[/B]

A car travels 71 feet each second.How many feet does it travel in 12 seconds? Distance = Rate * Time We're given a rate of 71 feet per second and a time of 12 seconds. So we plug this in: Distance = 71 feet/second * 12 seconds [URL='https://www.mathcelebrity.com/drt.php?d=+&r=71&t=+12&pl=Calculate+the+missing+Item+from+D%3DRT']Distance[/URL] = [B]852 feet[/B]

A car travels at 40 kilometers per hour. Write an expression for the distance traveled after h hours. Distance = rate * time, so we have: Distance = 40km/h * h Distance = [B]40h[/B]

a car was bought for $24300 and sold at a loss of $2290. Find the selling price. A loss means the car was sold for less than the buying price. Let the selling price be S. we have: 24300 - S = 2290 [URL='https://www.mathcelebrity.com/1unk.php?num=24300-s%3D2290&pl=Solve']Typing this equation into our search engine[/URL], we get: s = [B]22,010[/B]

A car who’s original value was $25600 decreases in value by $90 per month. How Long will it take before the cars value falls below $15000 Let m be the number of months.We have our Book Value B(m) given by: B(m) = 25600 - 90m We want to know when the Book value is less than 15,000. So we have an inequality: 25600 - 90m < 15000 Typing [URL='https://www.mathcelebrity.com/1unk.php?num=25600-90m%3C15000&pl=Solve']this inequality into our search engine and solving for m[/URL], we get: [B]m > 117.78 or m 118 months[/B]

A car worth $43,000 brand new, depreciates at a rate of $2000 per year. What is the formula that describes the relationship between the value of the car (C) and the time after it has been purchased (t)? Let t be the number of years since purchase. Depreciation means the value decreases, so we have: [B]C = 43000 - 2000t[/B]

a card is chosen at a random from a deck of 52 cards. it is then replaced and a second card is chosen. what is the probability of getting a jack and then an eight? Calculate the probability of drawing a jack from a full deck There are 4 jacks in a deck of 52 cards P(J) = 4/52 P(J) = 1/13 <-- We simplify 4/52 by dividing top and bottom of the fraction by 4 Calculate the probability of drawing an eight from a full deck There are 4 eights in a deck of 52 cards. We[I] replaced[/I] the first card giving us 52 cards to choose from. P(8) = 4/52 P(8) = 1/13 <-- We simplify 4/52 by dividing top and bottom of the fraction by 4 Since each event is independent, we multiply: P(J, 8) = P(J) * P(8) P(J, 8) = 1/13 * 1/13 P(J, 8) = [B]1/169[/B]

a card is drawn at random from a standard 52 card deck. find the probability that the card is not a king. There are 4 kings in a standard 52 card deck. To not get a king, we'd have 52 - 4 = 48 possible cards. The probability of not drawing a King is 48/52. But we can simplify this. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=48%2F52&frac2=3%2F8&pl=Simplify']type the fraction 48/52 into our search engine[/URL], and get: [B]12/13[/B]

A card is drawn from a pack of 52 cards. The probability that the card drawn is a red card is The deck is split evenly between red and black cards. So we have 52/2 = 26 red cards P(Red) = # of Red Cards / Total Deck Cards P(Red) = 26/52 We can simplify this fraction. [URL='https://www.mathcelebrity.com/fraction.php?frac1=26%2F52&frac2=3%2F8&pl=Simplify']Using our fraction calculator[/URL], we get: P(Red) = [B]1/2 or 0.5[/B]

A card is drawn from a standard deck of 52 cards. What is the probability of drawing an ace or a 6? There are 4 Ace's in a standard 52 card deck. There are 4 6's as well. So we have 4 + 4 = 8 possible cards out of 52: 8/52 To simplify, [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F52&frac2=3%2F8&pl=Simplify']we type this into our search engine[/URL] and we get: [B]2/13[/B]

A card is picked from a deck of 52 cards. Find the probability of getting a black ace or a red queen. In a standard deck of 52 cards, we have: [LIST] [*]2 black Aces with probability 2/52 = 1/26 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F52&frac2=3%2F8&pl=Simplify']using our fraction simplifier[/URL] [*]2 red Queens with probability 2/52 = 1/26 [URL='http://using our fraction simplifier']using our fraction simplifier[/URL] [/LIST] The problems asks for P(Red Queen Or Black Ace). Or means we add, so we have: P(Red Queen Or Black Ace) = P(Red Queen) + P(Black Ace) P(Red Queen Or P Black Ace) = 1/26 + 1/26 P(Red Queen Or P Black Ace) = 2/26 P(Red Queen Or P Black Ace) = [B]1/13[/B] [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F26&frac2=3%2F8&pl=Simplify']using our fraction simplifier[/URL]

a card selected from a deck of 52 cards what is the probability it is a black card or face card Facts: [LIST] [*]Half the cards in the deck are black (26/52) [*]There are 12 face cards (K, Q, J) in a deck (12/52) [*]Black and Face = 6/52 (Duplicates from above) [/LIST] P(Black or Face) = P(Black) + P(Face) - P(Black And Face) P(Black or Face) = 26/52 + 12/52 - 6/52 P(Black or Face) = 32/52 We can simplify this. We use our [URL='https://www.mathcelebrity.com/fraction.php?frac1=32%2F52&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL] to get: P(Black or Face) = [B]8/13[/B]

a carnival charges $6 admission and $2.50 per ride. You have $50 to spend at the carnival. Which of the following inequalities represents the situation if r is the number of rides? We set up our inequality using less than or equal to, since our cash is capped at $50. We use S for our : Cost per ride * r + Admission <= 50 Plugging in our numbers, we get: 2.50r + 6 <= 50 [B][/B] Now, if the problem asks you to put this in terms of r, then [URL='https://www.mathcelebrity.com/1unk.php?num=2.50r%2B6%3C%3D50&pl=Solve']we plug this inequality into our search engine[/URL] and we get: r <= 17.6 Since we cannot do fractional rides, we round down to 17: [B]r <= 17[/B]

A carnival charges a $15 admission price. Each game at the carnival costs $4. How many games would a person have to play to spend at least $40? Let g be the number of games. The Spend function S(g) is: S(g) = Cost per game * number of games + admission price S(g) = 4g + 15 The problem asks for g when S(g) is at least 40. At least is an inequality using the >= sign: 4g + 15 >= 40 To solve this inequality for g, we type it in our search engine and we get: g >= 6.25 Since you can't play a partial game, we round up and get: [B]g >= 7[/B]

A carpenter bought a piece of wood that was 43.32 centimeters long. Then she sawed 5.26 centimeters off the end. How long is the piece of wood now? When you saw off the end, the length decrease. So we subtract: New length = Original length - Sawed piec New length = 43.32 - 5.26 New length = [B]38.06[/B]

A carpenter wants to cut a 45 inch board into two pieces such that the longer piece will be 7 inches longer than the shorter. How long should each piece be Let the shorter piece of board length be s. Then the larger piece is: [LIST] [*]l = s + 7 [/LIST] And we know that: Shorter Piece + Longer Piece = 25 Substituting our values above, we have: s + s + 7 = 45 to solve this equation for s, we type it in our search engine and we get: s = [B]19[/B] Plugging this into our equation for l above means that: l = 19 + 7 l =[B] 26[/B]

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge of 25¢ per square foot for any footage that exceeds 180 sq ft and $1.30 per step for any carpeting on a staircase. A customers cleaning bill was $253.95. This included the cleaning of a staircase with 14 steps. In addition to the staircase, how many square feet of carpet did the customer have cleaned? Calculate the cost of the staircase cleaning. Staircase cost = $1.30 * steps Staircase cost = $1.30 * 14 Staircase cost = $18.20 Subtract this from the cost of the total cleaning bill of $253.95. We do this to isolate the cost of the carpet. Carpet cost = $253.95 - $18.20 Carpet cost = $235.75 Now, the remaining carpet cost can be written as: 75 + $0.25(s - 180) = $235.75 <-- were s is the total square foot of carpet cleaned Multiply through and simplify: 75 + 0.25s - 45 = $235.75 Combine like terms: 0.25s + 30 = 235.75 [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B30%3D235.75&pl=Solve']Type this equation into our search engine[/URL] to solve for s, and we get: s = [B]823[/B]

A car’s purchase price is $24,000. At the end of each year, the value of the car is three-quarters of the value at the beginning of the year. Write the first four terms of the sequence of the car’s value at the end of each year. three-quarters means 3/4 or 0.75. So we have the following function P(y) where y is the number of years since purchase price: P(y) = 24000 * 0.75^y First four terms: P(1) = 24000 * 0.75 = [B]18000[/B] P(2) = 18000 * 0.75 = [B]13500[/B] P(3) = 13500 * 0.75 = [B]10125[/B] P(4) = 10125 * 0.75 = [B]7593.75[/B]

A case of meatball costs $19.09. There are 320 meatballs in a case. How much does 1 meatball cost? Cost per meatball = Cost of case / Total Meatballs per case Cost per meatball = $19.09 / 320 Cost per meatball = [B]$0.06 per meatball[/B]

a cash prize of $4600 is to be awarded at a fundraiser. if 2300 tickets are sold at $7 each, find the expected value. Expected Value E(x) is: E(x) = Probability of winning * Winning Price - Probability of losing * Ticket Price [U]Since only 1 cash price will be given, 2299 will be losers:[/U] E(x) = 4600 * (1/2300) - 2299/2300 * 7 E(x) = 2 - 0.99956521739 * 7 E(x) - 2 - 7 E(x) = [B]-5[/B]

A cash register contains $5 bills and $20 bills with a total value of $180 . If there are 15 bills total, then how many of each does the register contain? Let f be the number of $5 dollar bills and t be the number of $20 bills. We're given the following equations: [LIST=1] [*]f + t = 15 [*]5f + 20t = 180 [/LIST] We can solve this system of equations 3 ways. We get [B]t = 7[/B] and [B]f = 8[/B]. [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Cramers+Method']Cramers Method[/URL] [/LIST]

A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How many of each type of bill does the cashier have? Let a be the amount of $10 bills and b be the amount of $20 bills. We're given two equations: [LIST=1] [*]a + b = 44 [*]10a + 20b = 730 [/LIST] We rearrange equation 1 in terms of a. We subtract b from each side and we get: [LIST=1] [*]a = 44 - b [*]10a + 20b = 730 [/LIST] Now we substitute equation (1) for a into equation (2): 10(44 - b) + 20b = 730 Multiply through to remove the parentheses: 440 - 10b + 20b = 730 Group like terms: 440 + 10b = 730 Now, to solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=440%2B10b%3D730&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]29 [/B] To get a, we take b = 29 and substitute it into equation (1) above: a = 44 - 29 a = [B]15 [/B] So we have [B]15 ten-dollar bills[/B] and [B]29 twenty-dollar bills[/B]

A cashier has a total of 52 bills in her cash drawer. There are only $10 bills and $5 bills in her drawer. The value of the bills is $320. How many $10 bills are in the drawer? Let f be the amount of $5 bills in her drawer. Let t be the amount of $10 bills in her drawer. We're given two equations: [LIST=1] [*]f + t = 52 [*]5f + 10t = 320 [/LIST] We have a system of equations. We can solve this 3 ways below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter what method we choose, we get: f = 40 and t = 12 So the answer for how many $10 bills are in the drawer is [B]12[/B]. Let's check our work for equation 1: 40 + 12 ? 52 52 = 52 <-- Confirmed Let's check our work for equation 2: 5(40) + 10(12) ? 320 200 + 120 ? 320 320 = 320 <-- Confirmed

A catering service offers 3 appetizers, 6 main courses, and 4 desserts. A customer is to select 2 appetizers, 3 main courses, and 3 desserts for a banquet. In how many ways can this be done? We use the combinations formula, and since each event is independent of the others, we multiply: 2 appetizers, 3 main courses, and 3 desserts = [URL='https://www.mathcelebrity.com/permutation.php?num=3&den=2&pl=Combinations']3C2[/URL] * [URL='https://www.mathcelebrity.com/permutation.php?num=6&den=3&pl=Combinations']6C3[/URL] * [URL='https://www.mathcelebrity.com/permutation.php?num=4&den=3&pl=Combinations']4C3[/URL] 2 appetizers, 3 main courses, and 3 desserts = 3 * 20 * 4 2 appetizers, 3 main courses, and 3 desserts = [B]240[/B]

A catering service offers 4 appetizers, 12 main courses, and 9 desserts. A customer is to select 3 appetizers, 10 main courses, and 5 desserts for a banquet. In how many ways can this be done? We use combinations, so we have: [LIST] [*][URL='https://www.mathcelebrity.com/permutation.php?num=4&den=3&pl=Combinations']4C3 appetizers[/URL] = 4 [*][URL='https://www.mathcelebrity.com/permutation.php?num=12&den=10&pl=Combinations']12C10 main courses[/URL] = 66 [*][URL='https://www.mathcelebrity.com/permutation.php?num=9&den=5&pl=Combinations']9C5 desserts[/URL] = 126 [/LIST] We multiply each of these together to get our total combinations: 4 * 66 * 126 = [B]33,264[/B]

A celebrity 50,000 followers on Instagram. The number of follower increases 45% each year. How many followers will they have after 8 years? We set up a growth equation for followers F(y), where y is the number of years passed since now: F(y) = 50000 * (1.45)^y <-- since 45% is 0.45 The problem asks for F(8): F(8) = 50000 * 1.45^8 F(8) = 50000 * 19.5408755063 F(8) = [B]977,044[/B]

A cell phone company charges 8$ per minute. How much do you pay for 60 minutes? Calculate the total bill: Total Bill = Cost per minute * number of minutes Total Bill = $8 * 60 Total Bill = [B]$480[/B]

A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for m minutes is $21.20. Write an equation that models this situation. Let m be the number of minutes. We have the cost equation C(m): [B]0.25m + 12.95 = $21.20[/B]

A cell phone costs $20 for 400 minutes and $2 for each extra minute. Gina uses 408 minutes. How much will it cost? Set up the cost function for minutes (m) if m is greater than or equal to 400 C(m) = 20 + 2(m - 400) For m = 408, we have: C(408) = 20 + 2(408 - 400) C(408) = 20 + 2(8) C(408) = [B]36[/B]

A cell phone plan charges $1.25 for the first 400 minutes and $0.25 for each additional minute, x. Which represents the cost of the cell phone plan? Let C(x) be the cost function where x is the number of minutes we have: [B]C(x) = 1.25(min(400, x)) + 0.25(Max(0, 400 - x))[/B]

A cell phone plan costs $20 a month and includes 200 free minutes. Each additional minute costs 5 cents. If you use your cell phone for at least 200 minutes a month, write a function C(x) that represents the total cost per x minutes. We add the flat rate per month to 5% of the number of minutes [U]over[/U] 200: [B]C(x) = 20 + 0.05(x - 200)[/B]

A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 per month. However, if you go over your 5 GB of data in a month, you have to pay an extra $10 for each GB. How many GB would be used to make both plans cost the same? Let g be the number of GB. The limited plan has a cost as follows: C = 10(g - 5) + 55 C = 10g - 50 + 55 C = 10g + 5 We want to set the limited plan equal to the unlimited plan and solve for g: 10g + 5 = 70 Solve for [I]g[/I] in the equation 10g + 5 = 70 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 5 and 70. To do that, we subtract 5 from both sides 10g + 5 - 5 = 70 - 5 [SIZE=5][B]Step 2: Cancel 5 on the left side:[/B][/SIZE] 10g = 65 [SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE] 10g/10 = 65/10 g = [B]6.5[/B] Check our work for g = 6.5: 10(6.5) + 5 65 + 5 70

A cellular offers a monthly plan of $15 for 350 min. Another cellular offers a monthly plan of $20 for 425 min. Which company offers the better plan? Let's figure out the unit cost of minutes per dollar: [LIST=1] [*]Plan 1: 350 minutes / $15 = 23.33 minutes per dollar [*]Plan 2: 425 minutes / $20 = 21.25 minutes per dollar [/LIST] [B]Plan 2 is better, because you get more minutes per dollar.[/B]

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute cost $.35. This month you used 750 minutes. How much do you owe? Calculate the excess minutes over the standard plan: Excess Minutes = 750 - 600 Excess Minutes = 150 Calculate additional cost: 150 additional minutes * 0.35 per additional minutes = $52.50 Add this to the standard plan cost of $49.99 $52.50 + $49.99 = [B]$102.49[/B]

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute costs $.35. This month you used 750 minutes. How much do you owe [U]Find the overage minutes:[/U] Overage Minutes = Total Minutes - Free Minutes Overage Minutes = 750 - 600 Overage Minutes = 150 [U]Calculate overage cost:[/U] Overage Cost = Overage Minutes * Overage cost per minute Overage Cost = 150 * 0.35 Overage Cost = $52.5 Calculate total cost (how much do you owe): Total Cost = Monthly Fee + Overage Cost Total Cost = $49.99 + $52.50 Total Cost = [B]$102.49[/B]

A cereal box has dimensions of 12" x 3" x 18". How many square inches of cardboard are used in its construction? A cereal box is a rectangular solid. The volume formula is V = lwh. Substituting these values of the cereal box in, we have: V = 12(3)(18) V = [B]648 cubic inches[/B]

A certain culture of the bacterium Streptococcus A initially has 8 bacteria and is observed to double every 1.5 hours.After how many hours will the bacteria count reach 10,000. Set up the doubling times: 0 | 8 1.5 | 16 3 | 32 4.5 | 64 6 | 128 7.5 | 256 9 | 512 10.5 | 1024 12 | 2048 13.5 | 4096 15 | 8192 16.5 | 16384 So at time [B]16.5[/B], we cross 10,000 bacteria.

A certain group of woman has a 0.69% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness? 0.69% = 0.0069. There exists a statistics theorem for an event A that states: P(A) + P(A') = 1 where A' is the event not happening In this case, A is the woman having red/green color blindness. So A' is the woman [U][B][I]not[/I][/B][/U][I] having red/green color blindness[/I] So we have: 0.0069 + P(A') = 1 Subtract 0.0069 from each side, we get: P(A') = 1 - 0.0069 P(A') = [B]0.9931[/B]

A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 people if 3 people initially exposes? Round to the nearest hour. Let h be the number of hours. We have the equation: 3 * (1.1)^h = 1,200 Divide each side by 3: 1.1^h = 400 [URL='https://www.mathcelebrity.com/natlog.php?num=1.1%5Eh%3D400&pl=Calculate']Type this equation into our search engine [/URL]to solve for h: h = 62.86 To the nearest hour, we round up and get [B]h = 63[/B]

Let x be the number. We have: x^2 + x = 30 Subtract 30 from each side: x^2 + x - 30 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-30%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get potential solutions of: [B]x = 5 or x = -6[/B] Check 5: 5 + 5^2 = 5 + 25 = [B]30[/B] Check -6 -6 + -6^2 = -6 + 36 = [B]30[/B]

A certain race is a distance of 26 furlongs. How far is the race in (a) miles? (b) yards? [URL='https://www.mathcelebrity.com/linearcon.php?quant=26&pl=Calculate&type=furlong']We type in [I]26 furlongs[/I] into our search engine[/URL] and we get: [LIST] [*][B]3.25 miles[/B] [*][B]5,720 yards[/B] [/LIST]

A certain species of fish costs $3.19 each. You can spend at most $35. How many of this type of fish can you buy for your aquarium? Let the number of fish be f. We have the following inequality where "at most" means less than or equal to: 3.19f <= 35 [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3.19f%3C%3D35&pl=Show+Interval+Notation']Typing this inequality into our search engine[/URL], we get: f <= 10.917 Since we need a whole number of fish, we can buy a maximum of [B]10 fish[/B].

A certain textbook cost $94. If the price increases each year by 3% of the previous year's price, find the price after 7 years. Using our [URL='https://www.mathcelebrity.com/apprec-percent.php?num=acertaintextbookcost94.ifthepriceincreaseseachyearby3%ofthepreviousyearspricefindthepriceafter7years&pl=Calculate']appreciation calculator[/URL], we get: [B]115.61[/B]

A certain type of an elephant would weigh 8 to 12 tons. How many pounds would it weigh? 1 ton = 2000 pounds. 8 tons = 8 * 2000 = 16000 pounds 12 tons = 12 * 20000 = 24000 pounds So the elephant weighs between 16000 and 24000 pounds

A chalkboard is 3 feet tall and 4 feet long. What is its perimeter A chalkboard is a rectangle. So the perimeter is: 2l + 2w Using [URL='https://www.mathcelebrity.com/rectangle.php?l=4&w=3&a=&p=&pl=Calculate+Rectangle']our rectangle calculator[/URL], we get: P = [B]14[/B]

A checking account is set up with an initial balance of $2400 and $200 are removed from the account each month for rent right and equation who solution is the number of months and it takes for the account balance to reach 1000 200 is removed, so we subtract. Let m be the number of months. We want the following equation: [B]2400 - 200m = 1000 [/B] Now, we want to solve this equation for m. So [URL='https://www.mathcelebrity.com/1unk.php?num=2400-200m%3D1000&pl=Solve']we type it in our search engine[/URL] and we get: m = [B]7[/B]

A cheetah travels at a rate of 90 feet per second. The distance d traveled by the cheetah is a function of seconds traveled t. Write a rule for the function. How far will the cheetah travel in 25 seconds? Distance, or D(t) is expressed as a function of rate and time below: Distance = Rate x Time For the cheetah, we have D(t) as: D(t) = 90ft/sec(t) The problem asks for D(25): D(25) = 90(25) D(25) = [B]2,250 feet[/B]

A chest of treasure was hidden in the year 64 BC and found in 284 AD. For how long was the chest hidden BC stands for Before Christ. Year 0 is when Christ was born. AD stands for After Death On a number line, the point of Christ's birth is 0. So BC is really negative AD is positive So we have: 284 - -64 284 + 64 [B]348 years[/B]

A chicken farm produces ideally 700,000 eggs per day. But this total can vary by as many as 60,000 eggs. What is the maximum and minimum expected production at the farm? [U]Calculate the maximum expected production:[/U] Maximum expected production = Average + variance Maximum expected production = 700,000 + 60,000 Maximum expected production = [B]760,000[/B] [U]Calculate the minimum expected production:[/U] Minimum expected production = Average - variance Minimum expected production = 700,000 - 60,000 Minimum expected production = [B]640,000[/B]

A child's bedroom is rectangular in shape with dimensions 17 feet by 15 feet. How many feet of wallpaper border are needed to wrap around the entire room? A rectangle has an Perimeter (P) of: P = 2l + 2w We're given l = 17 and w = 15. So we have: P = 2(17) + 2(15) P = 34 + 30 P = [B]64[/B]

A circle has a center at (6, 2) and passes through (9, 6) The radius (r) is found by [URL='https://www.mathcelebrity.com/slope.php?xone=6&yone=2&slope=+2%2F5&xtwo=9&ytwo=6&pl=You+entered+2+points']using the distance formula[/URL] to get: r = 5 And the equation of the circle is found by using the center (h, k) and radius r as: (x - h)^2 + (y - k)^2 = r^2 (x - 6)^2 + (y - 2)^2 = 5^2 [B](x - 6)^2 + (y - 2)^2 = 25[/B]

A circular balloon is inflated with air flowing at a rate of 10cm3/s. How fast is the radius of the ballon increasing when the radius is 2cm? [U]The volume (V) of the balloon with radius (r) is:[/U] V = 4/3?r^3 [U]Differentiating with respect to t, we get:[/U] dV/dt = 4/3? * 3r^2 * dr/dt dV/dt = 4?r^2 * dr/dt The rate of change of the volume is: dV/dt = 10cm^3s^?1 [U]So, we find dr/dt:[/U] dr/dt = 1/4?r^2 * dV/dt dr/dt = 10/4?r^2 dr/dt = 5/2?r^2 Therefore, dr/dt(2cm) is: dr/dt(2cm) = 5/2?(2)^2 dr/dt(2cm) = 5/2?4 dr/dt(2cm) = [B]5?/8[/B]

A city doubles its size every 48 years. If the population is currently 400,000, what will the population be in 144 years? Calculate the doubling time periods: Doubling Time Periods = Total Time / Doubling Time Doubling Time Periods = 144/48 Doubling Time Periods = 3 Calculate the city population where t is the doubling time periods: City Population = Initital Population * 2^t Plugging in our numbers, we get: City Population = 400,000 * 2^3 City Population = 400,000 * 8 City Population = [B]3,200,000[/B]

A city has a population of 240,000 people. Suppose that each year the population grows by 7.25%. What will the population be after 9 years? Let's build a population function P(t), where t is the number of years since right now. P(t) = 240,000(1.0725)^t <-- 7.25% as a decimal is 0.0725 The question asks for P(9) P(9) = 240,000(1.0725)^9 P(9) = 240,000(1.87748) P(9) = [B]450,596[/B]

A city has a population of 240,000 people. Suppose that each year the population grows by 8%. What will the population be after 5 years? [U]Set up our population function[/U] P(t) = 240,000(1 + t)^n where t is population growth rate percent and n is the time in years [U]Evaluate at t = 0.08 and n = 5[/U] P(5) = 240,000(1 + 0.08)^5 P(5) = 240,000(1.08)^5 P(5) = 240,000 * 1.4693280768 [B]P(5) = 352638.73 ~ 352,639[/B]

A city has a population of 260,000 people. Suppose that each year the population grows by 8.75% . What will the population be after 12 years? Use the calculator provided and round your answer to the nearest whole number. Using our [URL='http://www.mathcelebrity.com/population-growth-calculator.php?num=acityhasapopulationof260000people.supposethateachyearthepopulationgrowsby8.75%.whatwillthepopulationbeafter12years?usethecalculatorprovidedandroundyouranswertothenearestwholenumber&pl=Calculate']population growth calculator,[/URL] we get P = [B]711,417[/B]

A city’s budget is $8,000,000. It actually spends $12,000,000.What is the city’s deficit? Deficit = Budget - Spend Deficit = $8,000,000 - $12,000,000 Deficit = [B]-$4,000,000[/B]

A city’s population in the 1987 was 125,524. In 2007 the population was 436,884. Determine the population rate of increase or decrease [U]Find the population change:[/U] Population Change = New Population - Old Population Population Change = 436,884 - 125,524 Population Change = 311,360 [U]Since the population change increased, we calculate the rate of increase:[/U] Rate of increase = 100% * Population Change / Starting Population Rate of increase = 100% * 311,360 / 125,524 Rate of increase = 100% * 2.48 Rate of increase = [B]248%[/B]

a class has 24 people and 1/6 of them have blue eues. what fraction of the class has blue eyes, using 24 as the denominator Blue eyes = 1/6 * 24 Blue Eyes = 24/6 Blue Eyes = 4 Since 6*4 = 24, we have: 24/6 * 4/4 = [B]96/24[/B]

A class has 35 boys and girls. There are 7 more girls than boys. Find the number of girls and boys in the class Let the number of boys be b and the number of girls be g. We're given two equations: [LIST=1] [*]b + g = 35 [*]g = b + 7 (7 more girls means we add 7 to the boys) [/LIST] To solve for b, we substitute equation (2) into equation (1) for g: b + b + 7 = 35 To solve for b, we type this equation into our search engine and we get: b = [B]14[/B] Now, to solve for g, we plug b = 14 into equation (2) above: g = 14 + 7 g = [B]21[/B]

A class is made up of 6 boys and 12 girls. Half of the girls wear glasses. A student is selected at random from the class. What is the probability that the student is a girl with glasses? 1/2 of 6 is 3. So we want the probability we pick any of the 3 girls wearing glasses. We have a total of 6 + 12 = 18 people. Our probability is [B]3/18, or 1/6[/B].

A class of [I]n[/I] students was raising money for a field trip. They have earned $800 so far. Each student plans to work [I]x[/I] more hours at a wage of [I]y[/I] dollars per hour. When they are done, how much money will they have earned? Class of n students * x more hours worked * y dollars per hour = xyn Total dollars earned includes the $800 already earned: $800 + xyn

A classroom fish tank contains x goldfish. The tank contains 4 times as many guppies as goldfish. Enter an equation that represents the total number of guppies, y, in the fish tank. The phrase [I]4 times as many[/I] means we multiply the goldfish (x) by 4 to get the number of guppies (y): [B]y = 4x[/B]

A classroom had x students. Then 9 of them went home. There are now 27 students in the classroom. Take this one piece at a time: [LIST] [*]We start with x students [*]9 of them went home. This means we have 9 less students. So we subtract 9 from x: x - 9 [*]The phrase [I]there are now[/I] means an equation, so we set x - 9 equal to 27 [/LIST] x - 9 = 27 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-9%3D27&pl=Solve']type it in our search engine[/URL] and we get: x = [B]36[/B]

A clothing store buys shirts for [I]n[/I] dollars and then marks them up 50%. To reward their employees, the store gives a 50% discount to all employees. How much does an employee pay for a shirt? 50% = 0.5 Markup cost = (1 + 0.5)n Markup cost = 1.5n 50% discount: 1.5n/2 = [B]0.75n[/B]

A coat is on sale for 35% off. The regular price of the coat is p. Write and simplify and expression to represent the sale price of the coat. Show your work. The Sale price of the coat is: S = p(1 - 0.35) <-- Since 35% is 0.35 as a decimal [B]S = 0.65p[/B]

A coat normally costs $100. First, there was a 20% discount. Then, later, it was marked down 30% off of the discounted priced. How much does the coat cost now? Calculate discounted price: Discounted Price = Full Price * (1 - Discount Percentage) Discounted Price = 100 * (1 - 0.20) <-- Since 20% = 0.2 Discounted Price = 100 * (0.80) Discounted Price = 80 Now calculate marked down price off the discount price: Markdown Price = Discount Price * (1 - Markdown Percentage) Markdown Price = 80 * (1 - 0.30) <-- Since 30% = 0.3 Markdown Price = 80 * (0.70) Markdown Price = [B]56[/B]

A coffee franchise is opening a new store. The company estimates that there is a 75% chance the store will have a profit of $45,000, a 10% chance the store will break even, and a 15% chance the store will lose $2,500. Determine the expected gain or loss for this store. Calculate the expected value E(x). Expected value is the sum of each event probability times the payoff or loss: E(x) = 0.75(45,000) + 0.1(0) + 0.15(-2,500) <-- Note, break even means no profit and no loss and a loss is denoted with a negative sign E(x) = 33,750 + 0 - 375 E(x) = [B]33,375 gain[/B]

A coin is tossed 3 times. a. Draw a tree diagram and list the sample space that shows all the possible outcomes [URL='https://www.mathcelebrity.com/cointoss.php?hts=+HTHTHH&hct=+2&tct=+1&fct=+5>=no+more+than&nmnl=+2&htpick=heads&tossct=3&montect=3&calc=5&pl=Calculate+Probability']type in "toss a coin 3 times" and pick the probability option[/URL].

A coin is tossed and a die is rolled. Find the probability pf getting a head and a number greater than 4. Since each event is independent, we multiply the probabilities of each event. P(H) = 0.5 or 1/2 P(Dice > 4) = P(5) + P(6) = 1/6 + 1/6 = 2/6 = 1/3 P(H) AND P(Dice > 4) = 1/2 * 1/3 = [B]1/6 [MEDIA=youtube]ofsbmHmQmjs[/MEDIA][/B]

a collection of 7 pencils, every week 3 more pencils are added How many weeks will it take to have 30 pencils? Set up a function, P(w), where w is the number of weeks, and P(w) is the total amount of pencils after w weeks. We have: P(w) = 3w + 7 We want to know what w is when P(w) = 30 3w + 7 = 30 [URL='https://www.mathcelebrity.com/1unk.php?num=3w%2B7%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get: w = 7.6667 We round up to the nearest integer, so we get [B]w = 8[/B]

A collection of nickels and dime has a total value of $8.50. How many coins are there if there are 3 times as many nickels as dimes. Let n be the number of nickels. Let d be the number of dimes. We're give two equations: [LIST=1] [*]n = 3d [*]0.1d + 0.05n = 8.50 [/LIST] Plug equation (1) into equation (2) for n: 0.1d + 0.05(3d) = 8.50 Multiply through: 0.1d + 0.15d = 8.50 [URL='https://www.mathcelebrity.com/1unk.php?num=0.1d%2B0.15d%3D8.50&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]d = 34[/B] Now, we take d = 34, and plug it back into equation (1) to solve for n: n = 3(34) [B]n = 102[/B]

A college student earned $6000 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 8% and the rest at 6%. If the student received a total of $418 in interest at the end of the year, how much was invested at 8%? [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=6000&i1=8&i2=6&itot=418&pl=Calculate']Using our split fund interest calculator[/URL], we get: [B]$2,900 invested at 8%[/B] $3,100 invested at 6%

A college student earns $21 per day delivering advertising brochures door-to-door, plus 50 cents for each person he interviews. How many people did he interview on a day when he earned $61.50 Let each person interviewed be p. We have an earnings equation E(p): E(p) = 0.5p + 21 The problems asks for p when E(p) = 61.50 0.5p + 21 = 61.50 To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.5p%2B21%3D61.50&pl=Solve']type this equation in our search engine[/URL] and we get: p = [B]81[/B]

A colony of 100 bacteria doubles in size every 34 hours. What will the population be 68 hours from now T(0) = 100 T(34) = 100 * 2 = 200 T(68) = 200 * 2 = [B]400[/B]

A colony of 995 bacteria doubles in size every 206 minutes. What will the population be 618 minutes from now? Calculate the doubling time periods: Doubling Time Periods = Total Minutes From Now / Doubling Period in Minutes Doubling Time Periods = 618/206 Doubling Time Periods = 3 Calculate the new population using the doubling time formula below where t is the number of doubling periods: Population = Initial Population * 2^2 Population = 995 * 2^3 Population = 995 * 8 Population = [B]7,960[/B]

A combination lock open with the correct 4 letter code. Each wheel roared through letters A-L. How many different 4 letter codes are possible A-L = 12 letters Possible combinations is found by: 12 * 12 * 12 * 12 = [B]20,736 combinations[/B]

A combined total of $34,000 is invested in two bonds that pay 4% and 8.5% simple interest. The annual interest is $2,350. How much is invested in each bond Using our split fund interest calculator, we get; [LIST] [*][B]12,000[/B] in Fund 1 [*][B]22,000[/B] in Fund 2 [/LIST]

A combined total of $40,000 is invested in two bonds that pay 6% and 9% simple interest. The annual interest is $3,210.00. How much is invested in each bond? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=40000&i1=6&i2=9&itot=3210&pl=Calculate']split fund interest calculator[/URL], we get: Fund 1 at 6% = [B]13,000[/B] Fund 2 at 9% =[B] 27,000[/B]

A comet passes earth every 70 years. another comet passes earth every 75 years of both comets pass earth this year how many years will it be before they pass on the same year again. We want the least common multiple of (70, 75). [URL='https://www.mathcelebrity.com/gcflcm.php?num1=70&num2=75&num3=&pl=GCF+and+LCM']Using our LCM calculator[/URL], we find the answer is [B]1,050 years[/B]

A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 12 faculty members and 15 students eligible to serve on the committee. In how many ways can the committee be formed? We'll use combinations, so we have: [LIST] [*][URL='https://www.mathcelebrity.com/permutation.php?num=12&den=4&pl=Combinations']12 faculty members choose 4 faculty members --> 12 C 4[/URL] = 495 [*][URL='https://www.mathcelebrity.com/permutation.php?num=15&den=5&pl=Combinations']15 students choose 5 students --> 15 C 5[/URL] = 3,003 [/LIST] To get the total committees, we multiply the total faculty member choices by the total student choices: Total committees = total faculty members * total students Total committees = 495 * 3,003 Total committees = [B]1,486,485[/B]

A compact disc is designed to last an average of 4 years with a standard deviation of 0.8 years. What is the probability that a CD will last less than 3 years? Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=3&mean=4&stdev=0.8&n=1&pl=P%28X+%3C+Z%29']Z-score and Normal distribution calculator[/URL], we get: [B]0.10565[/B]

A company charges $7 for a T-Shirt and ships and order for $22. A school principal ordered a number of T-shirts for the school store. The total cost of the order was $1,520. Which equation can be used to find the number one f shirts ordered? Set up the cost equation C(f) where f is the number of shirts: C(f) = Cost per shirt * f + Shipping We're given C(f) = 1520, Shipping = 22, and cost per shirt is 7, so we have: [B]7f + 22 = 1520 [/B] To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=7f%2B22%3D1520&pl=Solve']type this equation in our search engine[/URL] and we get: f = [B]214[/B]

A company delivered 498 packages on Monday. On Tuesday they delivered 639 and on Wednesday they delivered 436. How many packages did the company deliver in all? Add up all the packages: 498 + 639 + 436 = [B]1573[/B]

A company had sales of $19,808 million in 1999 and $28,858 million in 2007. Use the Midpoint Formula to estimate the sales in 2003 2003 is the midpoint of 1999 and 2007, so we use our [URL='https://www.mathcelebrity.com/mptnline.php?ept1=19808&empt=&ept2=28858&pl=Calculate+missing+Number+Line+item']midpoint calculator[/URL] to get: [B]24,333[/B] sales in 2003

A company has 12,600 employees. Of these, 1/4 drive alone to work, 1/6 car pool, 1/8 use public transportation, 1/9 cycle, and the remainder use other methods of transportation. How many employees use each method of transportation? Find the remainder fraction: Remainder = 1 - (1/4 + 1/6 + 1/8 + 1/9) The least common multiple of 4, 6, 8, 9 is 72. So we divide 72 by each fraction denominator to get our multiplier: 1/4 = 18/72 1/6 = 12/72 1/8 = 9/72 1/9 = 8/72 Add those all up: (18 + 12 + 9 + 8)/72 47/72 Now subtract the other methods out from 1 to get the remainder of who use other methods: Remainder = 1 - 47/72 Since 1 = 72/72, we have: (72 - 47)/72 [B]25/72[/B]

A company has 3,100 employees and is expected to grow at a rate of 0.04 for the next six years. How many employees will they have in 6 years? Round to the nearest whole number. We build the following exponential equation: Final Balance = Initial Balance * (1 + growth rate)^time Final Balance = 3100(1.04)^6 Final Balance = 3100 * 1.2653190185 Final Balance = 3922.48895734 The problem asks us to round to the nearest whole number. Since 0.488 is less than 0.5, we round [U]down.[/U] Final Balance = [B]3,922[/B]

A company has 81 employees of whom x are members of a union how many are not in the union You can either be a union member or a non-union member. This is our sample space. If we have 81 employees and x are union members, this means that: Non-Union membes = [B]81 - x[/B]

A company has 95 employees. 4 get sacked. 57 quit. 52 are hired. How many employees are there now? Take this in pieces [LIST=1] [*]We start with 95 employees [*]4 get sacked (fired). So we subtract: 95 - 4 = 91 [*]57 quit. We subtract: 91 - 57 = 34 [*]52 are hired. We add: 34 + 52 = [B]86 employees[/B] [/LIST]

A company has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item that it makes has its own cost of $34. One month the company filled an order for 2400 of its tapestries, selling each item for $63. How much profit was generated by the order? [U]Set up Cost function C(t) where t is the number of tapestries:[/U] C(t) = Cost per tapestry * number of tapestries + Fixed Cost C(t) = 34t + 26000 [U]Set up Revenue function R(t) where t is the number of tapestries:[/U] R(t) = Sale Price * number of tapestries R(t) = 63t [U]Set up Profit function P(t) where t is the number of tapestries:[/U] P(t) = R(t) - C(t) P(t) = 63t - (34t + 26000) P(t) = 63t - 34t - 26000 P(t) = 29t - 26000 [U]The problem asks for profit when t = 2400:[/U] P(2400) = 29(2400) - 26000 P(2400) = 69,600 - 26,000 P(2400) = [B]43,600[/B]

A company has a fixed cost of $34,000 and a production cost of $6 for each unit it manufactures. A unit sells for $15 Set up the cost function C(u) where u is the number of units is: C(u) = Cost per unit * u + Fixed Cost C(u) = [B]6u + 34000[/B] Set up the revenue function R(u) where u is the number of units is: R(u) = Sale price per unit * u R(u) = [B]15u[/B]

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 + 100x dollars, where x is the number of units produced and sold. How many units will give a profit Profit P(x) is given by: R(x) - C(x) So we have: P(x) = 500x - (100x + 48,000) P(x) = 500x - 100x - 48,000 P(x) = 400x - 48,000 A profit is found when P(x) > 0, so we have: 400x - 48000 > 0 To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=400x-48000%3E0&pl=Solve']we type it into our search engine [/URL]and we get: [B]x > 120[/B]

A company is planning to manufacture a certain product. The fixed costs will be $474778 and it will cost $293 to produce each product. Each will be sold for $820. Find a linear function for the profit, P , in terms of units sold, x . [U]Set up the cost function C(x):[/U] C(x) = Cost per product * x + Fixed Costs C(x) = 293x + 474778 [U]Set up the Revenue function R(x):[/U] R(x) = Sale Price * x R(x) = 820x [U]Set up the Profit Function P(x):[/U] P(x) = Revenue - Cost P(x) = R(x) - C(x) P(x) = 820x - (293x + 474778) P(x) = 820x - 293x - 474778 [B]P(x) = 527x - 474778[/B]

a company made a profit of $4 million per month for 8 months, then lost $10 million per month for 4 months. What was their result for the year? Profits = 4 million per month * 8 months = 32,000,000 Losses = 10 million per month * 4 months = 40,000,000 Calculate results for the year: Result for the year = Profits - Losses Result for the year = 32,000,000 - 40,000,000 Result for the year = [B]8,000,000[/B]

A company makes a puzzle that is made of 53 small plastic cubes. The puzzles are shipped in boxes that each contain 52 puzzles. That boxes are loaded into trucks that each contain 53 boxes. What is the total number of small plastic cubes in each truck? 1 truck has 53 boxes, and each box contains 52 puzzles, and each puzzle has 53 small plastic cubes. We have 53 * 52 * 53 = [B]146,068 plastic cubes[/B]

A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat. They sell boats for $75 a piece. How many boats must be sold each month to break even? [U]Set up Cost function C(b) where t is the number of tapestries:[/U] C(b) = Cost per boat * number of boats + Fixed Cost C(b) = 50b + 1500 [U]Set up Revenue function R(b) where t is the number of tapestries:[/U] R(b) = Sale Price * number of boats R(b) = 75b [U]Break even is where Revenue equals Cost, or Revenue minus Cost is 0, so we have:[/U] R(b) - C(b) = 0 75b - (50b + 1500) = 0 75b - 50b - 1500 = 0 25b - 1500 = 0 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-1500%3D0&pl=Solve']type this equation in our math engine[/URL] and we get: b = [B]60[/B]

A company now has 4900 employees nationwide. It wishes to reduce the number of employees by 300 per year through retirements, until its total employment is 2560. How long will this take? Figure out how many reductions are needed 4900 - 2560 = 2340 We want 300 per year for retirements, so let x equal how many years we need to get 2340 reductions. 300x = 2340 Divide each side by 300 x = 7.8 years. If we want full years, we would do 8 full years

A company ordered 325 boxes of pens. Each box has 12 cases in it. Each case holds 24 pens. How many pens did the company order 325 boxes Each box has 12 cases Each case has 24 pens We have 325 boxes * 12 cases/box * 24 pens / box 325 * 12 * 24 = [B]93,600 pens[/B]

A company specializes in personalized team uniforms. It costs the company $15 to make each uniform along with their fixed costs at $640. The company plans to sell each uniform for $55. [U]The cost function for "u" uniforms C(u) is given by:[/U] C(u) = Cost per uniform * u + Fixed Costs [B]C(u) = 15u + 640[/B] Build the revenue function R(u) where u is the number of uniforms: R(u) = Sale Price per uniform * u [B]R(u) = 55u[/B] Calculate break even function: Break even is where Revenue equals cost C(u) = R(u) 15u + 640 = 55u To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=15u%2B640%3D55u&pl=Solve']type this equation into our search engine[/URL] and we get: u = [B]16 So we break even selling 16 uniforms[/B]

A company that makes superhero capes has 6,300 yards of fabric left. It uses 70 yards of fabric each day. How many days will it take the company to use all the fabric? 6300 yards / 70 yards per day = [B]90 days[/B]

A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each lamp, and the selling price is $150 per lamp. Set up the Cost Equation C(l) where l is the price of each lamp: C(l) = Variable Cost x l + Fixed Cost C(l) = 90l + 1800 Determine the revenue function R(l) R(l) = 150l Determine the profit function P(l) Profit = Revenue - Cost P(l) = 150l - (90l + 1800) P(l) = 150l - 90l - 1800 [B]P(l) = 60l - 1800[/B] Determine the break even point: Breakeven --> R(l) = C(l) 150l = 90l + 1800 [URL='https://www.mathcelebrity.com/1unk.php?num=150l%3D90l%2B1800&pl=Solve']Type this into the search engine[/URL], and we get [B]l = 30[/B]

A companys cost function is C(x) = 16x^2 + 900 dollars, where x is the number of units. Find the marginal cost function. Marginal Cost is the derivative of the Cost function. [B]C'(x) = 32x[/B]

A company’s number of personnel on active duty (not on sick leave or vacation leave) during the period 2000 - 2013 can be approximated by the cubic model f(x) = 2.5x^3 - 15x^2 - 80x + 1025, where x = 0 corresponds to 2000. Based on the model, how many personnel were on active duty in 2010? What is the domain of f? If x = 0 corresponds to 2000, when 2010 is 2010 - 2000 = 10. We want f(10): f(10) = 2.5(10)^3 - 15(10)^2 - 80(10) + 1025 f(10) = 2.5(1000) - 15(100) - 800 + 1025 f(10) = 2500 - 1500 - 800 + 1025 f(10) = [B]1,225[/B]

a computer is purchased for 800 and each year the resale value decreases by 25% what will be the resale value after 4 years Let the resale in year y be R(y). We have: R(y) = 800 * (1 - 0.25)^y R(y) = 800 * (0.75)^y The problem asks for R(4): R(4) = 800 * (0.75)^4 R(4) = 800 * 0.31640625 R(4) = [B]$253.13[/B]

A computer randomly generates a whole number from 1 to 25. Find the probability that the computer generates a multiple of 5 [URL='https://www.mathcelebrity.com/factoriz.php?num=25&pl=Show+Factorization']Multiples of 5[/URL]: {1, 5, 25} So we have the probability of a random number multiple of 5 is [B]3/25[/B]

A computer screen has a diagonal dimension of 19 inches and a width of 15 inches. Approximately what is the height of the screen? We have a right triangle, with hypotenuse of 19, and width of 15. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=15&hypinput=19&pl=Solve+Missing+Side']Using our right triangle calculator, we get [/URL][B]height = 11.662[/B]

A computer was on sale. The original cost of the computer was $900. It’s on sale for 5/6 the price. How much is the computer now? We want 5/6 of 900. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=900&frac2=5/6&pl=Multiply']type this in our search engine[/URL] and we get: [B]750[/B]

A construction company can remove 2/3 tons of dirt from a construction site each hour. How long will it take them to remove 30 tons of dirt from the site? Let h be the number of hours. We have the following equation: 2/3h = 30 Multiply each side by 3: 2(3)h/3 = 30 * 3 Cancel the 3 on the left side: 2h = 90 [URL='https://www.mathcelebrity.com/1unk.php?num=2h%3D90&pl=Solve']Type 2h = 90 into the search engine[/URL], we get [B]h = 45[/B].

A construction company needs to remove 24 tons of dirt from a construction site. They can remove 3/8 ton s of dirt each hour. How long will I it take to remove the dirt? Let h be the number of hours it takes, we have: 3/8h = 24 Multiply each side by 8/3 h = 24(8)/3 24/3 = 8, so we have: h = 8(8) h = [B]64 hours[/B]

A construction crew has just built a new road. They built 43.75 kilometers of road at a rate of 7 kilometers per week. How many weeks did it take them? Let w = weeks 7 kilometers per week * w = 43.75 To solve for w, we divide each side of the equation by 7: 7w/7 = 43.75/7 Cancel the 7's, we get: w = [B]6.25 [/B]

A construction crew has just built a new road. They built 8.75 kilometers of road in 7 weeks. At what rate did they build the road? Rate = Km of road / weeks Rate = 8.75 km / 7 weeks Rate = [B]1.25 km per week[/B]

A construction crew must build a road in 10 months or they will be penalized $500,000. It took 10 workers 6 months to build half of the road. How many additional workers must be added to finish the road in the remaining 4 months? Calculate unit rate per one worker: 10 workers * 6 months = 60 months for one worker Calculate workers needed: 60 months / 4 months = 15 workers Calculate additional workers needed: Additional workers needed = New workers needed - Original workers needed Additional workers needed = 15 - 10 Additional workers needed = [B]5 additional workers[/B]

A construction worker can lift 220 lb, while an architect can only lift 40 lb. The construction worker can lift how many times what the architect can lift? [URL='https://www.mathcelebrity.com/perc.php?num=220&den=40&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']We divide 220 by 40 to get the multiplier:[/URL] 220/40 = [B]5.5 times[/B]

A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 100 nails and each large box has 350 nails. How many nails are there in 6 small boxes and 3 large boxes? How many nails are there in a small boxes and l large boxes? [U]Calculate Small Nails[/U] Small Nails = Small Nail Boxes * Nails per Box Small Nails = 6 * 100 Small Nails = 600 [U] Calculate Large Nails[/U] Large Nails = Large Nail Boxes * Nails per Box LargeNails = 3 * 350 Large Nails = 1,050 [U]Calculate Total Nails[/U] Total Nails = Small Nails + Large Nails Total Nails = 600 + 1,050 Total Nails = [B]1,650[/B]

A contractor’s crew can frame 3 houses in a week. How long will it take them to frame 54 houses if they frame the same number each week? 54 houses / 3 houses per week = [B]18 weeks[/B]

A cook has 2 3/4 pounds of ground beef.How many quarter-pound burgers can he make? 2 & 3/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%263%2F4&frac2=3%2F8&pl=Simplify']converts to 11/4 in our fraction converter[/URL]. A quarter-pound burger is 1/4 of a pound. 11/4 = 1/4 * 11, so the cook can make [B]11 quarter-pound burgers[/B]

a cookie jar contains 3 vanilla, 2 chocolate chip, and 7 gingersnap cookies. Of one cookie is taken at random from the jar, what is the probability that it will be a vanilla cookie? Total cookies = 3 + 2 + 7 Total cookies = 12 P(Vanilla) = Vanilla Cookies / Total Cookies P(Vanilla) = 3/12 Simplified dividing top and bottom by 3, we have: P(Vanilla) = [B]1/4[/B]

A cookie jar contains 8 cookies. There are 4 children. How many cookies will each child receive? Cookies Per child = Total Cookies / Total Children Cookies Per child = 8/4 Cookies Per child = [B]2[/B]

A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8 1/4 cups, how much flour and how much sugar would it be? Let f be the number of cups of sugar. And let f be the number of cups of flour. We're given two equations: [LIST=1] [*]f = 10s [*]s + f = 8 & 1/4 [/LIST] Substitute (1) into (2): s + 10s = 8 & 1/4 11fs= 33/4 <-- 8 & 1/4 = 33/4 Cross multiply: 44s = 33 Divide each side by 44: s= 33/44 Divide top and bottom by 11 and we get s [B]= 3/4 or 0.75[/B] Now substitute this into (1): f = 10(33/44) [B]f = 330/44 or 7 & 22/44 or 7.5[/B]

A copy machine makes 28 copies per minute. how many copies does it make in 3 minutes and 45 seconds? 45 seconds = 45/60 = 3/4 of a minute. 3/4 = 0.75 So we have 3.75 minutes. Set up a proportion of copies to minutes where c is the number of copies made in 3 minutes and 45 seconds: 28/1 = c/3.75 [URL='https://www.mathcelebrity.com/prop.php?num1=28&num2=c&den1=1&den2=3.75&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our calculator[/URL], we get: c = [B]105[/B]

A copy machine makes 44 copies per minute. How many copies does it make in 5 minutes and 45 seconds Set up a proportion of copies to minutes where c is the number of copies for 5 minutes and 45 seconds. [URL='https://www.mathcelebrity.com/fraction.php?frac1=45%2F60&frac2=3%2F8&pl=Simplify']Since 45 seconds[/URL] is: 45/60 = 3/4 of a minute, we have: 5 minutes and 45 seconds = 5.75 minutes 44/1 = c/5.75 To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=44&num2=c&den1=1&den2=5.75&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: c = [B]253[/B]

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixed costs are $110,000 per month and the feed sells for $132 per ton, how many tons should be sold each month to have a monthly profit of $560,000? [U]Set up the cost function C(t) where t is the number of tons of cattle feed:[/U] C(t) = Variable Cost * t + Fixed Costs C(t) = 84t + 110000 [U]Set up the revenue function R(t) where t is the number of tons of cattle feed:[/U] R(t) = Sale Price * t R(t) = 132t [U]Set up the profit function P(t) where t is the number of tons of cattle feed:[/U] P(t) = R(t) - C(t) P(t) = 132t - (84t + 110000) P(t) = 132t - 84t - 110000 P(t) = 48t - 110000 [U]The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:[/U] 48t - 110000 = 560000 [U]To solve for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=48t-110000%3D560000&pl=Solve']type this equation into our search engine[/URL] and we get:[/U] t =[B] 13,958.33 If the problem asks for whole numbers, we round up one ton to get 13,959[/B]

A couple is opening a savings account for a newborn baby. They start with $3450 received in baby gifts. If no depositts or withdrawals are made, what is the balance of the account if it earns simple interest at 6% for 18 years? Using [URL='https://www.mathcelebrity.com/simpint.php?av=&p=3450&int=6&t=18&pl=Simple+Interest']our simple interest calculator[/URL], we get: [B]7,176[/B]

A coupon that was mailed to preferred customers of video village rentals is good for 15% on any video that is bought. How much savings is there using the coupon to purchase a $22 video? Savings = Full Price * Coupon Amount Savings = $22 * 0.15 Savings = $3.30

A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The total value of the items is $825. How many coins are there? Let c be the number of coins, and s be the number of stamps. We're given: [LIST=1] [*]c + s = 300 [*]3c + 1.5s = 825 [/LIST] We have a set of simultaneous equations, or a system of equations. We can solve this 3 ways: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Cramers+Method']Cramers Method[/URL] [/LIST] No matter which way we pick, we get: s = 50 c = [B]250[/B]

A credit plan charges interest rate of 36% compounded monthly. Find the effective rate. [U]Calculate Monthly Nominal Rate:[/U] Monthly Nominal Rate = Annual Rate / 12 months per year Monthly Nominal Rate = 36%/12 Monthly Nominal Rate = 3% [U]Since there are 12 months in a year, we compound 12 times to get the effective rate below:[/U] Effective Rate = (1 + Monthly Nominal Rate as a Decimal)^12 - 1 Since 3% = 0.03, we have: Effective Rate = 100% * ((1 + 0.03)^12 - 1) Effective Rate = 100% * ((1.03)^12 - 1) Effective Rate = 100% * (1.42576088685 - 1) Effective Rate = 100% * (0.42576088685) Effective Rate = [B]42.58%[/B]

A cube has an edge that is x cm long. What is the capacity of C(x)? Capacity is another word for volume, or the amount an object will hold. Given a side x, the capacity (volume) of a cube is: C(x) = [B]x^3[/B]

A cube is 1 meter long.What is the total length of all its edges? A cube has 12 edges. 12 edges x 1 meter for each edge = [B]12 meters[/B]

A cubical storage box has edges that are 2 feet 4 inches long. What is the volume of the storage box? Since 1 foot = 12 inches, we have: 2 feet 4 inches = 2(12) + 4 2 feet 4 inches = 24 + 4 2 feet 4 inches = 28 inches We type [URL='https://www.mathcelebrity.com/cube.php?num=28&pl=Side&type=side&show_All=1']cube side = 28[/URL] into our search engine to get: V = [B]21952 cubic inches[/B]

A cubicle is 6 1?2 feet by 8 3?4 feet. What is the area of the cubicle? Area of a cube is length times width: A = 8 & 3/4 * 6 & 1/2 We need to convert these to improper fractions. [LIST] [*]8 & 3/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%263%2F4&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 35/4 [*]6 & 1/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%261%2F2&frac2=3%2F8&pl=Simplify']converted to an improper fraction[/URL] is 13/2 [/LIST] Multiply the improper fractions together: A = 35/4 * 13/2 [URL='https://www.mathcelebrity.com/fraction.php?frac1=35%2F4&frac2=13%2F2&pl=Multiply']Using our fraction multiplier[/URL], we get: [B]455/8 sq ft[/B] If you want to convert this to a mixed fraction, we [URL='https://www.mathcelebrity.com/fraction.php?frac1=455%2F8&frac2=3%2F8&pl=Simplify']type this in our calculator [/URL]and get: [B]56 & 7/8 sq ft[/B]

A culture of bacteria doubles every hour. If there are 500 bacteria at the beginning, how many bacteria will there be after 9 hours? Assumptions and givens; [LIST] [*]h is the number of hours. [*]B(h) is the number of bacteria at time h [*]B(0) is the starting bacteria amount [*]Doubling means multiplying by 2, so we have: [/LIST] B(h) = B(0) * 2^h We want h = 9, so we have: B(9) = 500 * 2^9 B(9) = 500 * 512 B(9) = [B]256,000[/B]

A cup of coffee cost $4 and a cup of tea cost $3.50. If ray has $40 and has bought 6 cups of coffee, find the maximum cups of tea he can buy [U]Calculate total coffee spend:[/U] Total coffee spend = Cost per Cup of Coffee * Cups of Coffee Total coffee spend = 4 * 6 Total coffee spend = 24 [U]Calculate remaining amount to be spent on tea:[/U] Remaining tea money = Starting Money - Total Coffee spend Remaining tea money = 40 - 24 Remaining tea money = 16 [U]Calculate cups of tea Ray can buy:[/U] Cups of tea Ray can buy = Remaining Tea money / Cost per cup of tea Cups of tea Ray can buy = 16/3.50 Cups of tea Ray can buy = 4.57142857143 Since Ray can't buy partial cups, we round down and we get: Cups of tea Ray can buy = [B]4[/B]

A cup of coffee costs $1.75. A monthly unlimited coffee card costs $25.00. Which inequality represents the number x of cups of coffee you must purchase for the monthly card to be a better deal? Let c be the number of cups. We want to know how many cups (x) where: 1.75x > 25 Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.75x%3E25&pl=Show+Interval+Notation']inequality solver[/URL], we see: [B]x > 14.28[/B]

A cup that is filled with equal parts red, green, and blue dye spills half of its contents. Enough green dye is then poured into the cup to fill it again. What is the ratio of red to green to blue dye now? Original Cup: [LIST=1] [*]Blue [*]Green [*]Red [/LIST] Spilled Cup [LIST=1] [*]Empty [*]Blue [*]Green [*]Red [/LIST] Refilled Cup [LIST=1] [*]Green [*]Blue [*]Green [*]Red [/LIST] [B]1:4:1[/B]

A cupe-shaped tank has edge lengths of 1/2 foot. Sheldon used the expression s to the power of 3 = v to find the volume. What was the volume of the tank? 1/2 foot = 6 inches v = (6)^3 v = [B]216 cubic inches[/B]

A customer buys 5 pounds of apples at $0.79 a pound. They hand the cashier a $10 bill. How much change will they get back? Calculate the total bill: Total Bill = Pounds of Apples * Cost per pound Total Bill = 5 * 0.79 Total Bill = $3.95 Calculate Change: Change = Money Offered - Total Bill Change = $10 - $3.95 Change = [B]$6.05[/B]

A customer withdrew $100 from a bank account. The customer then deposited $33 the next day. Write and then evaluate an expression to show the net effect of these transactions. Withdrawals are negative since we take money away Deposits are positive since we add money So we have: [LIST] [*]100 withdrawal = -100 [*]33 deposit = +33 [/LIST] Our balance is: -100 + 33 = [B]-67 net[/B]

A dad gave his 3 sons each the same amount of money in an envelope. He took $20 from one son for getting a D on a math test and he gave another son an extra $35 for doing extra chores. Combined, the sons had $81. Figure out how much each son had. Let x, y, and z be the money each son received. To begin, x = y = z. But then, Dad took 20 from son X and gave it to son Y. So now, x = y - 20 Next, he gave Son Z an extra $35 for chores So z is now y + 35 since y and z used to be equal Combined, they all have 81. x + y + z = 181 But with the changes, it is: (y - 20) + y + (y + 35) Combine like terms: 3y - 20 + 35 = 81 3y + 15 = 81 Subtract 15 from each side: 3y = 66 Divide each side by 3 to isolate y y = 22 Since x = y - 20, x = 2 Since z = y + 35, we have z = 57 Checking our work, 2 + 22 + 57 = 81.

A daily pass costs $62. A season ski pass costs $450. The skier would have to rent skis with either pass for $30 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes? Let d be the number of days the skier attends. Calculate the daily cost: Daily Total Cost = Daily Cost + Rental Cost Daily Total Cost = 62d + 30d Daily Total Cost = 92d Calculate Season Cost: Season Total Cost = Season Fee + Rental Cost Season Total Cost = 450 + 30d Set the daily total cost and season cost equal to each other: 450 + 30d = 92d [URL='https://www.mathcelebrity.com/1unk.php?num=450%2B30d%3D92d&pl=Solve']Typing this equation into the search engine[/URL], we get d = 7.258. We round up to the next full day of [B]8[/B]. Now check our work: Daily Total Cost for 8 days = 92(8) = 736 Season Cost for 8 days = 30(8) + 450 = 240 + 450 = 710. Therefore, the skier needs to go at least [B]8 days[/B] to make the season cost less than the daily cot.

A delivery man had 3,456 bottles of water in his truck. The bottles were packages in cases. There were 48 bottles in each case. The driver delivered 192 bottles to a store. How many cases were in the truck after delivery? Total cases in the truck before delivery 3,456/48 = 72 cases Driver delivers 192 bottles to the store. 192 bottles / 48 bottles per case = 4 cases 72 cases before delivery - 4 cases for delivery = 68 cases after delivery

A department store buys 100 shirts at a cost of $600 and sells them at a selling price of 10 each find the percentage mark up Find Unit Cost: Unit Cost = Cost / Number of Shirts Unit Cost = 600 / 100 Unit Cost = 6 With a selling price of 10, our markup percentage is: Markup % = 100 * (New Price - Old Price)/Old Price Markup % = 100 * (10 - 6)/6 Markup % = 100 * 4/6 Markup % = 400/6 Markup % = [B]66.67%[/B]

A desk and a chair together cost $1550. If the cost of the chair is n, what is the cost of the desk? Let the cost of the desk be d. WE know that: d + n = 1550 Therefore, d = [B]1550 - n[/B]

A desk drawer contains 10 blue pencils, 7 red pencils, and 8 green pencils. Without looking, you draw out a pencil and then draw out a second pencil without returning the first pencil. What is the probability that the first pencil and the second pencil are both green? We are drawing without replacement. Take each draw probability: [LIST=1] [*]First draw, we have a total of 10 + 7 + 8 = 25 pencils to choose from. P(Green) = 8/25 [*]Next draw, we only have 24 total pencils, and 7 green pencils since we do not replace. Therefore, we have P(Green)= 7/24 [/LIST] Since both events are independent, we have: P(Green) * P(Green) = 8/25 * 7/24 P(Green) * P(Green) = 56/600 Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=56&num2=600&num3=&pl=GCF']GCF Calculator[/URL], we see the greatest common factor of 56 and 600 is 8. So we divide top and bottom of the fraction by 8. [B]P(Green) * P(Green) = 7/75[/B]

A dice has six sides. The dice is rolled once. What is the probability that a six will be the result. P(6) = [B]1/6[/B]

A die and a coin are tossed. What is the probability of getting a 6 and a tail? Roll a 6: P(6) = 1/6 Flip a tail: P(T) = 1/2 Probability of getting a 6 and a tail: Since both events are independent, we have: P(6 and T) = P(6) * P(T) P(6 and T) = 1/6 * 1/2 P(6 and T) = [B]1/12[/B]

A direct variation includes the points ( – 5, – 20) and (n,8). Find n. Slopes are proportional for rise over run. Set up a proportion of x's to y's: -5/n = -20/8 To solve this proportion for n, we [URL='https://www.mathcelebrity.com/prop.php?num1=-5&num2=-20&den1=n&den2=8&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get: n = [B]2[/B]

A discount store buys a shipment of fish bowls at a cost of $3.80 each. The fish bowls will be sold for $5.76 apiece. What is the mark-up, as a percentage? Using our [URL='https://www.mathcelebrity.com/markup.php?p1=3.80&m=&p2=5.76&pl=Calculate']markup calculator[/URL], we get: [B]51.58% markup[/B]

A dish company needs to ship an order of 893 glass bowls. If each shipping box can hold 19 bowls, how many boxes will the company need? Number of boxes needed = Total bowls / Glass bowls per box Number of boxes needed = 893/19 Number of boxes needed = [B]47[/B]

A diving board is 10 feet long and 1 foot wide. What is its area? A diving board is a rectangle. And the area of a rectangle is: A = lw Plugging in our numbers, we get: A = 10(1) A = [B]10 sq feet[/B]

A dog and a cat together cost $100. If the price of the dogs $90 more than the cat, what is the cost of the cat? Set up givens and equations [LIST] [*]Let the cost of the dog be d [*]Let the cost of the cat be c [/LIST] We're given 2 equations: [LIST=1] [*]c + d = 100 [*]d = c + 90 [/LIST] Substitute equation (2) into equation (1) for d c + c + 90 = 100 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=c%2Bc%2B90%3D100&pl=Solve']math engine[/URL], we see that: c = [B]5 [/B] Substitute c = 5 into equation (2) above: d = 5 + 90 d = [B]95[/B]

A dog on a 20-foot long leash is tied to the middle of a fence that is 100 feet long. The dog ruined the grass wherever it could reach. What is the area of the grass that the dog ruined. The leash forms a circle where the dog can get to. A = pi(r)^2 A = 3.1415(20)^2 A = 3.1415 * 400 A = 1256 square feet The fence blocks off half the circle where the dog can move to, so we have a half-circle area: A = 1256/2 A = [B]628 square feet[/B]

A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog walker charge for a 3 hour walk? Set up the cost equation C(h) where h is the number of hours: C(h) = Hourly rate * h + flat rate C(h) = 30h + 6 The question asks for C(h) when h = 3: C(3) = 30(3) + 6 C(3) = 90 + 6 C(3) = [B]96[/B]

A dormitory manager buys 38 bed sheets and 61 towels for $791.50. The manager get another 54 bed sheets and 50 towels for $923 from the same store. What is the cost of one bed sheet and one towel? Let s be bed sheets and t be towels. We have two equations: [LIST=1] [*]38s + 61t = 791.50 [*]54s + 50t = 923 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=38s+%2B+61t+%3D+791.50&term2=54s+%2B+50t+%3D+923&pl=Cramers+Method']system of equations calculator,[/URL] we get: [LIST] [*]s = 12 [*]t = 5.5 [/LIST]

A drawer is filled with 9 black shirts , 6 white shirts, and 5 gray shirts one shirt is chosen at random from the drawer find the probability that it is not a white shirt P(Not White) = P(Black or Gray) P(Black or Gray) = (Total Black + Total Gray)/Total Shirts P(Black or Gray) = (9 + 5)/(9 + 6 + 5) P(Black or Gray) = 14/20 Simplifying this [URL='https://www.mathcelebrity.com/fraction.php?frac1=14%2F20&frac2=3%2F8&pl=Simplify']using our fraction simplify calculator[/URL], we get: P(Black or Gray) = [B]7/10, or 0.7 or 70%[/B]

A dress is on sale for $33. This is 3/5 of the regular price. What is the regular price? Original price is p. We have: 3p/5 = 33 Cross multiply using our [URL='http://www.mathcelebrity.com/prop.php?num1=3p&num2=33&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]p = 55[/B].

A dresser has a length of 24 inches. What is the length of the dresser in centimeters? [SIZE=5][B]Convert 24 inches to centimeters[/B][/SIZE] centimeters = 2.54 x inches centimeters = 2.54 x 24 centimeters = [B]60.96[/B]

A driver drove at a speed of 42 mph for z hours. How far did the driver go? Distance = Rate * Time, so we have: Distance = [B]42z[/B]

A driver drove at a speed of 56 mph for z hours. How far did the driver go? Distance = Rate * time So we have: Distance = 56 mph * z Distance = [B]56z[/B]

A driver drove at a speed of 58 mph for t hours. How far did the driver go? Since distance = rate * time, we have distance D of: [B]D = 58t[/B]

A factory put cakes into boxes of 6 how many boxes can they fill with 3285 3285 cakes / 6 cakes per box = [B]547.5 boxes[/B]

A Fahrenheit thermometer shows that the temperature is 15 degrees below zero. Enter the integer that represents the temperature in degrees Fahrenheit. Below zero means negative in Fahrenheit, so we have: [B]-15[/B]

A fair charges an admission fee of 4 dollars for each person. Let C be the cost of admission (in dollars) for P people. Write an equation relating C to P. [B]C = 4P[/B]

A fair coin is tossed 4 times. a) How many outcomes are there in the sample space? b) What is the probability that the third toss is heads, given that the first toss is heads? c) Let A be the event that the first toss is heads, and B be the event that the third toss is heads. Are A and B independent? Why or why not? a) 2^4 = [B]16[/B] on our [URL='http://www.mathcelebrity.comcointoss.php?hts=+HTHTHH&hct=+2&tct=+1&fct=+5>=no+more+than&nmnl=+2&htpick=heads&tossct=+4&calc=5&montect=+500&pl=Calculate+Probability']coin toss calculator[/URL] b) On the link above, 4 of those outcomes have H and H in toss 1 and 3. So it's [B]1/4 or 0.25[/B] c) [B]Yes, each toss is independent of each other.[/B]

A fair die is rolled. What is the probability of rolling a 3 or a 6? P(3 or 6) can be written as: P(3) + P(6) A fair die means all faces have an equal probability of 1/6 P(3) = 1/6 P(6) = 1/6 P(3 or 6) = P(3) + P(6) P(3 or 6) = 1/6 + 1/6 P(3 or 6) = 2/6 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F6&frac2=3%2F8&pl=Simplify']Using our fractions simplifier for 2/6[/URL], we get: P(3 or 6) = [B]1/3[/B]

A fair six-sided die is rolled. Describe the sample space. [B]{1, 2, 3, 4, 5, 6}[/B]

A fake coin has heads on both sides, if the coin tossed once, what is the probability of getting a head? Since you always flip a head, we have: P(Head) = [B]1 or 100%[/B]

A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket that costs $19 per ticket. The Web site charges a fee of $16 for the entire purchase. The family is charged a total of $1132. How many tickets did the family buy? Let t be the number of tickets. We have the following equation with ticket price, insurance, and flat fee: 167t + 19t + 16 = 1132 Combine like terms: 186t + 16 = 1132 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=186t%2B16%3D1132&pl=Solve']equation calculator[/URL], we have: [B]t = 6[/B]

A family decides to rent a canoe for an entire day. The canoe rental rate is $50 for the first three hours and then 20$ for each additional hour. Suppose the family can spend $110 for the canoe rental. What is the maximum number of hours the family can rent the canoe? IF we subtract the $50 for the first 3 hours, we get: 110 - 50 = 60 remaining Each additional hour is 20, so the max number of hours we can rent the canoe is $60/20 = 3 hours additional plus the original 3 hours is [B]6 hours[/B]

A family has 4 children. Give the sample space in regards to the genders of the children. Children can either be male or female. Therefore, the sample space is 2 * 2 * 2 * 2 = 16 possible combinations. [LIST=1] [*]MMMM [*]MMMF [*]MMFM [*]MFMM [*]FMMM [*]MMFF [*]MFFM [*]FFMM [*]MFMF [*]FMFM [*]MMMF [*]FMMM [*]FFFM [*]MFFF [*]FMMF [*]FFFF [/LIST] [MEDIA=youtube]W0bthXg-368[/MEDIA]

A family is renting an apartment. For 2007, the rent is $1376 per month. The monthly rent in 2007 is 7.5% higher than the monthly rent in 2006. Determine the monthly rent in 2006. 7.5% as a decimal is 0.075 To increase a value by 7.5%, we multiply by 1.075 [U]Calculate Rent Increase[/U] R(2007) = R(2006) * 1.075 R(2007) = 1376 * 1.075 R(2007) = [B]1,479.20[/B]

A family is taking a cross-country trip of 3000 miles by car. They are bringing two spare tires with them and want all six tires to go an equal distance. How many miles will each tire go? 3000 * 4 tires = 12,000 miles traveled 12,000 / 6 tires = [B]2,000 miles[/B]

A family of 4 spent $78 at the exhibition. They spent $22 on rides and the rest on entrance fees. How much was the entrance fee per person We need to find the entrance fee per person. So subtract the cost of rides from the total spend: Entrance Fees = Total Spend - Cost of Rides Entrance Fees = 78 - 22 Entrance Fees = 56 [U]Now find the entrance fee per person:[/U] Entrance Fee Per Person = Entrance Fees / Total People in the Family Entrance Fee Per Person =56/4 Entrance Fee Per Person = [B]14[/B]

A family of four used about 11,370 gallons of water in their home last month. There were 30 days in the month. About how many gallons of water did each person use each day? 11370 gallons of water / (30 days in a month * 4 people) 11370 gallons of water / (120 people days) 94.75 [B]gallons[/B]

A family room measures 15.6 feet long and 18.4 feet wide. What is the area of the room? The room is rectangular. So our area A = lw. Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=15.6&w=18.4&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get: A = [B]287.04 square feet[/B]

a family went to a baseball game. the cost to park the car was $5 AND THE COST PER TICKET WAS $21. WRITE A LINEAR FUNCTION IN THE FORM Y=MX+B, FOR THE TOTAL COST OF GOING TO THE BASEBALL GAME,Y, AND THE TOTAL NUMBER PEOPLE IN THE FAMILY,X. We have: [B]y = 21x + 5[/B] Since the cost of each ticket is $21, we multiply this by x, the total number of people in the family. We add 5 as the cost to park the car, which fits the entire family, and is a one time cost.

A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at a profit of 4 per pig. His total profit was $56. How many pigs did he originally buy? Let p be the purchase price of pigs. We're given: [LIST] [*]Farmer originally bought [I]p [/I]pigs for 232 which is our cost C. [*]5 of them died, so he has p - 5 left [*]He sells 4(p - 5) pigs for a revenue amount R [*]Since profit is Revenue - Cost, which equals 56, we have: [/LIST] Calculate Profit P = R - C Plug in our numbers: 4(p - 5) - 232 = 56 4p - 20 - 232 = 56 To solve for p, [URL='https://www.mathcelebrity.com/1unk.php?num=4p-20-232%3D56&pl=Solve']we type this equation into our search engine[/URL] and we get: p = [B]77[/B]

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length x to be greater than 50 feet and the width y to be no more than 20 feet. Write a system to represent this situation. Perimeter of a rectangle: P = 2l + 2w We have P = 165 and l = x --> x>50 and width y <= 20. Plug these into the perimeter formula [B]165 = 2x + 2y where x > 50 and y <= 20[/B]

A farmer has a total of 200 ducks and cows in his barn. If he has n cows, how many total legs are there in the barn? (Make sure you include the farmer.) [LIST] [*]Number of cows = n [*]Legs per cow = 4 [*]Cows legs = 4n [*]Number of ducks = 200 - n [*]Legs per duck = 2 [*]Number of ducks legs = (200 - n) x 2 = 400 - 2n [*]Farmers legs = 2 [/LIST] Total legs = Cows legs + Ducks Legs + Farmers Legs Total legs = 4n + 400 - 2n + 2 Total legs = [B]2n + 402[/B]

A farmer has c chickens. She sells 3 of them for $6 each and the rest she sells for $5 each. How much money will she receive? Total money received = 3 * 6 + 5(c - 3) Total money received = 18 + 5c - 15 Total money received = [B]5c + 3[/B]

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over all the containers of eggs. Though she is unhurt, every egg is broken. So she goes to her insurance agent, who asks her how many eggs she had. She says she doesn't know, but she remembers somethings from various ways she tried packing the eggs. When she put the eggs in groups of two, three, four, five, and six there was one egg left over, but when she put them in groups of seven they ended up in complete groups with no eggs left over. What can the farmer figure from this information about the number of eggs she had? Is there more than one answer? We need a number (n) that leaves a remainder of 1 when divided by 2, 3, 4, 5, 6 but no remainder when divided by 7. 217 + 84 = [B]301[/B]. Other solutions are multiples of 3 x 4 x 5 x 7, but we want the lowest one here.

A Farmer Sell products at the market in 38- pound crates. If he sells 100 crates . How many pounds of produce has he sold [U]Calculate the pounds of produce:[/U] Pounds of Produce = Number of Crates * pounds per crate Pounds of Produce = 100 crates * 38 pounds per crates Pounds of Produce = [B]3,800 pounds of produce[/B]3

A farmer sold 250 of his sheep, bought 35 and then bought 68. If he now has 190, how many did he begin with? Let's start his count with x. We have: x - 250 + 35 + 68 = 190 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=x-250%2B35%2B68%3D190&pl=Solve']equation solver[/URL], we get x = [B]337[/B]

A farmer was 1/3 of his land to grow corn, a quarter of his land to grow lettuce, and 12.5% of his land to grow green beans. He uses the remaining 7 acres to grow wheat.How many total acres does the farmer own? Convert all land portions to fractions or decimals. We will do fractions: [LIST] [*]1/3 for corn [*][I]A quarter[/I] means 1/4 for lettuce [*]12.5% is 12.5/100 or 1/8 for green beans [/LIST] Now add all these up: 1/3 + 1/4 + 1/8 We need a common factor for 3, 4, and 8. Using our [URL='https://www.mathcelebrity.com/gcflcm.php?num1=3&num2=4&num3=8&pl=LCM']LCM Calculator[/URL], we get 24. 1/3 = 8/24 1/4 = 6/24 18 = 3/24 Add them all up: (8 + 6 + 3)/24 17/24 This means 17/24 of the land is used for everything but wheat. Wheat occupies (24-17)/24 = 7/24 of the land. We'll use a for the number of acres on the farm. 7a/24 = 7 [B]a = 24[/B]

A father is K years old and his son is M years younger. The sum of their ages is 53. Father's Age = K Son's Age = K - M and we know K + (K - M) = 53 Combine like terms: 2K - M = 53 Add M to each side: 2K - M + M = 53 + M Cancel the M's on the left side, we get: 2K = 53+ M Divide each side by 2: 2K/2 = (53 + M)/2 Cancel the 2's on the left side: K = [B](53 + M)/2[/B]

A faucet drips 15 milliliters of water every 45 minutes. How many milliliters of water will it drip in 3 hours? 3 hours = 60 * 3 = 180 minutes 180 minutes / 45 minutes = 4 So the faucet drips 15 milliliters 4 times 15 * 4 = [B]60 milliliters[/B]

A financial advisor has invested $7000 in two accounts. If one account contains x dollars, express the amount in the second account in terms of x The other account contains: [B]7000 - x[/B]

A financial analyst computed the ROI for all companies listed on the NYSE. She found that the mean of this distribution was 10% with standard deviation of 5%. She is interested in examining further those companies whose ROI is between 14% and 16% of the approximately 1,500 companies listed on the exchange, how many are of interest of her? First, use our [URL='http://www.mathcelebrity.com/zscore.php?z=p%280.14%3Cz%3C0.16%29&pl=Calculate+Probability']z-score calculator[/URL] to get P(0.14 < z < 0.16) = 0.007889 Divide that by 2 for two-tail test to get0.003944729 Use the NORMSINV(0.003944729) in Excel to get the Z value of 2.66 Therefore, the companies of interest are 2.66 * 1500 * 0.10 = [B]399[/B]

A firm wants to know with a 98% level of confidence if it can claim that the boxes of detergent it sells contain more than 500g of detergent. From past experience the firm knows that the amount of detergent in the boxes is normally distributed. The firm takes a random sample of n =25 and finds that X = 520 g and s = 75g. What's your final conclusion? (Ho: u = 500; Ha: u > 500) [URL='http://www.mathcelebrity.com/mean_hypothesis.php?xbar=520&n=25&stdev=75&ptype==&mean=500&alpha=0.02&pl=Mean+Hypothesis+Testing']Perform a hypothesis testing of the mean[/URL] [B]Yes, accept null hypothesis[/B]

A first number plus twice a second number is 10. Twice the first number plus the second totals 29. Find the numbers. Let the first number be x. Let the second number be y. We are given the following two equations: [LIST=1] [*]x + 2y = 10 [*]2x + y = 29 [/LIST] We can solve this 3 ways using: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Substitution']Substitution[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Elimination']Elimination[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] Using any of the 3 methods, we get the same answers of [B](x, y) = (16, -3)[/B]

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. Find the numbers. [U]The phrase [I]a number[/I] means an arbitrary variable[/U] A first number is written as x A second number is written as y [U]Twice a second number means we multiply y by 2:[/U] 2y [U]A first number plus twice a second number:[/U] x + 2y [U]A first number plus twice a second number is 10 means we set x + 2y equal to 10:[/U] x + 2y = 10 [U]Twice the first number means we multiply x by 2:[/U] 2x [U]Twice the first number plus the second:[/U] 2x + y [U]Twice the first number plus the second totals 35 means we set 2x + y equal to 35:[/U] 2x + y = 35 Therefore, we have a system of two equations: [LIST=1] [*]x + 2y = 10 [*]2x + y = 35 [/LIST] Since we have an easy multiple of 2 for the x variable, we can solve this by multiply the first equation by -2: [LIST=1] [*]-2x - 4y = -20 [*]2x + y = 35 [/LIST] Because the x variables are opposites, we can add both equations together: (-2 + 2)x + (-4 + 1)y = -20 + 35 The x terms cancel, so we have: -3y = 15 To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D15&pl=Solve']type it in our search engine[/URL] and we get: y = [B]-5 [/B] Now we substitute this y = -5 into equation 2: 2x - 5 = 35 To solve this equation for x, we[URL='https://www.mathcelebrity.com/1unk.php?num=2x-5%3D35&pl=Solve'] type it in our search engine[/URL] and we get: x = [B]20[/B]

A first number plus twice a second number is 11. Twice the first number plus the second totals 34. Find the numbers. Let the first number be x and the second number be y. We're given: [LIST=1] [*]x + 2y = 11 [*]2x + y = 34 [/LIST] Using our simultaneous equations calculator, we have 3 methods to solve this: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] All 3 methods give the same solution: [LIST] [*][B]x = 19[/B] [*][B]y = -4[/B] [/LIST]

A first number plus twice a second number is 14. Twice the first number plus the second totals 40. Find the numbers. [B][U]Givens and assumptions:[/U][/B] [LIST] [*]Let the first number be x. [*]Let the second number be y. [*]Twice means multiply by 2 [*]The phrases [I]is[/I] and [I]totals[/I] mean equal to [/LIST] We're given two equations: [LIST=1] [*]x + 2y = 14 [*]2x + y = 40 [/LIST] To solve this system, we can take a shortcut, and multiply the top equation by -2 to get our new system: [LIST=1] [*]-2x - 4y = -28 [*]2x + y = 40 [/LIST] Now add both equations together (-2 _ 2)x (-4 + 1)y = -28 + 40 -3y = 12 To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D12&pl=Solve']type it in our search engine[/URL] and we get: y = [B]-4 [/B] We substitute this back into equation 1 for y = -4: x + 2(-4) = 14 x - 8 = 14 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-8%3D14&pl=Solve']type it in our search engine[/URL] and we get: x = [B]22[/B]

A first number plus twice a second number is 22. Twice the first number plus the second totals 28. Find the numbers. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x + 2y = 22 <-- Since twice means multiply by 2 [*]2x + y = 28 <-- Since twice means multiply by 2 [/LIST] We have a set of simultaneous equations. We can solve this three ways [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28+&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter which method we use, we get the same answer: [LIST] [*][B]x = 11 & 1/3[/B] [*][B]y = 5 & 1/3[/B] [/LIST]

A first number plus twice a second number is 3. Twice the first number plus the second totals 24. Let the first number be x. Let the second number be y. We're given: [LIST=1] [*]x + 2y = 3 <-- Because [I]twice[/I] means multiply by 2 [*]2x + y = 24 <-- Because [I]twice[/I] means multiply by 2 [/LIST] We have a system of equations. We can solve it any one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which way we choose, we get: [LIST] [*]x = [B]15[/B] [*]y = [B]-6[/B] [/LIST]

A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Find the numbers. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x + 2y = 6 [*]2x + y = 15 [/LIST] Multiply the first equation by -2: [LIST=1] [*]-2x - 4y = -12 [*]2x + y = 15 [/LIST] Now add them -2x + 2x - 4y + y = -12 + 15 -3y = 3 Divide each side by -3: y = 3/-3 y =[B] -1[/B] Plug this back into equation 1: x + 2(-1) = 6 x - 2 = 6 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-2%3D6&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]8[/B]

A first number plus twice a second number is 7 Let the first number be x. Let the second number be y. We're given: [LIST] [*]A first number is x [*]A second number is y [*]Twice the second number means we multiply y by 2: 2y [*][I]Plus [/I]means we add x to 2y: x + 2y [*]The phrase [I]is[/I] means an equation, so we set x + 2y equal to 7 [/LIST] [B]x + 2y = 7[/B]

A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Find the numbers Let the first number be a and the second number be b. We have: [LIST=1] [*]a + 2b = 7 [*]2a + b = 23 [/LIST] Rearrange (1) into (3) (3) a = 7 - 2b Substitute (3) into (2): 2(7 - 2b) + b = 23 Multiply through: 14 - 4b + b = 23 Combine like terms: 14 - 3b = 23 Subtract 14 from each side: -3b = 9 Divide each side by -3 [B]b = -3[/B] Substitute this into (3) a = 7 - 2b a = 7 - 2(-3) a = 7 + 6 [B]a = 13[/B] [B](a, b) = (13, -3)[/B]

A flea is very small, but can jump very high. For example, a flea that is 1/8 inch tall can jump 12 inches in height. If a child who is 4 feet tall had the ability to jump like a flea, how high could she jump? Set up a proportion of height to jump height where j is the jump height of the child: 1/8/12 = 4/j Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=0.125&num2=4&den1=12&den2=j&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: j = [B]384 feet[/B]

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will its dimensions be? A flower bed has a rectangle shape, so the area is: A = lw We are given l = w + 3 Plugging in our numbers given to us, we have: 108 = w(w + 3) w^2 + 3w = 108 Subtract 108 from each side: w^2 + 3w - 108 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B3w-108%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get: w = (9, -12) Since length cannot be negative, w = 9. And l = 9 + 3 --> l = 12 So we have [B](l, w) = (12, 9)[/B] Checking our work, we have: A = (12)9 A = 108 <-- Match!

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day? Let the number of drinks be d. Let the number of salads be s. We're given two equations: [LIST=1] [*]2d + 6.50s = 836.50 [*]d + s = 209 [/LIST] We can use substitution to solve this system of equations quickly. The question asks for the number of salads (s). Therefore, we want all expressions in terms of s. Rearrange Equation 2 by subtracting s from both sides: d + s - s = 209 - s Cancel the s's, we get: d = 209 - s So we have the following system of equations: [LIST=1] [*]2d + 6.50s = 836.50 [*]d = 209 - s [/LIST] Substitute equation (2) into equation (1) for d: 2(209 - s) + 6.50s = 836.50 Multiply through to remove the parentheses: 418 - 2s + 6.50s = 836.50 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=418-2s%2B6.50s%3D836.50&pl=Solve']type it into our search engine and we get[/URL]: s = [B]93[/B]

A football gained 52 yards during the possession. In the next 3 possessions they gained the same amount of yards each time. If they gained a total of 256 yards, write and solve an equation for how many yards they gained in each of the last 3 possessions. Subtract 52 initial yards 256 - 52 = 204 Now, divide 204 by 3 possessions 204/3 = [B]68 yards[/B]

A football team gained 4 yards on a play,lost 8 on the next play ,then gained 2 yards on the third play write and addition expression Gains are expressed with positives (+) and losses are expressed with negatives (-): [LIST] [*]Gained 4 years: +4 [*]Lost 8 on the next play: -8 [*]Gained 2 yards on the third play: +2 [/LIST] Expression: [B]+4 - 8 + 2 = -2[/B]

A football team gained 8 yards on a first down, lost 12 yards on the second down, and gained 16 yards on the third down. How many yards did the team gain or lose? Assumptions: [LIST] [*]We reflect gains by adding [*]We reflect losses by subtracting [/LIST] Plays: [LIST] [*]Gain of 8 = +8 [*]Loss of 12 = -12 [*]Gain of 16 = +16 [/LIST] Net Gain/Loss +8 - 12 + 16 [B]+12 (gain)[/B]

A football team loses 27 yards total during its first 3 plays. On average, what is the yards per play for these 3 plays? A loss of yards means negative yardage. Average Yards per play = Total Yards / Total plays Average Yards per play = -27/3 Average Yards per play = -[B]9 or 9 yard loss[/B]

A football team loses 3 yards, gains 12 yards, gains 10 yards, and then loses 15 yards. Did the team gain yards or lose yards overall? How many yards We have: Gains - Losses -3 + 12 + 10 - 15 (12 + 10) - (3 + 15) 22 - 18 [B]4 yard gain[/B]

A football team lost 7 yards each play for four consecutive plays. Represent the team’s total change in position for the four plays as an integer. A net loss in yardage for 7 yards is written as -7 4 plays * -7 yards equals [B]-28[/B]

a football team won 3 more games than it lost.the team played 11 games.how many did it win? Let wins be w. Let losses be l. We're given two equations: [LIST=1] [*]w = l + 3 [*]l + w = 11 [/LIST] Plug equation (1) into equation (2) to solve for l: l + (l + 3) = 11 Group like terms: 2l + 3 = 11 [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B3%3D11&pl=Solve']Typing this equation into our search engine[/URL], we get: l = 4 To solve for w, we plug in l = 4 above into equation (1): w = 4 + 3 w = [B]7[/B]

A fraction has a value of 3/4. If 7 is added to the numerator, the resulting fraction is equal to the reciprocal of the original fraction. Find the original fraction. Let the fraction be x/y. We're given two equations: [LIST=1] [*]x/y = 3/4 [*](x + 7)/y = 4/3. [I](The reciprocal of 3/4 is found by 1/(3/4)[/I] [/LIST] Cross multiply equation 1 and equation 2: [LIST=1] [*]4x = 3y [*]3(x + 7) = 4y [/LIST] Simplifying, we get: [LIST=1] [*]4x = 3y [*]3x + 21 = 4y [/LIST] If we divide equation 1 by 4, we get: [LIST=1] [*]x = 3y/4 [*]3x + 21 = 4y [/LIST] Substitute equation (1) into equation (2) for x: 3(3y/4) + 21 = 4y 9y/4 + 21 = 4y Multiply the equation by 4 on both sides to eliminate the denominator: 9y + 84 = 16y To solve this equation for y, we type it in our math engine and we get: y = [B]12 [/B] We then substitute y = 12 into equation 1 above: x = 3 * 12/4 x = 36/4 x = [B]9 [/B] So our original fraction x/y = [B]9/12[/B]

A framed print measures 80cm by 65cm. The frame is 5cm wide. Find the area of the unframed print. We subtract 5 cm from the length and the width to account for the frame: Unframed Length: 80 - 5 = 75 Unframed Width: 65 - 5 = 60 Area of the unframed rectangle is: A = lw A = 75(60) A = [B]4,500 sq cm[/B]

A fruit basket contains 2 red apples and 2 green apples. What is the ratio of the number of red apples to the total number of apples? 2:2 = [B]1:1[/B] simplified

A fruit basket contains 458 apples And 139 oranges.How many more apples are there in the basket? We want Apples - Oranges: Apples - Oranges = 458 - 139 Apples - Oranges = [B]319[/B]

A fuel injection system is designed to last 18 years, with a standard deviation of 1.4 years. What is the probability that a fuel injection system will last less than 15 years? Using our [URL='https://www.mathcelebrity.com/probnormdist.php?xone=15&mean=18&stdev=14&n=1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that: P(X < 15) = [B]0.416834[/B]

A furniture company plans to have 25 employees at its corporate headquarters and 25 employees at each store it opens. Let s represent the number of stores and m represent the total number of employees. There is only one corporate headquarters. So we have the number of employees (m) as: m = Store Employees + Corporate Employees Each store has 25 employees. Total store employees equal 25 per store times the number of stores (s). [B]m = 25s + 25[/B]

A game show has 74 categories. There are 9,785 points in each category. How many points are there in total on the game show? Total points = Total categories * points per category Total points = 9785 * 74 Total points = [B]724,090[/B]

A garden has a length that is three times its width. If the width is n feet and fencing cost $8 per foot, what is the cost of the fencing for the garden? Garden is a rectangle which has Perimeter P of: P = 2l + 2w l = 3w P = 2(3w) + 2w P = 6w + 2w P = 8w Width w = n, so we have: P = 8n Cost = 8n * 8 = [B]64n dollars[/B]

A garden table and a bench cost $977 combined. The garden table costs $77 more than the bench. What is the cost of the bench? Let the garden table cost be g and the bench cost be b. We're given [LIST=1] [*]b + g = 977 [*]g = b + 77 <-- The phrase [I]more than[/I] means we add [/LIST] Substitute (2) into (1): b + (b + 77) = 977 Combine like terms: 2b + 77 = 977 [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B77%3D977&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]b = $450[/B]

A gardener plants flowers in the following order: carnations,daffodils, larkspurs, tiger lillies, and zinnias. if the gardener planted 47 plants, what kind of flower did he plant last? Let c be carnations, d be daffodils, l be larkspurs, t be tiger lillies, and z be zinnias. The order goes as follows: c, d, l, t, z. So each cycle of plants counts as 5 plants. We know that 9 * 5 = 45. So the gardener plants 9 full cycles. Which means they have 47 - 45 = 2 plans left over. In the order above, the second plant is the daffodil. So the gardener planted the [B]daffodil[/B] last. Now, can we shortcut this problem? Yes, using modulus. 47 plants, with 5 plants per cycle, we do [URL='https://www.mathcelebrity.com/modulus.php?num=47mod5&pl=Calculate+Modulus']47 mod 5 through our calculator[/URL], and get 2. So we have 2 plants left over, and the daffodil is the second plant.

A gardener wants to fence a circular garden of diameter 21cm. Find the length of the rope he needs to purchase, if he makes 2round of fence Also find the cost of the rope, if it costs Rs4 per meter (take pie as 22/7) Circumference of a circle = Pi(d). Given Pi = 22/7 for this problem, we have: C = 22/7(21) C = 22*3 [B]C = 66[/B]

A gas tank contains 5.3 gallons. The capacity of the tank is 12.5 gallons. How much will it cost to fill the tank at $1.30 per gallon. [U]Calculate the empty portion of the gas tank:[/U] Empty portion = Capacity - Gas gallons remaining Empty portion = 12.5 - 5.3 Empty portion (in gallons) = 7.2 [U]Calculate the cost to fill the tank:[/U] Cost to fill the tank = Empty portion (in gallons) * cost per gallon Cost to fill the tank = 7.2 * $1.30 Cost to fill the tank = [B]$9.36[/B]

A gasoline tank is leaking at a rate of n gallons in t hours. If the gasoline cost $2 per gallon, what is the value of the gasoline that will be lost in m minutes? n gallons / t hours = n/t gallons per hour are leaking The value of the gas that leaks each hour is $2, so we have: 2n/t dollar per hour is leaking Value per minute means we divide by 60: 2n/60t Dividing top and bottom by 2 to simplify, we have: n/30t Given m minutes, we multiply to get: [B]nm/30t[/B]

A giant burrito required 75.75 lb of cheese. About how many 12-lb boxes of cheese did the cooks use? 75.75/12 = [B]6.31 boxes [/B] We can round up to 7 full boxes

A giant tortoise can live 175 years in captivity. The gastrotrich, which is a small aquatic animal, has a life-span of only 3 days (72 hours). If a gastrotrich died after 36 hours, a giant tortoise that lived 87.5 yeas would live proportionally the same because they both would have died halfway through their life-span. How long would a giant tortoise live if it lived proportionally the same as a gastrotrich that died after 50 hours? Set up a proportion of hours lived to lifespan where n is the number of years the giant tortoise lives: 50/72 = n/175 Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=50&num2=n&den1=72&den2=175&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: n = [B]121.5[/B]

A girl is pedaling her bicycle at a velocity of 0.10 km/hr. How far will she travel in two hours? The distance formula is: d = rt We're given a rate (r) of 0.10km/hr We're given time (t) of 2 hours Plug these values into the distance formula and we get: d= 0.1 * 2 d = [B]0.2km [MEDIA=youtube]w80E_YM-tDA[/MEDIA][/B]

A girl is three years older than her brother. If their combined age is 35 years, how old is each Let the girl's age be g. Let the boy's age be b. We're given two equations: [LIST=1] [*]g = b + 3 ([I]Older means we add)[/I] [*]b + g = 35 [/LIST] Now plug in equation (1) into equation (2) for g: b + b + 3 = 35 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2Bb%2B3%3D35&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]16 [/B] Now, to solve for g, we plug in b = 16 that we just solved for into equation (1): g = 16 + 3 g = [B]19[/B]

A girl makes 12 foul shots for every eight that she misses how many shots did you make if she shot 125 foul shots This means she makes 12/20 We want to know x shots, if 12/20 = x/125. [URL='http://www.mathcelebrity.com/prop.php?num1=12&num2=x&den1=20&den2=125&propsign=%3D&pl=Calculate+missing+proportion+value']Enter this proportion into the search engine[/URL] to get [B]x = 75[/B]

A golf ball is selected at random from a golf bag. If the golf bag contains 5 type A balls, 4 type B balls, and 9 type C balls, find the probability that the golf ball is not a type A ball Not Type A means Type B or Type C. Our total balls = 5 + 4 + 9 = 18 P(B or C) = P(B) + P(C) P(B or C) = 4/18 + 9/18 P(B or C) = [B]13/18[/B]

A Government antipollution spokeperson asserts that more than 80% of the plants in the Glassboro area meet the antipollution standards. An antipollution advocate does not believe the government claim. She takes a random sample of published data on pollution emission for 64 plants in the area and finds that 56 plants meet the pollution standards. Do the sample data support the government claim at the 1% level of significance? (H0: ρ=0.8; H_a: ρ>0.8) [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=+56&n=64&ptype==&p=+0.8&alpha=+0.01&pl=Proportion+Hypothesis+Testing']Perform a hypothesis testing of a proportion[/URL] [B]Accept null hypothesis[/B]

A grandmother deposited $5,000 in an account that pays 8% per year compounded annually when her granddaughter was born. What will the value of the account be when the granddaughter reaches her 16th birthday? We have the accumulation function A(t) = 5,000(1.08)^t. For t = 16, we have: A(16) = 5,000(1.08)^16 A(16) = 5,000*3.42594264333 A(16) = [B]17,129.71[/B]

A grocer is selling oranges at 3 for $2. How much would it cost to buy a dozen oranges? Set up a proportion of oranges per cost where c is the cost of a dozen oranges: 3/2 = 12/c <-- A dozen equals 12 [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=12&den1=2&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get: c = [B]8[/B]

A grocery store is selling 6 cans of cat food for $3. Find the cost of a can of cat food Unit Cost = Cost / Quantity Unit Cost = $3 / 6 Unit cost = [B]0.50 per can[/B]

A grocery store sells 6 pounds of apples for $12. What is the unit price of the apples? Unit Price = Cost/Quantity Unit Price = 12/6 [B]Unit Price = $2/lb[/B]

A grocery store sells chili peppers at $2.04 for a dozen. At this rate, what's the cost per pepper? A dozen = 12 peppers, so our cost per pepper is: Cost per pepper = Cost per dozen / 12 per dozen Cost per pepper = 2.04/12 Cost per pepper = [B]0.17[/B]

A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience is 120. What theoretical probability of 5 students from your school being selected as contestants out of 9 possible contestant spots? We want the probability a student from your school is chosen out of total students times total ways to choose students from your school: [U]a) P(5 students being selected):[/U] 5/30 * 4/(120 - 30) 5/30 * 4/90 20/2700 [URL='https://www.mathcelebrity.com/fraction.php?frac1=20%2F2700&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get: 1/135 [U]b) Total Ways 9 students can be picked from your school:[/U] 9/120 [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F120&frac2=3%2F8&pl=Simplify']Simplifying this fraction[/URL], we get: 3/40 Divide a by b: 1/135 / 3/40 40/405 [URL='https://www.mathcelebrity.com/fraction.php?frac1=40%2F405&frac2=3%2F8&pl=Simplify']Simplifying[/URL], we get: [B]8/81[/B]

A group of 4 adults and 5 children is visiting an amusement park. Admission is $15 per adult and $9 per child. Find the total cost of admission for the group. Set up the cost function for adults and children: C(a, c) = 15a + 9c We want the cost for 4 adults and 5 children C(4, 5) = 15(4) + 9(5) C(4, 5) = 60 + 45 C(4, 5) = [B]105[/B]

A group of campers have 250 pounds of food. They plan to eat 12 pounds a day. How many days will it take them to eat the food. Write your answer in a linear equation. Let the number of days be d. We have the following equation: 12d = 250 To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=12d%3D250&pl=Solve']type this equation in our search engine[/URL] and we get: d = [B]20.833[/B]

A group of people was surveyed to determine what newspaper they read. 80% of those interviewed read the New York Times, while 50% read U.S.A. Today. If 35% read both papers, what percent read neither paper? New York Times: 80% - 35% for both = 45% USA Today: 50% - 35% for both = 15% 45% + 15% + 35% = 95% Which means 100% - 95% = [B]5% read neither[/B]

A group of people were asked if they had run a red light in the last year. 497 responded "yes", and 223 responded "no". Find the probability that if a person is chosen at random, they have run a red light in the last year. P(Run Red Light) = yes answers / total answers P(Run Red Light) = 497 / (497 + 223) P(Run Red Light) = 497 / 720 P(Run Red Light) = [B]0.6903[/B]

A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A started with 6000 cells and decreased at a constant rate of 2000 cells per hour after the chemical was applied. Strain B started with 2000 cells and decreased at a constant rate of 1000 cells per hour after the chemical was applied. When will the strains have the same number of cells? Explain. Set up strain equations where h is the number of hours since time 0: [LIST] [*]Strain A: 6000 - 2000h [*]Strain B: 2000 - 1000h [/LIST] Set them equal to each other 6000 - 2000h = 2000 - 1000h Using our [URL='http://www.mathcelebrity.com/1unk.php?num=6000-2000h%3D2000-1000h&pl=Solve']equation solver[/URL], we see that [B]h = 4[/B]

a group of students and teachers are going on a field trip. one ninth of the group will fit on 1/3 of a school bus how many buses are needed to transport the entire group 1/9g = 1/3b We want to find g, so we multiply each side through by 9 g = 9/3b Simplify: g = 3b, so we need [B]3 buses[/B]

A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4. (a) Everyone who scores in the top 30% of the distribution gets a certificate. (b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state? (a) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.70&pl=Calculate+Critical+Z+Value']Top 30% is 70% percentile[/URL] Inverse of normal distribution(0.7) = -0.5244005 Plug into z-score formula, -0.5244005 = (x - 25)/4 [B]x = 22.9024[/B] (b) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.95&pl=Calculate+Critical+Z+Value']Top 5% is 95% percentile[/URL] Inverse of normal distribution(0.95) = 1.644853627 Plug into z-score formula, 1.644853627 = (x - 25)/4 [B]x = 31.57941451[/B]

A group of workers can plant 54 acres in 6 days. What is their rate in acres per day? Acres per day = 54 acres / 6 days = [B]9 acres per day[/B]

A group of workers can plant 72 acres in 8 days what is the rate in acres per a day Acres per day = Total Acres / Total Days Acres per day = 72/8 Acres per day =[B] 9[/B]

A guitar that normally cost n dollars is on sale for 20% off. The tax is 8%. What is the total cost of the guitar including tax? Discount Amount = 0.2n Total paid after discount = n - 0.2n = 0.8n Tax amount: 0.8n * 0.08 = 0.064n After tax amount: 0.8n + 0.64n = [B]0.864n[/B]

A gym charges a $30 sign-up fee plus $20 per month. You have a $130 gift card for the gym. When does the total spent on your gym membership exceed the amount of your gift card? Subtract the sign up fee of $30 from your gift card amount: $130 - $30 = $100 Since each month costs $20, we have $100/$20 = 5 months. So if you go for [B]more than 5 months[/B], you'll exceed your gift card.

A gym has 18 exercise stations, including 2 rowing machines. What is the probability that a randomly selected exercise station will be a rowing machine? The probability is 2/18. We can simplify this fraction. Divide top and bottom by 2: [B]1/9[/B]

A gym has yoga classes. Each class has 11 students. If there are c classes, write an equation to represent the total number of students s taking yoga. Total students is the number of classes times the number of students in each class: [B]s = 11c[/B]

A gym has yoga classes. Each class has 14 students. If there are c classes write an equation to represent the total number of students s taking yoga s = students per class * number of classes [B]s = 14c[/B]

A gym membership has a $50 joining fee plus charges $17 a month for m months Build a cost equation C(m) where m is the number of months of membership. C(m) = Variable Cost * variable units + Fixed Cost C(m) = Months of membership * m + Joining Fee Plugging in our numbers and we get: [B]C(m) = 17m + 50 [MEDIA=youtube]VGXeqd3ikAI[/MEDIA][/B]

A heating company charges $60 per hour plus $54 for a service call. Let n be the number of hours the technician works at your house. The cost function C(n) where n is the number of hours is: C(n) = Hourly Rate * hours + Service Call Charge [B]C(n) = 60n + 54[/B]

A helicopter blade does 3206 full turns in 7 minutes , work out the number of full turns per minute 3206 full turns / 7 minutes [URL='https://www.mathcelebrity.com/fraction.php?frac1=3206%2F7&frac2=3%2F8&pl=Simplify']Divide the fraction by 7 to get turns per minute[/URL] [B]458 turns per minute[/B]

A helicopter is flying at an altitude of 785 feet. It descends 570 feet, and then ascends 595 feet. Write an expression to represent this situation. Then determine and interpret the sum. [LIST] [*]Start at +785 feet [*]Descend 570 feet means using a minus sign -570 [*]Ascend 595 feet means using a plus sign +595 [/LIST] [U]Calculate the sum:[/U] +785 - 570 + 595 [B]+810[/B]

A helicopter rose vertically 300 m and then flew west 400 m how far was the helicopter from it’s starting point? The distance forms a right triangle. We want the distance of the hypotenuse. Using our [URL='http://www.mathcelebrity.com/pythag.php?side1input=300&side2input=400&hypinput=&pl=Solve+Missing+Side']right triangle calculator[/URL], we get a distance of [B]500[/B]. We also could use a shortcut on this problem. If you divide 300 and 400 by 100, you get 3 and 4. Since we want the hypotenuse, you get the famous 3-4-5 triangle ratio. So the answer is 5 * 100 = 500.

A high school graduating class is made up of 440 students. There are 168 more girls than boys. How many boys are in the class? Let b be the number of boys and g be the number of girls. We're given 2 equations: [LIST=1] [*]b + g = 440 [*]g = b + 168 [/LIST] Substitute (2) into (1) b + (b + 168) = 440 Combine like terms: 2b + 168 = 440 [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B168%3D440&pl=Solve']Type this equation into the search engine[/URL], and we get: [B]b = 136[/B]

A high school with 1000 students offers two foreign language courses : French and Japanese. There are 200 students in the French class roster, and 80 students in the Japanese class roster. We also know that 30 students enroll in both courses. Find the probability that a random selected student takes neither foreign language course. Let F be the event a student takes French and J be the event a student takes Japanese P(F) = 200/1000 = 0.2 P(J) = 80/1000 = 0.08 P(F ? J) = 30/1000 = 0.03 From our [URL='http://www.mathcelebrity.com/probunion2.php?pa=+0.2&pb=0.08+&paintb=+0.03&aub=+&pl=Calculate']two event calculator[/URL], we get P(F U J) = 0.25 So we want P(F U J)^C = 1 - P(F U J) = 1 - 0.25 = [B]0.75[/B]

A hill rises 60 ft for every horizontal 96 ft. Find the slope. Slope = Rise / Run Slope = 60/96 Using [URL='https://www.mathcelebrity.com/fraction.php?frac1=60%2F96&frac2=3%2F8&pl=Simplify']our fraction simplifier, we reduce 60/96 [/URL]to [B]5/8[/B]

A holiday in Florida costs $876. A holiday in Bali costs $394. How much more expensive is the Florida holiday? We want the difference between Florida holiday costs and Bali holiday costs: $876 - $394 = [B]$482[/B]

A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 20 feet less than 3 times the width, what are the dimensions of the rectangular plot? [U]Set up equations:[/U] (1) 2l + 2w = 800 (2) l = 3w - 20 [U]Substitute (2) into (1)[/U] 2(3w - 20) + 2w = 800 6w - 40 + 2w = 800 [U]Group the w terms[/U] 8w - 40 = 800 [U]Add 40 to each side[/U] 8w = 840 [U]Divide each side by 8[/U] [B]w = 105 [/B] [U]Substitute w = 105 into (2)[/U] l = 3(105) - 20 l = 315 - 20 [B]l = 295[/B]

A hoodie sold for d dollars. Now, the new price of the hoodie can be represented by 1.3d. Which description could explain what happened to the price of the hoodie? We can rewrite this as: d(1 + 0.3) And in this format, we see that the [B]hoodie was increased by 30% [/B]which is also 1.3

a horse and a saddle cost $5,000. if the horse cost 4 times as much as the saddle, what was the cost of each? Let the cost of the horse be h, and the cost of the saddle be s. We're given: [LIST=1] [*]h + s = 5000 [*]h = 4s [/LIST] Substitute equation (2) into equation (1): 4s + s = 5000 [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2Bs%3D5000&pl=Solve']Type this equation into the search engine[/URL], we get: [B]s = 1,000[/B] Substitute s = 1000 into equation (2): h = 4(1000) [B]h = 4,000[/B]

A hot air balloon at 1120 feet descends at a rate of 80 feet per minute. Let y represent the height and let x represent the number of minutes the balloon descends. Descending means we subtract height, so we have: [B]y = 1120 - 80x[/B]

A hot dog costs $3 and a corn dog costs $1.50. If $201 was collected, write a mathematical sentence to represent this information Assumptions: [LIST] [*]Let the number of corn dogs be c [*]Let the number of hot dogs be h [/LIST] Since cost = price * quantity, we have: [B]1.50c + 3h = 201[/B]

A house costs 3.5 times as much as the lot. Together they sold for $135,000. Find the cost of each. Let the house cost be h, and the lot cost be l. We have the following equations: [LIST=1] [*]h = 3.5l [*]h + l = 135,000 [/LIST] Substitute (1) into (2) 3.5l + l = 135,000 Combine like terms: 4.5l = 135,000 Divide each side by 4.5 to isolate l [B]l = 30,000[/B] Substitute this back into equation (1) h = 3.5(30,000) [B]h = 105,000[/B]

A house has 8 rooms one quarter of the rooms are bedrooms how many of the rooms are bedrooms 1/4 * 8 = 8/4 = [B]2 rooms are bedrooms[/B]

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. How long is a job for which companies will charge the same amount? Set up the cost function C(h) where h is the number of hours. Company 1: C(h) = 12h + 376 Company 2: C(h) = 15h + 280 To see when the companies charge the same amount, set both C(h) functions equal to each other. 12h + 376 = 15h + 280 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B376%3D15h%2B280&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]32[/B]

A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. How long is a job for which both companies will charge the same amount? [U]Set up the cost function for the first company C(h) where h is the number of hours:[/U] C(h) = Hourly Rate * h + flat rate C(h) = 12h + 376 [U]Set up the cost function for the first company C(h) where h is the number of hours:[/U] C(h) = Hourly Rate * h + flat rate C(h) = 15h + 280 The problem asks how many hours will it take for both companies to charge the same. So we set the cost functions equal to each other: 12h + 376 = 15h + 280 Plugging this equation [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B376%3D15h%2B280&pl=Solve']into our search engine and solving for h[/URL], we get: h = [B]32[/B]

A house rental company charges a $700 for a week stay plus an additional $4 per night for a roll away bed. Your family rents a house for a week and pays $756. How many roll away beds did they rent? Roll Away Beds = (Total Rental Price - Weekly Charge)/Per night bed fee Plugging in our numbers, we get: Roll Away Beds = (756 - 700)/4 Roll Away Beds = 56/4 Roll Away Beds = [B]14[/B]

A house sold for $200,000 and the real estate agent earned a commission of $10,200.00. Find the commission rate. Commission Rate = 100 * Commission Amount / Sale Price Commission Rate = 100 * 10200/20000 Commission Rate = 100 * 0.051 Commission Rate = [B]5.51%[/B]

A house valued at 70,000 in 1989 increased in value to 125,000 in 2000. Find a function which gives the value of the house, v, as a function of y, the number of years after 1989. Let's determine the years: 2000 - 1989 = 11 Let's determine the change in value: 125,000 - 70,000 = 55,000 Assuming a linear progression, we have: 55,000/11 = 5,000 per year increase [B]y = 70,000 + 5,000v[/B] where v is the number of years after 1989 Plug in 11 to check our work y = 70,000 + 5,000(11) y = 70,000 + 55,000 y = 125,000

A hungry Emperor penguin was swimming 21 feet below sea level. It swam up 9 feet to eat a fish. What is the position of the penguin now relative to sea level? 21 feet below is written as -21 9 feet up is written as +9 So we have -21 + 9 = [B]-12 or 12 feet below sea level[/B]

The mean credit card debt among households in one state is $8400. A hypothesis test is to be performed to decide whether the mean credit card debt for households in the formerly affluent town of Rich-No-More differs from the mean credit card debt for the state.

A hypothetical population consists of eight individuals ages 14,15,17,20,26,27,28, and 30 years. What is the probability of selecting a participant who is at least 20 years old? At least 20 means 20 or older, so our selection of individuals is: {20, 26, 27, 28, 30} This is 5 out of a possible 8, so we have [URL='http://www.mathcelebrity.com/perc.php?num=5&den=8&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']5/8 of 0.625, which is 62.5%[/URL]

A is 0 and AR=19 what is the midpoint [URL='https://www.mathcelebrity.com/mptnline.php?ept1=0&empt=&ept2=19&pl=Calculate+missing+Number+Line+item']Using our midpoint calculator, with one point at 0, and the other point at 19[/URL], we get the midpoint M: M = [B]19/2 or 9.5[/B]

a is 2 years older than b who is twice as old as c. if the total ages of a,b and c is 42, then how old is b We're given 3 equations: [LIST=1] [*]a = b + 2 [*]b = 2c [*]a + b + c = 42 [/LIST] Substituting equation (2) into equation (1), we have: a = 2c + 2 Since b = 2c, we substitute both of these into equation (3) to get: 2c + 2 + 2c + c = 42 To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=2c%2B2%2B2c%2Bc%3D42&pl=Solve']type this equation into our math engine[/URL] and we get: c = 8 Now take c = 8 and substitute it into equation (2) above: b = 2(8) b = [B]16[/B]

A is the set of factors of 12 Type in [URL='https://www.mathcelebrity.com/factoriz.php?num=12&pl=Show+Factorization']factor 12[/URL] into our math engine and we get: A = {[B]1, 2, 3, 4, 6, 12[/B]}

A is the set of integers greater than or equal to -5 and less than or equal to -2 [B]-5 <= A <= -2[/B]

A is the set of odd integers between 4 and 12 Let A be the set of odd numbers between 4 and 12: [B]A = {5, 7, 9, 11}[/B]

A jar contains 7 red marbles, 8 green marbles, and 6 blue marbles. What is the probability that you draw 4 green marbles in a row if you do not replace the marbles after each draw? The key phrase in this problem is [I]do not replace[/I]. [U]Draw #1:[/U] P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar Total Green Marbles in the Jar = 8 Total Marbles in the Jar = 7 red + 8 green + 6 blue = 21 P(Green) = 8/21 [U]Draw #2:[/U] P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar Total Green Marbles in the Jar = 8 - 1 = 7 Total Marbles in the Jar = 7 red + 7 green + 6 blue = 20 P(Green) = 7/20 [U]Draw #3:[/U] P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar Total Green Marbles in the Jar = 7 - 1 = 6 Total Marbles in the Jar = 7 red + 6 green + 6 blue = 19 P(Green) = 6/19 [U]Draw #4:[/U] P(Green) = Total Green Marbles in the Jar / Total Marbles in the Jar Total Green Marbles in the Jar = 6 - 1 = 5 Total Marbles in the Jar = 7 red + 5 green + 6 blue = 18 P(Green) = 5/18 We want P(Green, Green, Green, Green) Because each draw is [U][B]independent[/B][/U] of all other draws, we multiply each draw to get the final probability P(Green, Green, Green, Green) = P(Green on Draw 1) * P(Green on Draw 2) * P(Green on Draw 3) * P(Green on Draw 4) * P(Green, Green, Green, Green) = 8/21 * 7/20 * 6/19 * 5/18 P(Green, Green, Green, Green) = 1680/143640 Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1680%2F143640&frac2=3%2F8&pl=Simplify']fraction simplifier[/URL], we get: P(Green, Green, Green, Green) = [B]2/171 [MEDIA=youtube]b2C_D4_d0Ug[/MEDIA][/B]

A jar contains 80 nickels and dimes worth $6.40. How many of each kind of coin are in the jar? Using our [URL='http://www.mathcelebrity.com/coin-word-problem.php?coinvalue=6.40&cointot=80&coin1=nickels&coin2=dimes&pl=Calculate+Coin+Quantities']coin combination word problem calculator[/URL], we get: [LIST] [*][B]48 dimes[/B] [*][B]32 nickels[/B] [/LIST]

a jar contains a $5 note, two $10 notes, a $20 note and a $50 note. if 2 notes are taken out by random, find the probability that their sum is $15 To get a sum of $15, we'd need to pull the $5 and the $10. Since both events are indepdenent, we have: P($5 or 10) or P(whatever is not pulled in the first pull) First Pull: 2/4 (We can pull either a $10 or a $5, so 2 choices out of 4 bills) Second Pull: 1/3 <-- since there are only 3 bills and 1 bill to pull Each pull is independent, so we multiply: 2/4 * 1/3 = 2/12 We can simply this, so [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F12&frac2=3%2F8&pl=Simplify']we type this fraction in our search engine[/URL] and we get: [B]1/6[/B]

A jet left Nairobi and flew east at an average speed of 231 mph. A passenger plane left four hours later and flew in the same direction but with an average speed of 385 mph. How long did the jet fly before the passenger plane caught up? Jet distance = 231t Passenger plane distance = 385(t - 4) 385(t - 4) = 231t 385t - 1540 = 231t Subtract 231t from each side 154t = 1540 [URL='https://www.mathcelebrity.com/1unk.php?num=154t%3D1540&pl=Solve']Type 154t = 1540[/URL] into the search engine, we get [B]t = 10. [/B] Check our work: Jet distance = 231(10) = 2,310 Passenger plane distance = 385(10 - 4) = 385 * 6 = 2,310

A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hours head start. How far from the starting point are the planes? Use the formula D = rt where [LIST] [*]D = distance [*]r = rate [*]t = time [/LIST] The plan traveling 150 mph for 3 hours: Time 1 = 150 Time 2 = 300 Time 3 = 450 Now at Time 3, the other plane starts Time 4 = 600 Time 5 = 750 Time 6 = 450 + 150t = 550t Subtract 150t 400t = 450 Divide each side by 400 t = 1.125 Plug this into either distance equation, and we get: 550(1.125) = [B]618.75 miles[/B]

A jet travels 832 km in 5 hours. At this rate, how far could the jet fly in 12 hours? What is the rate of speed of the jet? Distance = rate * time. We're given D = 832 and t = 5. Using our [URL='https://www.mathcelebrity.com/drt.php?d=+832&r=+&t=+5&pl=Calculate+the+missing+Item+from+D%3DRT']drt calculator[/URL], we solve or rate to get: [B]r = 166.4[/B] The problems asks for a distance D when t = 12 hours and r = 166.4 from above. Using our [URL='https://www.mathcelebrity.com/drt.php?d=&r=+166.4&t=+12&pl=Calculate+the+missing+Item+from+D%3DRT']drt calculator solving for d[/URL], we get: d = [B]1,996.8 km[/B]

A jet travels at 485 miles per hour. Which equation represents the distance, d, that the jet will travel in t hours. The distance formula is: d = rt We're given r = 485, so we have: [B]d = 485t[/B]

A job pays $56 for 8 hours of work. how much money does the job pay per hour Hourly Wage = Total Wages / Total Hours Worked $56/8 = [B]$7 per hour[/B].

A jug holds 1.2 litres of orange juice. All of the juice is poured equally into six glasses. How much orange is in each glass? 1.2 litres / 6 glasses = [B]0.2 litres[/B] in each glass.

A kilogram of chocolate costs8 dollars. Sally buys p kilograms. Write an equation to represent the total cost c that Sally pays. c[B] = 8p[/B]

A kilogram of rice costs $2.05.what is the cost of 30kg of the rice? We multiply the price for 1 kilogram by the 30 kilograms total: $2.05 * 30 = [B]$61.50[/B]

A kitchen measures 5 yd by 6 yd. How much would it cost to install new linoleum in the kitchen if the linoleum costs $2 per square foot? The kitchen has an area of 5yd x 6yd = 30 sq yards. If the linoleum costs $2 per square foot, we have 30 sq yards / $2 per square foot = [B]$15[/B]

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall, how high up the wall does the ladder reach? We have a right triangle, where the ladder is the hypotenuse, and we want the measurement of one leg. Set up the pythagorean theorem with these given items using our P[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=7&hypinput=25&pl=Solve+Missing+Side']ythagorean Theorem Calculator[/URL]. We get Side 1 = [B]24 feet.[/B]

A ladder is 25 ft long. The ladder needs to reach to a window that is 24 ft above the ground. How far away from the building should the bottom of the ladder be placed? We have a right triangle, where the ladder is the hypotenuse, and the window side is one side. Using our right triangle and the [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=24&hypinput=25&pl=Solve+Missing+Side']pythagorean theorem calculator[/URL], we get a length of [B]7 ft [/B]for the ladder bottom from the wall.

A ladder rests 2.5 m from the base of a house. If the ladder is 4 m long, how far up the side of the house will the ladder reach? We have a right triangle with the hypotenuse as 4, the one leg as 2.5 We want to solve for the other leg length. We use our [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=2.5&hypinput=4&pl=Solve+Missing+Side']right triangle solver[/URL] to get [B]3.122[/B]

A lady walks into a store and steals $100 bill from the register without the owners knowledge. She comes back 5 minutes later and buys $70 worth of goods with the $100 bill. The owner gives her $30 in change. How much did the owner lose? [LIST=1] [*]After the lady steals $100, the owner is down -$100. [*]The lady comes back, and buys $70 worth of goods. At this point, the owner has -$100 + $70 = $-30. [*]Next, the owner gives the lady another $30 in change, making the owner's loss -$30 - $30 = [B]-$60[/B]. [/LIST]

a landscaper buys 1 gallon of plant fertilizer. he uses 1/5 of the fertilizer, and then divides the rest into 3 smaller bottles. how many gallons does he put into each bottle? First, we find the remaining fraction of fertilizer after using 1/5. [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=1%2F5&pl=Subtract']Using our fraction calculator[/URL], we see: 1 - 1/5 = 4/5 To find the amount of fertilizer per bottle, we then [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F5&frac2=3&pl=Divide']divide 4/5 by 3 and we get[/URL]: [B]4/15 gallon per bottle[/B]

A laptop is purchased for $1700. After each year, the resale value decreases by 25%. What will be the resale value after 5 years? [U]Let R(t) be the Resale value at time t:[/U] R(t) = 1,700(1 - 0.25)^t [U]We want R(5)[/U] R(5) = 1,700(1 - 0.25)^5 R(5) =1,700(0.75)^5 R(5) =1,700 * 0.2373 R(5) = [B]$403.42[/B]

A large bag of candy contains 84 blue candies, 96 red candies, and 120 yellow candies. What percent of the candies are red? [U]Calculate total candies:[/U] Total Candies = Blue Candies + Red Candies + Yellow Candies Total Candies = 84 + 96 + 120 Total Candies = 300 [U]Now calculate the red candy percentage:[/U] Red Candy Percent = 100 * Red Candies / Total Candies Red Candy Percent = 100 * 96 / 300 Red Candy Percent = 9600 / 300 Red Candy Percent = [B]32%[/B]

a large fry has 120 more calories than a small. 5 large fries is the same amount of calories as 7 small. How many calories does each size fry have? Let the number of calories in large fries be l. Let the number of calories in small fries be s. We're given two equations: [LIST=1] [*]l = s + 120 [*]5l = 7s [/LIST] Substitute equation (1) into equation (2): 5(s + 120) = 7s [URL='https://www.mathcelebrity.com/1unk.php?num=5%28s%2B120%29%3D7s&pl=Solve']Type this equation into the search engine[/URL] and we get: s = [B]300[/B] Substitute s = 300 into equation (1): l = 300 + 120 l = [B]420[/B]

A large storage container is filled with 44.9 quarts of water. One quart of water is equivalent to 32 fluid ounces. How many fluid ounces of water are stored in the container? Round your answer to the nearest whole number. 44.9 quarts * 32 fluid ounce / quart = 1,436.8 if we found to the nearest whole number, we round up since 0.8 is greater than 0.5, so we get: [B]1,437 fluid ounces[/B]

A laundry basket contains 30 socks, of which 9 are black. What is the probability that a randomly selected sock will be black? P(Black) = 9/30 Simplifying, we can divide top and bottom by 3: [B]3/10 3/10 as a percentage is 30%[/B]

A lead pipe 20 ft long is 3/8 inch thick and has an inner diameter of 3 inches. Find the volume of lead in it. A lead pipe is a cylinder. We want the volume of a cylinder. Convert 20ft to inches: 20ft = 12(20) = 240 inches Find the inner radius: 1/2 * inner diameter 1/2 * 3 = 3/2 Now add the thickness for the total radius 3/2 + 3/8 = 12/8 + 3/8 = 15/8 Find volume of the lead where volume = pi r^2 h Lead vol (V) = Overall volume - inner volume Lead Vol = pi(15/8)^2(240) - pi(3/2)^2(240) Lead Vol = 240pi(225/64 - 9/4) 9/4 = 144/64 Lead Vol = 240pi(225/64 - 144/64) Lead Vol = 240pi(81/64) [B]Lead Vol = 303.75pi[/B]

a licence plate that has 3 numbers from 0 to 9 followed by 2 letters How many license plate combinations can we form? We multiply as follows: [LIST] [*][0-9] = 10 possible digits (D) [*]A-Z = 26 possible letters (L) [/LIST] The problem asks for this: DDDLL So we have: 10 * 10 * 10 * 26 * 26 = [B]676,000[/B] plates

a license plate has 3 letters followed by 4 numbers There are 26 letters A-Z and 10 numbers 0-9. So we have: 26 * 26 * 26 * 10 * 10 * 10 * 10 [B]175,760,000 different license plate combinations[/B]

A license plate is made up of 2 letter and 3 single digit numbers. There are 26 letters (A-Z). And there are 10 single digit numbers [0-9]. So our total combinations are: Letter - Letter - Number - Number - Number 26 * 26 * 10 * 10 * 10 = [B]676,000[/B]

A light bulb consumes 17100 watt-hours in 4 days and 18 hours. How many watt-hours does it consume a day? Since one day equals 24 hours, we have: 4 days and 18 hours equals: 4(24) + 18 hours 96 + 18 hours 114 hours Therefore, we have a proportion, where w is the number of watt-hours in a 24-hour period. 17,100 watt-hours/114 hours = w/24 [URL='https://www.mathcelebrity.com/prop.php?num1=17100&num2=w&den1=114&den2=24&propsign=%3D&pl=Calculate+missing+proportion+value']Typing 1711/114 = w/24 into our calculator[/URL], we get: [B]w = 3,600[/B]

A light flashes every 2 minutes a, second light flashes every 7 minutes, and a third light flashes every 8 minutes. If all lights flash together at 8 P.M., what is the next time of day they will all flash together [URL='https://www.mathcelebrity.com/gcflcm.php?num1=2&num2=7&num3=8&pl=LCM']We use our least common multiple calculator[/URL] to see when the 3 numbers have a common multiple: LCM of (2, , 8) = 56 minutes So this means we add 56 minutes to 8:00 P.M. and we get [B]8:56 P.M.[/B]

a lighthouse blinks every 12 minutes. A second lighthouse blinks every 10 minutes if they both blink at 8:10 P.M at what time will they next blink together We want the least common multiple of (10, 12). This will be the next time each number times a multiple equals the same number. [URL='https://www.mathcelebrity.com/gcflcm.php?num1=10&num2=12&num3=&pl=GCF+and+LCM']Typing in LCM 10,12 into our search engine[/URL], we get: 60 So if we start at 8:10, and 60 minutes later is when both lighthouses blink. 60 minutes equals 1 hour. So we add 1 hour to 8:10, we have [B]9:10[/B]

A lighthouse blinks every 12 minutes.A second lighthouse blinks every 10 minutes.If they both blink at 8:10 P.M., at what time will they next blink together? We want to know the least common multiple, so that 12 and 10 intervals meet again.[URL='https://www.mathcelebrity.com/gcflcm.php?num1=10&num2=12&num3=&pl=GCF+and+LCM'] We type in LCM(10,12) into our search engine[/URL] and we get 60. 60 minutes is 1 hour, so we add this to 8:10 to get [B]9:10[/B]

A limo costs $85 to rent for 3 hours plus a 7% sales tax. What is the total cost to rent the limo for 6 hours? Determine the number of 3 hour blocks: 3 hour blocks = Total Rental Time / 3 3 hour blocks = 6 hours / 3 3 hour blocks = 2 With 7% = 0.07, we have: Total Cost = $85 * / 3 hours * 2 (3 hour blocks) * 1.07 Total Cost = 85 * 2 * 1.07 Total Cost = [B]181.9[/B]

A line has a slope of 1/2 and a run of 50. Find the rise of the line. Slope = Rise/Run We're given a run of 50, so let the rise be r. We have: r/50 = 1/2 To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=r&num2=1&den1=50&den2=2&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: r = [B]25[/B]

A line has a slope of 7 and a y-intercept of -4. What is its equation in slope intercept form The slope-intercept equation for a line: y = mx + b where m is the slope Given m = 7, we have: y = 7x + b The y-intercept is found by setting x to 0: y = 7(0) + b y = 0 + b y = b We're given the y-intercept is -4, so we have: b = -4 So our slope-intercept equation is: [B]y = 7x - 4[/B]

A line in the xy-plane passes through the origin and has a slope of 4/5. What points lie on that line. Our line equation is: y = mx + b We're given: m = 4/5 (x, y) = (0, 0) So we have: 0 = 4/5(0) + b 0 = 0 + b b = 0 Therefore, our line equation is: y = 4/5x [URL='https://www.mathcelebrity.com/function-calculator.php?num=y%3D4%2F5x&pl=Calculate']Start plugging in values here to get a list of points[/URL]

A line joins A (1, 3) to B (5, 8). (a) (i) Find the midpoint of AB. We type in (1,3),(5,8) to our search engine. We [URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=3&slope=+2%2F5&xtwo=5&ytwo=8&pl=You+entered+2+points']choose our midpoint of 2 points calculator,[/URL] and we get: [B](3, 11/2)[/B]

A line passes through the point -3,4 and has a slope of -5 Using our [URL='http://A line passes through the point -3,4 and has a slope of -5']point slope calculator[/URL], we get a line equation of: y = -5x - 11

A line segment has the endpoints S(10, 7) and T(2, 7). Find the coordinates of its midpoint M. [URL='https://www.mathcelebrity.com/slope.php?xone=2&yone=7&slope=+&xtwo=10&ytwo=7&bvalue=+&pl=You+entered+2+points']Using our midpoint calculator[/URL], we get: M = [B](6, 7)[/B]

A line segment is 26 centimeters long. If a segment, x centimeters, is taken, how much of the line segment remains? This means the leftover segment has a length of: [B]26 - x[/B]

a lion can run 72 feet in one second how far can the lion run in one minute? Using our [URL='https://www.mathcelebrity.com/timecon.php?quant=1&pl=Calculate&type=minute']time conversions calculator by typing [I]1 minute[/I] into our search engine[/URL], we see: 1 minute = 60 seconds So 72 feet per second * 60 seconds / minute = [B]4,320 feet / minute[/B]

A loaf of bread has 35 slices. Ann eats 8 slices, Betty eats 6 slices, Carl eats 5, and Derrick eats 9 slices. What fraction of the loaf is left? [U]Calculate total slices eaten:[/U] Slices eaten = Ann + Betty + Carl + Derrick Slices eaten = 8 + 6 + 5 + 9 Slices eaten = 28 [U]Calculate remaining slices:[/U] Remaining slices = Slices in loaf - Slices Eaten Remaining slices = 35 - 28 Remaining slices = 7 [U]Calculate fraction of the loaf left:[/U] Fraction left = Remaining Slices / Slices in Loaf Fraction left = 7/35 We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=7%2F35&frac2=3%2F8&pl=Simplify']type 7/35 into our search engine[/URL], choose simplify, and we get: Fraction left = [B]1/5[/B]

A local bank charges 19 per month plus 3 cents per check. The credit union charges7 per month plus 7 cents per check. How many checks should be written each month to make the credit union a better deal? Set up the cost function B(c) for the local bank where c is the number of checks: B(c) = 0.03c + 19 Set up the cost function B(c) for the credit union where c is the number of checks: B(c) = 0.07c + 7 We want to find out when: 0.07c + 7 < 0.03c + 19 [URL='https://www.mathcelebrity.com/1unk.php?num=0.07c%2B7%3C0.03c%2B19&pl=Solve']Typing this inequality into our search engine[/URL], we get: c < 300

A local college classifies its students by major, year (Freshman, Sophomore, Junior, Senior) and sex (M, F). If the college offers 20 majors, how many combinations are possible? We have 20 majors, 4 grade levels, and 2 sexes. The total combinations = 20 * 4 * 2 = [B]160[/B]

A local Dunkin’ Donuts shop reported that its sales have increased exactly 16% per year for the last 2 years. This year’s sales were $80,642. What were Dunkin' Donuts' sales 2 years ago? Declare variable and convert numbers: [LIST] [*]16% = 0.16 [*]let the sales 2 years ago be s. [/LIST] s(1 + 0.16)(1 + 0.16) = 80,642 s(1.16)(1.16) = 80,642 1.3456s = 80642 Solve for [I]s[/I] in the equation 1.3456s = 80642 [SIZE=5][B]Step 1: Divide each side of the equation by 1.3456[/B][/SIZE] 1.3456s/1.3456 = 80642/1.3456 s = 59930.142687277 s = [B]59,930.14[/B]

A local radio station sells time slots for programs in 20-minute intervals. If the station operates 24 hours per day, what is the total number of 20-minute time slots the radio station can sell for Thursday and Friday? Thursday and Friday = 2 days With 24 hours per day, we have 24 * 2 = 48 hours for Thursday and Friday. Since 20 minutes is 1/3 of an hour, then we have 3 20-minute time slots per hour. 3 20-minute time slots * 48 hours = [B]144[/B] total 20-minute time slots

A local shop sold 499 hamburgers and cheese burgers. There were 51 fewer cheese burgers sold. How many hamburgers were sold? Let h = number of hamburgers sold and c be the number of cheeseburgers sold. We have two equations: (1) c = h - 51 (2) c + h = 499 Substitute (1) into (2) h - 51 + h = 499 Combine like terms 2h - 51 = 499 Add 51 to both sides 2h = 550 Divide each side by 2 to isolate h [B]h = 275[/B]

A local sports centre charges $8 per visit. For an annual membership fee of$45, the cost per visit is only $5.50. What is the least number of visits needed in a year in order for the membership to be a better deal? Set up the cost for the visitors plan C(v) where v is the number of visits: C(v) = 8v Set up the cost for the membership plan C(v) where v is the number of visits: C(v) = 5v + 45 The problem asks for v where: 5v + 45 < 8v [URL='https://www.mathcelebrity.com/1unk.php?num=5v%2B45%3C8v&pl=Solve']Type this inequality into our search engine[/URL] and get: v > 15 This means, the least number of visits is 1 more which is [B]16[/B]

A lottery offers 1 $1000 prize and 5 $100 prizes. 1000 tickets are sold. Find the expectation if a person buys 1 ticket for $5. Set up the expected values E(x): for the 1,000 price: E(x) = (1000 - 5) * 1/1000 = 995/1000 For the 5 $100 prizes: E(x) = (100 - 5) * 5/1000 = 475/1000 For the losing ticket. With 6 winning tickets, we have 1000 - 6 = 994 losing tickets: E(x) = -3 * 994/1000 = -2982/1000 We get our total expected value by adding all of these expected values up. Since they all have the same denominator, we add numerators: E(x) = (995 + 475 - 2982)/1000 E(x) = -1512/1000 E(x) = [B]-1.51[/B]

A lottery uses a container with 25 identical balls numbered 1 through 25, from which three balls are selected. What is the theoretical probability that the number 13 is picked first? P(1st ball being 13) = [B]1 /25[/B]

A luncheon for 14 guests cost $468.00. What was the average cost per guest? Average Cost per Guest = Total Cost / Number of Guests Average Cost per Guest = $468 / 14 Average Cost per Guest = [B]$33.43[/B]

a machine has a first cost of 13000 an estimated life of 15 years and an estimated salvage value of 1000.what is the book value at the end of 9 years? Using [URL='https://www.mathcelebrity.com/depsl.php?d=&a=13000&s=1000&n=15&t=9&bv=&pl=Calculate']our straight line depreciation calculator[/URL], we get a book value at time 9, B9 of: [B]5,800[/B]

A machine prints 230 movie posters each hour. Write and solve an equation to find the number of hours it takes the machine to print 1265 posters. Let h be the number of hours. We're given the following expression for the printing output of the machine: 230h The questions asks for how long (h) to print 1265 posters, so we setup the equation: 230h = 1265 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=230h%3D1265&pl=Solve']type this equation into our math engine[/URL] and we get: h = [B]5.5 hours[/B]

A machine shop employee earned $642 last week. She worked 40hours at her regular rate and 9 hours at a time and a half rate. Find her regular hourly rate. Let the regular hourly rate be h. We're given: 40h + 40(1.5)(h - 40) = 642 Multiply through and simplify: 40h + 60h - 2400 = 642 100h - 2400 = 642 [URL='https://www.mathcelebrity.com/1unk.php?num=100h-2400%3D642&pl=Solve']To solve for h, we type this equation into our search engine[/URL] and we get: h = [B]30.42[/B]

A magic box has pennies in it that double every minute. If the box takes a full hour to become completely full, how long does it take for the box to become half full? At the hour mark, it's 100% full. Half full means 50%. Since it doubles every minute, then at the [B]59th minute[/B], it's half full.

A mail courier charges a base fee of $4.95 plus $11.90 per package being delivered. If x represents the number of packages delivered, which of the following equations could be used to find y, the total cost of mailing packages? Set up the cost function y = C(x) [B]C(x) = 4.95 + 11.90x[/B]

A man bought a mobile phone for $800 and sold it for $1000. What was his profit as a percentage of the cost price Calculate Profit: Profit = Sales Price - Cost Profit = 1000 - 800 Profit = 200 Calculate profit percentage: Profit Percentage = Profit * 100 / Cost Profit Percentage = 800 * 100 / 200 Profit Percentage = [B]400%[/B]

A man invested part of $15,000 at 12% and the remainder at 8%. If his annual income from the investments is $1456, how much does he have invested at each rate? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=15000&i1=12&i2=8&itot=1456&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*]Fund 1 Investment @ 12% = [B]6,400[/B] [*]Fund 2 Investment @ 8% =[B] [B]8,600[/B][/B] [/LIST]

A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments is $194, how much money did he invest at each rate? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=5200&i1=4&i2=3&itot=194&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]Fund 1 = $3,800[/B] [*][B]Fund 2 = $1,400[/B] [/LIST]

A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100 Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given: [LIST=1] [*]m = w + 5 [*]d = 0.5m [*]d + m + w = 100 [/LIST] Rearrange equation 1 in terms of w my subtracting 5 from each side: [LIST=1] [*]w = m - 5 [*]d = 0.5m [*]d + m + w = 100 [/LIST] Substitute equation (1) and equation (2) into equation (3) 0.5m + m + m - 5 = 100 We [URL='https://www.mathcelebrity.com/1unk.php?num=0.5m%2Bm%2Bm-5%3D100&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get: m = [B]42 [/B] Now, substitute m = 42 into equation 2 to solve for d: d = 0.5(42) d = [B]21 [/B] Now substitute m = 42 into equation 1 to solve for w: w = 42 - 5 w = [B]37 [/B] To summarize our ages: [LIST] [*]Man (m) = 42 years old [*]Daughter (d) = 21 years old [*]Wife (w) = 37 years old [/LIST]

A man is four time as old as his son. How old is the man if the sum of their ages is 60? Let the son's age be a. Then the man's age is 4a. If the sum of their ages is 60, we have: a + 4a = 60 To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B4a%3D60&pl=Solve']type it in our math engine[/URL] and we get: a = 12 Therefore, the man's age is: 4(12) = [B]48[/B]

A man is four times as old as his son. In five years time he will be three times as old. Find their present ages. Let the man's age be m, and the son's age be s. We have: [LIST=1] [*]m = 4s [*]m + 5 = 3(s + 5) [/LIST] Substitute (1) into (2) 4s + 5 = 3s + 15 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=4s%2B5%3D3s%2B15&pl=Solve']equation calculator[/URL], and we get [B]s = 10[/B]. m = 4(10) [B]m = 40[/B]

A man is swimming at 10 feet below sea level. Then he descends 1 feet and then ascends 5 feet. What is the man's new location? 10 feet below sea level is written as -10 He descends 1 foot. Since descending is negative depth, we have: -10 - 1 = -11 Then he ascends 5 feet, so we add: -11 + 5 = [B]-6 or 6 feet below sea level[/B]

A man left a warehouse at 9:00 a.m. and travels 150 km to reach his home. What is the speed if he arrives at 11:00 a.m.? [LIST] [*]His trip took 2 hours (11 - 9) [*]He traveled 150 km in 2 hours [*]His speed is measured in km per hour [/LIST] If we have 150km/2 hours, we want his speed in km per hour Divide top and bottom by 2 [B]75km/hr[/B]

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket? Declare variables: [LIST] [*]Let a be the number of adult's tickets [*]Let c be the number of children's tickets [/LIST] Cost = Price * Quantity We're given two equations: [LIST=1] [*]a + c = 20 [*]15a + 10c = 225 [/LIST] Rearrange equation (1) in terms of a: [LIST=1] [*]a = 20 - c [*]15a + 10c = 225 [/LIST] Now that I have equation (1) in terms of a, we can substitute into equation (2) for a: 15(20 - c) + 10c = 225 Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225 We first need to simplify the expression removing parentheses Simplify 15(20 - c): Distribute the 15 to each term in (20-c) 15 * 20 = (15 * 20) = 300 15 * -c = (15 * -1)c = -15c Our Total expanded term is 300-15c Our updated term to work with is 300 - 15c + 10c = 225 We first need to simplify the expression removing parentheses Our updated term to work with is 300 - 15c + 10c = 225 [SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE] (-15 + 10)c = -5c [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] -5c + 300 = + 225 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 300 and 225. To do that, we subtract 300 from both sides -5c + 300 - 300 = 225 - 300 [SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE] -5c = -75 [SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE] -5c/-5 = -75/-5 c = [B]15[/B] Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a: a = 20 - 15 a = [B]5[/B]

A man stands at point p, 45 metres from the base of a building that is 20 metres high. Find the angle of elevation of the top of the building from the man. Draw a right triangle ABC where Side A is from the bottom of the building to the man and Side B is the bottom of the building to the top of the building. Using right triangle calculations, we want Angle A which is the angle of elevation. [URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=20&angle_b=&b=45&c=&pl=Calculate+Right+Triangle']Angle of Elevation[/URL] which is [B]23.9625°[/B]

A man's age (a) 10 years ago is 43 [U]10 years ago means we subtract 10 from a:[/U] a - 10 [U]The word [I]is[/I] means an equation. So we set a - 10 equal to 43 to get our algebraic expression[/U] [B]a - 10 = 43[/B] If the problem asks you to solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=a-10%3D43&pl=Solve']we type this equation into our search engine[/URL] and we get: a = 53

A man's age (a) 10 years ago is 43. Years ago means we subtract [B]a - 10 = 43 [/B] If the problem asks you to solve for a, we type this equation into our math engine and we get: Solve for [I]a[/I] in the equation a - 10 = 43 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -10 and 43. To do that, we add 10 to both sides a - 10 + 10 = 43 + 10 [SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE] a = [B]53[/B]

a mans age (a) ten years ago The problem asks for an algebraic expression for age. The phrase [I]ago[/I] means before now, so they were younger. And younger means we [B]subtract[/B] from our current age: [B]a - 10[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produced. The product sells for $22/unit. The cost function for each unit u is: C(u) = Variable Cost * Units + Fixed Cost C(u) = 10u + 100000 The revenue function R(u) is: R(u) = 22u We want the break-even point, which is where: C(u) = R(u) 10u + 100000 = 22u [URL='https://www.mathcelebrity.com/1unk.php?num=10u%2B100000%3D22u&pl=Solve']Typing this equation into our search engine[/URL], we get: u =[B]8333.33[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produced. The product sells for $20/unit [U]Cost Function C(u) where u is the number of units:[/U] C(u) = cost per unit * u + fixed cost C(u) = 12u + 100000 [U]Revenue Function R(u) where u is the number of units:[/U] R(u) = Sale price * u R(u) = 20u Break even point is where C(u) = R(u): C(u) = R(u) 12u + 100000 = 20u To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=12u%2B100000%3D20u&pl=Solve']type this equation into our search engine[/URL] and we get: u = [B]12,500[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produced. The product sells for $20/unit. Let u be the number of units. We have a cost function C(u) as: C(u) = Variable cost * u + Fixed Cost C(u) = 14u + 100000 [U]We have a revenue function R(u) with u units as:[/U] R(u) = Sale Price * u R(u) = 20u [U]We have a profit function P(u) with u units as:[/U] Profit = Revenue - Cost P(u) = R(u) - C(u) P(u) = 20u - (14u + 100000) P(u) = 20u - 14u - 100000 P(u) = 6u - 1000000

A manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produced. The product sells for $10/unit. Set up cost function where u equals each unit produced: C(u) = 7u + 25,500 Set up revenue function R(u) = 10u Break Even is where Cost equals Revenue 7u + 25,500 = 10u Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=7u%2B25500%3D10u&pl=Solve']equation calculator[/URL] to get [B]u = 8,500[/B]

A manufacturer has a monthly fixed cost of $52,500 and a production cost of $8 for each unit produced. The product sells for $13/unit. Using our [URL='http://www.mathcelebrity.com/cost-revenue-profit-calculator.php?fc=52500&vc=8&r=13&u=20000%2C50000&pl=Calculate']cost-revenue-profit calculator[/URL], we get the following: [LIST] [*]P(x) = 55x - 2,500 [*]P(20,000) = 47,500 [*]P(50,000) = 197,500 [/LIST]

a manufacturing company has a debt to equity ratio of 3 to 2. if the company has a debt of $12 million, how much does it have in equity? Set up a proportion of debt to equity 3/2 = 12/x Using our [URL='http://www.mathcelebrity.com/prop.php?num1=3&num2=12&den1=2&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: x = 8

A marathon runner took 2 hours and 15 minutes to complete the race. During that time he spent 50 minutes in the lead. Write down, in its simplest form, the fraction of time he spent in the lead. [U]Calculate total race time in minutes[/U] [URL='https://www.mathcelebrity.com/timecon.php?quant=2&pl=Calculate&type=hour']2 hours[/URL] = 120 minutes 120 minutes + 15 minutes = 135 minutes [U]Calculate fraction of lead time[/U] Fraction of lead time = Time spent in lead / total race time Fraction of lead time = 50/135 Simplifying this fraction, we get: [URL='https://www.mathcelebrity.com/fraction.php?frac1=50%2F135&frac2=3%2F8&pl=Simplify']Fraction of lead time[/URL] = [B]10/27[/B]

[SIZE=6][B]A quiz has 5 questions with 4 answer choices each find the number of possible outcomes[/B] [B][/B] [B]We have 4 * 4 * 4 * 4 * 4 = 1024 outcomes[/B][/SIZE]

A math teacher bought 40 calculators at $8.20 each and a number of other calculators costing$2.95 each. In all she spent $387. How many of the cheaper calculators did she buy Let the number of cheaters calculators be c. Since amount equals price * quantity, we're given the following equation: 8.20 * 40 + 2.95c = 387 To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=8.20%2A40%2B2.95c%3D387&pl=Solve']type it in our search engine [/URL]and we get: c = [B]20[/B]

A Math teacher gives one test a week to his class of 31 students. Estimate the number of tests the teacher will mark in 39 weeks. 31 students * 1 test per week * 39 weeks = [B]1,209 tests[/B]

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test? Let's call the 5 point questions m for multiple choice. Let's call the 2 point questions t for true-false. We have two equations: [LIST=1] [*]m + t = 38 [*]5m + 2t = 100 [/LIST] Rearrange (1) to solve for m - subtract t from each side: 3. m = 38 - t Now, substitute (3) into (2) 5(38 - t) + 2t = 100 190 - 5t + 2t = 100 Combine like terms: 190 - 3t = 100 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=190-3t%3D100&pl=Solve']equation solver[/URL], we get [B]t = 30[/B]. Plugging t = 30 into (1), we get: 30 + t = 38 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=m%2B30%3D38&pl=Solve']equation solver[/URL] again, we get [B]m = 8[/B]. Check our work for (1) 8 + 30 = 38 <-- Check Check our work for (2) 5(8) + 2(30) ? 100 40 + 60 ? 100 100 = 100 <-- Check You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+38&term2=5m+%2B+2t+%3D+100&pl=Cramers+Method']simultaneous equations calculator[/URL]

A mathematician has 8 favorite paintings and only 6 wall hooks to hang the paintings. How many different ways can she hang the paintings? 8 paintings taken 6 at a time is written as: [URL='https://www.mathcelebrity.com/permutation.php?num=8&den=6&pl=Permutations']8P6[/URL] = [B]20,160[/B]

A mechanic charges $45 per hour and parts cost $125. Write an expression for the total if the mechanic works h hours. Set up the cost function C(h) where h is the number of hours worked: C(h) = Hourly Rate * h + parts C(h) = [B]45h + 125[/B]

A mechanic charges $50 to inspect your heater, plus $80 per hour to work on it. You owe the mechanic a total of $310. Write and solve an equation to find the amount of time h (in hours) the mechanic works on your heater. We calculate the cost function C(h) as: C(h) = Hourly Rate * hours + Flat Fee Inspection C(h) = 80h + 50 <-- this is our cost equation Now, we want to solve for h when C(h) = 310 80h + 50 = 310 [URL='https://www.mathcelebrity.com/1unk.php?num=80h%2B50%3D310&pl=Solve']We type this equation into our search engine[/URL] and we get: h = [B]3.25[/B]

A mechanic will charge a new customer $45.00 for an initial diagnosis plus $20 an hour of labor. How long did the mechanic work on a car if he charged the customer $165? We set up a cost function C(h) where h is the number of hours of labor: C(h) = Hourly Labor Rate * h + Initial Diagnosis C(h) = 20h + 45 The problem asks for the number of hours if C(h) = 165. So we set our cost function C(h) above equal to 165: 20h + 45 = 165 To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B45%3D165&pl=Solve']we plug this equation into our search engine[/URL] and we get: h = [B]6[/B]

A medium orange has 70 calories. This is 10 calories less then 1/4 of the calories in a sugar krunchy. How many calories are in a sugar crunchy? Let s = calories in a sugar crunch. Let o = 70 be the calories in a medium orange. Set up the equation: o = 1/4s - 10 70 = 1/4s - 10 Add 10 to each side 1/4s = 80 Multiply each side by 4 [B]s = 320[/B]

A members-only speaker series allows people to join for $16 and then pay $1 for every event attended. What is the maximum number of events someone can attend for a total cost of $47? Subtract the join fee from the total cost: $47 - $16 = $31 Now divide this number by the cost per event: $31 / $1 = [B]31 events[/B]

A metal block is made of nickel and copper. The weight of metals in the block are in a ratio of 2:9. The weight of the block is 407 pounds. What is the weight of the nickel? Using our [URL='https://www.mathcelebrity.com/ratio.php?simpratio=100%3A350&rs=2%3A9&rtot=407&pl=Calculate+Ratio']ratio calculator[/URL], we get: [B]74 pounds[/B]

A meter is defined as the distance light travels in 1/299,792,458 of a second. How many meters does light travel in 1/8 of a second? 1/8 second / 1/299,792,458 299,792,458/8 = [B]37,474,057.25 meters[/B]

A Middleweight UFC fighter weighs between 170 lbs and 185 lbs. Let w be the UFC fighter's weight: We have a compound inequality. Right side includes 185 lbs. because between means includes 185lbs. Left side includes 170 lbs. because between means includes 17lb0s [B]170 <= w <= 185[/B]

A milk booth sells 445 litres of milk in a day. How many litres of milk will it sell in 4 years Calculate the number of days in 4 years: Days in 4 years = Days in 1 year * 4 Days in 4 years = 365 * 4 Days in 4 years = 1,460 Calculate litres of milk sold in 4 years: Litres of milk sold in 4 years = Litres of milk sold in 1 day * Days in 4 years Litres of milk sold in 4 years = 445 * 1,460 Litres of milk sold in 4 years = [B]649,700 litres[/B]

A monster energy drink has 164 mg of caffeine. Each hour your system reduces the amount of caffeine by 12%. Write an equation that models the amount of caffeine that remains in your body after you drink an entire monster energy. Set up a function C(h) where he is the number of hours after you drink the Monster energy drink: Since 12% as a decimal is 0.12, we have: C(h) = 164 * (1 - 0.12)^h <-- we subtract 12% since your body flushes it out [B]C(h) = 164 * (0.88)^h[/B]

a more than b is greater than 6 a more than b: b + a Is greater than 6 means an inequality using the > sign: [B]b + a > 6[/B]

A mother duck lines her 13 ducklings up behind her. In how many ways can the ducklings line up? In position one, we can have any of the 13 ducks. In position two, we can have 12 ducks, since one has to occupy position one. We subtract 1 each time until we fill up all 13 positions. We have: 13 * 12 * 11 * ... * 2 * 1 Or, 13!. [URL='https://www.mathcelebrity.com/factorial.php?num=13!&pl=Calculate+factorial']Typing 13! into our search engine[/URL], we get [B]6,227,020,800[/B] ways the ducklings can line up behind the mother duck.

A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight. If the baby gains 5 pounds every 2 months, then they gain 5/2 = 2.5 pounds per month. Let x be the number of months old for the baby, we have: The baby starts at 10 pounds. And every month (x), the baby's weight increases 2.5 pounds. Our equation is: [B]y = 2.5x + 10[/B]

A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx b that describes the baby's weight. The baby gains 4 pounds every month, where x is the number of months since birth. The baby boy starts life (time 0) at 6 pounds. So we have [B]y = 4x + 6[/B]

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight. Every month, the baby gains 2/3 of a pound. So we have: [B]y = 2/3x + 7 [/B] The baby starts off with 7 pounds. So we add 7 pounds + 2/3 times the number of months passed since birth.

A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? [U]Assumptions:[/U] [LIST] [*]B = the speed of the boat in still water. [*]S = the speed of the stream [/LIST] Relative to the bank, the speeds are: [LIST] [*]Upstream is B - S. [*]Downstream is B + S. [/LIST] [U]Use the Distance equation: Rate * Time = Distance[/U] [LIST] [*]Upstream: (B-S)6 = 258 [*]Downstream: (B+S)6 = 330 [/LIST] Simplify first by dividing each equation by 6: [LIST] [*]B - S = 43 [*]B + S = 55 [/LIST] Solve this system of equations by elimination. Add the two equations together: (B + B) + (S - S) = 43 + 55 Cancelling the S's, we get: 2B = 98 Divide each side by 2: [B]B = 49 mi/hr[/B] Substitute this into either equation and solve for S. B + S = 55 49 + S = 55 To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=49%2Bs%3D55&pl=Solve']type it in our search engine[/URL] and we get: S = [B]6 mi/hr[/B]

A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pass for $80. How many days must he work (i.e. pass through the toll) in order to break even? Let the number of days be d. Break even means both costs are equal. We want to find when: 4.75d = 80 To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.75d%3D80&pl=Solve']type this equation into our search engine[/URL] and we get: d = 16.84 days We round up to an even [B]17 days[/B].

A mountain with a base 6684 feet below sea level rises 22304 feet. What is the elevation above sea level of its peak? Below sea level is written as a negative, so we have: -6684 + 22304 = [B]15,620 feet above sea level[/B]

A movie started at 11:28 am and it ended at 2:49 pm. How long was the movie? Using our [URL='http://www.mathcelebrity.com/elaptime.php?num1=11%3A28&check1=1&num2=2%3A49&check2=2&pl=Calculate+Elapsed+Time']elapsed time calculator[/URL], we have [B]3 hours and 21 minutes[/B].

A movie theater charges $7 for adults and $3 for seniors on a particular day when 324 people paid an admission the total receipts were 1228 how many were seniors and how many were adults? Let the number of adult tickets be a. Let the number of senior tickets be s. We're given two equations: [LIST=1] [*]a + s = 324 [*]7a + 3s = 1228 [/LIST] We have a set of simultaneous equations we can solve using 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [LIST] [*][B]a = 64[/B] [*][B]s = 260[/B] [/LIST]

A movie theater charges 7.00 for adults and 2.00 for seniors citizens. On a day when 304 people paid for admission, the total receipt were 1118. How many who paid were adults ? How many were senior citizens? Let a be the number of adult tickets. Let s be the number of senior citizen tickets. We're given two equations: [LIST=1] [*]a + s = 304 [*]7a + 2s = 1118 [/LIST] We can solve this system of equations three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Cramers+Method']Cramer's Method[/URL] [/LIST] No matter which way we choose, we end up with the same answer: [LIST] [*]a = [B]102[/B] [*]s = [B]202[/B] [/LIST]

A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1030, How many children, students, and adults attended? Let c be the number of children's tickets, s be the number of student's tickets, and a be the number of adult's tickets. We have 3 equations: [LIST=1] [*]a + c + s = 143 [*]a = 0.5c [*]12a + 5c + 7s =1030 [/LIST] Substitute (2) into (1) 0.5c + c + s = 143 1.5c + s = 143 Subtract 1.5c from each side 4. s = 143 - 1.5c Now, take (4) and (2), and plug it into (3) 12(0.5c) + 5c + 7(143 - 1.5c) = 1030 6c + 5c + 1001 - 10.5c = 1030 Combine like terms: 0.5c + 1001 = 1030 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.5c%2B1001%3D1030&pl=Solve']equation calculator[/URL] to get [B]c = 58[/B]. Plug this back into (2) a = 0.5(58) [B]a = 29 [/B] Now take the a and c values, and plug it into (1) 29 + 58 + s = 143 s + 87 = 143 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B87%3D143&pl=Solve']equation calculator[/URL] again, we get [B]s = 56[/B]. To summarize, we have: [LIST] [*]29 adults [*]58 children [*]56 students [/LIST]

A mug has 3 inch diameter and is 3.5 inches tall how much water can it hold A mug is a cylinder. If the diameter is 3, then the radius is 3/2 = 1.5. Using our cylinder volume calculator, we get: [B]V = 7.875pi or 24.74 cubic inches[/B]

A music app charges $2 to download the app plus $1.29 per song download. Write and solve a linear equation to find the total cost to download 30 songs Set up the cost function C(s) where s is the number of songs: C(s) = cost per song * s + download fee Plugging in our numbers for s = 30 and a download fee of $2 and s = 1.29, we have: C(30) = 1.29(30) + 2 C(30) = 38.7 + 2 C(30) = [B]40.7[/B]

A music app charges $2 to download the app plus $1.29 per song downloaded Let d be the number of downloads. The cost function C(d) is: C(d) = cost per download * d + download fee [B]C(d) = 1.29d + 2[/B]

A music app charges $2 to download the app plus $1.29 per song downloaded. Write and solve a linear equation to find the total cost to download 30 songs. Let the number of songs be s. And the cost function be C(s). We have: C(s) = Price per song downloaded * s + app download charge C(s) = 1.29s + 2 The problem asks for C(30): C(3) = 1.29(30) + 2 C(3) = 38.7 +2 C(3) = $[B]40.7[/B]

a music app charges $5 to download the app plus $1.25 per song downloaded. write linear equation to calculate the cost for x number of songs With x songs, our Cost equation C(x) is: C(x) = cost per download * x downloads + app download fee [B]C(x) = 1.25x + 5[/B]

A music app charges 2$ to download the app plus 1.29$ per song download. Write and solve linear equation and a linear equation to find the total cost to download 30 songs Set up the equation C(d) where d is the number of downloads: C(d) = cost per download * d + download fee Plugging in our numbers, we get: C(d) = 1.29d + 2 The problem asks for C(30): C(30) = 1.29(30) + 2 C(30) = 38.7 + 2 C(30) = [B]40.70[/B]

A music camp with 50 students decided to break the students into barbershop quartets to see which combination of four students sounded the best. How many different barbershop quartets can be made with 50 students so that each possible combinations of four is tried? We want 50 combinations of 4. [URL='https://www.mathcelebrity.com/permutation.php?num=50&den=4&pl=Combinations']50C4 [/URL]= 230,300

A music teacher budgets $150 for new books. The minimum cost of a new book is $12. How many books can she buy? 150 / 12 per book = 12.5 So the teacher can buy [B]12 full books[/B].

A national political party has a budget of $30,000,000 to spend on the inauguration of the new president. 16% of the costs will be paid to personnel, 12% of the costs will go toward food, and 10% will go to decorations. How much money will go for personnel, food, and decorations? [LIST] [*]Personnel Costs = 0.16 * 30,000,000 = $4,800,000 [*]Food Costs = 0.12 * 30,000,000 = $3,600,000 [*]Decoration Costs = 0.10 * 30,000,000 = $3,000,000 [/LIST]

A necklace chain costs $15. Beads cost $2.75 each. You spend a total of $28.75 on a necklace and beads before tax. How many beads did you buy in addition to the necklace? [U]Calculate the amount left to spend on beads:[/U] Bead Spend = Total Spend - Necklace Cost Bead Spend = $28.75 - $15 Bead Spend = $13.75 [U]Calculate the number of beads you bought:[/U] Beads Bought = Bead Spend / Cost Per Bead Beads Bought = $13.75 / $2.75 Beads Bought = [B]$5[/B]

A new car worth $24,000 is depreciating in value by $3,000 per year , how many years till the cars value will be $9,000 We have a flat rate depreciation each year. Set up the function D(t) where t is the number of years of depreciation: D(t) = 24000 - 3000t The problem asks for the time (t) when D(t) = 9000. So we set D(t) = 9000 24000 - 3000 t = 9000 To solve for t, [URL='https://www.mathcelebrity.com/1unk.php?num=24000-3000t%3D9000&pl=Solve']we plug this function into our search engine[/URL] and we get: t = [B]5[/B]

A new car worth $30,000 is depreciating in value by $3,000 per year. After how many years will the cars value be $9,000 Step 1, the question asks for Book Value. Let y be the number of years since purchase. We setup an equation B(y) which is the Book Value at time y. B(y) = Sale Price - Depreciation Amount * y We're given Sale price = $30,000, depreciation amount = 3,000, and B(y) = 9000 30000 - 3000y = 9000 To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=30000-3000y%3D9000&pl=Solve']type this in our math engine[/URL] and we get: y = [B]7 [/B] To check our work, substitute y = 7 into B(y) B(7) = 30000 - 3000(7) B(7) = 30000 - 21000 B(7) = 9000 [MEDIA=youtube]oCpBBS7fRYs[/MEDIA]

A new company is projecting its profits over a number of weeks. They predict that their profits each week can be modeled by a geometric sequence. Three weeks after they started, the company's projected profit is $10,985.00 Four weeks after they started, the company's projected profit is $14,280.50 Let Pn be the projected profit, in dollars, n weeks after the company started tracking their profits. a. What is the common ratio of the sequence? b. Calculate the initial value c. Construct a recurrence relation that can be used to model the value of Pn a. 14,280.50/10,985.00 = [B]1.3[/B] b. 3 weeks ago, the Initial value is 10,985/1.3^3 = [B]$5,000 c. Pn = 5000 * 1.3^n[/B]

A new company president is said to have caused the company "to do a 180." Before the new president, the company was losing money. What is the company most likely doing under the new president? A 180 is a completely different direction. Since 180 degrees means the other way, a half-circle, a switch in direction. This means if the company was losing money, after doing a "180", they're making money.

a new savings account starts at $700 at a rate of 1.2% yearly. how much money will be in the account after 8 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=700&nval=8&int=1.2&pl=Annually']balance and interest calculator with annual (yearly) compounding[/URL], we have: [B]770.09[/B]

A non-profit organization is having a couple’s banquet for a fundraiser. The banquet hall will only hold 250 people. The President, Vice-President, two volunteers, and a guest speaker will be working the event. How many couples will be able to attend the banquet? We subtract the 5 people working the event to get: 250 - 5 = 245 A couple is 2 people, so we have 245/2 = 122.5 We round down to [B]122 couples[/B].

a number added to 5 minus p The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We add 5 minus p to this number x: [B]x + 5 - p[/B]

a number added to the product of y and x Since we're already using the variables x and y, we choose another arbitrary variable for the phrase [I]a number.[/I] a The product of y and x isL xy Then add a: [B]a + xy[/B]

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 3 and the coin toss is heads? Write your answer as a fraction in simplest form Let's review the vitals of this question: [LIST] [*]The probability of heads on a fair coin is 1/2. [*]On a fair die, greater than 3 means either 4, 5, or 6. Any die roll face is a 1/6 probability. [*]So we have a combination of outcomes below: [/LIST] Outcomes [LIST=1] [*]Heads and 4 [*]Heads and 5 [*]Heads and 6 [/LIST] For each of the outcomes, we assign a probability. Since the coin flip and die roll are independent, we multiply the probabilities: [LIST=1] [*]P(Heads and 4) = 1/2 * 1/6 = 1/12 [*]P(Heads and 5) = 1/2 * 1/6 = 1/12 [*]P(Heads and 6) = 1/2 * 1/6 = 1/12 [/LIST] Since we want any of those events, we add all three probabilities 1/12 + 1/12 + 1/12 = 3/12 This fraction is not simplified. S[URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F12&frac2=3%2F8&pl=Simplify']o we type this fraction into our search engine, and choose Simplify[/URL]. We get a probability of [B]1/4[/B]. By the way, if you need a decimal answer or percentage answer instead of a fraction, we type in the following phrase into our search engine: [URL='https://www.mathcelebrity.com/perc.php?num=1&den=4&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']1/4 to decimal[/URL] Alternative Answers: [LIST] [*]For a decimal, we get [B]0.25[/B] [*]For a percentage, we get [B]25%[/B] [/LIST]

The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e. Let's choose x. The phrase [I]increased by[/I] means we add 6 to x [B]x +6[/B]

a number increased by 8 and then tripled The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x Increased by 8 means we add 8 to x: x + 8 Then tripled means we multiply the expression x + 8 by 3: [B]3(x + 8)[/B]

a number is twice another number The phrase [I]a number[/I] means an arbitrary variable, let's call it x The phrase [I]another number [/I]means another arbitrary variable, let's call it y Twice means we multiply y by 2: 2y The phrase [I]is [/I]means an equation, so we set x equal to 2y: [B]x = 2y[/B]

A number K is doubled and then increased by 3 K is doubled means we multiply K by 2: 2K Increased by 3 means we add: [B]2K + 3[/B]

A number m is no less than -8 and fewer than 9. No less than means greater than or equal to: m >= -8 Fewer than 9 means less than 9: m < 9 Combine these two inequalities to get [B]-8 <= m < 9[/B]

A number multiplied by 6 and divided by 5 give four more than a number? A number is represented by an arbitrary variable, let's call it x. Multiply by 6: 6x Divide by 5 6x/5 The word "gives" means equals, so we set this equal to 4 more than a number, which is x + 4. 6x/5 = x + 4 Now, multiply each side of the equation by 5, to eliminate the fraction on the left hand side: 6x(5)/5 = 5(x + 4) The 5's cancel on the left side, giving us: 6x = 5x + 20 Subtract 5x from each side [B]x = 20[/B] Check our work from our original equation: 6x/5 = x + 4 6(20)/5 ? 20 + 4 120/5 ?24 24 = 24 <-- Yes, we verified our answer

A number n diminished by 8 gives 12 A number n can be written as n: n Diminished by means we subtract, so we subtract 8 from n: n - 8 The word [I]gives[/I] means an equation, so we set n - 8 equal to 12: [B]n - 8 = 12[/B]

A number n is no less than 2 and no more than 49. This is a compound inequality. Let's break it into parts. Step 1: No more than 49 means 49 or less. Or, less than or equal to 49 <= 49 Step 2: no less than 2 means 2 or greater. Or, greater than or equal to 2 >=2 Writing this in terms of the number n, we have: [B]2 <= n <= 49[/B]

a number of bacteria b tripled The word [I]tripled[/I] means we multiply by 3, so we have: [B]3b[/B]

A number of dogs are to equally share a bag of dog food. If there are [I]n[/I] dogs in the group and one dog eats its share, what percent of the bag is left? Fraction of the bag left is: (n - 1)/n Multiply by 100 to get a percentage: [B]100(n - 1)/n[/B]

a number of pennies splits into 4 equal groups The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We take x and divide it by 4 to get 4 equal groups: [B]x/4[/B]

A number p subtracted by its double is 10 The double of a number means we multiply p by 2: 2p A number p is subtracted by its double p - 2p The phrase [I]is[/I] means equal to, so we set p - 2p equal to 10: [B]p - 2p = 10[/B]

A number t is no less than 30 and fewer than 40. This is a compound inequality. Take it in 3 parts: Step 1: fewer than 40 means less than (does not include 40) t < 40 Step 2: no less than 30 means greater than or equal to t >= 30 Step 3: Combine these 2 statements into one compound inequality: [B]30 <= t < 40[/B]

A number y increased by itself increased by itself means we add the variable y to itself to get our final algebraic expression of: [B]y + y [/B] [I]If[/I] the problem asks you to simplify, we group like terms and get: [B]2y[/B]

A numerical pass code is required to open a car door. The pass code is five digits long and uses the digits 0-9. Numbers may be repeated in the pass code. How many different pass codes exist? 0-9 is 10 digits. Since digits can repeat, we use the fundamental rule of counting to get: 10 * 10 * 10 * 10 * 10 = [B]100,000 different pass codes[/B]

A pack of 12 tortillas cost $3.24. What is the price per tortilla? Price per tortilla = Total Cost / Total Tortillas Price per tortilla = $3.24/12 Price per tortilla = [B]$0.27[/B]

A pack of 36 black sharp tip markers costs $34.49. What is the price of one marker? Set up unit cost: 34.49/36 = [B]$0.96 per marker[/B]

A package of cookies cost $4.00 it has 20 cookies how much does each cookie cost? We want the cost per cookie: $4.00/20 cookies = [B]$0.20 or 20 cents per cookie[/B]

a package of soccer accessories costs $25 for cleats, $14 for shin guards , and $12 for a ball. Write two equivalent expressions for the total cost of 9 accessory package. Then find the cost. Let c be the number of cleats, s be the number of shin guards, and b be the number of balls. We have the following cost function for 9 accessory packages: [B]9(25c + 14s + 12b)[/B] But if we multiply through, we get an equivalent expression: [B]225c + 126s + 108b[/B]

A package that is heavier than 11 lbs and 8 oz will have a label that says HEAVY on it. Gloria packed 6 flowerpots to send to her customers. Each of the flowerpots weighs 1 lb and 12 oz. The packing material weighs 5 oz. Will her package be labeled as HEAVY? Calculate weight of flowerpots: Flowerpot weight = Weight per flowerpot * number of flowerpots Flowerpot weight = 1 lb 12 oz * 6 Flowerpot weight = 6 lb and 72 oz Since 72oz = 72/16 = 4 lbs and 8 oz, we have: Flowerpot weight = 6 lb 8 oz + 4 lbs and 8 oz = 12 lb 16 oz Since 16oz = 1 lb, we have: 13lb Add in the 5 oz of packing material, we have: 13lb 5 oz Since this is greater than 11lb 8oz, the package [B]will be labeled as HEAVY[/B]

A packing machine can package 236 first aid kit each hour. At this rate, find the number of first aid kit package in 24 hours Total First Aid Kits = Kits Per Hour * Number of Hours Total First Aid Kits = 236 * 24 Total First Aid Kits = [B]5,664[/B]

a painter is painting a circular sculpture. The sculpture has a radius of 5 meters. How much paint should she use to paint the sculpture Area of a circle (A) is: A = ?r² Substituting r = 5 into this formula, we get: A = ? * 5² A = [B]25?[/B]

A painter rented a wallpaper steamer at 9 a.m. and returned it at 4 p.m. He paid a total of $28.84. What was the rental cost per hour? 9am to 4pm is 7 hours. Cost per hour = Total Cost / Hours Cost per hour = 28.84 / 7 Cost per hour = [B]$4.12[/B]

A pair of dice are rolled. Find the probability for P(Not 2 or Not 12). P(Not 2 or Not 12) = 1 - P(2) - P(12) P(Not 2 or Not 12) = 1 - [URL='https://www.mathcelebrity.com/2dice.php?gl=1&pl=2&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']1/36[/URL] - [URL='https://www.mathcelebrity.com/2dice.php?gl=1&pl=12&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']1/36[/URL] P(Not 2 or Not 12) = 34/36 [URL='https://www.mathcelebrity.com/fraction.php?frac1=34%2F36&frac2=3%2F8&pl=Simplify']P(Not 2 or Not 12)[/URL] = [B]17/18[/B]

A pair of dice is cast. what is the probablitly that the sum is less than 5? Using our [URL='http://www.mathcelebrity.com/2dice.php?gl=4&pl=5&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']two dice calculator[/URL], we get 1/6 or 16.67%

A pair of dice is rolled. Find the probability of rolling a sum of not less than 5. The phrase [I]not less than[/I] also means greater than or equal to. So we [URL='https://www.mathcelebrity.com/2dice.php?gl=3&pl=5&opdice=1&rolist=+&dby=&ndby=&montect=+']use our 2 dice calculator for a sum roll of 5 or greater[/URL] and we get: [B]5/6[/B]

A pair of jeans are priced at $129.99 there is a discount of 20% and sales tax of 8% what is the final cost [U]Calculate discounted price:[/U] Discounted price = Full price * (100% - discount percent) Discounted price = 129.99 * (100% - 20%) Discounted price = 129.99 * 80% Since 80% = 0.8, we have: Discounted price = 129.99 * 0.8 Discounted price = 103.99 [U]Calculate after tax cost:[/U] Tax Rate = Tax percent/100 Tax Rate = 8/100 Tax Rate = 0.08 After Tax cost = Discounted price * (1 + Tax rate) After Tax cost = 103.99 * (1 + 0.08) After Tax cost = 103.99 * 1.08 After Tax cost = [B]112.31[/B]

A pair of numbers has an HCF (Highest Common Factor) of 3, and an LCM (Lowest Common Multiple) of 45 . If one of the numbers in the pair is 15 , what is the other number? [LIST=1] [*]Prime Factorization for 15 is 3 * 5 [*]Prime Factorization for 9 is 3 * 3 [*]LCM of (9, 15) = 35 [/LIST] [URL='https://www.mathcelebrity.com/gcflcm.php?num1=9&num2=15&num3=&pl=GCF+and+LCM']Check out this link here to see the details[/URL]

A pair of shoes cost $250. The price was decreased by 20%. A week later shoes were mark down again by 25%. What is the final price of the shoes? 20% is 0.2. 25% is 0.25. A decrease is a reduction, so we have: Final Price = 250 * (1 - 0.2) * (1 - 0.25) Final Price = 250 * 0.8 * 0.75 Final Price = [B]150[/B]

A pair of standard dice is rolled, how many possible outcomes are there? We want the number of outcomes in the sample space. The first die has 6 possibilities 1-6. The second die has 6 possibilities 1-6. Our sample space count is 6 x 6 = [B]36 different outcomes [/B] [LIST=1] [*](1, 1) [*](1, 2) [*](1, 3) [*](1, 4) [*](1, 5) [*](1, 6) [*](2, 1) [*](2, 2) [*](2, 3) [*](2, 4) [*](2, 5) [*](2, 6) [*](3, 1) [*](3, 2) [*](3, 3) [*](3, 4) [*](3, 5) [*](3, 6) [*](4, 1) [*](4, 2) [*](4, 3) [*](4, 4) [*](4, 5) [*](4, 6) [*](5, 1) [*](5, 2) [*](5, 3) [*](5, 4) [*](5, 5) [*](5, 6) [*](6, 1) [*](6, 2) [*](6, 3) [*](6, 4) [*](6, 5) [*](6, 6) [/LIST]

A Pairs of fair dice is tossed. What is the probability of not getting a sum 7 or 8? Not a 7 or 8 means 2 - 6 or 9 - 12 [URL='https://www.mathcelebrity.com/2dice.php?gl=5&pl=6&opdice=1&rolist=+&dby=&ndby=&montect=+']Using our 2-dice calculator[/URL], P(2 - 6) = 5/12 [URL='https://www.mathcelebrity.com/2dice.php?gl=3&pl=9&opdice=1&rolist=+&dby=&ndby=&montect=+']Using our 2-dice calculator[/URL], P(9 - 12) = 5/18 Since the sum could be either of these, we add probabilities: P(Not a 7 or 8) = P(2 - 6) + P(9 - 12) P(Not a 7 or 8) = 5/12 + 5/18 [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F12&frac2=5%2F18&pl=Add']P(Not a 7 or 8) [/URL]= [B]25/36[/B]

a paper boy delivers thirteen paper to an apartment complex. if these deliveries compose one-seventh of his route, how many papers does he deliver Let d be the total number of deliveries the paper boy makes on the route. d We're given, d/7 = 13 d = 13 * 7 d = [B]91 [MEDIA=youtube]HRviz-3fn5c[/MEDIA][/B]

A parabola has a Vertex at (4,-2) and a Focus at (6,-2). Find the equation of the parabola and the lotus rectum. Equation of a parabola given the vertex and focus is: ([I]x[/I] – [I]h[/I])^2 = 4[I]p[/I]([I]y[/I] – [I]k[/I]) The vertex (h, k) is 4, -2 The distance is p, and since the y coordinates of -2 are equal, the distance is 6 - 4 = 2. So p = 2 Our parabola equation becomes: (x - 4)^2 = 4(2)(y - -2) [B](x - 4)^2 = 8(y + 2)[/B] Latus rectum of a parabola is 4p, where p is the distance between the vertex and the focus LR = 4p LR = 4(2) [B]LR = 8[/B]

A parallelogram has a perimeter of 48 millimeters. Two of the sides are each 20 millimeters long. What is the length of each of the other two sides? 2 sides * 20 mm each is 40 mm subtract this from the perimeter of 48: 48 - 40 = 8 Since the remaining two sides equal each other, their length is: 8/2 = [B]4mm[/B]

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. What is the length of each of the other two sides? A parallelogram is a rectangle bent on it's side. So we have the perimeter formula P below: P = 2l + 2w We're given w = 17 and P = 54. So we plug this into the formula for perimeter: 2l + 2(17) = 54 2l + 34 = 54 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B34%3D54&pl=Solve']equation calculator[/URL], we get [B]l = 10[/B].

A park bench is 6 feet long. Convert the length to inches We [URL='https://www.mathcelebrity.com/linearcon.php?quant=6&pl=Calculate&type=foot']type in 6 feet into our search engine[/URL]. We get: 6 feet = [B]72 inches[/B]

A parking garage charges $5 plus $2 per hour. You have $16 to spend for parking. How many hours can you park? Subtract the flat rate to get the amount you have for hourly parking: 16 - 5 = 11 So we divide 11 dollars to park by 2 dollars per hour to get: 11/2 [B]5.5 hours[/B]

A parking lot has seventy-one parking spaces numbered from 1 to 71. There are no cars in the parking lot when Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she parks is greater than or equal to 31? Greater than or equal to means including 31 all the way through 71 31-71 is 40 spaces P(s>=31) = [B]40/71[/B]

A parking lot has sixty-eight parking spaces numbered from 1 to 68. There are no cars in the parking lot when Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she parks is greater than or equal to 21? We want P(X>=21). This is also found by taking 1 - P(X <= 20). P(X<=20) = 20/68. Reduced using a [URL='http://www.mathcelebrity.com/gcflcm.php?num1=20&num2=68&num3=&pl=GCF']GCF of 4[/URL], we get 5/17. P(X >=21) = 1 - 5/17 = [B]12/17[/B]

A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of each coin are there? Let d = the number of dimes and q = the number of quarters. We have two equations: (1) d + q = 146 (2) 0.1d + 0.25q = 27.05 Rearrange (1) into (3) solving for d (3) d = 146 - q Substitute (3) into (2) 0.1(146 - q) + 0.25q = 27.05 14.6 - 0.1q + 0.25q = 27.05 Combine q's 0.15q + 14.6 = 27.05 Subtract 14.6 from each side 0.15q = 12.45 Divide each side by 0.15 [B]q = 83[/B] Plugging that into (3), we have: d = 146 - 83 [B]d = 63[/B]

A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables is $37. The total cost to rent 2 chairs and 6 tables is $64. What is the cost to rent each chair and each table? Let c be the cost of renting one chair and t be the cost of renting one table. We're given two equations: [LIST=1] [*]5c + 3t = 37 [*]2c + 6t =64 [/LIST] We have a system of equations. Using our system of equations calculator, we can solve this problem any of 3 ways below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] All 3 methods give the same answer: [LIST] [*][B]Chairs (c) cost $1.25[/B] [*][B]Tables (t) cost $10.25[/B] [/LIST]

A passenger train left station A at 6:00 P.M. Moving with the average speed 45 mph, it arrived at station B at 10:00 p.m. A transit train left from station A 1 hour later than the passenger train, but it arrived at the station B at the same time with the passenger train. What was the average speed of the transit train? [U]Passenger Train[/U] [LIST] [*]45 miles per hour and it got there in 4 hours. [/LIST] Using our formula D = rt where: [LIST] [*]D = Distance [*]r = rate [*]t = time [/LIST] [LIST] [*]D = rt [*]D = 45(4) [*]D = 180 miles from Station A to Station B [/LIST] Transit Train [LIST] [*]It has to go the same distance, 180 miles, so D = 180 [*]It made it there in 3 hours. This is r [*]We want to solve for t [/LIST] D = rt 180 = 3r Divide each side by 3 [B]r = 60 miles per hour[/B]

A patient’s temperature was 103°. The temperature then fell by 4° and later rose by 2°. What was the patient’s final temperature Start with 103 Fell by 4 means we subtract 4: 103 - 4 = 99 Rose by 2 means we add 2L 99 + 2 = [B]101[/B]

A pawn broker buys a tv and a computer for $600. He sells the computer at a markup of 30% and the tv at a markup of 20%. If he makes a profit of $165 on the sale of the two items, what did he pay for the computer? Let c be the price of the computer and t be the price of the tv. WE have: [LIST=1] [*]c + t = 600 [*]c(1.3) + t(1.2) = 765 <-- (600 + 165 profit) [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+600&term2=1.3c+%2B+1.2t+%3D+765&pl=Cramers+Method']simultaneous equation calculator[/URL], we get: [B]c = 450[/B] t = 150

A peanut vendor has initial start up costs of $7600 and variable costs of $0.70 per bag of peanuts. What is the cost function? We set up the cost function C(b) where b is the number of bags: C(b) = Cost per bag * b + Start up costs Plugging in our numbers, we get: [B]C(b) = 0.70b + 7600[/B]

A penny has a diameter of 19 millimeters. What is the radius of the penny. D = 2r To solve for r, we divide each side by 2: r = D/2 Plugging in D = 19, we get: r = [B]19/2 or 9.5[/B]

A person has $13,000 invested in stock A and stock B. Stock A currently sells for $20 a share and stock B sells for $90 a share. If stock B triples in value and stock A goes up 50%, his stock will be worth $33,000. How many shares of each stock does he own? Set up the given equations, where A is the number of shares for Stock A, and B is the number of shares for Stock B [LIST=1] [*]90A + 20B = 13000 [*]3(90A) + 1.5(20B) = 33000 <-- [I]Triple means multiply by 3, and 50% gain means multiply by 1.5[/I] [/LIST] Rewrite (2) by multiplying through: 270A + 30B = 33000 Using our simultaneous equations calculator, we get [B]A = 100 and B = 200[/B]. Click the links below to solve using each method: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Cramers+Method']Cramers Method[/URL] [/LIST] Check our work using equation (1) 90(100) + 20(200) ? 13,000 9000 + 4000 ? 13,000 13000 = 13000

A person invested 30,000 in stocks and bonds. Her investment in bonds is 2000 more than 1-third her investments in stocks. How much did she invest in stocks? How much did she invest in bonds? Let the stock investment be s, and the bond investment be b. We're given: [LIST=1] [*]b + s = 30000 [*]b = 1/3s + 2000 [/LIST] Plug in (2) to (1): 1/3s + 2000 + s = 30000 Group like terms: (1/3 + 1)s + 2000 = 30000 Since 1 = 3/3, we have: 4/3s + 2000 = 30000 Subtract 2000 from each side: 4/3s + 2000 - 2000 = 30000 - 2000 Cancel the 2000's on the left side, we get: 4/3s = 28000 [URL='https://www.mathcelebrity.com/1unk.php?num=4%2F3s%3D28000&pl=Solve']Typing this equation into our calculator[/URL], we get: s = [B]21,000[/B]

A person invests $500 in an account that earns a nominal yearly rate of 4%. How much will this investment be worth in 10 years? If the interest was applied four times per year (known as quarterly compounding), calculate how much the investment would be worth after 10 years. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=500&nval=10&int=4&pl=Annually']compound interest calculator[/URL], $500 @ 4% for 10 years is: $[B]740.12 [/B] Using [URL='https://www.mathcelebrity.com/compoundint.php?bal=500&nval=40&int=4&pl=Quarterly']quarterly compounding in our compound interest calculator[/URL], we have 10 years * 4 quarters per year = 40 periods, so we have: [B]$744.43[/B]

A person invests $9400 in an account at 5% interest compound annually. When will the value of the investment be $12,800. Let's take it one year at a time: Year 1: 9,400(1.05) = 9,870 Year 2: 9,870(1.05) = 10,363.50 Year 3: 10,363.50(1.05) = 10,881.68 Year 4: 10.881.68(1.05) = 11,425.76 Year 5: 11,425.76(1.05) = 11,997.05 Year 6: 11,997.05(1.05) = 12.596.90 Year 7: 12,596.90(1.05) = 13,226.74 So it take [B][U]7 years[/U][/B] to cross the $12,800 amount.

A person is earning 600 per day to do a certain job. Express the total salary as a function of the number of days that the person works. Set up the salary function S(d) where d is the number of days that the person works: S(d) = Daily Rate * d [B]S(d) = 600d[/B]

A person paid $60 for a vase at an estate auction. She resold it to an antiques dealer for $50. What was her profit or loss She lost, since the sale price was less than the purchase price. The loss is calculated as: 50 - 60 = [B]-$10[/B]

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuously. Using the formula V = Pe^{rt}V=Pe^rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 20 years Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=230&int=6.8&t=20&pl=Continuous+Interest']continuous compounding calculator[/URL], we get: V = [B]896.12[/B]

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV = Pe^{rt} V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years. Substituting our given numbers in where P = 96,300, r = 0.028, and t = 7, we get: V = 96,300 * e^(0.028 * 7) V = 96,300 * e^0.196 V = 96,300 * 1.21652690533 V = [B]$117,151.54[/B]

A person that runs for 15 minutes burns 180 calories. If someone burns 300 calories, how long did tgey run for Set up a proportion of minutes to calories where m is the number of minutes per 300 calories: 15/180 = m/300 To solve for m, [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=m&den1=180&den2=300&propsign=%3D&pl=Calculate+missing+proportion+value']we type this proportion into our search engine[/URL] and we get: m = [B]25[/B]

A person who had $1,000,000 gave $100 to charity. How much must a student who has $100 give to charity to give proportionally the same as the millionaire? Set up a proportion of wealth owned to donation where x is the amount the student gives: 1000000/100 = 100/x Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=1000000&num2=100&den1=100&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: [B]x = 0.01[/B]

A person will devote 31 years to be sleeping and watching tv. The number of years sleeping will exceed the number of years watching tv by 19. How many years will the person spend on each of these activities Let s be sleeping years and t be tv years, we have two equations: [LIST=1] [*]s + t = 31 [*]s = t + 19 [/LIST] Substitute (2) into (1) (t + 19) + t = 31 Combine like terms: 2t + 19 = 31 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2t%2B19%3D31&pl=Solve']equation solver[/URL], we get [B]t = 6[/B]. Using equation (2), we have s = 6 + 19 s = [B]25[/B]

A person works 46 hours in one week and earns 440 dollars. They get time and a half for over 40 hours. What is their hourly salary? Let the hourly rate be r. Since time and a half is 1.5 the hourly rate, We're given: 40r + 6(1.5r) = 440 40r + 9r = 440 to solve this equation for r, we type it in our search engine and we get: r = [B]$8.98[/B]

A pet store has 10 rabbits. What’s the probability that they have at least 1 female rabbit. At least 1 female rabbit means we [U]must[/U] have a female rabbit First, we calculate the probability of 0 females A rabbit can be either male or female with equal probabilities of 1/2 or 0.5. Since each birth is independent, we can multiply to get the probability of all males: P(MMMMMMMMMM) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 P(MMMMMMMMMM) = 1/1024 Then, we subtract this probability from 1 to get the probability of [B]at least[/B] one female: P(At least one F) = 1 - 1/1024 Since 1 = 1024/1024, we have: P(At least one F) = (1024 - 1)/1024 P(At least one F) = [B]1023/1024[/B]

A pet supply chain called pet city has 15 hamsters and 12 gerbils for sale at its seaside location. At its livingston location there are 19 hamsters and 10 gerbils. Which location has a lower ratio of hamsters to gerbils? Seaside ratio 15/12 = 1.25 Livingston ratio 19/10 = 1.9 Since 1.25 < 1.9, Seaside has the lower ratio of hamsters to gerbils

A Petri dish contains 2000. The number of bacteria triples every 6 hours. How many bacteria will exist after 3 days? Determine the amount of tripling periods: [LIST] [*]There are 24 hours in a day. [*]24 hours in a day * 3 days = 72 hours [*]72 hours / 6 hours tripling period = 12 tripling periods [/LIST] Our bacteria population function B(t) where t is the amount of tripling periods. Tripling means we multiply by 3, so we have: B(t) = 2000 * 3^t with t = 12 tripling periods, we have: B(12) = 2000 * 3^12 B(12) = 2000 * 531441 B(12) = [B]1,062,882,000[/B]

A phone company charges a $30 usage fee $15 per 1GB of data. Write an expression that describes the monthly charge and use d to represent data We multiply gigabyte fee by d and add the usage fee: [B]15d + 30[/B]

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 8 cents per minute of use. In Plan B, the customer pays a monthly fee of $1.50 and then an additional 7 cents per minute of use. For what amounts of monthly phone use will Plan A cost more than Plan B? Set up the cost equations for each plan. The cost equation for the phone plans is as follows: Cost = Cost Per Minute * Minutes + Monthly Fee Calculate the cost of Plan A: Cost for A = 0.08m + 0. <-- Since there's no monthly fee Calculate the cost of Plan B: Cost for B = 0.07m + 1.50 The problem asks for what amounts of monthly phone use will Plan A be more than Plan B. So we set up an inequality: 0.08m > 0.07m + 1.50 [URL='https://www.mathcelebrity.com/1unk.php?num=0.08m%3E0.07m%2B1.50&pl=Solve']Typing this inequality into our search engine[/URL], we get: [B]m > 150 This means Plan A costs more when you use more than 150 minutes per month.[/B]

A photographer snapped 224 photos over a period of 15 days. At this rate, how many would he take in 45 days? Set up a proportion of photos to days where p is the number of photos snapped in 45 days: 224/15 = p/45 To solve this proportion for p, we [URL='https://www.mathcelebrity.com/prop.php?num1=224&num2=p&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get; p = [B]672[/B]

A piece of gym equipment which cost 450 including vat last year is now selling at 500 excluding vat. Calculate the percentage increase. Increase = (New Price - Old Price)/Old Price Increase = (500-450)/450 50/450 = 0.1111 To get the percentage, multiply by 100 [B]11.11%[/B]

A piece of pipe is 144 inches long. After 4 pieces, each 33 inches long are cut, what length of pipe is left? Calculate the length of cut pipe: 4 pieces * 33 inches per piece = 132 inches The remaining pipe is found by subtracting the original pipe length by the cut pipe length: 144 - 132 = [B]12 inches[/B]

a piece of ribbon is y cm long. Ashley cut it into 4 equal pieces to do her 4 sisters hair. write an expression for the amount of ribbon used for each sister We take y cm and divide it equal among 4 sisters: [B]y/4[/B]

A piggy bank contains $90.25 in dimes and quarters. Which equation represents this scenario? Let x represent the number of dimes, and let y represent the number of quarters. Since amount = cost * quantity, we have: [B]0.1d + 0.25q = 90.25[/B]

A pile of coins, consisting of quarters and half dollars, is worth 11.75. If there are 2 more quarters than half dollars, how many of each are there? Let h be the number of half-dollars and q be the number of quarters. Set up two equations: (1) q = h + 2 (2) 0.25q + 0.5h = 11.75 [U]Substitute (1) into (2)[/U] 0.25(h + 2) + 0.5h = 11.75 0.25h + 0.5 + 0.5h = 11.75 [U]Group h terms[/U] 0.75h + 0.5 = 11.75 [U]Subtract 0.5 from each side[/U] 0.75h = 11.25 [U]Divide each side by h[/U] [B]h = 15[/B] [U]Substitute h = 15 into (1)[/U] q = 15 + 2 [B]q = 17[/B]

A plain chocolate bar weights 40 grams. It contains 12 grams of fat. A milk chocolate bar is 30 grams. It contains 10 grams of fat. Which chocolate bar has the highest proportion of fat? Calculate the proportion of fat grams for each chocolate bar: [LIST] [*]Plain chocolate: 12/40 = 3/10 = 30% [*]Milk chocolate: 10/30 = 1/3 = 33% [/LIST] [B]Milk chocolate[/B] has the higher proportion of fat grams.

A plane is flying at an altitude of 45,000 feet. It begins to drop in altitude 3,000 feet per minute. What is the slope in this situation? Set up a graph where minutes is on the x-axis and altitude is on the y-axis. [LIST=1] [*]Minute 1 = (1, 42,000) [*]Minute 2 = (2, 39,000) [*]Minute 3 = (3, 36,000) [*]Minute 4 = (4, 33,000) [/LIST] You can see for every 1 unit move in x, we get a -3,000 unit move in y. Pick any of these 2 points, and [URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=42000&slope=+2%2F5&xtwo=2&ytwo=39000&bvalue=+&pl=You+entered+2+points']use our slope calculator[/URL] to get: Slope = -[B]3,000[/B]

A plane takes off at 11:53 and lands at 9 minutes to 2. How long is the flight? 9 minutes to 2 is 1:51 11:53 to 1:53 is exactly 2 hours. 1:51 is 2 minutes less than 1:53. So we have [B]1 hour and 58 minutes[/B]

A plant is 15 cm high and grows 4.5 cm every month. How many months will it take until the plant is 27.5 cm We set up the height function H(m) where m is the number of months since now. We have: H(m) = 4.5m + 15 We want to know when H(m) = 27.5, so we set our H(m) function equal to 27.5: 4.5m + 15 = 27.5 To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.5m%2B15%3D27.5&pl=Solve']type this equation into our search engine[/URL] and we get: m = 2.78 So we round up to [B]3 whole months[/B]

A playground requires 2,459 pounds of sand to cover the ground. If the sand comes in 60-pound bags, how many bags are needed Number of bags = Total Weight of Sand / Pounds per bag Number of bags = 2459/60 Number of bags = 40.9833

A playing card is 7 centimeters wide and 10 centimeters tall. What is its area? A playing card has a rectangle shape, so the area is l x w. A = l x w A = 10 cm x 7 cm A =[B] 70 cm^2[/B]

A plumber charges $45 for a house call plus $25 for each hour worked.Let h represent the number of hours worked. Write the expression that shows how much a plumber charges for a job. Then find how much the plumbers charges for a job lasting 4 hours [U]Set up the cost function C(h) where h is the number of hours:[/U] C(h) = Hours worked * hourly rate + house call fee [B]C(h) = 25h + 45 <-- This is the expression for how much the plumber charges for a job [/B] [U]Now determine how much the plumber charges for a job lasting 4 hours[/U] We want C(4) C(4) = 25(4) + 45 C(4) = 100 + 45 C(4) = [B]$145[/B]

A plumber charges $50 to visit a house plus $40 for every hour of work. Set up the cost function in terms of hours (h) using the flat fee of $50 [B]C(h) = 40h + 50[/B]

A plumber makes a starting $36,000 a year. They get paid semimonthly. They have a health insurance premium of $74.28 and $25 in union dues each paycheck. 1. What is their semimonthly salary? Calculate the number of semi-monthly periods per year: Semi-monthly periods per year = 12 Months per year * 2 Semi-monthly periods per year = 24 Calculate semi-monthly salary amount: Semi-monthly salary amount = Annual Salary / Semi-monthly periods per year Semi-monthly salary amount = $36,000 / 24 Semi-monthly salary amount = $1,500 Now, calculate the net pay each semimonthly period: Net pay = Semi-monthly salary amount - Health Insurance Premium - Union Dues Net pay = $1,500 - $74.28 - $25 Net pay = [B]$1,400.72[/B]

A police officer is trying to catch a fleeing criminal. The criminal is 20 feet away from the cop, running at a rate of 5 feet per second. The cop is running at a rate of 6.5 feet per second. How many seconds will it take for the police officer to catch the criminal? Distance = Rate * Time [U]Criminal:[/U] 5t + 20 [U]Cop[/U]: 6.5t We want to know when their distances are the same (cop catches criminal). So we set the equations equal to each other: 5t + 20 = 6.5t To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=5t%2B20%3D6.5t&pl=Solve']we type it in our search engine[/URL] and we get: t = 13.333 seconds

A pollster selected 4 of 7 people. How many different groups of 4 are possible? We want to use the combinations formula. [URL='https://www.mathcelebrity.com/permutation.php?num=7&den=4&pl=Combinations']So we type 7C4 into our search engine[/URL]. This is also known as 7 choose 4. We get [B]35[/B] different groups.

A pool is 5 meters wide and 21 meter long what is the area of the pool? A pool is a rectangle. So the area for a rectangle is: A = lw [I]where l is the length and w is the width.[/I] [URL='https://www.mathcelebrity.com/rectangle.php?l=21&w=5&a=&p=&pl=Calculate+Rectangle']Plugging in our width of 5 and length of 21 to our rectangle calculator[/URL], we get: A = [B]105 m^2[/B]

A population grows at 6% per year. How many years does it take to triple in size? With a starting population of P, and triple in size means 3 times the original, we want to know t for: P(1.06)^t = 3P Divide each side by P, and we have: 1.06^t = 3 Typing this equation into our search engine to solve for t, we get: t = [B]18.85 years[/B] Note: if you need an integer answer, we round up to 19 years

A population of 200 doubles in size every hour. What is the rate of growth of the population after 2.5 hours? Time 1: 400 Time 2: 800 Time 3: 1200 (Since it's only 1/2 of a period)

A population of wolves on an island starts at 5 if the population doubles every 10 years, what will be the population in 90 years? If the population doubles every 10 years, we have 90/10 = 9 doubling periods. Our population function P(t) is where t is the doubling period P(t) = 5(2^t) The problem asks for P(9): P(9) = 5(2^9) P(9) = 5(512) P(9) = [B]2,560[/B]

A postcard is 4 inches tall and 5 inches wide. What is its area? A postcard is a rectangle. The area is 4 x 5 = [B]20 square inches[/B]

A pot of soup, currently 66°C above room temperature, is left out to cool. If that temperature difference decreases by 10% per minute, then what will the difference be in 17 minutes? We set up the temperature function T(m), where m is the number of minutes of cooling. With 10% = 0.1, we have: T(m) = 66 * (1 - 0.10)^m The problem asks for T(17) [U]and[/U] the difference temperature: T(17) = 66 * 0.9^17 T(17) = 66 * 0.16677181699 T(17) = [B]11.01C[/B] [B][/B] [U]Calculate the difference in temperature[/U] Difference = Starting Temperature - Ending Temperature Difference = 66 - 11.01 Difference = 66 - 11.01 = [B]54.99 ~ 55[/B]

A pound of chocolate costs 6 dollars. Greg buys p pounds. Write an equation to represent the total cost c that Greg pays Since cost = price * quantity, we have: [B]c = 6p[/B]

A pound of chocolate costs 6 dollars. Ryan buys p pounds. Write an equation to represent the total cost c that Ryan pays Since cost = Price * Quantity, we have: [B]c = 6p[/B]

A pound of chocolate costs 7 dollars. Hong buys p pounds . Write an equation to represent the total cost c that Hong pays Our equation is the cost of chocolate multiplied by the number of pounds: [B]c = 7p[/B]

A pound of coffee costs $14.99. What is the cost per ounce? 1 pound = 16 ounces. So we have: $14.99/16 ounces [B]$0.94 per ounce[/B]

A pound of popcorn is popped for a class party. The popped corn is put into small popcorn boxes that each hold 120 popped kernels. There are 1,600 kernels in a pound of unpopped popcorn. If all the boxes are filled except for the last box, how many boxes are needed and how many popped kernels are in the last partially filled box? Using modulus calculator, we know [URL='https://www.mathcelebrity.com/modulus.php?num=1600mod120&pl=Calculate+Modulus']1600 mod 120[/URL] gives us [B]13 full boxes[/B] of unpopped popcorn. We also know that 13*120 = 1,560. Which means we have 1,600 - 1,560 = [B]40[/B] popped kernels left in the last box. FB Live: [URL='https://www.facebook.com/plugins/video.php?href=https%3A%2F%2Fwww.facebook.com%2FMathCelebrity%2Fvideos%2F10156733590718291%2F&show_text=0&width=560']https://www.facebook.com/plugins/video.php?href=https://www.facebook.com/MathCelebrity/videos/10156733590718291/&show_text=0&width=560[/URL]

A pound-and-a-half of candy costs $1.65. Find the cost of one pound 1.65/1.5 = [B]$1.10 per pound[/B]

A pretzel factory has daily fixed costs of $1100. In addition, it costs 70 cents to produce each bag of pretzels. A bag of pretzels sells for $1.80. [U]Build the cost function C(b) where b is the number of bags of pretzels:[/U] C(b) = Cost per bag * b + Fixed Costs C(b) = 0.70b + 1100 [U]Build the revenue function R(b) where b is the number of bags of pretzels:[/U] R(b) = Sale price * b R(b) = 1.80b [U]Build the revenue function P(b) where b is the number of bags of pretzels:[/U] P(b) = Revenue - Cost P(b) = R(b) - C(b) P(b) = 1.80b - (0.70b + 1100) P(b) = 1.80b = 0.70b - 1100 P(b) = 1.10b - 1100

A principal of $3300 is invested at 3.25% interest, compounded annually. How much will the investment be worth after 10 years? [URL='https://www.mathcelebrity.com/compoundint.php?bal=3300&nval=10&int=3.25&pl=Annually']Using our balance calculator with compound interest[/URL], we get: [B]$4,543.75[/B]

A printer can print 25 pages per minute. At this rate, how long will it take to print 2000 pages? Let m be the number of minutes it takes to print 2,000 pages. We have the equation: 25m = 2000 [URL='https://www.mathcelebrity.com/1unk.php?num=25m%3D2000&pl=Solve']Type this equation into our search engine[/URL], and we get: m = 80

a printer charges a $30 setup fee plus $2.00 per ticket. Write an algebraic expression for the cost of t tickets. What is the cost of 225 tickets? Algebraic Expression: Cost per ticket * t + set up fee [B]2t + 30[/B] How much for t = 225? 2(225) + 30 450 + 30 [B]480[/B]

A printer prints 2 photos each minute. Let P be the number of photos printed in M minutes. Write an equation relating P to M. Set up the equation P(M). [B]P(M) = 2M[/B] Read this as for every minute that goes by, 2 photos are printed.

A private high school charges $36,400 for tuition, but this figure is expected to rise 10% per year. What will tuition be in 10 years? Let the tuition be T(y) where y is the number of years from now. We've got: T(y) = 36400 * (1.1)^y The problem asks for T(10) T(10) = 36400 * (1.1)^10 T(10) = 36400 * 2.5937424601 T(10) = [B]94,412.23[/B]

A private high school charges $52,200 for tuition, but this figure is expected to rise 7% per year. What will tuition be in 3 years? We have the following appreciation equation A(y) where y is the number of years: A(y) = Initial Balance * (1 + appreciation percentage)^ years Appreciation percentage of 7% is written as 0.07, so we have: A(3) = 52,200 * (1 + 0.07)^3 A(3) = 52,200 * (1.07)^3 A(3) = 52,200 * 1.225043 A(3) = [B]63,947.25[/B]

A private jet flies the same distance in 4 hours that a commercial jet flies in 2 hours. If the speed of the commercial jet was 154 mph less than 3 times the speed of the private jet, find the speed of each jet. Let p = private jet speed and c = commercial jet speed. We have two equations: (1) c = 3p - 154 (2) 4p =2c Plug (1) into (2): 4p = 2(3p - 154) 4p = 6p - 308 Subtract 4p from each side: 2p - 308 = 0 Add 308 to each side: 2p = 308 Divide each side by 2: [B]p = 154[/B] Substitute this into (1) c = 3(154) - 154 c = 462 - 154 [B]c = 308[/B]

A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?" Let the number of children be c. Let the number of parents be p We're given: [LIST=1] [*]c = p + 9 [I](9 more children than parents)[/I] [*]c + p = 25 [/LIST] to solve this system of equations, we plug equation (1) into equation (2) for c: (p + 9) + p = 25 Group like terms: 2p + 9 = 25 To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=2p%2B9%3D25&pl=Solve']type it in our search engine[/URL] and we get: p = [B]8[/B]

A professor assumed there was a correlation between the amount of hours people were expose to sunlight and their blood vitamin D level. The null hypothesis was that the population correlation was__ a. Positive 1.0 b. Negative 1.0 c. Zero d. Positive 0.50 [B]c. Zero[/B] Reason: Since the professor wanted to assume a correlation (either positive = 1.0 or negative = -1.0), then we take the other side of that assumption for our null hypothesis and say that there is no correlation (Zero)

A professor wants to test all possible pairwise comparisons among three means. If we need to maintain an experiment-wise alpha of 0.05, what is the error rate per comparison after applying Bonferroni correction? We are given: [LIST] [*]? = 0.05 [*]n = 3 [/LIST] Bonferroni Correction = ?/n Bonferroni Correction = 0.05/3 Bonferroni Correction = [B]0.01666666667[/B]

A project requires a $5000 investment. It pays out $1000 at year 1, $2000 at year 2, $3000 at year 3. The discount rate is 5%. Should you invest? Using our [URL='https://www.mathcelebrity.com/npv.php?matrix1=0%2C-5000%0D%0A1%2C1000%0D%0A2%2C2000%0D%0A3%2C3000&irr=5&pl=NPV']NPV calculator,[/URL] we get: NPV = 357.94. Because NPV > 0, we [B]should invest [MEDIA=youtube]jXvwCTDwQ1o[/MEDIA][/B]

A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joe's phone bill was $60 under this promotional deal, how many minutes of phone calls did he make? Round to the nearest integer if necessary. Let m be the number of minutes Joe used. We have a cost function of: C(m) = 0.05m + 15 If C(m) = 60, then we have: 0.05m + 15 = 60 [URL='https://www.mathcelebrity.com/1unk.php?num=0.05m%2B15%3D60&pl=Solve']Typing this equation into our search engine[/URL], we get: m = [B]900[/B]

A property sold for $198,000 with a listing commission of 8%. The selling office is to receive 40% of the total commission. How much will the listing salesperson receive if she is paid 60% of the amount retained by listed broker. [U]Calculate commission amount:[/U] Commission amount = Sale Price * Commission Percent Commission amount = 198,000 * 8% [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=8&den1=198000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Commission amount [/URL]= 15,840 [U]Calculate listing salesperson commission amount:[/U] Listing salesperson commission amount = Commission Amount * Listing salesperson Percent Listing salesperson commission amount = 15,840 * 60% [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=60&den1=15840&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Listing salesperson commission amount[/URL] = [B]9,504[/B]

A quantity x is at least 10 and at most 20 The phrase [I]at most[/I] means less than or equal to The phrase [I]at least[/I] means greater than or equal to. So we have the following inequality [B]10 <= x <= 20[/B]

A quarter of a number is greater than or equal to 38. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. A quarter of a number means 1/4, so we have: x/4 The phrase [I]is greater than or equal to[/I] means an inequality, so we use the >= sign in relation to 38: [B]x/4 >= 38 <-- This is our algebraic expression [/B] If you want to solve this inequality, [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=38&propsign=%3E%3D&den1=4&den2=1&pl=Calculate+missing+proportion+value']we type it in the search engine[/URL] to get: x >= [B]152[/B]

A quarter of the learners in a class have blond hair and two thirds have brown hair. The rest of the learners in the class have black hair. How many learners in the class if 9 of them have blonde hair? Total learners = Blond + Brown + Black Total Learners = 1/4 + 2/3 + Black Total Learners will be 1, the sum of all fractions 1/4 + 2/3 + Black = 1 Using common denominators of 12, we have: 3/12 + 8/12 + Black = 12/12 11/12 + Black = 12/12 Subtract 11/12 from each side: Black = 1/12 Let t be the total number of people in class. We are given for blondes: 1/4t = 9 Multiply each side by 4 [B]t = 36[/B] Brown Hair 2/3(36) = 24 Black Hair 1/12(36) = 3

A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime. [B]2902 < u < 3098[/B] using our [URL='http://www.mathcelebrity.com/normconf.php?n=100&xbar=3000&stdev=500&conf=95&rdig=4&pl=Large+Sample']confidence interval for the mean calculator[/URL]

A random sample of 144 with a mean of 100 and a standard deviation of 70 is known from a population of 1,000. What is the 95% confidence interval for the unknown population? [URL='http://www.mathcelebrity.com/normconf.php?n=144&xbar=100&stdev=70&conf=95&rdig=4&pl=Large+Sample']Large Sample Confidence Interval Mean Test[/URL] [B]88.5667 < u < 111.4333[/B]

A random sample of 149 students has a test score average of 61 with a standard deviation of 10. Find the margin of error if the confidence level is 0.99. (Round answer to two decimal places) Using our [URL='https://www.mathcelebrity.com/normconf.php?n=149&xbar=61&stdev=10&conf=99&rdig=4&pl=Large+Sample']confidence interval of the mean calculator[/URL], we get [B]58.89 < u < 63.11[/B]

A random sample of 25 customers was chosen in CCP MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes). Checkout Time (in minutes) | Frequency | Relative Frequency 1.0 - 1.9 | 2 | ? 2.0 - 2.9 | 8 | ? 3.0 - 3.9 | ? | ? 4.0 - 5.9 | 5 | ? Total | 25 | ? (a) Complete the frequency table with frequency and relative frequency. (b) What percentage of the checkout times was less than 3 minutes? (c)In what class interval must the median lie? Explain your answer. (d) Assume that the largest observation in this dataset is 5.8. Suppose this observation were incorrectly recorded as 8.5 instead of 5.8. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Why? (a) [B]Checkout Time (in minutes) | Frequency | Relative Frequency 1.0 - 1.9 | 2 | 2/25 2.0 - 2.9 | 8 | 8/25 3.0 - 3.9 | 10 (since 25 - 5 + 8 + 2) = 10 | 10/25 4.0 - 5.9 | 5 | 5/25 Total | 25 | ?[/B] (b) (2 + 8)/25 = 10/25 = [B]40%[/B] c) [B]3.0 - 3.9[/B] since 2 + 8 + 10 + 5 = 25 and 13 is the middle value which occurs in the 3.0 - 3.9 interval (d) [B]Mean increases[/B] since it's a higher value than usual. Median would not change as the median is the most frequent distribution and assuming the 5.8 is only recorded once.

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.22 hours, with a standard deviation of 2.31 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.44 hours, with a standard deviation of 1.74 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children left parenthesis mu 1 minus mu 2 right parenthesis (?1 - ?2). Using our confidence interval for [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+40&xbar1=+5.22&stdev1=+2.31&n2=+40&xbar2=+4.44&stdev2=1.74&conf=+90&pl=Mean+Diff+Conf.+Interval+%28Large+Sample%29']difference of means calculator[/URL], we get: [B]0.0278 < ?1 - ?2 < 1.5322[/B]

A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.22 hours, with a standard deviation of 2.31 hours. A random sample of 40 adults with children under the age of 18 results in a mean daily leisure time of 4.29 hours, with a standard deviation of 1.58 hours. Construct and interpret a 90% confidence interval for the mean difference in leisure time between adults with no children and adults with children (u1 - u2) What is the interpretation of this confidence interval? A. There is 90% confidence that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours B. There is a 90% probability that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours C. There is 90% confidence that the difference of the means is in the interval. Conclude that there is a significant difference in the number of leisure hours D. There is a 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours 0.2021 < u1 - u2 < 1.6579 using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+40&xbar1=+5.22&stdev1=2.31&n2=40&xbar2=4.29&stdev2=1.58&conf=+90&pl=Mean+Diff+Conf.+Interval+%28Large+Sample%29']difference of means confidence interval calculator[/URL] [B]Choice D There is a 90% probability that the difference of the means is in the interval. Conclude that there is insufficient evidence of a significant difference in the number of leisure hours[/B]

A random sample of n = 10 flash light batteries with a mean operating life X=5 hr. And a sample standard deviation S = 1 hr. is picked from a production line known to produce batteries with normally distributed operating lives. What's the 98% confidence interval for the unknown mean of the working life of the entire population of batteries? [URL='http://www.mathcelebrity.com/normconf.php?n=10&xbar=5&stdev=1&conf=98&rdig=4&pl=Small+Sample']Small Sample Confidence Interval for the Mean test[/URL] [B]4.1078 < u < 5.8922[/B]

A random sample of STAT200 weekly study times in hours is as follows: 2 15 15 18 30 Find the sample standard deviation. (Round the answer to two decimal places. Show all work.) [B]9.98[/B] using [URL='http://www.mathcelebrity.com/statbasic.php?num1=+2,15,15,18,30&num2=+0.2,0.4,0.6,0.8,0.9&pl=Number+Set+Basics']our standard deviation calculator[/URL]

A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit a. Calculate the mean and standard deviation of this distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.) Using our [URL='http://www.mathcelebrity.com/uniform.php?a=+670&b=+770&x=+680&t=+3&pl=PDF']uniform distribution calculator[/URL], we get: [B]Mean = 720 Standard deviation = 28.87 [/B] b. What is the probability that X is less than 730? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Using our [URL='http://www.mathcelebrity.com/uniform.php?a=+670&b=+770&x=+730&t=+3&pl=CDF']uniform distribution calculator[/URL], we get: [B]0.6[/B]

A rational expression is undefined when what is 0? The [B]denominator[/B]. Because division by zero is undefined.

A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you get 92. What is the number? Let the rational number be x. We're given: 7x/3 - 3/2 = 92 Using a common denominator of 3*2 = 6, we rewrite this as: 14x/6 - 9/6 = 92 (14x - 9)/6 = 92 Cross multiply: 14x - 9 = 92 * 6 14x - 9 = 552 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=14x-9%3D552&pl=Solve']type this equation into our search engine [/URL]and we get: x = [B]40.07[/B]

A real estate agency receives 3.5% commission on the first $100,000 of a sale and 2.25% on the remainder. How much commission is received on the sale of a $450,000 property? Calculate commission on first $100,000 (Commission 1): Commission 1 = $100,000 * 0.035 Commission 1 = $3,500 Calculate commission on the remainder (Commission 2): Commission 2 = 0.025 * ($450,000 - $100,000) Commission 2 = 0.025 * ($350,000) Commission 2 = $8,750 Calculate Total Commission: Total Commission = Commission 1 + Commission 2 Total Commission = $3,500 + $8,750 Total Commission = [B]$12,250[/B]

A real estate agent has $920 to spend on newspaper ads. Each ad costs $6. After buying as many ads as she can afford, how much money will the real estate agent have left over? We want to know the remainder of 920/6. We can type 920 mod 6 into our search engine and get: [URL='https://www.mathcelebrity.com/modulus.php?num=920mod6&pl=Calculate+Modulus']920 mod 6[/URL] = [B]2[/B]

A real estate agent sells a house for $229,605. A sales commission of 6% is charged. The agent gets 45% of this commission. How much money does the agent get? The agents Commission (C) is: C = Sale price * sales commission percent * agent commission percent Since 6% = 0.06 and 45% = 0.45, we have: C = 229605 * 0.06 * 0.45 C = [B]6,199.34[/B]

A realtor makes an annual salary of $25000 plus a 3% commission on sales. If a realtor's salary is $67000, what was the amount of her sales? Total post-salary pay = $67,000 - $25,000 = $42,000 Let Sales be s. So 0.03s = $42,000 Divide each side by 0.03 s = $1,400,000

A recent survey showed that 44% of recent college graduates named flexible hours as their most desire employment benefit. In a graduating class of 870 college students, how many would you expect to rank flexible hours as their top priority in job benefits? Using our [URL='http://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=44&den1=870&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percentage calculator[/URL], 44% of 870 = 382.8 ~ [B]383[/B]

A recent survey showed that 49% of recent college graduates named flexible hours as their most desire employment benefit. In a graduating class of 820 college students, how many would you expect to rank flexible hours as their top priority in job benefits? 49% of 820, using our [URL='http://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=49&den1=820&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percentage calculator[/URL], we get: 401.8 ~ [B]402[/B]

a recipe of 20 bread rolls requires 5 tablespoons of butter. How many tablespoons of butter are needed for 30 bread rolls? Set up a proportion of bread rolls per tablespoons of butter where t is the amount of tablespoons of butter needed for 30 bread rolls: 20/5 = 30/t Cross multiply our proportion: Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2 20t = 30 * 5 20t = 150 Divide each side of the equation by 20: 20t/20 = 150/20 Cancel the 20's on the left side and we get: t = [B]7.5[/B]

A recipe that makes 25 oatmeal cookies calls for 2.5 cups of oats and one cup of sugar. Jerry needs to make 195 cookies for his school party. How many cups of oats will he need? Set up a proportion of oats to cookies where c is the number of cups needed to make 195 cookies 2.5/25 = c/195 Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=2.5&num2=c&den1=25&den2=195&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get: c = [B]19.5[/B]

A recipe calls for 2 tablespoons of olive oil for every 3 servings. How much olive oil will be needed for 6 servings? Set up a proportion of tablespoons to servings: 2/3 = o/6 where o is the number of tablespoons per 6 servings. [URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=o&den1=3&den2=6&propsign=%3D&pl=Calculate+missing+proportion+value']Type 2/3 = o/6 into our search engine[/URL], and we get [B]o = 4[/B].

a rectangle has a length of x-7 and a width of x + 5. Write an expression that represents the area of the rectangle in terms of x. Area of a rectangle (A) with length(l) and width (w) is expressed as follows: A = lw Plugging in our values given above, we have: [B]A = (x - 7)(x + 5)[/B]

A rectangle has a length that is 8.5 times its width. IF the width is n, what is the perimeter of the rectangle. w = n l = 8.5n P = 2(8.5n) + 2n P = 17n + 2n P = [B]19n[/B]

A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSIONS OF THE RECTANGLE? Whoa... stop screaming with those capital letters! But I digress... The perimeter of a rectangle is: P = 2l + 2w We're given two equations: [LIST=1] [*]P = 196 [*]l = 6w [/LIST] Plug these into the perimeter formula: 2(6w) + 2w = 196 12w + 2w = 196 [URL='https://www.mathcelebrity.com/1unk.php?num=12w%2B2w%3D196&pl=Solve']Plugging this equation into our search engine[/URL], we get: [B]w = 14[/B] Now we put w = 14 into equation (2) above: l = 6(14) [B]l = 84 [/B] So our length (l), width (w) of the rectangle is (l, w) = [B](84, 14) [/B] Let's check our work by plugging this into the perimeter formula: 2(84) + 2(14) ? 196 168 + 28 ? 196 196 = 196 <-- checks out

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions? We know the rectangle has the following formulas: Area = lw Perimeter = 2l + 2w Given an area of 238 and a perimeter of 62, we have: [LIST=1] [*]lw = 238 [*]2(l + w) = 62 [/LIST] Divide each side of (1) by w: l = 238/w Substitute this into (2): 2(238/w + w) = 62 Divide each side by 2: 238/w + w = 31 Multiply each side by w: 238w/w + w^2 = 31w Simplify: 238 + w^2 = 31w Subtract 31w from each side: w^2 - 31w + 238 = 0 We have a quadratic. So we run this through our [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2-31w%2B238%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL] and we get: w = (14, 17) We take the lower amount as our width and the higher amount as our length: [B]w = 14 l = 17 [/B] Check our work for Area: 14(17) = 238 <-- Check Check our work for Perimeter: 2(17 + 14) ? 62 2(31) ? 62 62 = 62 <-- Check

[SIZE=4]A rectangle is cut in half to create two squares that each has an area of 25. What is the perimeter of the original rectangle? A. 20 B. 25 C. 30 D. 50[/SIZE] [SIZE=4]Area of a square: A = s^2 We're given A = 25: s^2= 25 s = 5 This means the rectangle width is 5. The rectangle length is 2(5) = 10. Perimeter of a rectangle: P = 2l + 2w P = 2(10) + 2(5) P = 20 + 10 P = [B]30 (choice C)[/B] [B][/B] [B][MEDIA=youtube]tKpS1gQY68o[/MEDIA][/B][/SIZE]

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards because of a building code, what will the length need to be? Perimeter of a rectangle (P) with length (l) and width (w) is: 2l + 2w = P We're given P = 506 and w = 100. We plug this in to the perimeter formula and get: 2l + 2(100) = 506 To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B2%28100%29%3D506&pl=Solve']type it in our search engine[/URL] and we get: l = [B]153[/B]

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 feet longer than the width, then how wide is the field? We're given: [LIST=1] [*]l = w + 40 [/LIST] And we know the perimeter of a rectangle is: P = 2l + 2w Substitute (1) into this formula as well as the given perimeter of 1120: 2(w + 40) + 2w = 1120 Multiply through and simplify: 2w + 80 + 2w = 1120 Group like terms: 4w + 80 = 1120 [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B80%3D1120&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 260[/B]

A rectangular field is twice as long as it is wide. If the perimeter is 360 what are the dimensions? We are given or know the following about the rectangle [LIST] [*]l = 2w [*]P = 2l + 2w [*]Since P = 360, we have 2l + 2w = 360 [/LIST] Since l = 2w, we have 2l + (l) = 360 3l = 360 Divide by 3, we get [B]l = 120[/B] Which means w = 120/2 [B]w = 60[/B]

A rectangular fish tank has a base that is 8 inches by 7 inches. How much water will it take to a depth of 5 inches The volume (V) or a rectangular solid is: V = lwh Using l = 8, w = 7, and h = 5, we have: V = 8(7)(5) V = [B]280 cubic inches[/B]

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find its length and width. The area of a rectangle (A) is: A = lw --> where l is the length and w is the width We're given l = 2w, so we substitute this into the Area equation: A = (2w)w A = 2w^2 We're given the area of the pitch is 360, so we set: 2w^2 = 360 We [URL='https://www.mathcelebrity.com/1unk.php?num=2w%5E2%3D360&pl=Solve']type this equation into our search engine[/URL], follow the links, and get: w = [B]6*sqrt(5) [/B] Now we take this, and substitute it into this equation: 6*sqrt(5)l = 360 Dividing each side by 6*sqrt(5), we get: l = [B]60/sqrt(5)[/B]

A rectangular garden is 5 ft longer than it is wide. Its area is 546 ft2. What are its dimensions? [LIST=1] [*]Area of a rectangle is lw. lw = 546ft^2 [*]We know that l = w + 5. [/LIST] Substitute (2) into (1) (w + 5)w = 546 w^2 + 5w = 546 Subtract 546 from each side w^2 + 5w - 546 = 0 Using the positive root in our [URL='http://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B5w-546%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get [B]w = 21[/B]. This means l = 21 + 5. [B]l = 26[/B]

A rectangular hotel room is 4 yards by 5 yards. The owner of the hotel wants to recarpet the room with carpet that costs $76.00 per square yard. How much will it cost to recarpet the room? $ The area of a rectangle is length * width, so we have: A = 5 yards * 4 yards A = 20 square yards Total cost = Cost per square yard * total square yards Total Cost = $76 * 20 Total Cost = [B]$1520[/B]

A rectangular house is 68 yards wide and 112 yards long. What is its perimeter? The perimeter of a rectangle is: P = 2l + 2w Plugging in our length of 112 and our width of 68, we get: P = 2(112) + 2(68) P = 224 + 136 P = [B]360[/B]

A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards greater than the width. What is the width of the parking lot? The perimeter of a rectangle is: 2l + 2w = P. We're given 2 equations: [LIST=1] [*]2l + 2w = 152 [*]l = w + 12 [/LIST] Substitute equation (2) into equation (1) for l: 2(w + 12) + 2w = 152 2w + 24 + 2w = 152 Combine like terms: 4w + 24 = 152 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B24%3D152&pl=Solve']type this equation into our search engine[/URL] and we get: w =[B] 32[/B]

A rectangular piece of paper has the dimensions of 10 inches by 7 inches.What is the perimeter of the piece of paper Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=10&w=7&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get perimeter P: P = [B]34[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters Given l = length and w = width, The perimeter of a rectangle is 2l + 2w, we have: [LIST=1] [*]l = 3w [*]2l + 2w = 56 [/LIST] Substitute equation (1) into equation (2) for l: 2(3w) + 2w = 56 6w + 2w = 56 To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our math engine[/URL] and we get: w = [B]7 [/B] To solve for l, we substitute w = 7 into equation (1): l = 3(7) l = [B]21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. We're given the following: [LIST] [*]l = 3w [/LIST] We know the Perimeter (P) of a rectangle is: P = 2l + 2w Substituting l = 3w and P = 56 into this equation, we get: 2(3w) + 2w = 56 Multiplying through, we get: 6w + 2w = 56 (6 +2)w = 56 8w = 56 [URL='https://www.mathcelebrity.com/1unk.php?num=8w%3D56&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 7[/B] Substitute w = 7 into l = 3w, we get: l = 3(7) [B]l = 21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimensions of the room. We're given two items: [LIST] [*]l = 3w [*]P = 56 [/LIST] We know the perimeter of a rectangle is: 2l + 2w = P We plug in the given values l = 3w and P = 56 to get: 2(3w) + 2w = 56 6w + 2w = 56 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']plug this equation into our search engine[/URL] and we get: w = [B]7 [/B] To solve for l, we plug in w = 7 that we just found into the given equation l = 3w: l = 3(7) l = [B]21 [/B] So our dimensions length (l) and width (w) are: (l, w) = [B](21, 7)[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimension of the room. We're given: l = 3w The Perimeter (P) of a rectangle is: P = 2l + 2w With P = 56, we have: [LIST=1] [*]l = 3w [*]2l + 2w = 56 [/LIST] Substitute equation (1) into equation (2) for l: 2(3w) + 2w = 56 6w + 2w = 56 To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our search engine[/URL] and we get: w = [B]7 [/B] Now we plug w = 7 into equation (1) above to solve for l: l = 3(7) l = [B]21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 64 meters. Find the dimension of the room. We're given: [LIST] [*]l = 3w [*]P = 64 [/LIST] We also know the perimeter of a rectangle is: 2l + 2w = P We plugin l = 3w and P = 64 into the perimeter equation: 2(3w) + 2w = 64 Multiply through to remove the parentheses: 6w + 2w = 64 To solve this equation for w, we type it in our search engine and we get: [B]w = 8[/B] To solve for l, we plug w = 8 into the l = 3w equation above: l = 3(8) [B]l = 24[/B]

A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimension of the room The perimeter of a rectangle is P = 2l + 2w. We're given two equations: [LIST=1] [*]l = 4w [*]2l + 2w = 80. <-- Since perimeter is 80 [/LIST] Plug equation (1) into equation (2) for l: 2(4w) + 2w = 80 8w + 2w = 80 [URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B2w%3D80&pl=Solve']Plugging this equation into our search engine[/URL], we get: w = [B]10[/B] To get l, we plug w = 10 into equation (1): l = 4(10) l = [B]40[/B]

A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation to determine the break even point? Set up the cost functions for Rental Truck 1 (R1) and Rental Truck 2 (R2) where m is the number of miles R1(m) = 0.59m + 49.95 R2(m) = 0.99m + 39.95 Break even is when we set the cost functions equal to one another: 0.59m + 49.95 = 0.99m + 39.95 [URL='https://www.mathcelebrity.com/1unk.php?num=0.59m%2B49.95%3D0.99m%2B39.95&pl=Solve']Typing this equation into the search engine[/URL], we get [B]m = 25[/B].

A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour. Write and solve an equation to find the number of hours spent repairing the car. Let h be the number of hours spent repairing the car. We set up the cost function C(h): C(h) = Labor Cost per hour * h + Parts Cost We're given C(h) = 648.85, parts cost = 265.95, and labor cost per hour of 85, so we have: 85h + 265.95 = 648.85 To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=85h%2B265.95%3D648.85&pl=Solve']type this into our search engine[/URL] and we get: h = [B]4.5[/B]

A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and solve an equation to find the number of hours of labor spent repairing the car Set up the cost equation C(h) where h is the number of labor hours: C(h) = Labor Cost per hour * h + Parts Cost We're given C(h) = 553, Parts Cost = 265, and Labor Cost per Hour = 48. So we plug these in: 48h + 265 = 553 To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=48h%2B265%3D553&pl=Solve']type it in our math engine[/URL] and we get: h = [B]6 hours[/B]

A repair will require 3 hours at $40 per hour. How much will the total/labor cost be for this job? Total cost = Hourly Labor Rate * hours Total cost = $40 * 3 Totaal cost = [B]$120[/B]

a repairman charged $93.06. The price included 2 hours of labor and a $40 service charge. How much does the repairman charge per hour? Subtract the service charge: 93.06 - 40 = 53.06 53.06/2 hours = [B]$26.53 per hour[/B].

A researcher believed that there was a difference in the amount of time boys and girls at 7th grade studied by using a two-tailed t test. Which of the following is the null hypothesis? a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per day b. Mean of hours that boys studied per day was greater than mean of hours that girls studied per day c. Mean of hours that boys studied per day was smaller than mean of hours that girls studied per day d. Mean of hours that boys studied per day was smaller than or equal to mean of hours that girls studied per day [B]a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per day[/B] Reason is that in hypothesis testing, you take a position other than what is assumed or what is being tested as the null hypothesis

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 120 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 6.0. What's the absolute value of the difference between means? |70 -65| = |5| = 5

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What is the standard error of the difference in means? [B]0.707106781187[/B] using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+100&xbar1=70&stdev1=5&n2=+100&xbar2=65&stdev2=5&conf=+99&pl=Hypothesis+Test']difference of means calculator[/URL]

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What's the t-value (two-tailed) for the null hypothesis that boys and girls have the same test scores? t = 7.07106781187 using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+100&xbar1=70&stdev1=5&n2=+100&xbar2=65&stdev2=5&conf=+99&pl=Hypothesis+Test']difference of means calculator[/URL]

A restaurant bill comes to $28.35. Find the total cost if the tax is 6.25% and a 20% tip is left on the amount before tax. Calculate the tip: Tip = Bill Before Tax * Tip % Tip = $28.35 * 20% Tip = $5.67 Calculate Tax: Tax = Bill without Tip * Tax % Tax = $28.35 * 6.25% Tax = $1.77 Total Cost = Bill + Tax + Tip Total Cost = $28.35 + $5.67 + $1.77 Total Cost = [B]$35.79[/B]

A restaurant chain sells 15,000 pizzas each month, and 70% of the pizzas are topped with pepperoni. Of these, 2/3 also have peppers. How many pizzas have pepperoni and peppers? We multiply the pizzas sold by the percentage of pepperoni times the fraction of peppers. Since 70% is 7/10, we have: Pizzas with pepperoni and peppers = 15,000 * 7/10 * 2/3 7/10 * 2/3 = 14/30. [URL='https://www.mathcelebrity.com/fraction.php?frac1=14%2F30&frac2=3%2F8&pl=Simplify']Using our fraction simplifier calculator[/URL], we can reduce this to 7/15 Pizzas with pepperoni and peppers = 15,000 * 7/15 Pizzas with pepperoni and peppers = [B]7,000[/B]

A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount x (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Let Sunday's earnings be s. With 3 days, we divide our sum of earnings for 3 days by 3 to get our 1,000 average, so we have: (1073 + 1108 + s)/3 = 1000 Cross multiply: 1073 + 1108 + s = 1000 * 3 1073 + 1108 + s = 3000 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=1073%2B1108%2Bs%3D3000&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]819[/B]

A restaurant has 8 pizza toppings to choose from. How many different 2 topping pizzas are possible? We want 8 combinations of 2, denoted as 8 C 2, or 8 choose 2. [URL='https://www.mathcelebrity.com/permutation.php?num=8&den=2&pl=Combinations']Typing 8 C 2 into the search engine[/URL], we get [B]28[/B] different 2 topping pizzas

A restaurant is going to raise all their prices by 5%. If the current price of an item is p dollars, write an expression for the price after the increase. 5% = 0.05 as a decimal. New price = Old Price * (1 + decimal increase) New price = p * (1 + 0.05) New price = [B]1.05p[/B]

A restaurant is going to raise all their prices by 7%. If the current price of an item is p dollars, write an expression for the price after the increase. A 7% increase on price means we multiply the current price of p by 1.07. So our algebraic expression is: [B]1.07p[/B]

A restaurant is open for 10 ½ hours during the day. The restaurant has 5 ½ families coming and leaving every hour. A family has 4 members. How many people have visited the restaurant during the day? [U]Given:[/U] [LIST] [*]10 & 1/2 = 10.5 hours [*]5 & 1/2 = 5.5 families [/LIST] Total Visitors = Hours Open * Families per hour * member per family Total Visitors = 10.5 * 5.5 * 4 Total Visitors = [B]231[/B]

A restaurant offers 20 appetizers and 40 main courses, how many ways can a person order a two course meal? Using the fundamental rule of counting, we can have: 20 appetizers * 40 main courses = [B]800 possible two-course meals[/B]

A restaurant offers a special pizza with any 5 toppings. If the restaurant has 17 topping from which to choose, how many different special pizzas are possible? We have 17 choose 5, or 17C5. [URL='https://www.mathcelebrity.com/permutation.php?num=17&den=5&pl=Combinations']Type this into the search engine[/URL], and we get [B]6,188[/B] different special pizzas available.

A restaurant offers the following options: [LIST] [*]Starter – soup or salad [*]Main – chicken, fish or vegetarian [*]Dessert – ice cream or cake [/LIST] How many possible different combinations of starter, main and dessert are there? Using the fundamental rule of counting, we have: 2 starters * 3 main courses * 2 desserts = [B]12 different combinations [MEDIA=youtube]-N9j7FQ8Le4[/MEDIA][/B]

A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $584. What was the simple interest rate of the bonds? For simple interest, we have: Balance * interest rate = Interest payment 8000i = 584 Divide each side of the equation by 8000 to isolate i: 8000i/8000 = 584/8000 Cancelling the 8000's on the left side, we get: i = 0.073 Most times, interest rates are expressed as a percentage. Percentage interest = Decimal interest * 100% Percentage interest = 0.073 * 100% Multiplying by 100 is the same as moving the decimal point two places right: Percentage interest = [B]7.3%[/B]

A revenue function is R(x) = 22x and a cost function is C(x) = -9x + 341. The break-even point is Break even is when C(x) = R(x). So we set them equal and solve for x: -9x + 341 = 22x Typing[URL='https://www.mathcelebrity.com/1unk.php?num=-9x%2B341%3D22x&pl=Solve'] this equation into our search engine[/URL], we get: x = [B]11[/B]

A right triangle has legs of 9 feet and 12 feet. How long is the hypotenuse? A common right triangle ratio is 3:4:5 9 = 3 * 3 12 = 3 * 4 3 * 5 = 15, so we have [B]15 feet[/B]

A river is rising at a rate of 3 inches per hour. If the river rises more than 2 feet, it will exceed flood stage. How long can the river rise at this rate without exceeding flood stage? Let the number of inches be i. Remember 12 inches to a foot, so we have 2 feet = 12*2 = 24 inches. [LIST] [*]Inequality: 3i <= 24. (since more than means the river can go [U]up to[/U] 2 feet or 24 inches [/LIST] To solve the inequality for I, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=3i%3C%3D24&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get: [B]I <= 8 This means after 8 hours, the river will flood[/B]

A road construction team built a 114 mile road over a period of 19 months what was their average building distance per a month Average building distance = miles built / months of building Average building distance = 114/19 Average building distance = [B]6 miles per month[/B]

a rocket is propelled into the air. its path can be modeled by the relation h = -5t^2 + 50t + 55, where t is the time in seconds, and h is height in metres. when does the rocket hit the ground We set h = 0: -5t^2 + 50t + 55 = 0 Typing this quadratic equation into our search engine to solve for t, we get: t = {-1, 11} Time can't be negative, so we have: t = [B]11[/B]

A rocket travels at a rate of 160 meters in 3 seconds. What is the speed of the rocket in meters per second? 160 meters /3 seconds = [B]53.333333333 meters per second[/B]

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the coaster after the first descent. 90 feet above and then we descend 105 feet, meaning we subtract: 90 - 105 = -15. We read this [B]15 feet below ground level[/B]

A roller coaster begins at 90 feet above ground level. Then it descends 105 feet. Find the height of the roller coaster after the first descent. 90 feet above ground level is written as +90 Descending 105 feet means we subtract 105 feet to get: +90 - 105 = [B]-15 or 15 feet below ground level[/B]

A roller coaster car carriers 32 people every 10 minutes there are 572 people in line in front of Ruben how long will it take for Ruben to ride the roller coaster 527/32 = 17.875 Which means on the 18th ride, Ruben will get a seat. 18 rides * 10 minutes per ride = [B]180 minutes, or 3 hours.[/B]

a roller coaster has 6 trains. each train has 3 cars, and each car seats 4 people. write and simplify an expression including units to find the total number of people that can ride the roller coaster at one time 6 trains * 3 cars per train * 4 people per car = [B]72 people[/B]

A roof drops 4 feet for every 12 feet forward. Determine the slope of the roof. Slope = Rise or Drop / Run Slope = 4/12 We can simplify this fraction. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F12&frac2=3%2F8&pl=Simplify']type 4/12 into our search engine[/URL] and get: Slope. = [B]1/3[/B]

A room is 15 ft long and 12 feet wide. What are the length and width of the room in yards? Since 3 feet = 1 yard, we have: Length in yards = Length in feet / 3 Length in yards = 15/3 Length in yards = 5 Width in yards = Width in feet / 3 Width in yards = 12/3 Width in yards = 4

A salary after a 4.6% increase, of the original salary is x dollars 4.6% is also written as 0.046. Our formula for the new salary S is: S = (1 + 0.046)x [B]S = 1.046x[/B]

A sales clerk receives a monthly salary of $750 plus a commission of 4% on all sales over $3900. What did the clerk earn the month that she sold $12,800 in merchandise? [U]Calculate Commission Sales Eligible Amount:[/U] Commission Sales Eligible Amount = Sales - 3900 Commission Sales Eligible Amount = 12800 - 3900 Commission Sales Eligible Amount = 8900 [U]Calculate Commission Amount:[/U] Commission Amount = Commission Sales Eligible Amount * Commission Percent Commission Amount = [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=4&den1=8900&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']8900 * 4%[/URL] Commission Amount = 356 [U]Calculate total earnings:[/U] Total Earnings = Base Salary + Commission Amount Total Earnings = 750 + 356 Total Earnings = [B]1106[/B]

A Sales Manager buys antacid in bottles by the gross. If he goes through 3 bottles of antacid everyday, how long will the gross last? [U][B]Calculate a gross[/B][/U] [URL='https://en.wikipedia.org/wiki/Gross_(unit)#:~:text=A%20gross%20refers%20to%20a,cubic%20dozen%2C%20123).']A gross equals[/URL] 144 because 1 gross = 12 dozen 12 dozen * 12 items/dozen = 144 [B] [U]Answer[/U][/B] Days lasted = Total Bottles / Bottles per day Days lasted = 144 bottles / 3 days [B]Days lasted = 48 days[/B]

Set up a function where t is the number of hours driven, and f(t) is the distance driven after t hours: [B]f(t) = 9t[/B]

A salesperson earns a commission of $364 for selling $2600 in merchandise. Find the commission rate. Write your answer as a percentage. Commission percentage = Commission Amount / Sales Price Commission percentage = 364 / 2600 Commission percentage = 0.14 Multiply by 100 to get the percentage: 0.14 * 100 = [B]14%[/B]

A salesperson receives a base salary of $300 per week and a commission of 15% on all sales over $5,000. If x represents the salesperson’s weekly sales, express the total weekly earnings E(x) as a function of x and simplify the expression. Then find E(2,000) and E(7,000) and E(10,000). 15% as a decimal is written as 0.15. Build our weekly earnings function E(x) = Commission + Base Salary E(x) = 0.15(Max(0, x - 5000)) + 300 Now find the sales salary for 2,000, 7,000, and 10,000 in sales E(2,000) = 0.15(Max(0,2000 - 5000)) + 300 E(2,000) = 0.15(Max(0,-3000)) + 300 E(2,000) = 0.15(0) + 300 [B]E(2,000) = 300 [/B] E(7,000) = 0.15(Max(0,7000 - 5000)) + 300 E(7,000) = 0.15(Max(0,2000)) + 300 E(7,000) = 0.15(2,000) + 300 E(7,000) = 300 + 300 [B][B]E(7,000) = 600[/B][/B] E(10,000) = 0.15(Max(0,10000 - 5000)) + 300 E(10,000) = 0.15(Max(0,5000)) + 300 E(10,000) = 0.15(5,000) + 300 E(10,000) = 750+ 300 [B][B]E(10,000) = 1,050[/B][/B]

A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $24. Option B is a commission rate of 4% on weekly sales. How much does he need to sell this week to earn the same amount with the two options? Option A payment function: 24h With a 40 hour week, we have: 24 * 40 = 960 Option B payment function with sales amount (s): 0.04s We want to know the amount of sales (s) where Option A at 40 hours = Option B. So we set both equal to each other: 0.04s = 960 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.04s%3D960&pl=Solve']type it in our math engine[/URL] and we get: s = [B]24,000[/B]

A sample of 71 college students yields a mean annual income of $3595. Assuming that ? = $898, find the margin of error in estimating µ at the 99% level of confidence

A sample of 71 college students yields a mean annual income of $3595. Assuming that ? = $898, find the margin of error in estimating µ at the 99% level of confidence

A savings account earns 15% interest annually. What is the balance after 8 years in the savings account when the initial deposit is 7500 Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=7500&nval=8&int=15&pl=Annually']compound interest with balance calculator,[/URL] we get a balance of: [B]22,942.67[/B]

A school bus can safely carry as many as 76 students. If 19 students are already on the bus, how many more can board the bus? Remaining boarders = total capacity - students on the bus Remaining boarders = 76 - 19 Remaining boarders = [B]57[/B]

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis? Slope is y/x,so we have 27/36. [URL='https://www.mathcelebrity.com/fraction.php?frac1=27%2F36&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we can reduce 27/36 to 3/4. So this is our slope. [B]3/4[/B]

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis? Slope = Rise/Run or y/x Since tests are on the y-axis and time is on the x-axis, we have: Slope = 27/36 We can simplify this, so we [URL='https://www.mathcelebrity.com/fraction.php?frac1=27%2F36&frac2=3%2F8&pl=Simplify']type in 27/36 into our search engine[/URL], and get: [B]Slope = 3/4[/B]

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 9 sophomores, 7 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen? We want combinations for freshmen, sophomores, juniors, and seniors. [LIST] [*]Freshmen choices: [URL='https://www.mathcelebrity.com/permutation.php?num=6&den=2&pl=Combinations']6 C 2[/URL] = 15 [*]Sophomore choices: [URL='https://www.mathcelebrity.com/permutation.php?num=9&den=3&pl=Combinations']9 C 3[/URL] = 84 [*]Junior choices: [URL='https://www.mathcelebrity.com/permutation.php?num=7&den=4&pl=Combinations']7 C 4[/URL] = 35 [*]Senior choices: [URL='https://www.mathcelebrity.com/permutation.php?num=7&den=5&pl=Combinations']7 C 5 [/URL]= 21 [/LIST] The number of committees we can choose is the product of combinations of freshmen, sophomores, juniors, and seniors. Total Committees = Freshmen choices * Sophomore choices * Junior choices * Senior choices Total Committees = 15 * 84 * 35 * 21 Total Committees = [B]926,100[/B]

A school dance had 675 cookies each student took 3 cookies and there were 15 cookies leftover how many students attended the dance Let each student be s. We have: 3s + 15 = 675 To solve this equation for s, [URL='https://www.mathcelebrity.com/1unk.php?num=3s%2B15%3D675&pl=Solve']we type it in our search engine[/URL] and we get: s = [B]220[/B]

A school has a boy to girl ratio of 6:7. If there are 288 boys, how many girls are there? 6 boys/7 girls = 288 boys/g girls Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=6&num2=288&den1=7&den2=g&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: g = [B]336 [MEDIA=youtube]P7x_u9oAkEc[/MEDIA][/B]

A school spent $150 on advertising for a breakfast fundraiser. Each plate of food was sold for $8.00 but cost the school $2.00 to prepare. After all expenses were paid, the school raised $2,400 at the fundraiser. Which equation can be used to find x, the number of plates that were sold? Set up the cost equation C(x) where x is the number of plates sold: C(x) = Cost per plate * x plates C(x) = 2x Set up the revenue equation R(x) where x is the number of plates sold: R(x) = Sales price per plate * x plates C(x) = 8x Set up the profit equation P(x) where x is the number of plates sold: P(x) = R(x) - C(x) P(x) = 8x - 2x P(x) = 6x We're told the profits P(x) for the fundraiser were $2,400, so we set 6x equal to 2400 and solve for x: 6x = 2400 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x%3D2400&pl=Solve']type it in our math engine[/URL] and we get: x =[B]400 plates[/B]

A school theater group is selling candy to raise funds in order to put on their next performance. The candy cost the group $0.20 per piece. Plus, there was a $9 shipping and handling fee. The group is going to sell the candy for $0.50 per piece. How many pieces of candy must the group sell in order to break even? [U]Set up the cost function C(p) where p is the number of pieces of candy.[/U] C(p) = Cost per piece * p + shipping and handling fee C(p) = 0.2p + 9 [U]Set up the Revenue function R(p) where p is the number of pieces of candy.[/U] R(p) = Sale price * p R(p) = 0.5p Break-even means zero profit or loss, so we set the Cost Function equal to the Revenue Function 0.2p + 9 = 0.5p To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B9%3D0.5p&pl=Solve']type it in our math engine[/URL] and we get: p = [B]30[/B]

A school wants to buy a chalkboard that measures 1 yard by 2 yards. The chalkboard costs $27.31 per square yard. How much will the chalkboard cost? Area of a chalkboard is denoted as : A = lw Given 1 yard width and 2 years length of the chalkboard, we have: A = 2(1) A = 2 square yards Therefore, total cost is: Total Cost = $27.31 * square yards Total Cost = $27.31(2) Total Cost = [B]$54.62[/B]

A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds later. At what rate is the scuba diver going deeper down in the water If we take these as coordinates on a graph, where y is the depth and x is the time, we calculate our slope or rate of change where (x1, y1) = (10, 30) and (x2, y2) = (40, 100) Rate of change = (y2 - y1)/(x2 - x1) Rate of change = (100 - 30)/(40 - 10) Rate of change = 70/30 Rate of change =[B] 2.333 feet per second[/B]

A scuba diver swam 96ft under the sea and then went back up 34ft. What is the depth of the diver at this point? 96 - 34 = [B]62 ft[/B]

A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number? Take this algebraic expression in pieces: [LIST] [*]Let the secret number be n. [*]Added to means we add 6 to n: n + 6 [*]The total is multiplied by 5: 5(n + 6) [*]The phrase [I]to get[/I] means equal to, so we set 5(n + 6) equal to 50 [/LIST] 5(n + 6) = 50 To solve this equation for n, we type it in our search engine and we get: n = [B]4[/B]

A segment has an endpoint at (2, 1). The midpoint is at (5, 1). What are the coordinates of the other endpoint? The other endpoint is (8,1) using our [URL='http://www.mathcelebrity.com/mptnline.php?ept1=2&empt=5&ept2=&pl=Calculate+missing+Number+Line+item']midpoint calculator.[/URL]

A Septon said that he has a collection of 1,000,000 stones in his house. How many stones is that in base 10? The 1 is in decimal position 7, or 6th power. [URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=7%5E6&pl=Calculate']1 * 7^6[/URL] = [B]117,649[/B]

A Septonian said he had eaten .5 of his cookie while an American said he had eaten .5 of his cookie. Who ate more? Why? [LIST] [*]The Septon ate 5 groups of 1/7 or 5/7 [*]The American ate 5 groups of 1/10 or 5/10 which is 1/2 [/LIST] [URL='https://www.mathcelebrity.com/fraction.php?frac1=5/7&frac2=5/10&pl=Compare']5/7 is larger[/URL], so the Septoian ate more.

A Septonian said that his exact weight is 250.346 pounds (base 7). Translate this into base 10. Start the conversion: 2 * 7^2 + 5 * 7^1 + 0 * 7^0 + 3 * 1/7 + 4 * (1/7)^2 + 6 * (1/7)^3 2 * 49 + 5 * 7 + 0 * 1 + 3/7 + 4 * 1/49 + 6 * 1/343 98 + 35 + 3/7 + 4/49 + 6/343 [B]133 & 181/343[/B]

A Septonian won the lottery in the United States and won $1,000,000. How many dollars in that in base 7? Using our [URL='https://www.mathcelebrity.com/binary.php?num=1000000&check1=7&bchoice=7&pl=Convert']base change calculator[/URL], we get: 1,000,000 in base 7 = [B]11,333,311[/B]

A service charges a $1.95 flat rate plus $0.05 per mile. Jason only has $12 to spend on a a ride. Set up the cost equation C(m) where m is the number of miles: C(m) = 0.05m + 1.95 The problems asks for the number of miles (m) when C(m) = 12: 0.05m + 1.95 = 12 [URL='https://www.mathcelebrity.com/1unk.php?num=0.05m%2B1.95%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get: m = [B]201[/B]

A set has a cardinality of 9. How many proper subsets does the set have? The set has 2^9 = [B]512 proper subsets[/B]

A set of 19 scores has a mean of 6.3. A new score of 8 is then included in the data set. What is the new mean? We know the mean formula is: Sum of scores / Number of Scores = Mean We're given mean = 6.3 and number of scores = 19, so we have: Sum of scores / 19 = 6.3 Cross multiply: Sum of scores = 19 * 6.3 Sum of scores = 119.7 Now a new score is added of 8, so we have: Sum of scores = 119.7 + 8 = 127.7 Number of scores = 19 + 1 = 20 So our new mean is: Mean = Sum of scores / Number of Scores Mean = 127.7/20 Mean = [B]6.385[/B] [COLOR=rgb(0, 0, 0)][SIZE=5][FONT=arial][B][/B][/FONT][/SIZE][/COLOR]

A set of 4 consecutive integers adds up to 314. What is the least of the 4 integers? First integer is x. The next 3 are x + 1, x + 2, and x + 3. Set up our equation: x + (x + 1) + (x + 2) + (x + 3) = 314 Group x terms and group constnats (x + x + x + x) + (1 + 2 + 3) = 314 Simplify and combine 4x + 6 = 314 [URL='http://www.mathcelebrity.com/1unk.php?num=4x%2B6%3D314&pl=Solve']Enter this in the equation solver[/URL] [B]x = 77[/B]

A set of 6 wooden chairs costs $444. A set of 8 metal chairs costs $720. How much more do the metal chairs cost per chair? [U]Wooden Chair Unit Cost:[/U] Unit Cost = Total Cost / Quantity Unit Cost = 444/6 Unit Cost = 74 [B][/B] [U]Metal Chair Unit Cost:[/U] Unit Cost = Total Cost / Quantity Unit Cost = 720/8 Unit Cost = 90 [B][B][/B][/B] Find the difference (how much more) Difference = Metal Chair Unit Cost - Wooden Chair Unit Cost Difference = 90 - 74 Difference = [B]16[/B]

A set of data has a range of 30. The least value in the set of data is 22. What is the greatest value in the set of data? High Value - Low Value = Range Let the high value be h. We're given: h - 22 = 30 We [URL='https://www.mathcelebrity.com/1unk.php?num=h-22%3D30&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]52[/B]

A sewing class has 205 yards off a bric to make quilts. Each quilt requires 7 yards off a bric. How much will remain after all the quilts are made? Calculate the number of full quilts: 205/7 = 29.2857 so 29 full quilts. 29 * 7 = 203 205 - 203 = [B]2 yards remaining[/B]. You can also use the [URL='http://www.mathcelebrity.com/modulus.php?num=205mod7&pl=Calculate+Modulus']modulus calculator[/URL]

A ship is traveling at an average velocity of 28 miles per hour. How far will the ship travel in two days? 28 miles/1 hour * 24 hours/1 day * 2 days 28 * 24 * 2 = [B]1,344 miles[/B]

A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package weight. Write an equation to represent the price P of shipping a package that weighs x ounces, for any whole number of ounces greater than or equal to 1. Set up the price function P(x) [B]P(x) = 0.43 + 0.29(x - 1)[/B]

A shirt costs 15 and jeans costs 25. write an expressions for the costs of j jeans and s shirts. Cost equals quantity times price, so we have the total cost C: [B]C(s, j) = 15s + 25j[/B]

A shoe store was having a sale where 2 pairs of Brand A shoes cost $23.10 and 3 pairs of Brand B shoes cost $35.85. Which brand is the better buy? [URL='https://www.mathcelebrity.com/betterbuy.php?p1=23.10&p2=35.85&q1=2&q2=3&pl=Better+Buy']Using our better buy calculator[/URL]: [SIZE=5][B]Calculate Unit Price[/B][/SIZE] Unit Price = Price/Quantity [SIZE=5][B]Calculate Unit Price 1:[/B][/SIZE] Unit Price Brand A = P1/Q1 Unit Price Brand A = 23.10/2 Unit Price Brand A = 11.55 [SIZE=5][B]Calculate Unit Price 2:[/B][/SIZE] Unit Price Brand B = P2/Q2 Unit Price Brand B = 35.85/3 Unit Price Brand B = 11.95 Since Brand A's Unit price is lower, [B]Brand A is the better buy [MEDIA=youtube]Q16iZn6Uer8[/MEDIA][/B]

a shop has a sale of 1/5 off all items in stock. if the original price of a dress is £45, what would be its sale price? [URL='https://www.mathcelebrity.com/fraction.php?frac1=45&frac2=1/5&pl=Multiply']1/5 of 45[/URL] = 9 45 - 9 = [B]36[/B]

A shopkeeper buys a box of 20 cans of cola for $10. He sells the cans for 65 cents each. Work out his percentage profit. [U]Calculate Revenue[/U] Revenue = Sale price per can * number of cans Revenue = 0.65 * 20 Revenue = 13 [U]Calculate Profit given a cost of $10:[/U] Profit = Revenue - Cost Profit = 13 - 10 Profit = 3 [U]Calculate Percentage Profit:[/U] Percentage Profit = Profit/Revenue * 100% Percentage Profit = 3/13 * 100% Percentage Profit = 0.23076923076 * 100% Percentage Profit = [B]23.08%[/B]

A shopper paid $51.93 including tax for an item marked $48.99. What would she pay for another item marked $75? Set up a proportion, assuming identical tax rates: 51.93/48.99 = 75/x where x is the after-tax amount Using our [URL='http://www.mathcelebrity.com/prop.php?num1=51.93&num2=75&den1=48.99&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: [B]x = 70.75[/B]

A single card is drawn from a standard 52 card deck. What is the possibility that the card drawn is either a 4 or a 6 There are 4 (4's) and 4 (6's) in a standard 52 card deck. P(4 or 6) = P(4) + P(6) P(4 or 6) = 4/52 + 4/52 P(4 or 6) = 8/52 We can simplify this fraction by [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F52&frac2=3%2F8&pl=Simplify']typing it in our search engine and choosing simplify[/URL]: P(4 or 6) = [B]2/13[/B]

A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $75. A season ski pass costs $350. The skier would have to rent skis with either pass for $20 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes? Let d be the number of days: Daily Plan cost: 75d + 20d = 95d Season Pass: 350 + 20d We want to find d such that 350 + 20d < 95d Subtract 20d from each side 75d > 350 Divide each side by 75 d > 4.66667 [B]d = 5[/B]

A skydiver falls 144 feet in three seconds. How far does the skydiver fall per second? 144 feet/3 seconds Divide top and bottom by 3 to get feet per second [B]48 feet per second[/B]

A small theater had 6 rows of 24 chairs each. An extra 7 chairs have just been brought in. How many chairs are in the theater now? Calculate the chairs in the theater before the extra chairs were brought in: Chairs in theater (before) = Rows * Chairs per row Chairs in theater (before) = 6 * 24 Chairs in theater (before) = 144 To get the chairs in the theater after the extra, we have: Chairs in theater = Chairs in theater (before) + extra chairs Chairs in theater = 144 + 7 Chairs in theater = [B]151[/B]

A small theater had 9 rows of 24 chairs each. An extra 8 chairs have just been brought in. How many chairs are in the theater now? [LIST=1] [*]9 rows x 24 chairs per row = 216 chairs. [*]Add an extra 8 chairs, we get 216 + 8 = [B]224 chairs[/B] [/LIST]

A soccer team has picked its five best players to take part in penalty kicks to determine the winner of a soccer match that is tied. Each of the five players will get one shot against the opposing team's goalie. The coach needs to decide the order in which the five players will take their shots. How many possible ways are there to arrange the five players? First shot, 5 players can take the shot. Next shot is 4, then 3, then 2, then 1 5! = 5 x 4 x 3 x 2 x 1 = [B]120 ways[/B]

A soccer team is buying T-shirts to sell as a fundraiser. The team pays a flat fee of $35 for a logo design plus $7.00 per T-shirt. Set up the cost function C(t) where t is the number of t-shirts: C(t) = Cost per t-shirt * number of t-shirts + Flat Fee [B]C(t) = 7t + 35[/B]

A soccer team lost 30% of their games and drew 15% and they played 67 games. How many games did they win If they lost 30% and they drew (tied) 15%, then they won the following: Wins = 100% - Losses - Drew Wins = 100% - 30% - 15% Wins = 55% So we want 55% of 67. We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=55&den1=67&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type this expression into our search engine[/URL] and we get: [B]36.85 ~ 37 games[/B]

A social networking site currently has 38,000 active members per month, but that figure is dropping by 5% with every month that passes. How many active members can the site expect to have in 7 months? Setup an equation S(m) where m is the number of months that pass: S(m) = 38000 * (1 - 0.05)^t S(m) = 38000 * (0.95)^t The problem asks for S(7): S(7) = 38000 * (0.95)^7 S(7) = 38000 * (0.69833729609) S(7) = 26,536.82 We round down to a full person and get: S(7) = [B]26,536[/B]

A soda cost $100. What is the cost of y sodas? Total cost = price * quantity Total Cost = [B]100y[/B]

A soft drink costs $1.65, and each refill for the drink costs $0.95. If you have $4.50, how many refills can you purchase? Subtract the first drink: 4.50 - 1.65 = 2.85 Now, we need to find out how many refills we get for 2.85. 2.85/0.95 = [B]3 refills[/B]

We take the ratio of hits to at bats: 13/25 = 0.52 To get the percent, we multiply by 100: 100 * 0.52 = 52%

A software company, in 3 consecutive years, makes profits of -3 million dollars, 10 million dollars, and -2 million dollars. What was its profit over the 3 year period? Profit = -3,o00,000 + 10,000,000 - 2,000,000 Profit = [B]5,000,000[/B]

a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age. Declare variables: [LIST] [*]Let f be the father's age [*]Let s be the son's age [/LIST] We're given two equations: [LIST=1] [*]s = f/4 [*]f - s = 30. [I]The reason why we subtract s from f is the father is older[/I] [/LIST] Using substitution, we substitute equaiton (1) into equation (2) for s: f - f/4 = 30 To remove the denominator/fraction, we multiply both sides of the equation by 4: 4f - 4f/4 = 30 *4 4f - f = 120 3f = 120 To solve for f, we divide each side of the equation by 3: 3f/3 = 120/3 Cancel the 3's on the left side and we get: f = [B]40[/B]

A spacecraft with a volume of 800 cubic feet is leaking air at a rate of .4 cubic feet every [I]n[/I] minutes. How many minutes until the spacecraft has no air? 800 cubic feet / .4 cubic feet every n minutes = 2000 (n minute parts) Total time = [B]2000n[/B]

A spherical water tank holds 11,500ft^3 of water. What is the diameter? The tank holding amount is volume. And the volume of a sphere is: V = (4pir^3)/3 We know that radius is 1/2 of diameter: r =d/2 So we rewrite our volume function: V = 4/3(pi(d/2)^3) We're given V = 11,500 so we have: 4/3(pi(d/2)^3) = 11500 Multiply each side by 3/4 4/3(3/4)(pi(d/2)^3) = 11,500*3/4 Simplify: pi(d/2)^3 = 8625 Since pi = 3.1415926359, we divide each side by pi: (d/2)^3 = 8625/3.1415926359 (d/2)^3 = 2745.42 Take the cube root of each side: d/2 = 14.0224 Multiply through by 2: [B]d = 28.005[/B]

A spider has 8 legs. How many legs are there for k spiders? We multiply legs per spider * spiders [B]8k[/B]

A spinner has 10 equally sized sections, 2 are gray 8 are blue. The spinner is spun twice. What is the probability that the first spin lands on blue and the second lands on gray? P(blue) = Blue sections / Total Sections P(blue) = 8/10 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F10&frac2=3%2F8&pl=Simplify']Reducing this using our simplified fraction calculator[/URL], we get: P(blue) = 4/5 P(gray) = Gray sections / Total Sections P(blue) = 2/10 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F10&frac2=3%2F8&pl=Simplify']Reducing this using our simplified fraction calculator[/URL], we get: P(gray) = 1/5 We want the probability of blue,gray. Since each spin is independent, we multiply the two probabilities to get our answer: P(blue, gray) = P(blue) * P(gray) P(blue, gray) = 4/5 * 1/5 P(blue, gray) = [B]4/25[/B]

A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 white. The pointer is spun and a marble is picked at random. a) Use a tree diagram to list the possible outcomes. [LIST=1] [*][B]A, Grey[/B] [*][B]A, Black[/B] [*][B]A, White[/B] [*][B]B, Grey[/B] [*][B]B, Black[/B] [*][B]B, White[/B] [*][B]C, Grey[/B] [*][B]C, Black[/B] [*][B]C, White[/B] [/LIST] b) What is the probability of: i) spinning A? P(A) = Number of A sections on spinner / Total Sections P(A) = [B]1/3[/B] --------------------------------- ii) picking a grey marble? P(A) = Number of grey marbles / Total Marbles P(A) = [B]1/3[/B] --------------------------------- iii) spinning A and picking a white marble? Since they're independent events, we multiply to get: P(A AND White) = P(A) * P(White) P(A) was found in i) as 1/3 Find P(White): P(White) = Number of white marbles / Total Marbles P(White) = 1/3 [B][/B] Therefore, we have: P(A AND White) = 1/3 * 1/3 P(A AND White) = [B]1/9[/B] --------------------------------- iv) spinning C and picking a pink marble? Since they're independent events, we multiply to get: P(C AND Pink) = P(C) * P(Pink) Find P(C): P(C) = Number of C sections on spinner / Total Sections P(C) = 1/3 [B][/B] Find P(Pink): P(Pink) = Number of pink marbles / Total Marbles P(Pink) = 0/3 [B][/B] Therefore, we have: P(C AND Pink) = 1/3 * 0 P(C AND Pink) = [B]0[/B]

A spinner has 6 equal sections, of which 2 are green. If you spin the spinner once, what is the probability that it will land on a green section? Write your answer as a fraction or whole number. P(green) = Total Green / Total spaces P(green) = 2/6 We can simplify this fraction. So we [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F6&frac2=3%2F8&pl=Simplify']type 2/6 into our search engine[/URL], choose Simplify, and we get: P(green) = [B]1/3[/B]

A spinner is divided into 4 equal sections numbered 1 to 4. The theoretical probability of the spinner stopping on 3 is 25%. Which of the following is most likely the number of 3s spun in 10,000 spins? We want Expected Value of s spins. Set up the expected value formula for any number 1-4 E(s) = 0.25 * n where n is the number of spins. Using s = 3, n = 10,000, we have: E(10,000) = 0.25 * 10,000 E(10,000) = [B]2,500[/B]

A sports store near Big Bear Lake is having a 20% off sale on all water skis. What will the sale price be for water skis which regularly sell for $248? [U]Calculate Sale Price:[/U] Sale Price = Full Price * (1 - sale discount) Sale Price = 248 * (1 - 0.2) <-- since 20% is 0.2 Sale Price = 248 * (0.8) Sale Price = [B]198.40[/B]

A sports tournament has c teams. Each team has 17 players. Using c, write an expression for the total number of players in the tournament. Total Players = Total Teams * Players Per Team Total Players =[B] 17c[/B]

A sports tournament has d teams. Each team has 14 players. Using d, write an expression for the total number of players in the tournament. Tournament Players = Players per team * Number of Teams Tournament Players = [B]14d[/B]

A sprinter runs 400 meters in 54 seconds. What is the runners average running rate in meters per second? 400 meters/54 seconds = [B]7.407 meters per second[/B].

A square has a perimeter of 24 inches. What is the area of the square? Perimeter of a square = 4s where s = the length of a side. Therefore, we have: 4s = P 4s = 24 Using our equation solver, [URL='https://www.mathcelebrity.com/1unk.php?num=4s%3D24&pl=Solve']we type in 4s = 24[/URL] and get: s = 6 The problems asks for area of a square. It's given by A = s^2 Plugging in s = 6, we get: A = 6^2 A = 6 * 6 A = [B]36 [/B] Now if you want a shortcut in the future, type in the shape and measurement you know. Such as: [I][URL='https://www.mathcelebrity.com/square.php?num=24&pl=Perimeter&type=perimeter&show_All=1']square perimeter = 24[/URL][/I] From the link, you'll learn every other measurement about the square.

A square of an integer is the integer. Find the integer. Let the integer be n. The square means we raise n to the power of 2, so we have: n^2 = n Subtract n from each side: n^2 - n = n - n n^2 - n = 0 Factoring this, we get: n(n - 1) = 0 So n is either [B]0 or 1[/B].

A stack of boards is 21 inches high. Each board is 1¾ inches thick. How many boards are there? We want 21 / 1 & 3/4 Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=21&frac2=1%263%2F4&pl=Divide']fraction operation calculator[/URL], we get: [B]12 boards[/B]

A stack of lumber is 8 feet wide, 5 feet high, and 2 feet long. Give the volume of the stack The lumber stack is a rectangular solid. The Volume V is found from the length (l), width (w), and height (h) by: V = lwh Plugging in our given values, we get: V = 2 * 8 * 5 V = [B]80 cubic feet[/B]

A standard die is rolled. Find the probability that the number rolled is greater than 3. Using our [URL='http://www.mathcelebrity.com/1dice.php?gl=2&pl=3&opdice=1&rolist=+2%2C3%2C4&dby=+2%2C3%2C5&montect=+100']dice calculator[/URL], the probability is [B]1/2 or 0.5[/B]

A standard volleyball court has an area of 1800ft. The length is 60. What is the width of the volleyball court Plugging [URL='https://www.mathcelebrity.com/rectangle.php?l=60&w=&a=1800&p=&pl=Calculate+Rectangle']this into our rectangle calculator[/URL] and we get: w = [B]30[/B]

A state park charges a $6.00 entry fee plus $7.50 per night of camping. Write an algebraic expression for the cost in dollars of entering the park and camping for n nights. The cost in dollars C is found below: [B]C = 7.50n + 6[/B]

A state park charges a $6.00 entry fee plus $7.50 per night of camping. Write an algebraic expression for the cost in dollars of entering the park and camping for n nights. We write this as: cost per night of camping * n nights + entry fee [B]7.50n + 6[/B]

A stick that is ten feet tall casts a shadow of 12 feet. If a tree has a 96 foot shadow, how tall is the tree? Set up a proportion of wood height to shadow length where h is the height of the tree: 10/12 = h/96 Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=10&num2=h&den1=12&den2=96&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: h = [B]80 feet[/B]

a stone mason builds 7 houses in 3 days. How many days does it take to build 11 houses? The build rate of houses per days is proportional. Set up a proportion of [I]houses to days[/I] where d is the number of days it takes to build 11 houses: 7/3 = 11/d Cross multiply: Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2 7d = 11 * 3 7d = 33 Divide each side of the equation by 7: 7d/7 = 33/7 d = [B]4.7142857142857[/B]

A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. What is the height of the box? The volume of the box is l x w x h. We're given l and w = 4. So we want height: 56 = 4 x 4 x h 16h = 56 [URL='https://www.mathcelebrity.com/1unk.php?num=16h%3D56&pl=Solve']Type this equation into our search engine[/URL] and we get: h = [B]3.5[/B]

A store had 600 pounds of feed. After delivering equal amounts to 4 farmers, there are 60 pounds left. How many pounds did each farmer receive? If there were 60 pounds left, then the store had 600 - 60 = 540 pounds delivered. 540 pounds delivered in equal amounts to 4 farmers means each farmer got: 540/4 = [B]135 pounds of feed[/B]

A store is offering a 11% discount on all items. Write an equation relating the final price 11% discount means we pay 100% - 11% = 89% of the full price. Since 89% as a decimal is 0.89. With a final price f and an original price p, we have: [B]F = 0.89p[/B]

A store is offering a 15% discount on all items. Write an equation relating the sale price S for an item to its list price L If we give a discount of 15%, then we pay 100% - 15% = 85% of the list price. 85% as a decimal is 0.85, So we have: L = 0.85S

A store is offering a 18% discount on all items. Write an equation relating the sale price S for an item to its list price L. 18% discount means we subtract 18% (0.18) as a decimal, from the 100% of the price: S = L(1 - 0.18) [B]S = 0.82L[/B]

A store manager must calculate the total number of winter hats available to sell in the store from a starting number of 293. In the past month, the store sold 43 blue hats, 96 black hats, 28 red hats, and 61 pink hats. The store received a shipment of 48 blue hats, 60 black hats, 18 red hats, and 24 pink hats. How many total hats does the store have for sale? [LIST=1] [*]We start with 293 hats [*]We calculate the hats sold: (43 + 96 + 28 + 61) = 228 [*]We subtract Step 2 from Step 1 to get remaining hats before the shipment: 293 - 228 = 65 [*]Now we calculate the number of hats received in the shipment: (48 + 60 + 18 + 24) = 150 [*]We add Step 4 to Step 3: 65 + 150 = [B]215 hats for sale[/B] [/LIST]

A store owner bought 240 cartons of eggs. The owner sold 5/8 of the eggs and set aside 5 cartons. How many cartons of eggs did the owner have left to sale? If the owner sold 5/8 of the eggs, they have 1 - 5/8 left. 1 = 8/8, so we have 8/8 - 5/8 = 3/8 left 3/8 (240 cartons) = 90 cartons remaining The owner set aside 5 cartons. We're left with 90 cartons - 5 cartons = [B]85 cartons[/B]

a store sells a certain toaster oven for 35. The store offers a 30% discount and charges 8% sales tax. How much will the toaster oven cost? [U]Calculate discounted price:[/U] Discounted Price = Full Price * (1 - Discount Percent) Since 30% = 0.3, we have Discounted Price = 35 * (1 - 0.3) Discounted Price = 35 * 0.7 Discounted Price = 24.5 Calculate after-tax amount: After-tax amount = Discounted Price * (1 + Tax Percent) Since 8% = 0.08, we have Discounted Price = 24.5 * (1 + 0.08) Discounted Price = 24.5 * 1.08 Discounted Price = [B]26.46[/B]

A store sells about $45 a day 7 days a week about how many gigs is my the stores sell in 4 weeks 4 weeks = 7 * 4 = 28 days. $45 per day * 28 days = [B]$1,260[/B]

A store sells books for 50% off on Sundays. The store advertises that on Easter Sunday the store takes an additional 25% off. What would a pile of books cost on Easter Sunday that normally sell for $100 on a Thursday? 50% off means we'd pay 100% - 50% = 50% An additional 25% off means we'd pay 100% - 25% = 75% Build this percentage paid stack below 100 * 50% * 75% = [B]37.50[/B]

A store sells small notebooks for $6 and large notebooks for $12. If a student buys 6 notebooks and spends $60, how many of each did he buy? Let the amount of small notebooks be s. Let the amount of large notebooks be l. We're given two equations: [LIST=1] [*]l + s = 6 [*]12l + 6s = 60 [/LIST] Multiply equation (1) by -6 [LIST=1] [*]-6l - 6s = -36 [*]12l + 6s = 60 [/LIST] Now add equation 1 to equation 2: 12l - 6l + 6s - 6s = 60 - 36 Cancel the 6s terms, and we get: 6l = 24 To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=6l%3D24&pl=Solve']type this equation into our search engine[/URL] and we get: l = [B]4 [/B] Now substitute this into equation 1: 4 + s = 6 To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=4%2Bs%3D6&pl=Solve']we type this equation into our search engine[/URL] and we get: s = [B]2[/B]

A straight line has the equation ax + by=23. The points (5,-2) and (1,-5) lie on the line. Find the values of a and b. plug in both points and form 2 equations: [LIST=1] [*]5a - 2b = 23 [*]1x - 5b = 23 [/LIST] We can solve this simultaneous equations any one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]a = 3[/B] [*][B]b = -4[/B] [/LIST]

A straight road to the top of a hill is 2500 feet long and makes an angle of 12 degrees with the horizontal. Find the height of the hill. Height = Distance * Sin(Horizon Angle) Height = 2500 * [URL='http://www.mathcelebrity.com/anglebasic.php?entry=12&coff=&pl=sin']Sin(12)[/URL] Height = 2500 * 0.207911691 Height = [B]519.78 feet[/B]

a string measures 20 inches is cut into pieces. Let z represent the length of one of the resulting pieces. express length of the second piece in terms of the length z of the first pice Second piece length = [B]20 - z[/B]

A student and the marine biologist are together at t = 0. The student ascends more slowly than the marine biologist. Write an equation of a function that could represent the student's ascent. Please keep in mind the slope for the marine biologist is 12. Slope means rise over run. In this case, rise is the ascent distance and run is the time. 12 = 12/1, so for each second of time, the marine biologist ascends 12 units of distance If the student ascends slower, than the total distance gets reduced by an unknown factor, let's call it c. So we have the student's ascent function as: [B]y(t) = 12t - c[/B]

a student has $50 in saving and earns $40 per week. How long would it take them to save $450 Set up the savings function S(w), where w is the number of weeks. The balance, S(w) is: S(w) = Savings Per week * w + Initial Savings S(w) = 40w + 50 The problems asks for how many weeks for S(w) = 450. So we have; 40w + 50 = 450 To solve for w, we[URL='https://www.mathcelebrity.com/1unk.php?num=40w%2B50%3D450&pl=Solve'] type this equation in our search engine[/URL] and we get: w = [B]10[/B]

A student has an average mark of 68 from 10 tests. What mark must be gained in the next test to raise their average to 70? This is a missing average problem. We use our [URL='http://www.mathcelebrity.com/missingaverage.php?num=68%2C68%2C68%2C68%2C68%2C68%2C68%2C68%2C68%2C68&avg=70&pl=Calculate+Missing+Score']missing average calculator[/URL]. The student's next score must be a [B]90[/B].

A student hypothesized that girls in his class had the same blood pressure levels as boys. The probability value for his null hypothesis was 0.15. So he concluded that the blood pressures of the girls were higher than boys'. Which kind of mistake did he make? a. Type I error b. Type II error c. Type I and Type II error d. He did not make any mistake [B]d. He did not make any mistake[/B] [I]p value is high, especially using a significance level of 0.05[/I]

A student posed a null hypothesis that during the month of September, the mean daily temperature of Boston was the same as the mean daily temperature of New York. His alternative hypothesis was that mean temperatures in these two cities were different. He found the P value of his null hypothesis was 0.56. Thus, he could conclude: a. In September, Boston was colder than New York b. In September, Boston was warmer than New York c. He may reject the null hypothesis d. He failed to reject the null hypothesis [B]d. He failed to reject the null hypothesis[/B] [I]Higher p value tells us we cannot reject the null hypothesis[/I]

A student walks 1500 meters to school in 30 minutes. What is their average speed in meters per minute? 1500 meters / 30 minutes Divide top and bottom by 30 [B]50 meters / minute[/B]

A submarine at an elevation of -185 meters descends to 3 times that elevation. Then, it elevates 90 meters. What is the submarines new elevation? 3 times the current elevation is: 3 * -185 = -555 Elevating 90 meters means we have a positive change: -555 + 90 = [B]-465[/B]

A submarine dove 132.58 meters to reach a resting depth of 700 meter below sea level. What was it's original depth Below sea level is a negative amount. So they end up at -700. To go back up toward sea level, we'd be at: -700 + 132.58 = -567.42 Negative numbers mean below sea level, so the original depth was [B]567.42 meters below sea level[/B]

A submarine hovers at 240 meters below sea level. If it descends 160 meters and then ascends 390 meters, what is its new position? 240 meters below sea level means a negative number, so we start with: -240 Descending 160 meters means our depth decreases, so we subtract: -240 - 160 = -400 Ascends means our depth increases, so we add: -400 + 390 = [B]-10 or 10 feet below sea level [MEDIA=youtube]ngToCpLBgH4[/MEDIA][/B]

a submarine is 450 feet below sea level. It descends 300 feet. What is its new position? We start at 450 feet below sea level. We descend another 300 feet, so we're now at: -450 - 300 = -750 Negative depth means below sea level, so the submarine is at [B]750 feet below sea level[/B]

A submarine is 75 feet below sea level. It descends another 25 feet every 10 seconds for 3 minutes. What integer represents the submarines current location? Assumptions and givens: [LIST] [*]Let m be the number of minutes [*]10 seconds is 1/6 of a minute, 6 (10) seconds blocks per minute * 3 minutes = 18 (10 second blocks) [*]Below sea level is a negative number [/LIST] [U]Current depth:[/U] -25(18) - 75 -450 - 75 [B]-525[/B]

A submarine sits at –300 meters in relation to sea level. Then it descends 115 meters. What is its new position in relation to sea level? Descending means we go down in sea level, so we subtract: -300 - 115 = [B]-415 or 415 meters below sea level[/B]

A suitcase contains nickels, dimes and quarters. There are 2&1/2 times as many dimes as nickels and 5 times the number of quarters as the number of nickels. If the coins have a value of $24.80, how many nickels are there in the suitcase? Setup number of coins: [LIST] [*]Number of nickels = n [*]Number of dimes = 2.5n [*]Number of quarters = 5n [/LIST] Setup value of coins: [LIST] [*]Value of nickels = 0.05n [*]Value of dimes = 2.5 * 0.1n = 0.25n [*]Value of quarters = 5 * 0.25n = 1.25n [/LIST] Add them up: 0.05n + 0.25n + 1.25n = 24.80 Solve for [I]n[/I] in the equation 0.05n + 0.25n + 1.25n = 24.80 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (0.05 + 0.25 + 1.25)n = 1.55n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 1.55n = + 24.8 [SIZE=5][B]Step 3: Divide each side of the equation by 1.55[/B][/SIZE] 1.55n/1.55 = 24.80/1.55 n = [B]16[/B] [B] [URL='https://www.mathcelebrity.com/1unk.php?num=0.05n%2B0.25n%2B1.25n%3D24.80&pl=Solve']Source[/URL][/B]

A sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a. 40 years b. 50 years c. 30 years d. 60 years e. 80 years Simple interest formula if we start with 1 dollar and double to 2 dollars: 1(1 + i(20)) = 2 1 + 20i = 2 Subtract 1 from each side: 20i = 1 Divide each side by 20 i = 0.05 Now setup the same simple interest equation, but instead of 2, we use 3: 1(1 + 0.05(t)) = 3 1 + 0.05t = 3 Subtract 1 from each side: 0.05t = 2 Divide each side by 0.05 [B]t = 40 years[/B]

A super deadly strain of bacteria is causing the zombie population to double every day. Currently, there are 25 zombies. After how many days will there be over 25,000 zombies? We set up our exponential function where n is the number of days after today: Z(n) = 25 * 2^n We want to know n where Z(n) = 25,000. 25 * 2^n = 25,000 Divide each side of the equation by 25, to isolate 2^n: 25 * 2^n / 25 = 25,000 / 25 The 25's cancel on the left side, so we have: 2^n = 1,000 Take the natural log of each side to isolate n: Ln(2^n) = Ln(1000) There exists a logarithmic identity which states: Ln(a^n) = n * Ln(a). In this case, a = 2, so we have: n * Ln(2) = Ln(1,000) 0.69315n = 6.9077 [URL='https://www.mathcelebrity.com/1unk.php?num=0.69315n%3D6.9077&pl=Solve']Type this equation into our search engine[/URL], we get: [B]n = 9.9657 days ~ 10 days[/B]

A survey of 75 people found 45 like rabbits, 32 like hamsters, and 15 like both animals. How many people like neither animal? People who like either rabbits or hamsters = Rabbit liners + hamster likes - both likers People who like either rabbits or hamsters = 45 + 32 - 15 People who like either rabbits or hamsters = 62 People who like neither = 75 - People who like either rabbits or hamsters People who like neither = 775 - 62 People who like neither = [B]13[/B]

A survey of 950 college students found that 85% of the men and 90% of the women identified math as their favorite subject. If altogether 834 students reported math to be their favorite subject how many men and women participated in the survey Let m be the number of men and w be the number of women. We are given 2 equations [LIST=1] [*]m + w = 950 [*]0.85m + 0.90w = 834 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+w+%3D+950&term2=0.85m+%2B+0.90w+%3D+834&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: [LIST] [*]m = [B]420[/B] [*]w = [B]530[/B] [/LIST]

A survey was conducted that asked 1007 people how many books they had read in the past year. Results indicated that x overbarequals11.3 books and sequals16.6 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval. x bar = 11.3 s = 16.6 n = 1007 [URL='https://www.mathcelebrity.com/normconf.php?n=1007&xbar=11.3&stdev=16.6&conf=90&rdig=4&pl=Not+Sure']We use our confidence interval calculator[/URL] and get [B]10.4395 < u < 12.1605[/B]. [B][I]We interpret this as: If we repeated experiments, the proportion of such intervals containing u would be 90%[/I][/B]

A survey was given to 120 6th grade students at middle school. It showed the 42 students said they like playing at the park. What % of the students said they like playing there? We want [I][URL='https://www.mathcelebrity.com/perc.php?num=42&den=120&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']42 is what percent of 120[/URL][/I] Using our calculator above, we get [B]35%[/B]

A sweater costs $40. That is 5 times as much as a shirt. What is the price of the shirt? State this as an equation. Let the price of the shirt be s. 5 times as much means we multiply s by 5: 5s = 40 [URL='https://www.mathcelebrity.com/1unk.php?num=5s%3D40&pl=Solve']Type this equation into the search engine[/URL], we get: s = [B]8[/B]

A sweater that you love costs $32. You really want the sweater but only have $35. If there’s a sales tax of 4% on the item, do you have enough to buy the sweater? Calculate after-tax amount: After tax amount = Sale Price * (1 + sales tax percent) After tax amount = 32 * (1 + 0.04) <-- Since 4% = 0.04 After tax amount = 32 * (1.04) After tax amount = $33.28 [B]Yes[/B], since $33.28 is less than or equal to $35, you have enough to buy the sweater.

A tablet of Tylenol contains 35 mg of the active ingredient acetaminophen. If you take 140 mg of acetaminophen, how many tablets did you take? 140/35 = 4 tablets

A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take for the tank to be empty Assumptions and givens: [LIST] [*]Let the number of seconds be s. [*]An empty tank means 0 liters of water. [*]Leaks mean we subtract from the starting volume. [/LIST] We have the following relation: 800 - 12s = 0 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=800-12s%3D0&pl=Solve']type it in our search engine[/URL] and we get: s = 66.67 seconds

A tank used 22 gallons of gas to go 17.6 miles. How many miles per gallon did the tank use? 17.6 miles / 22 gallons = [B]0.8 miles per gallon[/B]

A taxi cab in Chicago charges $3 per mile and $1 for every person. If the taxi cab ride for two people costs $20. How far did the taxi cab travel. Set up a cost function C(m) where m is the number of miles driven: C(m) = cost per mile * m + per person fee [U]Calculate per person fee:[/U] per person fee = $1 per person * 2 people per person fee = $2 [U]With a cost per mile of $3 and per person fee of $2, we have:[/U] C(m) = cost per mile * m + per person fee C(m) = 3m + 2 The problem asks for m when C(m) = 20, so we set 3m + 2 equal to 20: 3m + 2 = 20 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%2B2%3D20&pl=Solve']plug it in our search engine[/URL] and we get: m = [B]6[/B]

A taxi cab in nyc charges a pick up fee of $5.00 . The customer must also pay $2.59 for each mile that the taxi must drive to reach their destination. Write an equation Set up a cost function C(m) where m is the number of miles: C(m) = Mileage Charge * m + pick up fee [B]C(m) = 2.59m + 5[/B]

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel? Set up the travel cost equation where m is the number of miles: C(m) = 0.8m + 1.50 If Samantha wants to spend less than 12 per ride, we have an inequality where C(m) < 12: [B]0.8m + 1.50 < 12[/B]

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel? [LIST] [*]Each ride will cost 1.50 + 0.8x where x is the number of miles per trip. [*]This expression must be less than 12. [/LIST] [U]Setup the inequality:[/U] 1.5 + 0.8x < 12 [U]Subtracting 1.5 from each side of the inequality[/U] 0.8x < 10.5 [U]Simplifying even more by dividing each side of the inequality by 0.8, we have:[/U] [B]x < 13.125[/B]

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel? Set up a cost function C(m), where m is the number of miles: C(m) = Cost per mile * m + flat rate C(m) = 0.65m + 1.75 The problem asks for m when C(m) = 10 0.65m + 1.75 = 10 [URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get: m = [B]12.692 miles[/B]

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel Set up a cost function C(m), where m is the number of miles Erica can travel. We have: C(m) = 0.65m + 1.75 If C(m) = 10, we have: 0.65m + 1.75 = 10 [URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into our search engine[/URL], we get: m = 12.69 miles If the problem asks for complete miles, we round down to 12 miles.

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel? Set up the cost function C(m) where m is the number of miles: C(m) = 0.65m + 1.75 If Erica has $10, then C(m) = 10, so we have: 0.65m + 1.75 = 10 [URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get m = 12.69 if the answer asks for whole number, then we round down to m = 12

A taxi charges a flat rate of 1.75, plus an additional 0.65 per mile. If Erica has at most 10 to spend on the cab ride, how far could she travel? Setup an equation where x is the number of miles traveled: 0.65x + 1.75 = 10 Subtract 1.75 from each side: 0.65x = 8.25 Divide each side by 0.65 [B]x = 12.69 miles[/B] If we do full miles, we round down to 12. [MEDIA=youtube]mFqUe2mjX-w[/MEDIA]

A taxi service charges an initial fee of $3 plus $1.80 per mile. How far can you travel for $12? Given m for miles, we have the equation: 1.80m + 3 = 12 We [URL='https://www.mathcelebrity.com/1unk.php?num=1.80m%2B3%3D12&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get: m = [B]5[/B]

A teacher assumed that the average of grades for a math test was 80. Imagine 20 students took the test and the 95% confidence interval of grades was (83, 90). Can you reject the teacher's assumption? a. Yes b. No c. We cannot tell from the given information [B]a. Yes[/B] [I]At the 0.05 significance level, yes since 80 is not in the confidence interval.[/I]

A teacher had 54 pencils gave p pencils to each of his s students. How many pencils does he have left? If the teacher gave p pencils to each of his s students, then he gave away ps total pencils. He's left with: [B]54 - ps[/B]

A teacher hypothesized that in her class, grades of girls on a chemistry test were the same as grades of boys. If the probability value of her null hypothesis was 0.56, it suggested: a. We failed to reject the null hypothesis b. Boys' grades were higher than girls' grades c. Girls' grades were higher than boys' grades d. The null hypothesis was rejected [B]a. We failed to reject the null hypothesis[/B] Due to a high probability.

a teacher puts 1125 marbles into 9 containers to put the same number of marbles into each container how many marbles does the teacher put into each container marbles per container = Total marbles / total containers marbles per container = 1125/9 marbles per container = [B]125[/B]

A teacher who makes $54000 per year $8400 in taxes, and $1200 in union does what fraction of the teacher’s income does she have left Calculate Net Income: Net income = Earnings - Taxes - Union Dues Net income = 54000 - 8400 - 1200 Net income = 44,400 Net Income Percent = 100% * Net Income / Earnings Net Income Percent = 100% * 44,400/54,000 Net Income Percent = 100% * 0.8222 Net Income Percent = [B]82.22%[/B]

A teacher’s salary was $3300 after she had received an increase of 10%. Calculate the teacher’s salary if she has received an increase of 20% instead. First, we need to find the starting salary. Let the starting salary be s. Since 10% as a decimal is 0.10, We're given: s*(1.10) = 3300 1.10s = 3300 To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=1.10s%3D3300&pl=Solve']we type this equation into our search engine[/URL] and we get: s = [B]3000[/B] The problem asks for the new salary if the teacher's starting salary was increased by 20%. 20% as a decimal is 0.20, so we have: 3000(1.2) = $[B]3,600[/B]

A television sells for $750. Instead of paying the total amount at the time of the purchase, the same television can be bought by paying $100 down and $50 a month for 14 months. How much is saved by paying the total amount at the time of the purchase? Option 2: 100 + 50(14) 100 + 700 800 800 - 750 = [B]$50 saved [MEDIA=youtube]XAixLxvelcg[/MEDIA][/B]

A test has three true-false questions. Find the total number of ways you can answer the three questions We can either choose T or F. So we have: Question 1: 2 choies Question 2: 2 choices Question 3: 2 choices 2 * 2 * 2 = [B]8 choices [/B] [LIST=1] [*][B]TTT[/B] [*][B]TTF[/B] [*][B]TFT[/B] [*][B]FTT[/B] [*][B]FTF[/B] [*][B]FFT[/B] [*][B]TFF[/B] [*][B]FFF[/B] [/LIST]

A test has twenty questions worth 100 points . The test consist of true/false questions worth 3 points each and multiple choice questions worth 11 points each . How many multiple choice questions are on the test? Set up equations where t = true false and m = multiple choice: [LIST=1] [*]t + m = 20 [*]3t + 11m = 100 [/LIST] Use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=t+%2B+m+%3D+20&term2=3t+%2B+11m+%3D+100&pl=Cramers+Method']simultaneous equation calculator[/URL]: [B]t = 15, m = 5[/B]

A test has twenty questions worth 100 points total. the test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many true/false questions are on the test? Let m be the number of multiple choice questions and t be the number of true/false questions. We're given: [LIST=1] [*]m + t = 20 [*]11m + 3t = 100 [/LIST] We can solve this system of equations 3 ways below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the following answers: [LIST] [*][B]m = 5[/B] [*][B]t = 15[/B] [/LIST] Check our work in equation 1: 5 + 15 ? 20 [I]20 = 20[/I] Check our work in equation 2: 11(5) + 3(15) ? 100 55 + 45 ? 100 [I]100 = 100[/I]

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test? Let the number of true/false questions be t. Let the number of multiple choice questions be m. We're given two equations: [LIST=1] [*]m + t = 20 [*]11m + 3t = 100 [/LIST] We have a set of simultaneous equations. We can solve this using 3 methods: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we pick, we get the same answer: [LIST] [*][B]m = 5[/B] [*][B]t = 15[/B] [/LIST]

A text message plan costs $7 per month plus $0.28 per text. Find the monthly cost for x text messages. We set up the cost function C(x) where x is the number of text messages per month: C(x) = Cost per text * x + Monthly cost Plugging in our given numbers, we get: [B]C(x) = 0.28x + 7[/B]

a textbook store sold a combined total of 296 sociology and history text books in a week. the number of history textbooks sold was 42 less than the number of sociology textbooks sold. how many text books of each type were sold? Let h = history book and s = sociology books. We have 2 equations: (1) h = s - 42 (2) h + s = 296 Substitute (1) to (2) s - 42 + s = 296 Combine variables 2s - 42 = 296 Add 42 to each side 2s = 338 Divide each side by 2 s = 169 So h = 169 - 42 = 127

A textbook store sold a combined total of 307 biology and chemistry textbooks in a week. The number of chemistry textbooks sold was 71 less than the number of biology textbooks sold. How many textbooks of each type were sold? Let b be the number of biology books and c be the number of chemistry books. We have two equations: [LIST=1] [*]b + c = 307 [*]c = b - 71 [/LIST] Substitute (2) into (1) for c b + (b - 71) = 307 Combine like terms: 2b - 71 = 307 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2b-71%3D307&pl=Solve']equation solver[/URL], we get: [B]b = 189[/B] Now substitute that into (2): c = 189 - 71 [B]c = 118[/B]

A theater has 1200 seats. Each row has 20 seats. Write and solve an equation to find the number x of rows in the theater. Let x be the number of rows in the theater: x = Total Seats / Seats per row x = 1200/20 x = [B]60[/B]

A theater is 3/4 full. When 96 people leave, the theater is only 35% full. How many seats are there? Let the full capacity of seats in the theater be s. We're given: 3/4s - 96 = 0.35s (Since 35% is 0.35) We also know that 3/4 = 0.75, so let's use this to have decimals: 0.75s - 96 = 0.35s To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75s-96%3D0.35s&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]240[/B]

A theatre contains 459 seats and the ticket prices for a recent play were $53 for adults and $16 for children. If the total proceeds were $13,930 for a sold- out matinee, how many of each type of ticket were sold? Let a be the number of adult tickets and c be the number of children tickets. We have the following equations: [LIST=1] [*]a + c =459 [*]53a + 16c = 13930 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a%2Bc%3D459&term2=53a+%2B+16c+%3D+13930&pl=Cramers+Method']simultaneous equation calculator[/URL], we have: [B]a = 178 c = 281[/B]

A theatre sold 67 tickets to a show. 43 tickets were for children up to 12 years old. How many tickets were for people older than 12 67 tickets - 43 tickets for 12 and under = [B]24 tickets[/B] for people older than 12

A thermometer has a range of 1.5 degrees of the temperature, what is the maximum and minimum at 87.4 degrees Range = Max - Min Divide this by 2 to get the lesser half and larger half: Half-Range = 1.5/2 Half-Range = 0.75 [U]Our Maximum temperature is:[/U] Max Temp = Current Temp + Half-Range Max Temp = 87.4 + 0.75 Max Temp = [B]88.15 [/B] [U]Our Minimum temperature is:[/U] Min Temp = Current Temp - Half-Range Min Temp = 87.4 - 0.75 Min Temp = [B][B]86.65[/B][/B]

A third of a pizza is 400 calories. How many calories in the whole pizza? Let c be the number of calories in the whole pizza. WE have: c/3 = 400 To solve this proportion for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=c&num2=400&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and get: c = [B]1,200[/B]

A three digit number, if the digits are unique [LIST=1] [*]For our first digit, we can start with anything but 0. So we have 9 options [*]For our second digit, we can use anything but 9 since we want to be unique. So we have 9 options [*]For our last digit, we can use anything but the first and second digit. So we have 10 - 2 = 8 options [/LIST] Our total 3 digit numbers with all digits unique is found by the fundamental rule of counting: 9 * 9 * 8 = [B]648 possible 3 digit numbers[/B]

a times b divided by the quantity a minus b a times b: ab a minus b: a - b Now divide a times b by a minus b: [B]ab/(a - b)[/B]

A times r squared multiplied by h r squared means we raise r to the power of 2: r^2 a times r squared: ar^2 Multiplied by h: [B]ahr^2[/B]

A tire repair shop charges $5 for tool cost and $2 for every minute the worker spends on the repair. A) Write an equation of the total cost of repair, $y, in terms of a total of x minutes of repair. y = Variable Cost + Fixed Cost y = Cost per minute of repair * minutes of repair + Tool Cost [B]y = 2x + 5[/B]

A toad croaks every 8seconds and a frog croaks every 6 seconds .They both croak at the same .After how many seconds will they next croak at the same time again. We want the least common multiple of 8 and 6. We type in [URL='https://www.mathcelebrity.com/gcflcm.php?num1=6&num2=8&num3=&pl=GCF+and+LCM']LCM(6, 8) into our search engine[/URL] and we get [B]24[/B]

A toffee jar contains 225 toffees . How many toffees will be there in 62 such toffee jars ? Total Toffees = Toffee per jar * number of jars Total Toffees = 225 * 62 Total Toffees = [B]13,950 toffees[/B]

a tomato plant has 5 leaves on day 1, 7 on day 3 and 9 on day 5. what is the rate it is growing? Day 1 = 5 leaves Day 3 = 7 leaves Day 5 = 9 leaves [B]Growth Rate = 2 leaves per day[/B]

A tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For how many minutes does it walk? Distance formula (d) for a rate (r) and time (t) is: d = rt We're given d = 12.5 and r = 5 12.5 = 5t 5t = 12.5 Solve for t. Divide each side of the equation by 5: 5t/5 = 12.5/5 Cancel the 5's on left side and we get: t = [B]2.5[/B]

a total of $4000 is invested: part at 10% and the remainder at 15%. How much is invested at each rate if the annual interest is $430? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=4000&i1=10&i2=15&itot=430&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]3,400[/B] @ 10% [*][B]600[/B] @ 15% [/LIST]

A total of $4300 was invested, part of it at 6% interest and the remainder at 9%. If the total yearly interest amounted to $315, how much was invested at each rate? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=4300&i1=6+&i2=9&itot=315&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]Fund 1: 2,400[/B] [*][B]Fund 2: 1,900[/B] [/LIST]

A total of $6,000 was invested, a portion at 6% and the remainder at 8%. The total amount of interest earned was $450. How much was invested at each rate? Using our split fund interest calculator, we get: [LIST] [*][B]1500 in 6% fund[/B] [*][B]4500 in 8% fund[/B] [/LIST]

A total of $7000 is invested: part at 7% and the remainder at 9%. How much is invested at each rate if the annual interest is $550? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=7000&i1=7&i2=9&itot=550&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]Fund 1: $4,000[/B] [*][B]Fund 2: $3,000[/B] [/LIST]

a total of 6000 is invested part at 8% and the remainder at 13%. how much is invested at each rate if the annual interest is 710 Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=6000&i1=8&i2=13&itot=710&pl=Calculate']split fund interest calculator[/URL], we get: 1,400 4,600

A total of 7000 is invested part at 7% and the reminder at 11% .how much is invested at each rate of the annual interest is 640 Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=7000&i1=7&i2=11&itot=640&pl=Calculate']split fund interest rate calculator[/URL], we get: [LIST] [*]Fund 1 = [B]3250[/B] [*]Fund 2 = [B]3750[/B] [/LIST]

A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was Marcos car towed if he received a bill for $71 Set up a cost equation C(m) where m is the number of miles: C(m) = Cost per mile * m + Service Fee Plugging in the service fee of 50 and cost per mile of 1.75, we get: C(m) = 1.75m + 50 The question asks for what m is C(m) = 71. So we set C(m) = 71 and solve for m: 1.75m + 50 = 71 Solve for [I]m[/I] in the equation 1.75m + 50 = 71 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 50 and 71. To do that, we subtract 50 from both sides 1.75m + 50 - 50 = 71 - 50 [SIZE=5][B]Step 2: Cancel 50 on the left side:[/B][/SIZE] 1.75m = 21 [SIZE=5][B]Step 3: Divide each side of the equation by 1.75[/B][/SIZE] 1.75m/1.75 = 21/1.75 m = [B]12[/B]

A town has a population of 12000 and grows at 5% every year. What will be the population after 12 years, to the nearest whole number? We calculate the population of the town as P(t) where t is the time in years since now. P(t) = 12000(1.05)^t The problem asks for P(12) P(12) = 12000(1.05)^12 P(12) = 12000(1.79585632602) P(12) = [B]21550[/B] <- nearest whole number

A town has a population of 25,000 and grows at 7.7% every 4 months. What will be the population after 6 years? [LIST] [*]1 year = 12 months [*]12 months / 4 months = 3 compounding periods per year [*]3 compounding periods per year * 6 years = 18 compounding periods [/LIST] So we have our population growth as follows: 25,000(1.077)^18 25,000 * 3.8008668804 95,021.67 ~ [B]95,021[/B]

A town has a population of 50,000. Its rate increases 8% every 6 months. Find the population after 4 years. Every 6 months means twice a year. So we have 4 years * twice a year increase = 8 compounding periods. Our formula for compounding an initial population P at time t is P(t) at a compounding percentage i: P(t) = P * (1 + i)^t Since 8% is 0.08 as a decimal and t = 4 *2 = 8, we have: P(8) = 50000 * (1.08)^8 P(8) = 50000 * 1.85093 P(8) = 92,546.51 Since we can't have a partial person, we round down to [B]92,545[/B]

A towns population is currently 500. If the population doubles every 30 years, what will the population be 120 years from now? Find the number of doubling times: 120 years / 30 years per doubling = 4 doubling times Set up our growth function P(n) where n is the number of doubling times: P(n) = 500 * 2^n Since we have 4 doubling times, we want P(4): P(4) = 500 * 2^4 P(4) = 500 * 16 P(4) = [B]8,000[/B]

A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. The company sells each bear for $12.00 each. How many bears must this company sell in order to break even? [U]Set up the cost function C(b) where b is the number of bears:[/U] C(b) = Cost per bear * b + factory expenses C(b) = 8b + 1500 [U]Set up the revenue function R(b) where b is the number of bears:[/U] R(b) = Sale Price per bear * b R(b) = 12b [U]Break-even is where cost equals revenue, so we set C(b) equal to R(b) and solve for b:[/U] C(b) = R(b) 8b + 1500 = 12b To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B1500%3D12b&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]375[/B]

A toy factory makes 5,000 teddy bears per day. The supervisor randomly selects 10 teddy bears from all 5,000 teddy bears and uses this sample to estimate the mean weight of teddy bears and the sample standard deviation. How many degrees of freedom are there in the estimate of the standard deviation? DF = n - 1 DF = 10 - 1 [B]DF = 9[/B]

A tractor tire has a radius of 24 inches. If the tire rotates one time around, about how many inches of ground will it cover? Use 3.14 for pi. A tractor tire is a circle. We want the circumference, which is the distance around the tire. C = 2pir C = 2(3.1415)24 [B]C ~ 150.8[/B]

A train leaves San Diego at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 30mph faster than the first. If the second train overtakes the first at 6:00 PM, what is the speed of each of the two trains? Distance = Rate x Time Train 1: d = rt t = 1:oo PM to 6:00 PM = 5 hours So we have d = 5r Train 2: d = (r + 30)t t = 3:oo PM to 6:00 PM = 3 hours So we have d = 3(r + 30) Set both distances equal to each other since overtake means Train 2 caught up with Train 1, meaning they both traveled the same distance: 5r = 3(r + 30) Multiply through: 3r + 90 = 5r [URL='https://www.mathcelebrity.com/1unk.php?num=3r%2B90%3D5r&pl=Solve']Run this equation through our search engine[/URL], and we get [B]r = 45[/B]. This is Train 1's Speed. Train 2's speed = 3(r + 30). Plugging r = 45 into this, we get 3(45 + 30). 3(75) [B]225[/B]

A train ticket is 8 centimeters tall and 10 centimeters long. What is its area? The ticket is a rectangle. The area is: A = lw Plugging in our numbers, we get: A = (8)(10) A = 80

A train traveled at 66km an hour for four hours. Find the distance traveled Distance = Rate * Time Distance = 66km/hr * 4 hours Distance = [B]264 miles[/B]

A trapezoid has one base that is 120% of the length of the other base. The two sides are each 1/2 the length of the smaller base. If the perimeter of the trapezoid is 54.4 inches, what is the length of the smaller base of the trapezoid? Setup measurements: [LIST] [*]Small base = n [*]Large base = 1.2n [*]sides = n/2 [*]Perimeter = n + 1.2n + 0.5n + 0.5n = 54.4 [/LIST] Solve for [I]n[/I] in the equation n + 1.2n + 0.5n + 0.5n = 54.4 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 1.2 + 0.5 + 0.5)n = 3.2n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 3.2n = + 54.4 [SIZE=5][B]Step 3: Divide each side of the equation by 3.2[/B][/SIZE] 3.2n/3.2 = 54.4/3.2 n = [B]17[/B] [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B1.2n%2B0.5n%2B0.5n%3D54.4&pl=Solve']Source[/URL]

A traveler is walking on a moving walkway in an airport. the traveler must walk back on the walkway to get a bag he forgot. the traveler's ground speed is 2 ft/s against the walkway and 6 ft/s with the walkway. what is the traveler's speed off the walkway? What is the speed of the moving walkway. We have two equations, where w is the speed of the walkway and t is the speed of the traveler. [LIST=1] [*]t - w = 2 [*]t + w = 6 [*]Rearrange (1) to solve for t: t = w + 2 [/LIST] Now plug (3) into (2) (w + 2) + w = 6 Combine like terms: 2w + 2 = 6 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B2%3D6&pl=Solve']equation solver[/URL], we get [B]w = 2[/B] Plug this into (1) t - 2 = 2 Add 2 to each side [B]t = 4[/B]

A tree grows 35 cm in 2 years. If it continues to grow at the same rate determine how long it would take to grow 85 cm We set up a proportion of cm to years where y is the number of years it takes to grow 85 cm: 35/2 = 85/y To solve this proportion for y, [URL='https://www.mathcelebrity.com/prop.php?num1=35&num2=85&den1=2&den2=y&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get: [B]y = 4.86[/B]

A tree is 23.1 feet tall. What is its height in meters ? Use the following conversion: 1 meter is 3.3 feet 23.1 feet * 1 meter / 3.3 feet = [B]7 meters[/B]

A trench is 40 feet long and the trencher goes 2 feet per minute. How long does it take to dig the trench? 2 feet per minute * x minutes = 40 feet Divide each side by 2 [B]x = 20 minutes[/B]

a triangle has side lengths of 12,16, and 20 centimeters. is it a right triangle? First, we see if we can simplify. So we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=12&num2=16&num3=20&pl=GCF']type GCF(12,16,20) [/URL]and we get 4. We divide the 3 side lengths by 4: 12/4 = 3 16/4 = 4 20/4 = 5 And lo and behold, we get a Pythagorean Triple of 3, 4, 5. So [B]yes, this is a right triangle[/B].

A truck driver took 7 hours and 45 minutes to travel 426.25 miles. What was the average speed of the truck driver? 45/60 = 0.75 of an hour 7 hours and 45 minutes = 7.75 hours 426.25 miles / 7.75 hours miles = [B]55 miles per hour[/B]

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle travels at a constant speed of 20 feet per minute for the entire 100 feet. The rabbit travels at a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then continuous at a constant speed of 40 feet per minute for the last 50 feet. (i) Determine which animal won the race. (ii). By how much time the animal won the race. (iii) Explain one life lesson from the race. We know the distance formula is: d = rt For the turtle, he has a rate (r) of 20 feet / minute and distance (d) of 100. We want to solve for time: [URL='https://www.mathcelebrity.com/drt.php?d=+100&r=+20&t=&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get: t = 5 The rabbit has 3 parts of the race: Rabbit Part 1: Distance (d) = 50 and rate (r) = 40 [URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get: t = 1.25 Rabbit Part 2: The rabbit stops for 3 minutes (t = 3) Rabbit Part 3: Distance (d) = 50 and rate (r) = 40 [URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get: t = 1.25 Total time for the rabbit from the 3 parts is (t) = 1.25 + 3 + 1.25 Total time for the rabbit from the 3 parts is (t) = 5.5 [LIST] [*](i) The [B]turtle won[/B] the race because he took more time to finish and they both started at the same time [*](ii) We subtract the turtles time from the rabbit's time: 5.5 - 5 = [B]0.5 minutes which is also 30 seconds[/B] [*](iii) [B]Slow and Steady wins the race[/B] [/LIST]

A tv is originally priced at $69.99 is reduced to $42.50. Find the % decrease in price Using our [URL='https://www.mathcelebrity.com/markup.php?p1=+69.99&m=+&p2=42.50&pl=Calculate']markdown calculator[/URL], we get: [B]-39.28%[/B]

A TV that usually sells for $192.94 is on sale for 15% off. If sales tax on the TV is 6%, what is the price of the TV, including tax? Find the discounted price: 15% off of 192.94 Discounted Price = 192.94 * (1 - 0.15) <-- 15% as a decimal is 0.15, and 1 is 100%, so we subtract to get 85% of the original price Discounted Price =192.94(0.85) Discounted Price = $164 Now, add in the sales tax of 6% to the Discounted Price Price after sales tax = Discounted Price * 1.06 Price after sales tax = $164 * 1.06 [B]Price after sales tax = $173.84[/B]

A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 85 and 125 points? For x = 125, our z-score and probability is seen [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+125&mean=+105&stdev=+20&n=+1&pl=P%28X+%3C+Z%29']here[/URL] Z = 1 P(x < 1) = 0.841345 For x = 85, our z-score and probability is seen [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+85&mean=+105&stdev=+20&n=+1&pl=P%28X+%3C+Z%29']here[/URL] Z = -1 P(x < -1) = 0.158655 So what we want is the probability between these values:
0.841345 - 0.158655 = [B]0.68269[/B]

A typical human adult weighs 150 pounds, while a human newborn weighs approximately 7 pounds. An adult female Western Grey Kangaroo weighs about 30 kilograms and gives birth to babies who are approximately one gram. If human babies were proportionally the same weight as adults as Western Grey Kangaroos babies, how much would a human newborn weigh? Set up a proportion of adult weight to baby weight where n is the weight of a human baby: 30000/1 = 150/n Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=30000&num2=150&den1=1&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get: n = [B]0.005 or 1/200 of a pound[/B]

A typist is paid a basic wage of $22.50 per hour for a 40-hour week. Calculate the typist's basic weekly wage Basic Weekly Wage = Hourly Rate * Hours Worked Basic Weekly Wage = $22.50 * 40 Basic Weekly Wage = [B]$900[/B]

A U ? = A Let x ? [I]S[/I], where [I]S[/I] is the universal set. First we show that if A ? Ø ? A. Let x ? A ? Ø. Then x ? A or x ? Ø. by definition of the empty set, x cannot be an element in Ø. So by assumption, x ? A ? Ø, x must be in A. So A ? Ø ? A. Next, we show that A ? A ? Ø. This is true because the set resulting from the union of two sets contains both of the sets forms the union Since A ? Ø ? A and A ? A ? Ø, we have that A ? Ø = A.

A used automobile dealership recently reduced the price of a used compact car by 6%. If the price of the car before discount was $18,100, find the discount and the new price. Using our [URL='http://www.mathcelebrity.com/markup.php?p1=&m=+6&p2=++18100&pl=Calculate']discount calculator[/URL], we get: [B]Discount = $1,086 New Price = $17,014[/B]

A used automobile dealership recently reduced the price of a used compact car by 6%. If the price of the car before discount was 18,400, find the discount and the new price. First, find the discount amount: Discount Amount = 6% * 18,400 = [B]1,104 [/B] [U]Calculate discounted price:[/U] Discounted Price = Full Price - Discount Amount Discounted Price = 18,400 - 1,104 Discounted Price = 18,400 - 1,104 = [B]17,296[/B]

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold Let c be the number of CDs sold, and v be the number of videos sold. We're given 2 equations: [LIST=1] [*]c + v = 40 [*]4c + 6v = 180 [/LIST] You can solve this system of equations three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter what method we choose, we get [B]c = 30, v = 10[/B]. Now let's check our work for both given equations for c = 30 and v = 10: [LIST=1] [*]30 + 10 = 40 <-- This checks out [*]4c + 6v = 180 --> 4(30) + 6(10) --> 120 + 60 = 180 <-- This checks out [/LIST]

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold. Let the number of cd's be c and number of videos be v. We're given two equations: [LIST=1] [*]c + v = 40 [*]4c + 6v = 180 [/LIST] We can solve this system of equations using 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [B]c = 30 v = 10[/B]

A used bookstore sells paperback fiction books in excellent condition for $2.50 and in fair condition for $0.50. Write an expression for the cost of buying x excellent-condition paperbacks and f fair-condition paperbacks. Cost = Price * Quantity, so we have: [B]2.50x + 0.50f[/B]

A varies directly as B and inversely as C. There exists a constant k such that: [B]a = kb/c [/B] Inversely means we divide by and directly means we multiply by

a varies directly with b and inversely with c Direct variation means we multiply. Inverse variation means we divide. There exists a constant k such that: [B]a = kb/c[/B]

A vehicle purchased for $25,000 depreciates at a constant rate of 5%. Determine the approximate value of the vehicle 11 years after purchase. Round to the nearest whole dollar. Depreciation at 5% means it retains 95% of the value. Set up the depreciation equation to get Book Value B(t) at time t. B(t) = $25,000 * (1 - 0.05)^t Simplifying, this is: B(t) = $25,000 * (0.95)^t The problem asks for B(11) B(11) = $25,000 * (0.95)^11 B(11) = $25,000 * 0.5688 B(11) = [B]$14,220[/B]

A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost? Let the cost of the soda be p. So the cost of a hot dog is 2p. The total cost of hot dogs: 2hp The total cost of sodas: ps The total cost of both equals d. So we set the total cost of hots dogs plus sodas equal to d: 2hp + ps = d We want to know the cost of a soda (p). So we have a literal equation. We factor out p from the left side: p(2h + s) = d Divide each side of the equation by (2h + s) p(2h + s)/(2h + s) = d/(2h + s) Cancel the (2h + s) on the left side, we get: p = [B]d/(2h + s[/B])

A vertical line that passes through the point (3, -2). Identify TWO additional points on the line. A vertical line runs straight up, so the x-coordinate is always the same. We use x = 3 and any y point: (3, -1) (3, 0) (3, 1)

A vial contains 150 cc of penicillin. How many 5 cc injections can be administered from the vial? 150cc / 5cc per injection = [B]30 injections[/B]

A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company? Set up a cost function C(m) where m is the number of movies you rent: C(m) = Rental cost per movie * m + Membership Fee [U]Video Store 1 cost function[/U] C(m) = 1m + 7.5 Video Store 2 cost function: C(m) = 2.50m We want to know when the costs are the same. So we set each C(m) equal to each other: m + 7.5 = 2.50m To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B7.5%3D2.50m&pl=Solve']we type it in our search engine[/URL] and we get: m = [B]5[/B]

A virus is spreading exponentially. The initial amount of people infected is 40 and is increasing at a rate of 5% per day. How many people will be infected with the virus after 12 days? We have an exponential growth equation below V(d) where d is the amount of days, g is the growth percentage, and V(0) is the initial infected people: V(d) = V(0) * (1 + g/100)^d Plugging in our numbers, we get: V(12) = 40 * (1 + 5/100)^12 V(12) = 40 * 1.05^12 V(12) = 40 * 1.79585632602 V(12) = 71.8342530409 or [B]71[/B]

A washer and a dryer cost 600 combined. The cost of the washer is 3 times the cost of the dryer. What is the cost of the dryer? Let w be the cost of the washer. Let d be the cost of the dryer. We have 2 given equations: [LIST=1] [*]w + d = 600 [*]w = 3d [/LIST] Substitute (2) into (1) (3d) + d = 600 4d = 600 [URL='http://www.mathcelebrity.com/1unk.php?num=4d%3D600&pl=Solve']Run it through our equation calculator[/URL], to get [B]d = 150[/B].

A watch was bought for $250 and sold for $375. What was the profit on the sale of the watch? Profit = Revenue (Sales) - Cost Profit = $375 - $250 Profit = [B]$125[/B]

A water tank holds 236 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds 354 gallons but is leaking at a rate if 5 gallons per week. After how many weeks will the amount of water in the two tanks be the same Let w be the number of weeks of leaking. We're given two Leak equations L(w): [LIST=1] [*]L(w) = 236 - 3w [*]L(w) = 354 - 5w [/LIST] When the water in both tanks is the same, we can set both L(w) equations equal to each other: 236 - 3w = 354 - 5w To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=236-3w%3D354-5w&pl=Solve']type it in our search engine[/URL] and we get: w = [B]59[/B]

a well driller charges $9.00 per foot for the first 10 feet, 9.10 per foot for the next 10 feet, $9.20 per foot for the next 10 feet, and so on, at a price increase of $0.10 per foot for succeeding intervals of 10 feet. How much does it cost to drill a well to a depth of 150 feet? Set up the cost function C(f) where f is the number of feet: Cost = 9(10) + 9.1(10) + 9.2(10) + 9.3(10) + 9.4(10) + 9.5(10) + 9.6(10) + 9.7(10) + 9.8(10) + 9.9(10) + 10(10) + 10.1(10) + 10.2(10) + 10.3(10) + 10.4(10) Cost = [B]1,455[/B]

A wide receiver sprints at a speed of 8.6 feet per second. How many feet would he expect the wide receiver to run in 25 seconds? 8.6 feet per second * 25 seconds = [B]212.5 feet[/B]

A wildlife reserve has a population of 180 elephants. A group of researchers trapped 60 elephants and recorded their vital statistics. Of the trapped elephants, 12 were female. If that rate holds true for the entire population of 180 elephants, how many female elephants are on the wildlife reserve? Set up a proportion of female to trapped elephants: 12/60 = f/180 Using our [URL='http://www.mathcelebrity.com/prop.php?num1=12&num2=f&den1=60&den2=180&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we see that f = [B]36[/B]

A woman dies at the age of 100 and her son is 35 years old how old was she when she gave birth to him. 35 years ago meant she was 100 - 35 = [B]65 years[/B].

A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages? Let the woman's age be w. Let the mother's age be m. We're given two equations: [LIST=1] [*]w = m/2 [*]m + w = 75 [/LIST] Substitute equation (1) into equation (2) for w: m + m/2 = 75 To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%2F2%3D75&pl=Solve']type this equation into our search engine [/URL]and we get: m = [B]50 [/B] To solve for w, we plug m = 50 into equation (1): w = 50/2 w = [B]25[/B]

A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and walked back to the starting point along the same path. She walks 4mph on level ground, 3 mph uphill, and 6 mph downhill. Find the distance she walked. Hint: Think about d = rt, which means that t = d/r. Think about each section of her walk, what is the distance and the rate. You know that the total time is 5 hours, so you know the sum of the times from each section must be 5. Let Level distance = L and hill distance = H. Add the times it took for each section of the walk: L/4 + H /3 + H/6 + L/4 = 5 The LCD of this is 12 from our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=3&num3=6&pl=LCM']LCD Calculator[/URL] [U]Multiply each side through by our LCD of 12[/U] 3L + 4H + 2H + 3L = 60 [U]Combine like terms:[/U] 6L + 6H = 60 [U]Divide each side by 3:[/U] 2L + 2H = 20 The woman walked [B]20 miles[/B]

A woman whose income for the year was $42,800 paid $10,700 in taxes. What percent of her income did she pay in taxes? Tax Percent = Tax Amount / Income * 100% Tax Percent = $10,700 / $42,800 * 100% Tax Percent = 0.25 * 100% Tax Percent = [B]25%[/B]

A wood screw advances 1/16 inch for each complete turn. How far will the screw advance in 8 complete turns 1/6 inch per turn x 8 complete turns = 8/16. Enter 8/16 into the search engine. Choose simplify. Using our [URL='http://www.mathcelebrity.com/fraction.php?frac1=8%2F16&frac2=3%2F8&pl=Simplify']simplify fraction calculator,[/URL] we get 8/16 simplified is [B]1/2[/B] of a turn.

a writer can write a novel at a rate of 3 pages per 5 hour work. if he wants to finish the novel in x number of pages, determine a function model that will represent the accumulated writing hours to finish his novel if 3 pages = 5 hours, then we divide each side by 3 to get: 1 page = 5/3 hours per page So x pages takes: 5x/3 hours Our function for number of pages x is: [B]f(x) = 5x/3[/B]

A yard is 33.21 meters long and 17.6 meters wide. What length of fence must be purchased to enclose the entire yard? The yard is a rectangle. The perimeter of a rectangle is: P = 2l + 2w where l is the length and w is the width. Evaluating, using our [URL='https://www.mathcelebrity.com/rectangle.php?l=33.21&w=17.6&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get P = [B]101.62[/B]

A yard with dimensions of 15m x 10m has a flower garden in the middle. The flower garden has a dimensions of 4m x 7m. What Is the area of the yard without the flower garden? Find the area of the yard: AY = l x w AY = 15 x 10 AFY= 150 Find the area of the flower garden: AFG = l x w AFG = 7 x 14 AFG = 28 Take the area of the remaining piece of the flower garden: ARP = AY - AFG A = 150 - 28 [B]A = 122[/B]

A yardstick casts a shadow of 8 inches. At the same time, a tree casts a shadow of 52 feet. How tall is the tree? Setup a proportion of height to shadow distance where h is the height of the tree: 36/8 = h/52 Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=36&num2=h&den1=8&den2=52&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: h = [B]234 feet[/B]

A yoga member ship costs $16 and additional $7 per class. Write a linear equation modeling the cost of a yoga membership? Set up the cost function M(c) for classes (c) [B]M(c) = 16 + 7c[/B]

A young dad, who was a star football player in college, set up a miniature football field for his five-year-old young daughter, who was already displaying an unusual talent for place-kicking. At each end of the mini-field, he set up goal posts so she could practice kicking extra points and field goals. He was very careful to ensure the goalposts were each straight up and down and that the crossbars were level. On each set, the crossbar was six feet long, and a string from the top of each goalpost to the midpoint between them on the ground measured five feet. How tall were the goalposts? How do you know this to be true? The center of each crossbar is 3 feet from each goalpost. We get this by taking half of 6, since midpoint means halfway. Imagine a third post midway between the two goal posts. It has the same height as the two goalposts. From the center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=3&hypinput=5&pl=Solve+Missing+Side']Using the Pythagorean Theorem[/URL], the other leg -- the height of each post -- is 4 feet.

A young snake measures 0.23 meters long. During the course of his lifetime,he will grow to be 13 times his current length what will be his length be when he is full grown Full Grown Length = Current Length * Growth Multiplier Full Grown Length = 0.23 * 13 Full Grown Length = [B]2.99 meters[/B]

A zoo has 15 Emperor penguins. The Emperor penguins make up 30% percent of all the penguins at the zoo. How many penguins live at the zoo? Let p be the total number penguins at the zoo. We're told: 30% of p = 15 Since 30% = 0.3, we have: 0.3p = 15 Solve for [I]p[/I] in the equation 0.3p = 15 [SIZE=5][B]Step 1: Divide each side of the equation by 0.3[/B][/SIZE] 0.3p/0.3 = 15/0.3 p = [B]50[/B]

a ^5 x a ^2 without exponents When we multiply the same variable or number, we add exponents, so we have: a^(5 + 2) a^7 To write a variable raised to an exponent without exponents, we break it up. The formula to do this is: a^n = a times itself n times a^7 = [B]a * a * a * a * a * a * a[/B]

A ________ ________ is the value of a statistic that estimates the value of a parameter. [B]Point Estimate[/B]. A point [B]estimate[/B] is a single [B]value[/B] (statistic) used to [B]estimate[/B] a population [B]value[/B]([B]parameter[/B])

a/m - b = c for m Add b to both sides: a/m - b + b = c + b Cancel b on both sides: a/m = c + b Multiply each side by m: am/m = m(c + b) Cancel the m's on the left side: a = m(c + b) Divide each side by (c + b) a/(c + b) = m(c + b)/(c + b) Cancel the (c + b) on the right side, and we get: m[B] = a/(c + b)[/B]

Multiply through using the distributive property, so we have: A = 2l + 2w Subtract 2l from each side 2w = A - 2l Divide each side by w w = (A - 2l)/2 [MEDIA=youtube]Nm-tYD4aEY4[/MEDIA]

A=a+b+c+d÷4 for c Assume A and a are different variables: Cross multiply: a + b + c + d = 4A Subtract a, b, and d from each side: a + b + c + d - (a + b + d) = 4A - (a + b + d) Cancel the a + b + d on the left side [B]c = 4A - a - b - d[/B]

A={2,8,1} and B={4,3,1}.find the Cartesian product A×B. Click [URL='http://www.mathcelebrity.com/cartprod.php?num1=2%2C8%2C1&num2=4%2C3%2C1&pl=Cartesian+Product']here[/URL] to find the answer

Aaron bought a bagel and 3 muffins for $7.25. Bea bought a bagel and 2 muffins for $6. How much is bagel and how much is a muffin? Let b be the number of bagels and m be the number of muffins. We have two equations: [LIST=1] [*]b + 3m = 7.25 [*]b + 2m = 6 [/LIST] Subtract (2) from (1) [B]m = 1.25 [/B] Plug this into (2), we have: b + 2(1.25) = 6 b + 2.5 = 6 Subtract 2.5 from each side [B]b = 3.5[/B]

Aaron bought a guitar for n dollars. The tax in his state is 6%. What is the total cost of the guitar including tax? Sale price is n Tax on sale is 0.06n Add them together n + 0.06n = [B]1.06n[/B]

Aaron buys a bag of cookies that contains 8 chocolate chip cookies, 6 peanut butter cookies,7 sugar cookies and 6 oatmeal raisin cookies. What it’s the probability that Aaron randomly selects a peanut butter cookie from the bag, eats it,, then randomly selects another peanut butter cookie? First draw out of the bag is a peanut butter cookie: P(PB) = Total Peanut Butter Cookies / Total Cookies P(PB) = 6/27 Second draw out of the bag is a peanut butter cookie, but we have one less since Aaron ate one: P(PB) = Total Peanut Butter Cookies - 1 / Total Cookies - 1 P(PB) = (6 - 1)/(27 - 1) P(PB) = 5/26 Now, since each event is independent, we multiply them to see the probability of choosing a peanut butter cookie, eating it, then reaching in and choosing another peanut butter cookie: P(PB, PB) = 6/27 * 5/26 [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F27&frac2=5%2F26&pl=Multiply']P(PB, PB)[/URL] = [B]5/117[/B]

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying [I]x[/I] nights? [LIST] [*]The Room cost equals 99.95 times x where x is the number of rooms [*]We express an 8% tax by multiplying the room cost by 1.08 [*]Finally, we add on $5, which is [I]untaxed[/I] [/LIST] [I][/I] Take this in pieces: Room Cost: 99.95x Tax on Room 1.08(99.95x) Add on $5 which is untaxed: [B]1.08(99.95x) + 5[/B]

ab/d + c = e for d I know this is a literal equation because we are asked to solve for a variable [U]in terms of[I] another variable [/I][/U] Subtract c from each side to isolate the d term: ab/d + c - c = e - c Cancel the c's on the left side and we get: ab/d = e - c Cross multiply: ab = d(e - c) Divide each side of the equation by (e - c): ab/(e - c)= d(e - c)/(e - c) Cancel the (e - c) on the right side, and we get: d = [B]ab/(e - c)[/B]

Abbey knew that the combination for her locker had the numbers 36, 12, 8, and 40, but she couldn't remember the right order of the numbers. How many different possibilities are there for the lock combination using the four numbers? First number could be 4 choices, then 3, then 2, then 1. So we have: 4! = 4 x 3 x 2 x 1 = [B]24 possibilities[/B]

About 3/5th of the registered voters participated in 2016 election. California has 25 million registered voters. Find the number of registered voters who participated in 2016 election. 3[URL='https://www.mathcelebrity.com/fraction.php?frac1=25000000&frac2=3/5&pl=Multiply']/5 of 25000000[/URL] = [B]15,000,000[/B]

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Free Absolute Difference Calculator - Calculates the absolute difference between 2 numbers

absolute value of x is less than or equal to 4 Absolute value of x: |x| Set up an inequality where this is less than or equal to 4: [B]|x| <= 4 [/B] <-- This is our algebraic expression To solve this, we have the following compound inequality: -4 < x < 4

These are now available as shortcuts. You can type any number or variable in the following forms: [LIST] [*]Absolute value of x less than 8 [*]Absolute value of x less than or equal to 8 [*]Absolute value of x greater than 8 [*]Absolute value of x greater than or equal to 8 [*]Absolute value of x equal to 8 [/LIST]

Free Acceleration Calculator - Solves for any of the 4 items in the acceleration equation including initial velocity, velocity, and time.

According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24. Over your lifetime, how many years will you spend on each of these activities? Assumptions: [LIST] [*]Let years eating be e [*]Let years sleeping be s [/LIST] We're given: [LIST=1] [*]s = e + 24 [*]e + s = 32 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for s: e + e + 24 = 32 To solve this equation for e, we [URL='https://www.mathcelebrity.com/1unk.php?num=e%2Be%2B24%3D32&pl=Solve']type it in our math engine[/URL] and we get: e = [B]4 [/B] Now, we take e = 4 and substitute it into equation (1) to solve for s: s = 4 + 24 s = [B]28[/B]

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acw+cz=y for a Solve this literal equation: Subtract cz from each side: acw + cz - cz = y - cz Cancel the cz on the left side: acw = y - cz Divide each side by cw to isolate a: acw/cw = (y - cz)/cw Cancel cw on the left side: [B]a = (y - cz)/cw[/B]

Adam ate 1/5 of a cake and Matt ate the rest. What fraction did Matt eat? The rest of the cake is 1 - 1/5. 1 as a fraction is 5/5. So we have: 5/5 - 1/5 Using our f[URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F5&frac2=1%2F5&pl=Subtract']raction calculator[/URL], we get [B]4/5[/B]

Adam drove the 10 miles to school at a speed of 60 mph. On his way home, due to traffic, his speed was 30 mph. What was his average speed for the round trip to school and back? D = rt To school: 60 miles in 60 minutes = 10 miles in 10 minutes To home: 30 miles in 60 minutes = 10 miles in 20 minutes Total time: 10 + 20 = 30 minutes or 0.5 hours With a speed of s, we have: d = st 20 = 0.5s Divide each side by 2: s = [B]40 mph[/B]

Adam has 20 sweets he eats a quarter of them how many does he have left? A quarter means 1/4. There's 2 ways you can approach this problem. [B][U]Approach #1:[/U][/B] Adam eats a quarter, or 1/4 of the sweets. So he eats: 20 * 1/4 = 5 Remaining sweets = Total Apples - Eaten Apples Remaining sweets = 0 - 5 Remaining sweets= 15 [U][B]Approach #2:[/B][/U] If Adam eats 1/4 of the sweets, this means he has: 1 - 1/4 sweets remaining. Since 1 equals 4/4, we have: 4/4 - 1/4 = 3/4 Therefore, he has 20 * 3/4 sweets remaining. This is 60/4, or [B]15[/B]

Adam took money from his savings account to use as spending money on a trip to San Antonio. On Monday, he spent half his money. On Tuesday, he sp ent half of what was left. On Wednesday, he again spent half of his remaining money. On Thursday, he work up with very little money left, but again spent half of it. If Adam started the vacation with n dollars, how much money did he have at the end of Thursday? [LIST] [*]Start with: n [*]Monday: n * 1/2 = n/2 [*]Tuesday: n/2 * 1/2 = n/4 [*]Wednesday: n/4 * 1/2 = n/8 [*]Thursday: n/8 * 1/2 = [B]n/16[/B] [/LIST]

Adam, Bethany, and Carla own a painting company. To paint a particular home, Adam estimates it would take him 4 days. Bethany estimates 5.5 days. Carla estimates 6 days. How long would it take them to work together to paint the house. Our combined work function for time (t) using a = Adam's time, b = Bethany's time, and c = Carla's time is: 1/a + 1/b + 1/c = 1/t Plugging in a, b, and c, we get: 1/4 + 1/5.5 + 1/6 = 1/t 0.25 + 0.181818 + 0.1667 = 1/t 1/t = 0.59848 t = [B]1.67089 days[/B]

Add 2 and z, then subtract y from the result Add 2 and z 2 + z Subtract y from the result: [B]2 + z - y[/B]

add 3 and 9, then multiply n by the result Add 3 and 9 3 + 9 12 Then multiply n by the result: [B]12n[/B]

Add 3 to 6, subtract w from the result, then triple what you have Add 3 to 6; 3 + 6 Subtract w from the result; 3 + 6 - w Triple what you have (means multiply by 3): [B]3(3 + 6 - w)[/B]

add 4 to the sum of 5 and z The sum of 5 and z 5 + z Add 4 to this 4 + (5 + z) Simplified: [B]9 + z[/B]

Add 5 and 6 and then multiply by 3 Add 5 and 6: (5 + 6) Then multiply by 3: [B]3(5 + 6) [/B] If you want to evaluate this term, then we [URL='https://www.mathcelebrity.com/distributive-property.php?a=3&b=5&c=6&pl=Distributive']type it into the math engine[/URL] and we get: [B]33[/B]

Add 5 to p, then divide the sum by 4 Add 5 to p: p + 5 Divide the sum by 4: [B](p + 5)/4 [/B] note: B[I]ecause this is a sum, we wrap it in parentheses to divide the sum by a number[/I]

Add 5 to the sum of 2x and y The sum of 2x and y means we add y to 2x: 2x + y Add 5 [B]2x + y + 5[/B]

add 7 and 2, raise the result to the 6th power, then add what you have to s Add 7 and 2: 7 + 2 Simplify this, we get:9 Raise the result to the 6th power: 9^6 [URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=9%5E6&pl=Calculate']Simplifying this using our exponent calculator[/URL], we get: 531,441 Now, we add what we have (our result) to s to get our final algebraic expression: [B]s + 531,441[/B]

Add 7 to a, and divide the sum by b Add 7 to a: a + 7 Divide the sum by b: [B](a + 7)/b[/B]

add 8 and 10 then divide u Add 8 and 10 8 + 10 Divide by u (8 + 10)/u Simplified, it is 18/u

Add 8 and 7, and then multiply by 2. Add 8 and 7: 8 + 7 Then multiply by 2: 2(8 + 7) If you want to evaluate this order of operations, then [URL='https://www.mathcelebrity.com/distributive-property.php?a=2&b=8&c=7&pl=Distributive']type it in our search engine[/URL] to get: [B]30[/B]

Add all the whole numbers 1 through 100 [URL='https://www.mathcelebrity.com/inclusnumwp.php?num1=1&num2=100&pl=Sum']Using our inclusive number word problem calculator[/URL], we get: 5,050

Add b and 9, then add c to the result Add b and 9 b + 9 Add c to the result [B]b + 9 + c[/B]

add c and b, multiply the result by a, then double what you have Take this algebraic expression in pieces: [LIST] [*]add c and b: c + b [*]Multiply the result by a: a(c + b) [*]Double what you have means take the last step result, and multiply it by 2: [/LIST] [B]2a(c + b)[/B]

add c to b, subtract d from the result, then double what you have Add c to b: b + c Subtract d from the result: b + c - d Double what you have means multiply the entire expression by 2: [B]2(b + c - d)[/B]

add c to d, multiply a by the result, then divide what you have by b Add c to d: d + c Multiply a by the result: a(d + c) then divide what you have by b: [B]a(d + c)/b[/B]

add c to d, then multiply 9 by the result Add c to d c + d Multiply 9 by the result: [B]9(c + d)[/B]

add d to 5, raise the result to the 9th power, then subtract what you have from 2 Add d to 5: d + 5 Raise the result to the 9th power means we raise (d + 5) to the 9th power using an exponent: (d + 5)^9 the subtract what we have (the result) from 2: [B]2 - (d + 5)^9[/B]

add f and g, then triple the result Add f and g f + g Triple the result means we multiply f + g by 3 [B]3(f + g)[/B]

Add h and 7, then triple the result Add h and 7 h + 7 Triple the result: [B]3(h + 7)[/B]

add p to 7, add the result to 10, then multiply 4 by what you have Add p to 7: p + 7 Add the result to 10: p + 7 + 10 p + 17 <-- combine like terms Then multiply 4 by what you have: [B]4(p + 17)[/B]

Add q and t, subtract s from the result, then multiply by r Take this algebraic expression in parts: [LIST] [*]Add q and t: q + t [*]Subtract s from the result: q + t - s [*]Multiply by r means we multiply the entire expression by r: [/LIST] [B]r(q + t - s)[/B]

Add q to p, add a to the result, then divide r by what you have Add q to p: p + q Add a to the result: p + q + a Then divide r by what you have: [B]r/(p + q + a)[/B]

add r and q, divide the result by s, then triple what you have Add r and q: r + q Divide the result by s. The result above is r + q, so we have: (r + q)/s Triple what you have means we multiply the expression above by 3: [B]3(r + q)/s[/B]

add r and s, add the result to q, then subtract what you have from p Take this algebraic expression in 3 parts: [LIST=1] [*]Add r and s: r + s [*]Add the result to q: r + s + q [*]Subtract what we have from p: [/LIST] [B]p - (r + s + q)[/B]

add r to 3, triple the result, then divide s by what you have Take this algebraic expression in parts: [LIST=1] [*]Add r to 3: 3 + r [*]Triple the result means multiply the result above by 3: 3(3 + r) [*]Then divide s by what you have. [B]s/3(3 + r)[/B] [/LIST]

Add r to the difference of s and t, then add q to the result the difference of s and t s - t Add r to the difference of s and t s - t + r Add r to the difference of s and t, then add q to the result [B]s - t + r + q[/B]

add s and 2 then subtract 4 Add s and 2 s + 2 Subtract 4: [B]s + 2 - 4[/B]

add s and t, multiply the result by u, then add r to what you have. Take this algebraic expression in 3 parts: [LIST=1] [*]Add s and t: s + t [*]Multiply the result by u means me multiply (s + t) times u: u(s + t) [*]Then add r to what you have. [I]what you have means the result in #2.[/I] [/LIST] [B]u(s + t) + r[/B]

add s to r, double the result Add s to r: r + s Double the result means multiply r + s by 2: [B]2(r + s)[/B]

add s to r, subtract q from the result Add s to r: r + s Subtract q from the result: [B]r + s - q[/B]

add s to v, multiply the result by u, then multiply t by what you have Take this algebraic expression in parts: [LIST] [*]Add s to v: v + s [*]Multiply the result by u: u(v + s) [*]Then multiply t by what you have: [/LIST] [B]tu(v + s)[/B]

add t and r and double the result Add t and r: t + r Double the result means multiply by 2: [B]2(t + r)[/B]

add the sum of 9 and q to r The sum of 9 and q 9 + q Add this to r [B]9 + q + r[/B]

add u and t divide s by the result then triple what you have Take this algebraic expression in parts: [LIST] [*]Add u and t: u + t [*]Divide s by the result: s/(u + t) [*]Triple what you have means we you multiply s/(u + t) by 3 [/LIST] [B]3s/(u + t)[/B]

Add u and w, triple the result, then add what you have to v Add u and w u + w Triple the result means multiply the sum of u and w by 3: 3(u + w) Then add what you have to v: [B]v + 3(u + w)[/B]

add v to t, add the result to u, then subtract what you have from s Add v to t: t + v Add the result to u: t + v + u Then subtract what you have from s: [B]s - (t + v + u)[/B]

add w and u, subtract t from the result Add w and u: w + u Subtract t from the result: [B]w + u - t[/B]

add w to t, add u to the result, then divide what you have by v Take this algebraic expression in parts: [LIST] [*]Add w to t: t + w [*]Add u to the result: t + w + u [*]Divide what you have by v: [/LIST] ([B]t + w + u)/v[/B]

add w to u, triple the result, then add v to what you have Take this algebraic expression in parts: [LIST] [*]add w to u: w + u [*]triple the result means we multiply w + u by 3: 3(w + u) [*]Then add v to what you have [/LIST] [B]3(w + u) + v[/B]

Add x and 3 x + 3 Then multiply by y (they mean the total) [B]y(x + 3)[/B]

Free Addition and Multiplication Tables (Times Tables) Calculator - Shows the color coded addition or multiplication table entries and answer for any 2 numbers 1-15.

Free Addition Equality Property Calculator - Demonstrates the Addition Equality Property Numerical Properties

Free Addition Property Of Inequality Calculator - Demonstrates the Addition Property Of Inequality. Numerical Properties

Free Additive Identity Property Calculator - Displays the line by line proof for the additive identity property Numerical Properties

Free Additive Inverse Property Calculator - Demonstrates the Additive Inverse property using a number. A + (-A) = 0 Numerical Properties

ADG,BEH,CFI,___,___,___ Looking at this pattern, we see: [LIST=1] [*]the first term starts with A and increments by 1 letter [*]the second term starts with D and increments by 1 letter [*]the third term starts with G and increments by 1 letter [/LIST] So terms 4, 5, and 6 are: [LIST] [*][B]DGJ[/B] [*][B]EHK[/B] [*][B]FIL[/B] [/LIST]

Admir works at a coffee shop and earns $9/hour he also works at a grocery store and earns $15/hour. Last week he earned $500 dollars. Write an equation that represents the situation. [LIST] [*]Let c be the hours Admir works at the coffee shop. [*]Let g be the hours Admir works at the grocery store. [/LIST] Since earnings equal hourly rate times hours, We have the following equation: [B]9c + 15g = 500[/B]

Admission to a baseball game is $2.00 for general admission and $5.50 for reserved seats. The receipts were $3577.00 for 1197 paid admissions. How many of each ticket were sold? Let g be the number of tickets for general admission Let r be the number of tickets for reserved seats We have two equations: [LIST=1] [*]g + r = 1197 [*]2g + 5.50r = 3577 [/LIST] We can solve this a few ways, but let's use substitution using our [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=g+%2B+r+%3D+1197&term2=2g+%2B+5.50r+%3D+3577&pl=Substitution']simultaneous equations calculator[/URL]: [LIST] [*][B]r = 338[/B] [*][B]g = 859[/B] [/LIST]

admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were collected for a total of 10,078.75, how many students attended the fair Let the number of students be s and the others be o. We're given two equations: [LIST=1] [*]o + s = 2848 [*]3.75o + 2.50s = 10078.75 [/LIST] Since we have no coefficients for equation 1, let's solve this the fast way using substitution. Rearrange equation 1 by subtracting o from each side to isolate s [LIST=1] [*]o = 2848 - s [*]3.75o + 2.50s = 10078.75 [/LIST] Now substitute equation 1 into equation 2: 3.75(2848 - s) + 2.50s =10078.75 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3.75%282848-s%29%2B2.50s%3D10078.75&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]481[/B]

Adrienne brings home $1580 per month. She spends $316 on food. What is the fraction of what she spends on food Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=316%2F1580&frac2=3%2F8&pl=Simplify']fraction calculator[/URL], we see that: 316/1580 = [B]1/5[/B]

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After 20 minutes, Juan had completed 12 questions, which is 0.7 of his assignment. What percent of the assignment has Juan NOT completed? We know that 0.7 as a percentage is: 0.7 * 100% = 70% In this problem, we have either or. Juan either completed the question or DID NOT complete the question. 100% of questions has one of two classifications - Completed or not completed. This means Juan did not complete the following amount of questions: 100% - 70% = [B]30%[/B]

After 5 years, a car is worth $22,000. It’s value decreases by $1,500 a year, which of the following equations could represent this situation? Group of answer choices Let y be the number of years since 5 years. Our Book value B(y) is: [B]B(y) = 22,000 - 1500y[/B]

After a 33 percent reduction, you purchase a television for $281.40. What was the televisions price before the reduction? Using our [URL='http://www.mathcelebrity.com/markup.php?p1=++281.40&m=+33&p2=&pl=Calculate']markup/markdown calculator[/URL], we get: Original Sale Price = [B]$374.26[/B]

After a long journey, you finally arrive at the edge o a deep gorge where there are two identical bridges from which to choose your path to the other side. One bridge is safe, while the other is very dangerous and has caused the deaths of hundreds of travelers. The owner of the first bridge is a talking rat, while the owner of the second bridge is a talking frog. Friends told you before you left that one of the bridge owners always tells the truth, while the other always lies. You are allowed one question to ask of either the frog or the rat to find out which bridge is the safe bridge. What is the question that you would ask? [B]Ask the frog the following question: "If I were to ask the rat which bridge is the same bridge, which one would he point to?" [/B] If the frog is the truth teller, he would tell you that the rat would point to the dangerous bridge. If the frog is the liar, the truth telling rat would point out the safe bridge, but the lying frog would tell you he said the dangerous bridge. In both situations, the dangerous bridge would be pointed to. Take the other bridge.

After an explosion of an oxygen tank, three astronauts were forced to move into the lunar lander that was attached to their spacecraft. If the lunar lander had enough oxygen to last 2 people for 6 days, is there enough oxygen for 3 astronauts if their journey back to earth will take 4 days? 2 people * 6 days = 12 days of oxygen for 1 person. 12 days of oxygen per person / 3 astronauts = [B]4 days of oxygen The answer is yes, there IS ENOUGH oxygen[/B]

After buying some tickets for $19.00, Ann has $18.00 left. How much money did Ann have to begin with? Let the beginning amount be b. We're given: b - 19 = 18. <-- [I]We subtract 19 because a purchase is a spend reducing the original amount[/I] To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b-19%3D18&pl=Solve']type the equation b - 19 = 18 into our search engine [/URL]and we get: b = [B]37[/B]

After paying 7 dollars for the pie, Keith has 64 dollars left. How much money did he have before buying the pie? we add the 7 dollars back in to find Keith's original total t: t = 64 + 7 t = [B]$71[/B]

Free Age Difference Calculator - Determines the ages for an age difference word problem.

I brute forced this and got a wrong answer, logic tells me is right. I tried the calculator here but maybe messed up the equation using another users problem as an example. Having no luck. Problem: Jacob is 4 times the age of Clinton. 8 years ago Jacob was 9 times the age of Clinton. How old are they now and how old were they 8 years ago?

she wrote it down wrong! The 9 should have been a 10. So I tried 4c-8=40c-80 in the equation solver and it also came back with C=2 which was the same answer you got before?

she wrote it down wrong! The 9 should have been a 10. So I tried 4c-8=40c-80 in the equation solver and it also came back with C=2 which was the same answer you got before? [QUOTE="Drew, post: 1161, member: 63"]she wrote it down wrong! The 9 should have been a 10. So I tried 4c-8=40c-80 in the equation solver and it also came back with C=2 which was the same answer you got before?[/QUOTE] oh and my brute force answer was 12-48 and 8 years earlier was 4-40

I read it wrong before. Here you go: Jacob is 4 times the age of Clinton. 8 years ago Jacob was 10 times the age of Clinton. How old are they now and how old were they 8 years ago? [LIST=1] [*]j = 4c [*]j - 8 = 10(c - 8) [/LIST] Substitute (1) into (2) (4c) - 8 = 10c - 80 [URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D10c-80&pl=Solve']Equation solver[/URL] gives us [B]c = 12[/B] which means j = 4(12) = [B]48[/B]. 8 years ago,[B] j = 40 and c = 4[/B] which holds the 10x rule.

[QUOTE="math_celebrity, post: 1163, member: 1"]I read it wrong before. Here you go: Jacob is 4 times the age of Clinton. 8 years ago Jacob was 10 times the age of Clinton. How old are they now and how old were they 8 years ago? [LIST=1] [*]j = 4c [*]j - 8 = 10(c - 8) [/LIST] Substitute (1) into (2) (4c) - 8 = 10c - 80 [URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D10c-80&pl=Solve']Equation solver[/URL] gives us [B]c = 12[/B] which means j = 4(12) = [B]48[/B]. 8 years ago,[B] j = 40 and c = 4[/B] which holds the 10x rule.[/QUOTE] Thank you, I see what I did wrong!

The age of the older of the two boys is twice that of the younger. 5 years ago it was three times that of the younger. Find the age of each

Age of the older boy is o, younger boy is y. We have the following equations: [LIST=1] [*]o = 2y [*]o - 5 = 3(y - 5) [/LIST] Plug (1) into (2) (2y) - 5 = 3y - 15 Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=2y-5%3D3y-15&pl=Solve']equation solver[/URL], we get: [B]y = 10[/B] Plug that into (1), we get: o = 2(10), [B]o = 20[/B]

A father is three times as old as the son, and the daughter is 3 years younger than the son. If the sum of their ages 3 years ago was 63 Find the present age of the father

Let f be the age of the father and d be the age of the daughter and s be the age of the son. We have: [LIST=1] [*]f = 3s [*]d = s - 3 [*]d - 3 + f - 3 + s - 3 = 63 [/LIST] Simplify (3) d + f + s - 9 = 63 d + f + s = 72 Now, substitute (1) and (2) into the modified (3) (s - 3) + 3s + s = 72 Combine like terms: 5s - 3 = 72 Add 3 to each side 5s = 75 Divide each side by 5 s = 15 We want f, so we substitute s = 15 into (1) f = 3(15) [B]f = 45[/B]

Ages are consecutive integers. The sum of ages are 111. What are the ages In the search engine, we type [I][URL='http://www.mathcelebrity.com/consecintwp.php?num=111&pl=Sum']sum of 2 consecutive integers is 111[/URL][/I]. We get [B]55 and 56[/B].

Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total value of $3.50. How many of each type of coin does Ahmad have? Let the number of 5-cent coins be f. Let the number of 20-cent coins be t. We're given two equations: [LIST=1] [*]f + t = 31 [*]0.05f + 0.2t = 3.50 [/LIST] We can solve this simultaneous system of equations 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter which method we choose, we get: [LIST] [*][B]f = 18[/B] [*][B]t = 13[/B] [/LIST]

Ahmed was born in 530 B.C.E. and lived for 60 years, in which year did he die? In B.C.E., the year decreases as time goes on until we get to year 0. So we have the year of death as: 530 - 60 = [B]470 B.C.E.[/B]

The seven pencils cost $24 - $10 = $14. $14 / 7 pencils = [B]$2 per pencil[/B].

Al's Rentals charges $25 per hour to rent a sailboard and a wetsuit. Wendy's Rentals charges $20 per hour plus $15 extra for a wetsuit. Find the number of hours for which the total charges for both companies would be the same. Al's Rentals Cost Equation C(h) where h is the number of hours you rent a sailboard and wetsuit: C(h) = 25h Wendy's Rentals Cost Equation C(h) where h is the number of hours you rent a sailboard and wetsuit: C(h) = 20h + 15 We want to set both cost equation equal to each other, and solve for h: 20h + 15 = 25h [URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B15%3D25h&pl=Solve']Typing this equation into our search engine[/URL], we get: h = [B]3[/B]

Alan is y years old. Beth is 3 years old than Alan.Write an expression for how old Beth is? The word [I]older[/I] means we add 3 to Alan's age of y. So Beth's age is: [B]y + 3[/B]

Alana puts $700.00 into an account to use for school expenses. The account earns 8% interest, compounded annually. How much will be in the account after 4 years? We use our [URL='https://www.mathcelebrity.com/compoundint.php?bal=700&nval=8&int=4&pl=Annually']balance with interest calculator[/URL] and we get: [B]$958[/B]

Alberto and Willie each improved their yards by planting daylilies and ivy. They bought their supplies from the same store. Alberto spent $64 on 3 daylilies and 8 pots of ivy. Willie spent $107 on 9 daylilies and 7 pots of ivy. What is the cost of one daylily and the cost of one pot of ivy? Assumptions: [LIST] [*]Let d be the cost of one daylily [*]Let i be the cost of one pot of ivy [/LIST] Givens: [LIST=1] [*]3d + 8i = 64 [*]9d + 7i = 107 [/LIST] To solve this system of equations, you can use any of three methods below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3d+%2B+8i+%3D+64&term2=9d+%2B+7i+%3D+107&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3d+%2B+8i+%3D+64&term2=9d+%2B+7i+%3D+107&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3d+%2B+8i+%3D+64&term2=9d+%2B+7i+%3D+107&pl=Cramers+Method']Cramer's Method[/URL] [/LIST] No matter what method we use, we get the same answer: [LIST] [*][B]d = 8[/B] [*][B]i = 5[/B] [/LIST] [B][MEDIA=youtube]K1n3niERg-U[/MEDIA][/B]

Alberto’s salary was $1500 greater than 5 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y. Let x be Alberto's salary. Let y be Nick's salary. We have: Let's break this down: [LIST=1] [*]5 times Nick's salary (y), means we multiply the variable y by 5 [*]$1500 greater means we add $1500 to 5y [/LIST] [B]x = 5y - 1500[/B]

Alec had c caramels. Then, Alecs sister took 85 of the caramels. Choose the expression that shows the number of caramels Alec has left. Alec starts with c caramels. His sister took 85. The word [I]took[/I] means subtract, so we have: [B]c - 85[/B]

alex burns approximately 650 calories in a 1.25-hour game. Daniellle enjoys kickboxing and burns approximately 420 calories in 45 minute class. who burns calories at the higher rate? We want a calories to minutes measure. [LIST] [*][URL='https://www.mathcelebrity.com/timecon.php?quant=1.25&pl=Calculate&type=hour']1.25 hours[/URL] = 75 minutes [/LIST] Alexa's unit calorie burn: 650/75 = 8.67 Danielle's unit calorie burn: 420/45 = 9.33 So [B]Danielle[/B] burns calories at a higher rate.

Alex rode his bike to school at a speed of 12 mph. He then walked home at a speed of 5 mph. What was Alex's average speed for his trip to school and back? Say the distance was 1 mile from school to home D = rt To school 1 = 12t t = 1/12 From school: 1 = 5t t = 1/5 1/2(1/12 + 1/5) [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F24&frac2=1%2F10&pl=Add']1/24 + 1/10[/URL] = 17/120 120 = Average speed * 17 Average speed = 120/17 = [B]7.06 mph[/B]

Alex says all factors of 16 are even why is she wrong. [URL='https://www.mathcelebrity.com/factoriz.php?num=16&pl=Show+Factorization']Type in factor 16[/URL] into our search engine. We get the following factor of 16: 1, 2, 4, 8, 16 [B]All of these are even [I]except[/I] 1, which is odd. This is why Alex is wrong.[/B]

Alex sells cars at Keith Palmer ford. He earns 400 dollars a week plus 150 dollars per car he sells. If he earned 1450 dollars last week, how many cars did he sell? Subtract the base salary of $400 $1,450 - 400 =$1,050 Divide this by 150 per car $1,050/$150 = [B]7 cars[/B]

Alexandra was given a gift card for a coffee shop. Each morning, Alexandra uses the card to buy one cup of coffee. The original amount of money on the gift card was $45 and each cup of coffee costs $2.50. Write an equation for A(x),A(x), representing the amount money remaining on the card after buying xx cups of coffee. We start with 45, and each cup of coffee decreases our balance by 2.50, so we subtract: [B]A(x) = 45 - 2.50x[/B]

Alexis is working at her schools bake sale. Each mini cherry pie sells for $4 and each mini peach pie sells for $3. Alexis sells 25 pies and collects $84. How many pies of each kind does she sell? Let each cherry pie be c and each peach pie be p. We have the following equations: [LIST=1] [*]c + p = 25 [*]4c + 3p = 84 [/LIST] You can solve this system of equations 3 ways. [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c%2Bp%3D25&term2=4c+%2B+3p+%3D+84&pl=Substitution']Substitution Rule[/URL] [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c%2Bp%3D25&term2=4c+%2B+3p+%3D+84&pl=Elimination']Elimination Rule[/URL] [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c%2Bp%3D25&term2=4c+%2B+3p+%3D+84&pl=Cramers+Method']Cramers Rule[/URL] No matter which way you choose, you get [B]c = 9 and p = 16[/B].

Alfred carries a load of 12 kilograms. He finds it heavy so he removes a weight of 4 kilograms. What is the weight of the remaining load? Removes means he subtract weight. So we have: 12 kilograms - 4 kilograms = [B]8 kilograms[/B]

Free Algebra Master (Polynomials) Calculator - Given 2 polynomials this does the following:
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algebraic expression for the sum of x and double the value of y Double the value of y means we multiply y by 2: 2y The sum of x and 2y means we add 2y to x: [B]x + 2y[/B]

Free Algebraic Expressions Calculator - This calculator builds algebraic expressions based on word representations of numbers using the four operators and the words that represent them(increased,product,decreased,divided,times) Also known as Mathematical phrases

Free Algebraic Substitutions Calculator - Given an algebraic statement with variables [a-z], this calculator takes a set of given substitution values, i.e., x=2,y=3,z=4, and evaluates your statement using the substitution values.

Let the first number equal x. The second number is 3 more than twice the first number. Express the second number in terms of the first number x. [LIST] [*]Let the second number be y. [*]Twice means multiply by 2 [*]3 more than means we add 3 [/LIST] So we have the following algebraic expression: [B]y = 2x + 3[/B]

Ali buys 6 sunglasses which cost $1.84 each, calculate the total cost. Total Cost = Quantity * Price Total Cost = 6 * $1.84 Total Cost = [B]$11.04[/B]

Ali needs to make a total of 90 deliveries this week. So far he has completed 72 of them. What percentage of his total deliveries has Ali completed [URL='https://www.mathcelebrity.com/perc.php?num=72&den=90&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Enter 72/90 into our search engine and choose the percentage option[/URL] and we get [B]80%[/B].

Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today? Let m be the number of minutes. The phrase [I]at least[/I] means an inequality, also known as greater than or equal to. So we have: m >= 11*6 [B]m >= 66 You can read this as Ali will run 66 or more minutes today. Or at least 66 minutes. Or greater than or equal to 66 minutes[/B]

Ali spent $60 at the grocery store. Of this amount, he spent $51 on fruit. What percentage of the total did he spend on fruit? 51/60 = 0.85 Multiply 0.85 by 100 to get the percentage 0.85 * 100 = [B]85%[/B]

Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara? Let a be Alice's age, b be Barbara's age, and c be Carol's age. We have 3 given equations: [LIST=1] [*]a = b - 3 [*]b = c - 5 [*]a + b + c = 68 [/LIST] Rearrange (2) c = b + 5 Now plug in (1) and (2) revised into (3). We want to isolate for b. a + b + c = 68 (b - 3) + b + (b + 5) = 68 Combine like terms: (b + b + b) + (5 - 3) = 68 3b + 2 = 68 Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=3b%2B2%3D68&pl=Solve']equation calculator[/URL], and we get b = [B]22[/B]

Alice is a machinist in a shirt factory. For the first 180 shirts she is paid $2.20 and then $2.90 per garment thereafter. What are her gross wages for a week in which she produces 240 shirts? Calculate commission on the first 180 shirts (Commission 1): Commission 1 = Shirts (up to 180) * $2.20 Commission 1 = 180 * $2.20 Commission 1 = $396 Calculate commission on the rest of the shirts about 180 (Commission 2): Commission 2 = Shirts Above 180 * $2.90 Commission 2 = (240 - 180) * $2.90 Commission 2 = 60 * $2.90 Commission 2 = $174 Calculate Total Commission: Total Commission = Commission 1 + Commission 2 Total Commission = $396 + $174 Total Commission = [B]$570[/B]

Alice is making a sandwich to pack in her lunch. She has 2 different kinds of bread, 3 cheeses, 4 lunch meats, and 2 condiments to choose from. Assuming she uses one of each of bread, cheese, meat, and condiment, how many different sandwiches can she make? We use the Fundamental Rule of Counting [LIST] [*]Bread: 2 [*]Cheeses: 3 [*]Lunch Meats: 4 [*]Condiments: 2 [/LIST] 2 * 3 * 4 * 2 = [B]48 different sandwiches[/B]

Alicia deposited $41 into her checking account. She wrote checks for $31 and $13. Now her account has a balance of $81. How much did she have in her account to start with? We start with a balance of b. Depositing 41 means we add to the account balance: b + 41 Writing checks for 31 and 13 means we subtract from the account balance: b + 41 - 31 - 13 The final balance is 81, so we set b + 41 - 31 - 13 equal to 81: b + 41 - 31 - 13 = 81 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B41-31-13%3D81&pl=Solve']type this equation into our math engine[/URL] and we get: b = [B]84[/B]

Alisha is 5 years younger than her brother. If the age of her brother is y years then age of Alisha in terms of her brother Younger means we subtract. If her brother is y years of age, then Alisha is: [B]y - 5[/B]

Aliyah had $24 to spend on seven pencils after buying them she had $10 how much did each pencil cost? If Aliyah had $24 to spend, and $10 left over, then she spent $24 - $10 = $14 on pencils Find the cost per pencil: Cost per pencil = Pencil Spend / Number of Pencils Cost per pencil = 14/7 Cost per pencil = [B]$2[/B]

Aliyah had $24 to spend on seven pencils. After buying them she had $1. How much did each pencil cost? Let each pencil cost p. We're given the following equation: 7p + 1 = 24 [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B1%3D24&pl=Solve']Type this equation into our search engine[/URL] and we get: p = [B]$3.29[/B]

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost? Let p be the number of pencils. We're given the following equation: 7p + 10 = 24 To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B10%3D24&pl=Solve']type it in our math engine[/URL] and we get: p = [B]2 [/B]

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost? Let the number of pencils be p. We have: 7p + 10 = 24 To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B10%3D24&pl=Solve']type it in our math engine[/URL] and we get: p = [B]2[/B]

Aliyah has $24 to spend on 7 pencils. After buying them she had $10. How much did each pencil cost? Let the cost of each pencil be p. The phrase [I]leftover[/I] means we add to the cost of the pencils after buying them. We're given the equation: 7p + 10 = 24 To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B10%3D24&pl=Solve']type this equation into our search engine[/URL] and we get: p = [B]2[/B]

We have two expressions here, so we need a union since we have the word [U]or[/U]. First, All real numbers less than or equal to -1 is x <= -1. All real numbers greater than 5 is x > 5 So we have x <= -1 U x > 5 [MEDIA=youtube]boOueZTCSuU[/MEDIA]

all real numbers y greater than or equal to 12 Greater than or equal to means we use the sign >= [B]y >= 12[/B]

All squares are rectangles and all rectangles are parallelograms, therefore all squares are parallelograms. Is this true? [B]Yes.[/B] This is similar to A implies B and B implies C so A implies C also known as transitive property

All the colors of the rainbow You can find this with the acronym: ROYGBIV [LIST=1] [*][B]Red[/B] [*][B]Orange[/B] [*][B]Yellow[/B] [*][B]Green[/B] [*][B]Blue[/B] [*][B]Indigo[/B] [*][B]Violet[/B] [/LIST] [U]Written as a set, we have 7 elements:[/U] {[B]Red, Orange, Yellow, Green, Blue, Indigo, Violet[/B]}

Allan built an additional room onto his house. The length of the room is 3 times the width. The perimeter of the room is 60 feet. What is the length of the room A room is a rectangle. We know the perimeter of a rectangle is: P = 2l + 2w We're given two equations: [LIST=1] [*]l = 3w [*]P = 60 [/LIST] Plug (1) and (2) into our rectangle perimeter formula: 2(3w) + w = 60 6w + w = 60 [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2Bw%3D60&pl=Solve']Type this equation into our search engine[/URL] to solve for w: w = 8.5714 Now plug w = 8.5714 into equation 1 to solve for l: l = 3(8.5714) l = [B]25.7142[/B]

Allison can pay her gym membership fee monthly but if she pays for her entire year at one she gets a $53 discount her discounted bill at the end of the year was 463 what is her monthly fee Her full annual bill is found by adding the discounted annual bill to the discount amount: Full annual bill = Discounted annual bill + discount amount Full annual bill = 463 + 53 Full annual bill = 516 Her monthly gym membership is found by the following calculation: Monthly Gym Membership = Full Annual Bill / 12 Monthly Gym Membership = 516 / 12 Monthly Gym Membership = [B]$43[/B]

Alonzo needs to buy some pencils. Brand A has a pack of 36 pencils for $8.52. Brand B has a pack of 48 pencils for $9.98. Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent. Using our [URL='http://www.mathcelebrity.com/betterbuy.php?p1=8.52&p2=9.98&q1=36&q2=48&pl=Better+Buy']better buy calculator[/URL], we see the following unit prices: [LIST] [*][B]Brand A = $0.24[/B] [*][B]Brand B = $0.21[/B]. [*][B]Brand B has the better unit price by 3 cents.[/B] [/LIST]

Alonzo runs each lap in 4 minutes. He will run at most 32 minutes today. What are the possible numbers of laps he will run today? 32 minutes / 4 minutes per lap =[B] 8 laps maximum[/B]. He can also run less than 8 laps if his lap time gets slower.

Alorah joins a fitness center. She pays for a year plus a joining fee of $35. If the cost for the entire year is $299, how much will she pay each month? We set up the cost function C(m) where m is the number of months of membership: C(m) = cost per month * m + joining fee Plugging in our numbers from the problem with 12 months in a year, we get: 12c + 35 = 299 To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=12c%2B35%3D299&pl=Solve']type it in our search engine [/URL]and we get: c = [B]22[/B]

Alvin is 12 years younger than Elga. The sum of their ages is 60 . What is Elgas age? Let a be Alvin's age and e be Elga's age. We have the following equations: [LIST=1] [*]a = e - 12 [*]a + e = 60 [/LIST] Plugging in (1) to (2), we get: (e - 12) + e = 60 Grouping like terms: 2e - 12 = 60 Add 12 to each side: 2e = 72 Divide each side by 2 [B]e = 36[/B]

Alvin is 34 years younger than Elga. Elga is 3 times older than Alvin. What is Elgas age? Let a be Alvin's age. Let e be Elga's age. We're given: [LIST=1] [*]a = e - 34 [*]e = 3a [/LIST] Substitute (2) into (1): a = 3a - 34 [URL='https://www.mathcelebrity.com/1unk.php?num=a%3D3a-34&pl=Solve']Typing this equation into the search engine[/URL], we get a = 17 Subtitute this into Equation (2): e = 3(17) e = [B]51[/B]

Alvin planted t fewer trees than Danielle. Danielle planted 56 trees. Write an expression that shows how many trees Alvin planted. The word [I]fewer[/I] means we subtract, so we have Alvin's tree planting of: [B]56 - t[/B]

Alvin, an HR Director has 12 employees in his department. There are still 3 positions to be filled up. What fraction of the entire staff are still available? If 3 spots need to be filled, then we have 12 - 3 = 9 people still available. [URL='https://www.mathcelebrity.com/fraction.php?frac1=9%2F12&frac2=3%2F8&pl=Simplify']9/12 =[/URL] 3[B]/4[/B]

Alya loves to read. She reads 90 pages in half an hour. How many pages does she read per minute? Set up a proportion of pages to minutes. Since 30 minutes is a half hour, we have the number of pages (p) for 1 minute as: 90/30 = p/1 To solve this proportion for p, [URL='https://www.mathcelebrity.com/prop.php?num1=90&num2=p&den1=30&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get: p = [B]3[/B]

Alyssa had 87 dollars to spend on 6 books. After buying them she had 15 dollars . How much did each book cost ? Let b be the cost of each book. We're given: 87 - 6b = 15 [URL='https://www.mathcelebrity.com/1unk.php?num=87-6b%3D15&pl=Solve']Typing this equation into search engine[/URL], we get: [B]b = 12[/B]

Alyssa has $952 and is spending $27 each week (w) for math tutoring write an algebraic expression to model the situation Alyssa's balance is found by using this expression: [B]952 - 27w[/B]

Amanda runs each lap in 4 minutes. She will run less than 44 minutes today. What are the possible number of laps she will run today? Notes for this problem: [LIST] [*]Let laps be l. [*]Lap time = Time per lap * number of laps (l) [*]Less than means we have an inequality using the < sign [/LIST] We have the inequality: 4l < 44 To solve this inequality for l, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4l%3C44&pl=Show+Interval+Notation']type it in our math engine[/URL] and we get: [B]l < 11[/B]

Amanda spent 2/5 of her time after school doing homework and ¼ of her remaining time riding her bike. If she rode her bike for 45 minutes in a week, how much time did she devote to homework in the same week If Amanda spent 2/5 of her time after school doing homework, she has 1 - 2/5 time left over. We convert 1 to a fraction using a denominator of 5, we get: 5/5 - 2/5 = 3/5 And Amanda spent 1/4 of 3/5 of her time bike riding, which means she spent: 1(3)/4(5) = 3/20 of her time. If the total time after school is t, we have: 3t/20 = 45 [URL='https://www.mathcelebrity.com/prop.php?num1=3t&num2=45&den1=20&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Typing in 3t/20 = 45 to our search engine[/URL], we get t = 300. So Amanda has 300 total minutes after school, which means she spent 2/5(300) = [B]120 minutes (2 hours)[/B] doing homework.

Amar goes to the dance class every fourth day. Karan goes to the dance class every fifth day. Both met at the dance class today. After how many days will they meet at the dance class again? We want the least common multiple of 4 and 5. We type in [URL='https://www.mathcelebrity.com/gcflcm.php?num1=4&num2=5&num3=&pl=GCF+and+LCM']LCM(4,5)[/URL] into our search engine and we get [B]20. So 20 days from now, Amar and Karen will meet again.[/B]

Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal? Let the number of tv's be t. Set up the salary function S(t): S(t) = Commision * tv's sold + Salary Company A: S(t) = 100t + 17,000 Company B: S(t) = 20t + 29,000 The problem asks for how many tv's it takes to make both company salaries equal. So we set the S(t) functions equal to each other: 100t + 17000 = 20t + 29000 [URL='https://www.mathcelebrity.com/1unk.php?num=100t%2B17000%3D20t%2B29000&pl=Solve']Type this equation into our search engine[/URL] and we get: t = [B]150[/B]

Amount you spend if you buy a shirt for $20 and jeans for j dollars We want an algebraic expression for our total spend. We add the $20 for a shirt plus j for the jeans: [B]20 + j[/B]

Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and inside. Amy charges 40$ and Ryan charges 50$ . In addition they charge a hourly rate. Amy charges $35/h and ryan charges $30/h. How many hours does amy and ryan have to work to make the same amount of money? Set up the cost functions C(h) where h is the number of hours. [U]Amy:[/U] C(h) = 35h + 40 [U]Ryan:[/U] C(h) = 30h + 50 To make the same amount of money, we set both C(h) functions equal to each other: 35h + 40 = 30h + 50 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=35h%2B40%3D30h%2B50&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]2[/B]

Amy deposits 4000 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in the first 4 years? Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=4000&int=6&t=4&pl=Simple+Interest']simple interest calculator[/URL], we get an accumulated value of 4,960 Interest Paid = Accumulated Value - Principal Interest Paid = 4960 - 4000 Interest Paid = [B]960[/B]

Amy has n decks of cards. Each deck has 52 cards in it. Using n, write an expression for the total number of cards Amy has. [B]52n[/B]

An 8 yard gain and a 3 yard loss results in what kind of gain or loss? [LIST=1] [*]Start with 0 yards [*]Gains means we add, so we have 0 + 8 = 8 [*]Losses mean we subtract, so we have 8 - 3 = 5 [/LIST] The overall result is a [B]5 yard gain[/B]

An air horn goes off every 48 seconds,another every 80 seconds. At 5:00 pm the two go off simultaneously. At what time will the air horns blow again at the same time? We want to find the least common multiple of (48, 80). So we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=48&num2=80&num3=&pl=GCF+and+LCM']type this in our search engine[/URL], and we get: 240. So 240 seconds is our next common meeting point for each air horn. When we [URL='https://www.mathcelebrity.com/timecon.php?quant=240&pl=Calculate&type=second']type 240 seconds into our search engine[/URL], we get 4 minutes. We add the 4 minutes to the 5:00 pm time to get [B]5:04 pm[/B].

An airplane carries 500 passengers 45% are men, 20% are children. The number of women in the airplane is If we assume the sample space is either men, women, or children to get 100% of the passengers, we have: PercentWomen = 100% - Men - Children PercentWomen = 100% - 45% - 20% PercentWomen = 35% Calculate Women passengers Women passengers = Total passengers * Percent Women Women passengers = 500 * 35% Women passengers = [B]175[/B]

An airplane is flying at 38,800 feet above sea level. The airplane starts to descend at a rate of 1800 feet per minute. Let m be the number of minutes. Which of the following expressions describe the height of the airplane after any given number of minutes? Let m be the number of minutes. Since a descent equals a [U]drop[/U] in altitude, we subtract this in our Altitude function A(m): [B]A(m) = 38,800 - 1800m[/B]

An airport has 13 scheduled arrivals every day. This week, 28 private planes also landed there. How many planes flew into the airport this week? A week has 7 days. 13 scheduled arrivals per day times 7 days = 91 scheduled planes Next, we add 28 private planes: 91 + 28 = [B]119 planes[/B]

An alligators tail length, T, varies directly as its body length, B. An alligator with a body length of 5.6 feet has a tail length of 4.9 feet. What is the tail length of an alligator whos body length is 4.8 feet Set up a proportion of T/B 5.6/4.9 = t/4.8 Using our [URL='http://www.mathcelebrity.com/prop.php?num1=5.6&num2=t&den1=4.9&den2=4.8&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]t = 5.49[/B].

An Amazon delivery package receives a bonus if he delivers a package to a costumer in 20 minutes plus or minus 5 minutes. Which inequality or equation represents the drivers allotted time (x) to receive a bonus 20 plus 5 minutes = 25 minutes 20 minus 5 minutes = 15 minutes So we have the inequality: [B]15 <= x <= 25[/B]

An analysis of the final test scores for Managerial Decision Making Tools reveals the scores follow the normal probability distribution. The mean of the distribution is 75 and the standard deviation is 8. The instructor wants to award an "A" to students whose score is in the highest 10 percent. What is the dividing point for those students who earn an "A"? Top 10% is equivalent to the 90th percentile. Using our [URL='http://www.mathcelebrity.com/percentile_normal.php?mean=+75&stdev=8&p=+90&pl=Calculate+Percentile']percentile calculator[/URL], the 90th percentile cutoff point is [B]85.256[/B]

An ancient Greek was said to have lived 1/4 of his live as a boy, 1/5 as a youth, 1/3 as a man, and spent the last 13 years as an old man. How old was he when he died? Set up his life equation per time lived as a boy, youth, man, and old man 1/4 + 1/5 + 1/3 + x = 1. Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=3&num3=5&pl=LCM']LCM Calculator[/URL], we see the LCM of 3,4,5 is 60. This is our common denominator. So we have 15/60 + 12/60 + 20/60 + x/60 = 60/60 [U]Combine like terms[/U] x + 47/60 = 60/60 [U]Subtract 47/60 from each side:[/U] x/60 = 13/60 x = 13 out of the 60 possible years, so he was [B]60 when he died[/B].

An angle is 30 degrees less than 5 times it's complement. Find the angle. Let the angle be a. The complement of a is 90 - a. We're given the following equation: a = 5(90 - a) - 30 <-- Less means we subtract Multiplying though, we get: a = 450 - 5a - 30 a = 420 - 5a [URL='https://www.mathcelebrity.com/1unk.php?num=a%3D420-5a&pl=Solve']Typing this equation into our search engine[/URL], we get: a =[B] 70[/B]

An auto repair bill is $126 for parts and $35 for each hour of labor. If h is the number of hours of labor, express the amount of the repair bill in terms of number of hours of labor. Set up cost function, where h is the number of hours of labor: [B]C(h) = 35h + 136[/B]

An auto repair bill was $563. This includes $188 for parts and $75 for each hour of labor. Find the number of hours of labor Let the number of hours of labor be h. We have the cost function C(h): C(h) = Hourly Labor Rate * h + parts Given 188 for parts, 75 for hourly labor rate, and 563 for C(h), we have: 75h + 188 = 563 To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=75h%2B188%3D563&pl=Solve']type it in our search engine[/URL] and we get: h = [B]5[/B]

An avocado is not ripe until 4 days after picking and will go bad after 7 days after picking. Represent the days the avocado is ripe Our sweet spot for ripeness is 4 days or more but not more than 7 days. Using d as our days, we have the following inequality: [B]4 <= d <= 7[/B]

an earthworm moves at distance of 45cm in 90 seconds what is the speed Using our [URL='https://www.mathcelebrity.com/drt.php?d=45&r=+&t=90&pl=Calculate+the+missing+Item+from+D%3DRT']distance, rate, time calculator[/URL], we have: Rate = [B]1/2cm or 0.5cm per second[/B]

An eccentric millionaire decided to give away $1,000,000 if Janelle took one die and rolled a "4". He wanted Janelle to have a better than 1 in 6 chance of winning, so before she rolled the die he told her that she could roll the die 3 times. If any roll was a "4", she would win the million dollars. What are Janelle's chances of winning the million dollars? Chance of winning each roll is 1/6. Which means the chances of losing each roll are 1 - 1/6 = 5/6 Calculate the probability of 3 straight losing rolls: P(Lose) = P(Loser) * P(Loser) * P(Loser) = 5/6 * 5/6 * 5/6 = 125/216 P(Win) = 1 - P(Lose) P(Win) = 1 - 125/216 P(Win) = 216/216 -125/216 P(Win) = [B]91/216[/B]

An eccentric millionaire has 5 golden hooks from which to hang her expensive artwork. She wants to have enough paintings so she can change the order of the arrangement each day for the next 41 years. (The same five paintings are okay as long as the hanging order is different.) What is the fewest number of paintings she can buy and still have a different arrangement every day for the next 41 years? 365 days * 41 years + 10 leap year days = 14,975 days what is the lowest permutations count of n such that nP5 >= 14,975 W[URL='https://www.mathcelebrity.com/permutation.php?num=9&den=5&pl=Permutations']e see that 9P5[/URL] = 15,120, so the answer is [B]9 paintings[/B]

An electrician starts off the day with 600 feet of copper wiring on his truck. During the course of the day he uses pieces 100, 82, 25, and 40 feet long. The next day, he purchases another 400 feet and puts it on his truck and later in the day uses pieces of 41, 39, and 44 feet long. How many feet of wiring are still on the truck at the end of the second day? If the electrician uses pieces, we subtract. If he purchases pieces, we add. So we have: 600 - 100 - 82 - 25 - 40 + 400 - 41 - 39 - 44 = [B]629 feet[/B]

An elevator can hold less than 2700 pounds of extra weight. If an average person weighs 150 pounds, what is the maximum number of people (p) that can be on the elevator at one time? Total weight = average weight per person * Number of people Total weight = 150p We know from the problem that: 150p < 2700 We want to solve this inequality for p. Divide each side of the inequality by 150: 150p/150 < 2700/150 Cancel the 150's on the left side and we get: p < [B]18[/B]

An elevator can safely lift at most 4400 1bs. A concrete block has an average weight of 41 lbs. What is the maximum number of concrete blocks that the elevator can lift? Total blocks liftable = Lift Max / Weight per block Total blocks liftable = 4400 / 41 Total blocks liftable = 107.31 We round down to whole blocks and we get [B]107[/B]

An elevator has a maximum weight of 3000 pounds. How many 150-pound people can safely ride the elevator? (Use "p" to represent the number of people) Maximum means less than or equal to. We have the inequality: 150p <= 3000 To solve this inequality for p, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=150p%3C%3D3000&pl=Show+Interval+Notation']type it in our search engine[/URL] and we get: [B]p <= 20[/B]

An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hours over 35. One weeks paycheck (before deductions) was for $308.00. How many hours did the employee work? Let's first check to see if the employee worked overtime: Regular Hours: 35 * 7 = 245 Since the employee made $308, they worked overtime. Let's determine how much overtime money was made: 308 - 245 = 63 Now, to calculate the overtime hours, we divide overtime pay by overtime rate 63/10.50 = 6 Now figure out the total hours worked in the week: Total Hours = Regular Pay Hours + Overtime Hours Total Hours = 35 + 6 [B]Total Hours = 41[/B]

An equilateral triangle has three sides of equal length. What is the equation for the perimeter of an equilateral triangle if P = perimeter and S = length of a side? P = s + s + s [B]P = 3s[/B]

An estate has 6 houses and each house has x lighting fittings which need 1 lamp each, and y fittings which need 3 lamps each. Write a formula to find z, the total number of lamps needed on the estate. z = 6(x * 1 + 3 * y) z = [B]6(x + 3y)[/B]

An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 6400 dollars. If she earns a total of 87400 dollars per year, what is her monthly salary in dollars? Calculate the annual salary without bonus: Annual Salary = Total Pay - Christmas Bonus Annual Salary = 87400 - 6400 Annual Salary = 81000 Now calculate the monthly salary. [I]Note: there are 12 months in a year[/I]: Monthly Salary = Annual Salary / 12 Monthly Salary = 81000/12 [URL='https://www.mathcelebrity.com/fraction.php?frac1=81000%2F12&frac2=3%2F8&pl=Simplify']Monthly Salary[/URL] = [B]6750[/B]

An executive invests $21,000, some at 8% and the rest at 7% annual interest. If he receives an annual return of $1,600, how much is invested at each rate? Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=21000&i1=8&i2=7&itot=1600&pl=Calculate']split fund calculator[/URL], we get: [LIST] [*][B]Fund 1 = 13,000[/B] [*][B]Fund 2 = 8,000[/B] [/LIST]

An executive invests $22,000, some at 7% and the rest at 6% annual interest. If he receives an annual return of $1,420, how much is invested at each rate Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=22000&i1=7&i2=6&itot=1420&pl=Calculate']split fund interest calculator[/URL], we get: [LIST] [*][B]10,000[/B] @ 7% [*][B]12,000[/B] @ 6% [/LIST]

An executive invests $23,000, some at 8% and some at 4% annual interest. If he receives an annual return of $1,560, how much is invested at each rate? Let x be the amount invested at 8% and y be the amount invested at 4%. We have two equations: [LIST=1] [*]x + y = 23,000 [*]0.08x + 0.04y = 1,560 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y+%3D+23000&term2=0.08x+%2B+0.04y+%3D+1560&pl=Cramers+Method']system of equations calculator[/URL], we get: [B]x = 16,000 y = 7,000[/B]

An executive invests $29,000, some at 8% and the rest at 6% annual interest. If he receives an annual return of $2,020, how much is invested at each rate? Using our [URL='http://www.mathcelebrity.com/split-fund-interest-calculator.php?p=29000&i1=8&i2=6&itot=2020&pl=Calculate']split fund calculator[/URL], we get: [LIST] [*]Fund 1: $14,000 [*]Fund 2: $15,000 [/LIST]

An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 10 hours. How long would it take the experienced accountant working alone? Person A: x/2 job per hour Person B: 1/x job per hour Set up our equation: 1/x + 1/(2x) = 1/10 Multiply the first fraction by 2/2 to get common denominators; 2/(2x) + 1/(2x) = 1/10 Combine like terms 3/2x = 1/10 Cross multiply: 30 = 2x Divide each side by 2: [B]x = 15[/B]

An ice cream shop carries 6 ice cream flavors, 3 sauces, and 4 toppings. If a sundae has one scoop of ice cream, one sauce, and one topping, how many different sundaes can be created? Using the rule of counting, we have: We have 6 possible ice cream flavors * 3 possible sauces * 4 possible toppings = [B]72 possible sundaes[/B]

An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people below. One bucket dumps water every 18 minutes. The other bucket dumps water every 21 minutes. It is currently 1:15 P.M. and both buckets dumped water 5 minutes ago. Find the next two times that both buckets dump water at the same time. We want to find the Least Common Multiple between 18 minutes and 21 minutes. This shows us when both bucket dumping cycles happen simultaneously. So we[URL='https://www.mathcelebrity.com/gcflcm.php?num1=18&num2=21&num3=&pl=GCF+and+LCM'] type in LCM(18,21) into our search engine and we get[/URL]: LCM(18, 21) = 126 This means, in 126 minutes, both buckets will dump water. Since 60 minutes is in an hour, we find out how many full hours we have. To find the full hours and remainder, we [URL='https://www.mathcelebrity.com/modulus.php?num=126mod60&pl=Calculate+Modulus']type in 126 mod 60[/URL] into our search engine and we get: 6. This means 126 minutes is 2 hours and 6 minutes. Find the next bucket dumping time: [LIST=1] [*]We start at 1:15 PM [*]Add 2 hours and we get 3:15 PM [*]Add 6 minutes and we get [B]3:21 PM[/B] [/LIST]

An initial deposit of $50 is now worth $400. The account earns 5.2% interest compounded continuously. Determine how long the money has been in the account. [URL='https://www.mathcelebrity.com/simpint.php?av=400&p=50&int=5.2&t=&pl=Continuous+Interest']Using our continuous interest compound calculator solving for t[/URL], we get: t =[B] 39.99 periods[/B]

An interior designer charges $100 to visit a site, plus $55 to design each room. Identify a function that represents the total amount he charges for designing a certain number of rooms. What is the value of the function for an input of 6, and what does it represent? [U]Set up the cost function C(r) where r is the number of room to design:[/U] C(r) = Cost per room * r + Site Visit Fee C(r) = 55r + 100 [U]Now, the problem asks for an input of 6, which is [I]the number of rooms[/I]. So we want C(6) which is the [I]cost to design 6 rooms[/I]:[/U] C(6) = 55(6) + 100 C(6) = 330 + 100 C(6) = [B]430[/B]

An investor has $300,000 to invest, part at 12% and the remainder in a less risky investment at 7%. If the investment goal is to have an annual income of $27,000, how much should be put in each investment? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=300000&i1=12&i2=7&itot=27000&pl=Calculate']split-fund interest calculator[/URL], we get: [LIST] [*][B]$120,000 in the 12% Fund[/B] [*][B]$180,000 in the 7% Fund[/B] [/LIST]

An investor invests $1000. Part of the investment is made at 5% interest and part of the investment is made at 10% interest. How much should be invested at 5% so the total interest in the first year is $80? Using our [URL='https://www.mathcelebrity.com/split-fund-interest-calculator.php?p=1000&i1=5&i2=10&itot=80&pl=Calculate']split fund interest calculator[/URL], we get: [B]$400[/B]

An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three times as long as the shortest side. The remaining two sides are each 8m longer than the shortest side. The perimeter of the Pentagon is 79m. Find the length of each side of the Pentagon. Let long sides be l. Let short sides be s. Let medium sides be m. We have 3 equations: [LIST=1] [*]2l + 2m + s = 79 [*]m = s + 8 [*]l = 3s [/LIST] Substitute (2) and (3) into (1): 2(3s) + 2(s + 8) + s = 79 Multiply through and simplify: 6s + 2s + 16 + s = 79 9s + 16 = 79 [URL='https://www.mathcelebrity.com/1unk.php?num=9s%2B16%3D79&pl=Solve']Using our equation calculator[/URL], we get [B]s = 7[/B]. This means from Equation (2): m = 7 + 8 [B]m = 15 [/B] And from equation (3): l = 3(7) [B]l = 21[/B]

An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the measure of all 3 angles? Let the congruent angles measurement be c. And the non-congruent angle measurement be n. We're given: [LIST=1] [*]n = 2c + 16 <-- Twice means we multiply by 2, and more than means we add 16 [*]2c + n = 180 <-- Since the sum of angles in an isosceles triangle is 180 [/LIST] Substitute (1) into (2): 2c + (2c + 16) = 180 Group like terms: 4c + 16 = 180 [URL='https://www.mathcelebrity.com/1unk.php?num=4c%2B16%3D180&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]c = 41[/B] Substituting this value into Equation 1, we get n = 2(41) + 16 n = 82 + 16 [B]n = 98[/B]

An item cost $370 before tax, and the sales tax is 25.90 what is the percentage? Sales Tax = Tax Amount/Original Bill Sales Tax = 25.90/370 Sales Tax = 0.07 Multiply by 100 to convert to a percent, we have[B] 7%[/B]

An item costs $470 before tax, and the sales tax is $14.10. Find the sales tax rate. Write your answer as a percentage. Sales Tax Percent = 100% * Sales Tax / Before Tax Amount Sales Tax Percent = 100% * 14.10 / 470 Sales Tax Percent = 100% * 0.03 Sales Tax Percent = [B]3%[/B]

An oil tank contains 220.2 gallons of oil. Whenever the amount of oil drops below 90 gallons, an alarm sounds. If 145.3 gallons are pumped into a delivery truck, how many gallons must be pumped back into the tank in order to shut off the alarm? I'm doing a remedial math course and I need help with a lot of questions..

An operation is defined by a*b=3a-b.Calculate the exact value of 2*3 We're given a = 2 and b = 3. So the operator says: 3(2) - 3 6 - 3 [B]3[/B]

An orchard has 378 orange trees. The number of rows exceeds the number of trees per row by 3. How many trees are there in each row? We have r rows and t trees per row. We're give two equations: [LIST=1] [*]rt = 378 [*]r = t + 3 [/LIST] Substitute equation (2) into equation (1) for r: (t + 3)t = 378 Multiply through: t^2 + 3t = 378 We have a quadratic equation. To solve this equation, we [URL='https://www.mathcelebrity.com/quadratic.php?num=t%5E2%2B3t%3D378&pl=Solve+Quadratic+Equation&hintnum=+0']type it in our search engine [/URL]and we get: t = 18 and t = -21 Since t cannot be negative, we get trees per row (t): [B]t = 18[/B]

An orchard has 816 apple trees. The number of rows exceeds the number of trees per row by 10. How many trees are there in each row? Let the rows be r and the trees per row be t. We're given two equations: [LIST=1] [*]rt = 816 [*]r = t + 10 [/LIST] Substitute equation (2) into equation (1) for r: (t + 10)t = 816 t^2 + 10t = 816 Subtract 816 from each side of the equation: t^2 + 10t - 816 = 816 - 816 t^2 + 10t - 816 = 0 We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=t%5E2%2B10t-816%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type it in our search engine [/URL]and we get: t = (24, -34) Since the number of trees per row can't be negative, we choose [B]24[/B] as our answer

An ordinary fair die is rolled twice. The face value of the rolls is added together. Compute the probability of the following events: Event A: The sum is greater than 6. Event B: The sum is divisible by 5 or 6 or both. [URL='http://www.mathcelebrity.com/2dice.php?gl=2&pl=6&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum greater than 6[/URL] = [B]7/12[/B] Sum is divisible by 5 or 6 or both This means a sum of 5, a sum of 6, a sum of 10, or a sum of 12. [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=5&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 5[/URL] = 1/9 or 4/36 [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=6&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 6[/URL] = 5/36 [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=10&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 10[/URL] = 1/12 or 3/36 [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=12&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']Sum of 12[/URL] = 1/36 Adding all these up, we get: (4 + 5 + 3 + 1)/36 [B]13/36[/B]

An organic juice bottler ideally produces 215,000 bottle per day. But this total can vary by as much as 7,500 bottles. What is the maximum and minimum expected production at the bottling company? Our production amount p is found by adding and subtracting our variance amount: 215,000 - 7,500 <= p <= 215,000 + 7,500 [B](min) 207,500 <= p <=222,500 (max)[/B]

Ana has 24 carrots, 12 cucumbers, and 36 radishes. She wants to make identical vegetable baskets using all of the vegetables. What is the greatest number of baskets she can make The key to solving this problem is asking what is the common factor between the 3 numbers. We want the greatest common factor or GCF [URL='https://www.mathcelebrity.com/gcflcm.php?num1=12&num2=24&num3=36&pl=GCF']GCF(12, 24, 36) [/URL]= [B]12[/B] We divide up our 12 baskets into carrots, cucumbers, and radishes. Each basket of the 12 baskets has the following: [LIST=1] [*]12 cucumbers / GCF of 12 = [B]1 cucumber per basket[/B] [*]24 carrots / GCF of 12 = [B]2 carrots per basket[/B] [*]36 radishes / GCF of 12 = [B]3 radishes per basket[/B] [/LIST] [B][MEDIA=youtube]D1KTOP0h2P4[/MEDIA][/B]

Ana was y years old 7 years ago. Represent her age twenty years from now twenty years from now, means we add 7 years to get to now and another 20 years to get to twenty years from now: y + 7 + 20 [B]y + 27[/B]

Unscramble the anagram: [B]ANENXPOITLE [/B] Hint: Think finance

Ande has 8 pints of milk. If he drinks 1/4 of a pint of milk each day, how long will the 8 pints of milk last him? Milk Days = Total Pints of Milk / pints drank per day Milk Days = 8 / 1/4 Dividing by a fraction is the same as multiplying by it's reciprocal. The [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=3%2F8&pl=Reciprocal']reciprocal of[/URL] 1/4 is 4/1, so we have: 8 * 4/1 = [B]32 days[/B]

Andrea has 6 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 7mph and walks back at a speed of 3mph, how long should she plan to spend walking back? Let the distance be d. Running full speed one way, 7d Walking back the opposite way, 3d And we know 7d + 3d = 6 hours 10d = 6 hours d =3/5 hour

Andrea has one hour to spend training for an upcoming race she completes her training by running full speed in the distance of the race and walking back the same distance to cool down if she runs at a speed of 9 mph and walks back at a speed of 3 mph how long should she plan on spending to walk back Let r = running time. Let w = walking time We're given two equations [LIST=1] [*]r + w = 1 [*]9r = 3w [/LIST] Rearrange equation (1) by subtract r from each side: [LIST=1] [*]w = 1 - r [*]9r = 3w [/LIST] Now substitute equation (1) into equation (2): 9r = 3(1 - r) 9r = 3 - 3r To solve for r, [URL='https://www.mathcelebrity.com/1unk.php?num=9r%3D3-3r&pl=Solve']we type this equation into our search engine[/URL] and we get: r = 0.25 Plug this into modified equation (1) to solve for w, and we get: w = 1. 0.25 [B]w = 0.75[/B]

Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What was the original number? The phrase [I]a number[/I] means an arbitrary variable, let's call it n. [LIST] [*]Start with n [*]Add 20 to it: n + 20 [*]Double it means we multiply the expression by 2: 2(n + 20) [*]Get an answer of 53: means an equation, so we set 2(n + 20) equal to 53 [/LIST] 2(n + 20) = 53 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%28n%2B20%29%3D53&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]6.5[/B]

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community college charges a $35 registration fee plus $375 per course, what is the greatest number of courses for which Angelica can register? We set up the Tuition function T(c), where c is the number of courses: T(c) = Cost per course * c + Registration Fee T(c) = 35c + 375 The problem asks for the number of courses (c) where her tuition [I]cannot exceed[/I] $1000. The phrase [I]cannot exceed[/I] means less than or equal to, or no more than. So we setup the inequality for T(c) <= 1000 below: 35c + 375 <= 1000 To solve this inequality for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=35c%2B375%3C%3D1000&pl=Solve']type it in our search engine and we get[/URL]: c <= 17.85 Since we cannot have fractional courses, we round down and get: c[B] <= 17[/B]

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Kenny buys 1 software package and 1 month of game play. Each software package costs $25. If their total cost is $155, what is the cost of one month of game play. Let s be the cost of software packages and m be the months of game play. We have: [LIST] [*]Angie: 2s + 4m [*]Kenny: s + m [/LIST] We are given each software package costs $25. So the revised equations above become: [LIST] [*]Angie: 2(25) + 4m = 50 + 4m [*]Kenny: 25 + m [/LIST] Finally, we are told their combined cost is 155. So we add Angie and Kenny's costs together: 4m + 50 + 25 + m = 155 Combine like terms: 5m + 75 = 155 [URL='http://www.mathcelebrity.com/1unk.php?num=5m%2B75%3D155&pl=Solve']Typing this into our search engine[/URL], we get [B]m = 16[/B]

Angie is 11, which is 3 years younger than 4 times her sister's age. Let her sister's age be a. We're given the following equation: 4a - 3 = 11 To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=4a-3%3D11&pl=Solve']type this equation into our math engine[/URL] and we get: [B]a = 3.5[/B]

Angie knew 90% of the answers on a worksheet. What fraction of the answers did she know? We [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=90&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type [I]90% as a fraction[/I] into our search engine[/URL] and we get: [B]9/10[/B]

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Ann purchased 8 packs of grape gum, 12 packs of cherry gum, and 6 packs of strawberry gum. If there are 6 pieces in each pack, how many pieces of gum did Ann purchased? Total Pieces = Packs x pieces per pack Total Pieces = (8 + 12 + 6) x 6 Total Pieces = 26 x 6 Total Pieces = [B]156[/B]

Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of $5 Ann paid a total of $49.10. Set up the cost function C(m) where m is the number of miles: C(m) = Mileage Rate x m + Tip 2.10m + 5 = 49.10 [URL='https://www.mathcelebrity.com/1unk.php?num=2.10m%2B5%3D49.10&pl=Solve']Type 2.10m + 5 = 49.10 into the search engine[/URL], and we get [B]m = 21[/B].

Anna has 50 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exactly four times as many pennies as dimes, how many pennies are in her piggy bank? Let d be the number of dimes, and p be the number of pennies. We're given: [LIST=1] [*]d + p = 50 [*]p = 4d [/LIST] Substitute (2) into (1) d + 4d = 50 [URL='https://www.mathcelebrity.com/1unk.php?num=d%2B4d%3D50&pl=Solve']Type that equation into our search engine[/URL]. We get: d = 10 Now substitute this into Equation (2): p = 4(10) [B]p = 40[/B]

Anna is collecting boxes of cereal to deliver in a food bank. The volume of each cereal box is 324 cubic inches. The picture shows the cereal boxes she has collected so far. A large delivery box holds three times as many boxes as Anna collected. About what is the volume of the delivery box? The picture has 12 cereal boxes. Since the delivery box holds three times as many cereal boxes as Anna collected, the delivery box holds 12 * 3 = 36 cereal boxes. With each cereal box having a volume of 324 cubic inches, we have the total volume as: V = 324 cubic inches * 36 cereal boxes V = [B]11,664 cubic inches[/B]

Anna made $60 babysitting. She spent 4/5 of the money on new shoes. How much money does she have left? [U]Calculate shoe spend[/U] [URL='https://www.mathcelebrity.com/fraction.php?frac1=60&frac2=4/5&pl=Multiply']4/5 of 60[/URL] = 48 [U]Calculate leftover money[/U] Leftover money = Babysitting money - shoe spend Leftover money = 60 - 48 Leftover money = [B]12[/B]

Anna painted 1/6 of a wall, Eric painted 1/5 of the wall, and Meadow painted 1/4 of the wall. There are now 3910 square feet left to paint. How many square feet did Anna paint? [URL='https://www.mathcelebrity.com/gcflcm.php?num1=4&num2=5&num3=6&pl=LCM']Using 60 as a common denominator through least common multiple[/URL], we get: 1/6 = 10/60 1/5 = 12/60 1/4 = 15/60 10/60 + 12/60 + 15/60 = 37/60 Remaining part of the wall is 60/60 - 37[B]/[/B]60 = 23/60 3910/23 = 170 for each 1/60 of a wall Anna painted 1/6 or 10/60 of the wall. So we multiply 170 * 10 = [B]1,700 square feet[/B]

Anna paints a fence in 4 hours wile her brother paints it in 5 hours. If they work together, how long will it take them to paint the fence? Set up unit rates per hour: [LIST] [*]Anna paints 1/4 of a fence per hour [*]Brother paints 1/5 of a fence per hour [*]Combined, they paint [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Add']1/4 + 1/5[/URL] = 9/20 of a fence per hour [/LIST] Setup a proportion of time to hours where h is the number of hours needed to paint the fence 9/20 of a fence the first hour 18/20 of a fence the second hour 2/20 is left. Each 1/20 of the fence takes 60/9 = 6 & 2/3 minutes 6 & 2/3 minutes * 2 = 13 & 1/3 minutes Final time is: [B]2 hours and 13 & 1/3 minutes[/B]

Anna’s age increased by 3 times her age, the result is 72. Let a be Anna's age. We have: a + 3a = 72 Combine like terms: (1 + 3)a = 72 4a = 72 [URL='https://www.mathcelebrity.com/1unk.php?num=4a%3D72&pl=Solve']Type 4a = 72 into our calculator[/URL], and we get [B]a = 18[/B].

Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure 6 inches wide by 2 feet long, how many boards will she need to complete the job? Area of platform which is a rectangle: A = lw A = 10 * 7 A = 70 Area of boards which are rectangles: A = lw A = 2 * 6 A = 12 We divide our platform area by our board area to get the number of boards needed: Boards needed = Platform Area / Board Area Boards needed = 70/12 Boards needed = 5.83333 We round up if we want full boards to be [B]6[/B]

Annie got a new video game. She scored 152 points on the first level, 170 points on the second level, 188 points on the third level, and 206 points on the fourth level. What kind of sequence is this? This is an [URL='https://www.mathcelebrity.com/sequenceag.php?num=152%2C170%2C188%2C206&n=10&pl=Calculate+Series&a1=&d=']arithmetic series as seen on our calculator[/URL]:

Annuity that pays 6.6% compounded monthly. If $950 is deposited into this annuity every month, how much is in the account after 7 years? How much of this is interest? Let's assume payments are made at the end of each month, since the problem does not state it. We have an annuity immediate formula. Interest rate per month is 6.6%/12 = .55%, or 0.0055. 7 years * 12 months per year gives us 84 deposits. Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=950&n=84&i=0.55&check1=1&pl=Calculate']present value of an annuity immediate calculator[/URL], we get the following: [LIST=1] [*]Accumulated Value After 7 years = [B]$101,086.45[/B] [*]Principal = 79,800 [*]Interest Paid = (1) - (2) = 101,086.45 - 79,800 = [B]$21,286.45[/B] [/LIST]

Free Annulus Calculator - Calculates the area of an annulus and the equation of the annulus using the radius of the large and small concentric circles.

Answer an electrician charges a base fee of $75. plus a $50 for each hour of work. The minimum the electrician charges is $175. Create a table that shows the amount the electrician charges for 1,2,3, and 4 hours of work. The hourly cost for h hours worked is C(h): C(h) = Max(175, 50h + 75) 1 hour cost: C(1) = Max(175, 50(1) + 75) C(1) = Max(175, 50 + 75) C(1) = Max(175, 125) [B]C(1) = 175[/B] 2 hour cost: C(2) = Max(175, 50(2) + 75) C(2) = Max(175, 100 + 75) C(2) = Max(175, 175) [B]C(2) = 175[/B] 3 hour cost: C(3) = Max(175, 50(3) + 75) C(3) = Max(175, 150 + 75) C(3) = Max(175, 225) [B]C(3) = 225[/B] 4 hour cost: C(4) = Max(175, 50(4) + 75) C(4) = Max(175, 200 + 75) C(4) = Max(175, 275) [B]C(4) = 275[/B]

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Approximately 2,800 red blood cells are created in the bone marrow each second. How many red blood cells would be created in .03125 seconds? 2800 red blood cells / second * .01325 seconds = [B]87.5 red blood cells[/B]

April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that June has. April has two-thirds of the number of sweets that May has. How many sweets does June have? Let the April sweets be a. Let the May sweets be m. Let the June sweets be j. We're given the following equations: [LIST=1] [*]m = 3j/4 [*]a = 2m/3 [*]a + j + m = 90 [/LIST] Cross multiply #2; 3a = 2m Dividing each side by 2, we get; m = 3a/2 Since m = 3j/4 from equation #1, we have: 3j/4 = 3a/2 Cross multiply: 6j = 12a Divide each side by 12: a = j/2 So we have: [LIST=1] [*]m = 3j/4 [*]a = j/2 [*]a + j + m = 90 [/LIST] Now substitute equation 1 and 2 into equation 3: j/2 + j + 3j/4 = 90 Multiply each side by 4 to eliminate fractions: 2j + 4j + 3j = 360 To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%2B4j%2B3j%3D360&pl=Solve']type it in our search engine[/URL] and we get: j = [B]40[/B]

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Free Area Conversions Calculator - This calculator converts between the following area measurements:
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area of a rectangle Let l be the length and w be the width of a rectangle. The Area (A) is: A = [B]lw[/B]

Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total? Total shots = Shots made + shots missed Total shots = 1 + 2 Total shots = [B]3[/B]

Free Arithmetic and Geometric and Harmonic Sequences Calculator - This will take an arithmetic series or geometric series or harmonic series, and an optional amount (n), and determine the following information about the sequence
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3) The sum of the first (n) terms of the sequence Also known as arithmetic sequence, geometric sequence, and harmonic sequence

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Arizona became a state in 1912. This was 5 years after Oklahoma became a state. Which equation can be used to find the year Oklahoma became a state? In what year did Oklahoma become a state? Let o be the year Oklahoma became a state: o = 1912 - 5 o = [B]1907[/B]

Arnie bought some bagels at 20 cents each. He ate 4, and sold the rest at 30 cents each. His profit was $2.40. How many bagels did he buy? Let x be the number of bagels Arnie sold. We have the following equation: 0.30(x - 4) - 0.20(4) = 2.40 Distribute and simplify: 0.30x - 1.20 - 0.8 = 2.40 Combine like terms: 0.30x - 2 = 2.40 Add 2 to each side: 0.30x = 4.40 Divide each side by 0.3 [B]x = 14.67 ~ 15[/B]

Arthur had $90. He spent $40 and gave $20 to his brother. What fraction of Arthur's money is left? Arthur starts with $90. He gives away $40, so now he has $90 - $40 = $50. Next, he gives $20 to his brother, so now he has $50 - $20 = $30. So Arthur has 30/90 left. [URL='https://www.mathcelebrity.com/fraction.php?frac1=30%2F90&frac2=3%2F8&pl=Simplify']We type 30/90 into our search engine[/URL] and simplify to get: [B]1/3[/B]

Arvin is twice as old as Cory. The sum of their ages is 42. What are their ages? Let Arvin's age be a. Let Cory's age be c. We're given two equations: [LIST=1] [*]a = 2c [*]a + c = 42 [/LIST] Plug equation (1) into equation (2): 2c + c = 42 [URL='https://www.mathcelebrity.com/1unk.php?num=2c%2Bc%3D42&pl=Solve']Plug this into our search engine[/URL] and we get: [B]c = 14[/B] Now, we plug c = 14 into equation 1 to solve for a: a = 2(14) [B]a = 28[/B]

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum amount of sales you need to make in order to receive a total income of at least $1500 per month. Let the amount of sales be s. The phrase [I]at least[/I] means greater than or equal to. Since 20% is 0.2, We want to know when: 0.20s + 600 >= 1500 We [URL='https://www.mathcelebrity.com/1unk.php?num=0.20s%2B600%3E%3D1500&pl=Solve']type this inequality into our search engine to solve for s[/URL] and we get: s >= [B]4500[/B]

As a salesperson, Lauren earns a base salary of $94 per week plus a commission of 10% of sales. If she had $90 in sales last week, what was her total pay? [B][U]Use the Base plus Commission formula above[/U][/B] Salary = Base Salary + 10%(Total Sales) Salary = $94 + 0.1(90) Salary = $94 + $9 Salary = [B]$103[/B]

As a salesperson, you are paid $50 per week plus $2 per sale. This week you want your pay to be at least $100. What is the minimum number of sales you must make to earn at least $100? Set up the inequality where s is the amount of sales you make: 50 + 2s >= 100 We use >= because the phrase [I]at least[/I] 100 means 100 or more Subtract 50 from each side: 2s >= 50 Divide each side by 2 [B]s >= 25[/B]

As the sample size increases, we assume: a. ? increases b. ? increases c. The probability of rejecting a hypothesis increases d. Power increases [B]d. Power increases[/B] [LIST] [*]Power increases if the standard deviation is smaller. [*]If the difference between the means is bigger, the power is bigger. [*]Sample size also increases power [/LIST]

Ashley age is 2 times Johns age. The sum of their ages is 63. What is Johns age? Let Ashley's age be a. Let John's age be j. We have two equations: [LIST=1] [*]a = 2j [*]a + j = 63 [/LIST] Now substitute (1) into (2) (2j) + j = 63 Combine like terms: 3j = 63 [URL='http://www.mathcelebrity.com/1unk.php?num=3j%3D63&pl=Solve']Typing 3j = 63 into our search engine[/URL], we get [B]j = 21[/B]

Ashley deposited $4000 into an account with 2.5% interest, compounded semiannually. Assuming that no withdrawals are made, how much will she have in the account after 10 years? Semiannual means twice a year, so 10 years * 2 times per year = 20 periods. We use this and [URL='https://www.mathcelebrity.com/compoundint.php?bal=4000&nval=20&int=2.50&pl=Semi-Annually']plug the numbers into our compound interest calculator[/URL] to get: [B]$5,128.15[/B]

Jason decided that he will sell his stocks if their values per share (x) goes below $5 or above $15. Write a compound inequality represents the values at which Jason will sell his stocks? Below $5 is also known as less than $5: x < 5 Above $15 is also known as greater than $15 x > 15 We write the compound inequality: [B]x < 5 U x > 15[/B]

Free Associative Property Calculator - Demonstrates the associative property using 3 numbers. Covers the Associative Property of Addition and Associative Property of Multiplication. Also known as the Associative Law of Addition and Associative Law of Multiplication Numerical Properties

Assume that a balloon is spherical shaped. If you have a balloon with the radius of 3, what’s the volume? Using our [URL='https://www.mathcelebrity.com/sphere.php?num=3&pl=Radius']sphere calculator[/URL], we get Volume (V): V = [B]36pi or 113.0973[/B]

Assume that in your Abnormal Psychology class you have earned test scores of 74%, 78%, and 63%, and only one test remains. If you need a mean score of 80% to earn a B for you final grade, is it possible for you to accomplish this? Assume there is no extra credit. Show work and explain why or why not. Hint: you're taking 4 tests total. Using our [URL='https://www.mathcelebrity.com/missingaverage.php?num=74%2C78%2C63&avg=80&pl=Calculate+Missing+Score']missing average calculator with our 3 given scores and target average[/URL], we get: A 4th score needed of 105. Since the most you can score on an exam is 100, [B][I]this is impossible[/I][/B].

Assume that you make random guesses for 5 true-or-false questions. (a) What is the probability that you get all 5 answers correct? (Show work and write the answer in simplest fraction form) (b) What is the probability of getting the correct answer in the 5th question, given that the first four answers are all wrong? (Show work and write the answer in simplest fraction form) (c) If event A is “Getting the correct answer in the 5th question” and event B is “The first four answers are all wrong”. Are event A and event B independent? Please explain. (a) Correct Answer on each one is 1/2 or 0.5. Since all are independent events, we have: (1/2)^5 = [B]1/32[/B] (b) We have [B]1/2[/B] (1/2)^4 * 1/2/((1/2)^4) c) [B]Independent since you could have gotten correct or wrong on any of the 4 and the probability does not change[/B]

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph. a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit? b. What proportion of the vehicles would be going less than 50 mph? c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion? d. In what way do you think the actual distribution of speeds differs from a normal distribution? a. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=65&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<65) = [B]22.66%[/B] b. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+50&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<50) = [B]0.4269%[/B] c. [URL='http://www.mathcelebrity.com/zcritical.php?a=0.9&pl=Calculate+Critical+Z+Value']Inverse of normal for 90% percentile[/URL] = 1.281551566 Plug into z-score formula: (x - 71)/8 = 1.281551566 [B]x = 81.25241252[/B] d. [B]The shape/ trail differ because the normal distribution is symmetric with relatively more values at the center. Where the actual has a flatter trail and could be expected to occur.[/B]

Assume you have a laptop worth 2900. There is a 3 percent chance of it getting lost what’s the fair premium insurance? Fair premium Insurance = Price * probability of loss: Fair premium Insurance = 2,900 * 3% Fair premium Insurance = [B]87[/B]

assume your math class has 10 sophomores and 7 juniors. there are 3 female sophomores and 4 male juniors. what is the probability of randomly selecting a student who is a female or a junior [U]Sophomores:[/U] 10 sophomores: 3 female male = 10 - 3 = 7 [U]Juniors:[/U] 7 juniors 4 males female = 7 - 4 = 3 [U]Females:[/U] Total Females = Female Sophomores + Female Juniors Total Females = 3 + 3 Total Females = 6 [U]Total Students:[/U] Total Students = Total Sophomores + Total Juniors Total Students = 10 + 7 Total Students = 17 [U]We want P(female or Junior). We use the formula below to avoid duplicates:[/U] P(female or Junior) = P(female) + P(junior) - P(female and junior) P(female or Junior) = Total Females / Total Students + Total Juniors / Total Students - Total Female Juniors / Total Students P(female or Junior) = 6/17 + 7/17 - 3/17 P(female or Junior) = [B]10/17[/B]

Assuming a standard 52-card deck, what's the probability of dealing three eights in a row when the cards are returned and the deck is shuffled between each draw? There are four (8's) in a standard 52 card deck. The probability of drawing an 8 is: 4/52 [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F52&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we get: 1/13 Now, with each draw, we replace the deck. So each draw of an 8 has a 1/13 probability. And since each of the three draws is independent, we multiply each probability: 1/13 * 1/13 * 1/13 = [B]1/2197 or 0.00045516613[/B]

Exam Questions from the Armed Services Vocational Aptitude Battery (ASVAB)

At 1:00 pm you have 24 megabytes of a movie and at 1:15 pm you have 96 megabytes of a movie. What is the download rate in megabytes per minute? First, find the number of minutes: 1:15 - 1:00 = 15 minutes Next, determine the difference in megabytes 96 - 24 = 72 Finally, determine the download rate: 72 megabytes / 15 minutes = [B]4.8 megabytes per minute [MEDIA=youtube]RCvs3TQMzdM[/MEDIA][/B]

At 2:18 Pm, a parachutist is 4900 feet above the ground. At 2:32 pm, the parachutist is 2100 above the ground. Find the average rate of change in feet per minute Average Rate of Change = Change in Distance / Change in time Average Rate of Change = (4900 - 2100) / (2:32 - 2:18) Average Rate of Change = 2800 / 14 Average Rate of Change = [B]200 feet per minute[/B]

At 4am the outside temperature was -28 By 4pm it rose 38° What was the temperature at 4pm -28 + 38 = [B]10 degrees (above zero)[/B]

At 7:00 AM, the temperature started dropping 1 degree Celsius per hour until it reached 30 degrees Celsius at 12:00 PM. What was the temperature at 7:00 AM? 7:00 AM to 12:00 PM is 5 hours. 1 degree per hour * 5 hours = 5 degrees. If it's 30 degrees at 12 pm, then it was 30 + 5 = 35 degrees Celsius at 7:00 AM, since it dropped each hour.

at 9:30am you enter a parking garage. It cost $3.25 for each hour to park your car. You leave the garage at 2:00pm. How much does it cost to park? [U]Calculate Hours:[/U] 9:30 am to 10:00 am is 0.5 hours 10 am to 2 pm is 4 hours So our total time is 4.5 hours [U]Calculate Total Cost[/U] Total Cost = Hours * Cost per hour Total Cost = 4.5 * 3.25 Total Cost = [B]$14.63[/B]

at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slices of pie costs $20.20. what is the cost of one cupcake? Let the number of cupcakes be c Let the number of pie slices be p Total Cost = Unit cost * quantity So we're given two equations: [LIST=1] [*]1c + 2p = 12.40 [*]2c + 3p = 20.20 [/LIST] We can solve this system of equations any one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]c = 3.2[/B] [*]p = 4.6 [/LIST]

At a birthday party, 13 children ate cake, 9 ate ice cream, 7 ate both cake and ice cream, and one child had neither cake nor ice cream. How many children were at the party? We have one of three scenarios [LIST=1] [*]A child ate cake (possibly ice-cream) [*]A child ate ice cream (possible cake) [*]A child ate neither [/LIST] We have cake + ice cream + neither - both cake and ice cream. We subtract both cake and ice cream to avoid duplicates 13 + 9 + 1 - 7 = 16 kids at the party

At a carnival, Diane bought 14 packs of 7 tickets each. She also found 9 more tickets on the ground. How many tickets did Diane have in all? 14 packs * 7 tickets/pack = 98 tickets Now add the 9 tickets on the ground: 98 + 9 = [B]107 tickets[/B]

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 more child tickets than adult tickets were sold. If a total of $6360 was collected from the total ticket sale that day, how many child tickets were sold? Let the number of adult tickets be a. Let the number of child tickets be c. We're given two equations: [LIST=1] [*]c = a + 30 [*]6a + 4c = 6360 [/LIST] Substitute equation (1) into equation (2): 6a + 4(a + 30) = 6360 Multiply through to remove parentheses: 6a + 4a + 120 = 6360 T[URL='https://www.mathcelebrity.com/1unk.php?num=6a%2B4a%2B120%3D6360&pl=Solve']ype this equation into our search engine[/URL] to solve for a and we get: a = 624 Now substitute a = 624 back into equation (1) to solve for c: c = 124 + 30 c = [B]154[/B]

At a certain university, 60% of the students enrolled in a math course, 50% are enrolled in an English course, and 40% are enrolled in both. What percentage of the students are enrolled in an English course and/or a math course? Let M be a math course, E be an english course, We are given: [LIST] [*]P(M) = 0.6 [*]P(E) = 0.5 [*]P(E AND M) = 0.4 [*]We want P(E U M) [/LIST] Using [URL='http://www.mathcelebrity.com/probunion2.php?pa=0.6+&pb=+0.5&paintb=+0.4&aub=+&pl=Calculate']two event probability[/URL], we get [B]P(E U M) = 0.7[/B]

At a concert there were 25 more women than men. The total number of people at the concert was 139. Find the number of women and the number of men at the concert. Let men be m and women be w. We're given two equations. [LIST=1] [*]w = m + 25 [*]m + w = 139 [/LIST] Substitute equation (1) into equation (2): m + m + 25 = 139 To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%2B25%3D139&pl=Solve']type this equation into our search engine[/URL] and we get: m = [B]57 [/B] To find w, we substitute m = 57 into equation (1): w = 57 + 25 w = [B]82[/B]

At a concert, 20% of the audience members were teenagers. If the number of teenagers at the concert was 360, what was the total number of audience members? We're looking for total audience members where [I]20% of what equals 360[/I]? [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=360&pct1=20&pcheck=2&pct2=+70&den1=+80&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Type this expression into our search engine[/URL] and we get: Audience = [B]1,800[/B]

At a festival, Cherly bought 5 ride tokens and 9 game tokens. She spent $59. Let x represent the cost of ride tokens and let y represent the cost of game tokens. Write an equation in standard for that can be used to determine how much each type of token costs. We know that: Token Cost + Game Cost = Total Cost Since cost = price * quantity, we have: [B]5x + 9y = 59[/B]

At a football game, a vender sold a combined total of 117 sodas and hot dogs. The number of hot dogs sold was 59 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold. [U]Let h = number of hot dogs and s = number of sodas. Set up our given equations:[/U] [LIST=1] [*]h + s = 117 [*]h = s - 59 [/LIST] [U]Substitute (2) into (1)[/U] (s - 59) + s = 117 [U]Combine s terms[/U] 2s - 59 = 117 [U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2s-59%3D117&pl=Solve']equation solver[/URL], we find:[/U] [B]s = 88 [/B] [U]Plug s = 88 into (2)[/U] h = 88 - 59 [B]h = 29[/B]

At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers for $1.35 each. They sold 40 more slices of pizza than hamburgers, and sales totaled $292.5. How many slices of pizza did they sell Let the number of pizza slices be p and the number of hamburgers be h. We're given two equations: [LIST=1] [*]p = h + 40 [*]1.35h + 0.75p = 292.50 [/LIST] [I]Substitute[/I] equation (1) into equation (2) for p: 1.35h + 0.75(h + 40) = 292.50 1.35h + 0.75h + 30 = 292.50 2.10h + 30 = 292.50 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.10h%2B30%3D292.50&pl=Solve']plug this equation into our search engine[/URL] and we get: h = 125 The problem asks for number of pizza slices sold (p). So we substitute our value above of h = 125 into equation (1): p = 125 + 40 p = [B]165[/B]

At a light bulb factory 4 out of every 25 light bulbs are defective. How many light bulbs would you excpect to be defective out of 350 light bulbs Set up a proportion of light bulbs to defects where d is the number of defects per 350 light bulbs: 4/25 = b/350 [URL='https://www.mathcelebrity.com/prop.php?num1=4&num2=b&den1=25&den2=350&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into our search engine[/URL], and we get: b = [B]56[/B]

At a local fitness center, members pay a $10 membership fee and $3 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members and nonmembers be the same? Set up the cost functions where x is the number of aerobics classes: [LIST] [*]Members: C(x) = 10 + 3x [*]Non-members: C(x) = 5x [/LIST] Set them equal to each other 10 + 3x = 5x Subtract 3x from both sides: 2x = 10 Divide each side by 2 [B]x = 5 classes[/B]

At a local fitness center, members pay an $8 membership fee and $3 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members be equal to nonmembers? Set up two cost equations C(x): [LIST=1] [*]Members: C(x) = 8 + 3x [*]Nonmembers: C(x) = 5x [/LIST] Set the two cost equations equal to each other: 8 + 3x = 5x Subtract 3x from each side 2x = 8 Divide each side by 2 [B]x = 4[/B]

at a party, there are 72 people. The ratio of men to ladies to kids is 4 to 3 to 2. [LIST] [*]How many men at the party? [*]How many ladies at the party? [*]How many kids at the party? [/LIST] Our total ratio denominator is 4 + 3 + 2 = 9. To find the number of each type of person, we take their ratio divided by their ratio numerator times 72 people at the party [U]Calculate ratios:[/U] [LIST] [*]Men: [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F9&frac2=72&pl=Multiply']4/9 * 72[/URL] = [B]32[/B] [*]Ladies: [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F9&frac2=72&pl=Multiply']3/9 * 72[/URL] = [B]24[/B] [*]Kids: [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F9&frac2=72&pl=Multiply']2/9 * 72[/URL] = [B]16[/B] [/LIST] [U]Check our work:[/U] Men + Ladies + Kids = 32 + 24 + 16 Men + Ladies + Kids = 72 <-- This checks out!

At a rate of 4 gallons per min , how long will it take to fill a 300 gallon swimming pool Time to fill = Total Gallons of the Pool / Fill Rate Time to Fill = 300 gallons / 4 gallons per minute Time to Fill = [B]75 minutes[/B]

At a recent motorcycle rally, the number of men exceeded the number of women by 247. If x represents the number of women, write an expression for the number of men. [B]m = x + 247[/B]

At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 percent. Which expression represents how much she will receive in commission from the sale? Since 18 percent = 0.18, we have: Commission = Sales * Commission Percent Commission = 569 * 0.18 Commission = [B]$102.42[/B]

At Billy’s Baseball Dugout, they are having a sale on merchandise. All bats cost $45.00, sunflower seeds, $1.50, and cleats $85.00. Write an expression if you bought b bats, s sunflower seeds, and c cleats. Since amount = cost * quantity, we have a cost of: [B]45b + 1.50s + 85c[/B]

At Falling Creek Middle School, they noticed that 3 out of every 4 buses were on time. If there are a total of 32 buses that drop off at this school, how many buses will NOT be on time. If 3/4 are on time, we have 1 - 3/4 are not on time. 1 = 4/4 4/4 - 3/4 = 1/4 are not on time We multiply 1/4(32) = [B]8 buses will NOT be on time[/B].

At midnight in Winnipeg, the temperature was ?23°C. During the next 24 hours, the temperature rose 12°C, then dropped 8°C. What was the final temperature? We start with ?23°C Temperatures rising 12°C mean we add: -23 + 12 = -11 Temperatures dropping 8°C mean we subtract: -11 - 8 = [B]-19°C[/B]

At midnight, the temperature was -15 degrees Fahrenheit. By the next morning, the temperature had gone up to 20 degrees. What was the temperature then? The student meant to say gone up 20 degrees. We start with -15. We add 20 -15 + 20 = [B]5[/B]

At night, the average temperature on the surface of Saturn is -150 C. During the day, the temperature rises 27 C. What is the average temperature on the planet's surface during the day? Rising temperature means we add, so we have: -150+ 27 = [B]-123C[/B]

At Priscilla's school, the final grade for her Calculus course is weighted as follows: Tests: 50% Quizzes: 30% Homework: 20% Priscilla has an average of 87% on her tests, 100% on her quizzes, and 20% on her homework. What is Priscilla's weighted average? Weighted Average gives weights to each percent of the average as follows: Weighted Average = Average * weighting percent Weighted Average = Test Average * Test Weighting + Quiz Average. * Quiz Weighting + Homework Average * Homework Weighting Weighted Average = 87% * 50% + 100% * 30% + 20% * 20% Weighted Average = 43.5% + 30% + 4% Weighted Average = [B]77.5%[/B]

At Sams Club, 32 cans of Coke cost a total of $8.96. What is the cost per can? Unit Cost is Total Cost / Number of Units Unit Cost = $8.96/32 Unit Cost = [B]$0.28[/B]

At the 2002 Winter Olympics, Austria won 2 gold medals. This was 1/8 of the total medals Austria won. How many did Austria win? Let t be the total medals Austria won. We have: 2 = x/8 Cross multiply, we get: x = 2 * 8 x = [B]16[/B]

At the beginning of Jack's diet, he was 257 pounds. If he lost 3 pounds per week, find his weight after 12 weeks. A loss of weight means we subtract from Jack's current weight. New Weight = Current Weight - Weight Loss per week * number of weeks New Weight =257 - 3*12 New Weight =257 - 36 New Weight =[B] 221[/B]

At the end of the 2021 NBA season, the NY Knicks had 10 more wins than losses. This NBA season the NY Knicks played a total of 72 times. Find a solution to this problem and explain. Let w be the number of wins Let l be the number of losses We're given two equations: [LIST=1] [*]w = l + 10 [*]l + w = 72 [/LIST] To solve this system of equations, substitute equation (1) into equation (2) for w: l + l + 10 = 72 To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l%2Bl%2B10%3D72&pl=Solve']type it in our math engine[/URL] and we get: l = [B]31 [/B] To solve for w, we substitute l = 31 into equation (1): w = 31 + 10 w = [B]41[/B]

At the end of the day, a bakery had 1/2 of a pie left over. The 4 employees each took home the same amount of leftover pie. How much pie did each employee take home? We have 1/2 of the pie eaten, if 1/2 was left over. So 1/2 of a pie divided by 4 employees = [B]1/8 of a pie per person[/B]. To check our work, we have 4 * 1/8 = 4/8 = 1/2 of pie eaten.

At the end of the day, the temperature is -16°C. During the day it dropped 12°C. What was the temperature in the morning? Write an equation to represent, then solve and verify your answer let the starting temperature be s. If the temperature dropped, that means we subtract, so we have the following equation: s - 12 = -16 To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=s-12%3D-16&pl=Solve']type it in our search engine[/URL] and we get: s = [B]-4[/B]

At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on a movie and popcorn and another $1.35 on a pen. How much did she earn babysitting? Let the original amount of money earned for babysitting be b. We're given: [LIST=1] [*]Start with b [*]Spending 14.65 for a movie means we subtract 14.65 from b: b - 14.65 [*]Spending 1.35 on a pen means we subtract another 1.35 from step 2: b - 14.65 - 1.35 [*]Francesca has a third of her money left. So we set step 3 equal to 1/3 of b [/LIST] b - 14.65 - 1.35 = b/3 Multiply each side of the equation by 3 to remove the fraction 3(b - 14.65 - 1.35) = 3b/3 3b - 43.95 - 4.05 = b To solve this equation for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b-43.95-4.05%3Db&pl=Solve']we type it in our search engine[/URL] and we get: b =[B] 24[/B]

At the movie theater, Celeste bought 2 large drinks and 2 large popcorns for $8.50. She paid with a twenty-dollar bill. What is the fewest number of bills and coins that she could have received as change?r of bills and coins that she could have received as change? Calculate change: Change = Amount Paid - Bill Change = $20.00 - $8.50 Change = $11.50 Largest bill we can start with is a 10 dollar bill: $11.50 - 10 = $1.50 Next largest bill is a $1 bill $1.50 - $1 = 0.50 Now we're down to coins. Largest coin(s) we can use are quarters (assuming no half-dollars) 2 quarters equals 0.50 0.50 - 0.50 = 0 [U]Therefore, our answer is:[/U] [B]Ten dollar Bill, 1 dollar bill, and 2 quarters[/B]

[B]A[/B]t Zabowood’s Gadget Store, some items are paid on instalment basis through credit cards. Clariza was able to sell 10 cellphones costing Php 18,000.00 each. Each transaction is payable in 6 months equally divided into 6 equal instalments without interest. Clariza gets 2% commission on the first month for each of the 10 cellphones. Commission decreases by 0.30% every month thereafter and computed on the outstanding balance for the month. How much commission does Clariza receive on the third month? Calculate Total Sales Amount: Calculate Total Sales Amount = 10 cellphones * 18000 per cellphone Calculate Total Sales Amount = 180000 Calculate monthly sales amount installment: monthly sales amount installment = Total Sales Amount / 6 monthly sales amount installment = 180000/6 monthly sales amount installment = 30000 per month Calculate Third Month Commission: Third month commission = First Month Commission - 0.30% - 0.30% Third month Commission = 2% - 0.30% - 0.30% = 1.4% Calculate 3rd month commission amount: 3rd month Commission amount = 1.4% * 30000 3rd month Commission amount = [B]420[/B]

Austin deposited $4000 into an account with 4.8% interest, compounded monthly. Assuming that no withdrawals are made, how much will he have in the account after 4 years? Do not round any intermediate computations, and round your answer to the nearest cent. Using our [URL='http://www.mathcelebrity.com/compoundint.php?bal=40000&nval=4&int=4.8&pl=Annually']balance calculator[/URL], we get: [B]$48,250.87[/B]

Austin has 15 CDs, which is 3 less than his sister has. How many CDs does his sister have? Let s be the number of CD's his sister has and a be the number Austin has [LIST=1] [*]a = 15 [*]a = s - 3 [/LIST] Substitute (1) into (2) 15 = s - 3 Add 3 to each side [B]s = 18[/B]

Austin needs $240 to buy a new bike if he can save $16 per week and how many weeks can you purchase the bike? Set up the equation, where w equals the number of weeks needed. We have: 16w = 240 [URL='https://www.mathcelebrity.com/1unk.php?num=16w%3D240&pl=Solve']Typing this into our search engine[/URL], we get [B]w = 15[/B].

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Ava is 4 times as old as Peter. What equation can be used to find Peter’s age? [U]Assumptions[/U] Let a be Ava's age Let p be Peter's age We're given: a = 4p To find Peter's age, we divide each side of the equation by 4 to get: a/4 = 4p/4 p = [B]a/4[/B]

Ava set her watch 2 seconds behind, every day it sets back 1 second. How many days has it been since she last set her watch if it is 41 seconds behind? Right now: Watch is 2 seconds behind [U]Let d be the day after right now[/U] (1)d + 2 = 41 d + 2 = 41 [U]Subtract 2 from each side[/U] [B]d = 39[/B]

We are solving for x: Subtract b from each side: ax = cx - d - b Subtract cx from each side: ax - cx = -d - b Factor out x from the left side: x(a - c) = -d - b Divide each side by (a - c) x = (-d - b)/(a - c)

ax - mn = mn + bx for x Add mn to each side: ax - mn + mn = mn + bx + mn Cancel the mn terms on the left side and we get: ax = bx + 2mn Subtract bx from each side: ax - bx = bx - bx + 2mn Cancel the bx terms on the right side: ax - bx = 2mn Factor out x on the left side: x (a - b) = 2mn Divide each side of the equation by (a - b): x (a - b)/(a - b) = 2mn/(a - b) Cancel the (a - b) on the left side and we get: x = [B]2mn/(a - b)[/B]

a^2 + b^2 = c^2 for c Take the square root of each side: c = [B]sqrt(a^2 + b^2)[/B]

b bags of beans there are 7 beans in each bag This means we have 7 beans x b bags = 7b beans total beans.

B is the midpoint of AC and BC=5 Since the midpoint divides a segment into two equal segments, we know that: AB = BC So AB =[B] 5[/B] And AC = 5 + 5 = [B]10[/B]

B is the set of vowels in the English alphabet B = [B]{a, e, i, o, u} [MEDIA=youtube]-O686SiqLrk[/MEDIA][/B]

b more points than 75 Let b be the number of points b + 75

B out of 6 is 12 b out of 6: b/6 The phrase [I]is[/I] means an equation, so we set b/6 equal to 12: [B]b/6 = 12[/B]

b to the fifth power decreased by 7 Take this algebraic expression in steps: [LIST] [*]b to the fifth power: b^5 [*]Decreased by 7 means we subtract 7 from b^5: [B]b^5 - 7[/B] [/LIST]

b varies directly as the sum of x and y This is a direct variation problem. Direct variation means there exists a constant k such that: [B]b = k(x + y)[/B]

b/3d - h = 343 for b A literal equation means we solve for one variable in terms of another variable or variables Add h to each side to isolate the b term: b/3d - h + h = 343 + h Cancel the h's on the left side, we get: b/3d = 343 + h Cross multiply: b = [B]3d(343 + h)[/B]

Free Babylonian Method Calculator - Determines the square root of a number using the Babylonian Method.

Bacteria in a petra dish doubles every hour. If there were 34 bacteria when the experiment began, write an equation to model this. Let h be the number of hours since the experiment began. Our equation is: [B]B(h) = 34(2^h)[/B]

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Balls numbered 1 to 10 are placed in a bag. Two of the balls are drawn out at random. Find the probability that the numbers on the balls are consecutive. Build our sample set: [LIST] [*](1, 2) [*](2, 3) [*](3, 4) [*](4, 5) [*](5, 6) [*](6, 7) [*](7, 8) [*](8, 9) [*](9, 10) [/LIST] Each of these 9 possibilities has a probability of: 1/10 * 1/9 This is because we draw without replacement. To start, the bag has 10 balls. On the second draw, it only has 9. We multiply each event because each draw is independent. We have 9 possibilities, so we have: 9 * 1/10 * 1/9 Cancelling, the 9's, we have [B]1/10[/B]

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, about 170 million. The population growth rate in Bangladesh is assumed to be linear, and is about 1.5% per year of the base 170 million. Create a linear model for population growth in Bangladesh. Assume that y is the total population in millions and t is the time in years. At any time t, the Bangladesh population at year t is: [B]y = 170,000,000(1.015)^t[/B]

Barbara bought a piece of rope that was 7 1/3 meters long. She cut the rope into 3 equal pieces. How long is each piece of rope? Using our mixed number converter, we see that: [URL='https://www.mathcelebrity.com/fraction.php?frac1=7%261%2F3&frac2=3%2F8&pl=Simplify']7&1/3[/URL] = 22/3 Split into [URL='https://www.mathcelebrity.com/fraction.php?frac1=22%2F9&frac2=3&pl=Simplify']3 equal pieces[/URL], we have: 22/3 / 3 = 22/9 or 2&4/9

Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants cost $4 each. If she plans to spend at least $20 and purchase less than 15 plants in total, create a system of equations or inequalities that model the situation. Define the variables you use. [U]Define variables[/U] [LIST] [*]Let c be the number of corn plants [*]Let p be the number of potato plants [/LIST] Since cost = price * quantity, we're given two inequalities: [LIST=1] [*][B]3p + 4c >= 20 (the phrase [I]at least[/I] means greater than or equal to)[/B] [*][B]c + p < 15[/B] [/LIST]

Barney has $450 and spends $3 each week. Betty has $120 and saves $8 each week. How many weeks will it take for them to have the same amount of money? Let w be the number of weeks that go by for saving/spending. Set up Barney's balance equation, B(w). Spending means we [U]subtract[/U] B(w) = Initial Amount - spend per week * w weeks B(w) = 450 - 3w Set up Betty's balance equation, B(w). Saving means we [U]add[/U] B(w) = Initial Amount + savings per week * w weeks B(w) = 120 + 8w The same amount of money means both of their balance equations B(w) are equal. So we set Barney's balance equal to Betty's balance and solve for w: 450 - 3w = 120 + 8w Add 3w to each side to isolate w: 450 - 3w + 3w = 120 + 8w + 3w Cancelling the 3w on the left side, we get: 450 = 120 + 11w Rewrite to have constant on the right side: 11w + 120 = 450 Subtract 120 from each side: 11w + 120 - 120 = 450 - 120 Cancelling the 120's on the left side, we get: 11w = 330 To solve for w, we divide each side by 11 11w/11 = 330/11 Cancelling the 11's on the left side, we get: w = [B]30 [MEDIA=youtube]ifG_q-utgJI[/MEDIA][/B]

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based on a sample of size 41, a 95% confidence interval for the mean score of all students,µ, on an aptitude test is from 60 to 66. Find the margin of error

Did they give you a standard deviation?

Bashar just read that many more car accidents occur within 30 miles of one's home. He decided that he would wear his seat belt only when he is driving within 30 miles from his home and not on long trips because it is obviously safer to travel when you are more than 30 miles from your home. Explain why Bashar's logic is flawed. [B]More accidents occur within 30 miles of one's home because that is where a majority of the travel takes place.[/B]

Bashir finds some nickels and pennies under the couch cushions. How much money ( in dollars ) does he have if he has x nickels and y pennies Amount = Cost * Quantity, so we have: [B]0.01y + 0.05x[/B]

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Free Basic Math Operations Calculator - Given 2 numbers, this performs the following arithmetic operations:
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Free Basic Statistics Calculator - Given a number set, and an optional probability set, this calculates the following statistical items:
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Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign, then divided by 3. What was the original equation [LIST=1] [*]If we added 7 to both sides, that means we had a minus 7 (-7) to start with as a constant. Since subtraction undoes addition. [*]If we divided by 3, this means we multiplied x by 3 to begin with. Since division undoes multiplication [/LIST] So we have the start equation: 3x - 7 If the answer was x = -4, then we plug this in to get our number on the right side of the equation: 3(-4) - 7 -12 - 7 -19 This means our original equation was: [B]3x - 7 = -19[/B] And if we want to solve this to prove our answer, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D-19&pl=Solve']type the equation into our search engine [/URL]and we get: x = -4

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Because of the promotion, attendance exceeded normal by 275 percent. If the normal attendance was 6600 people, how many people attended? Find the exceeded multiplier: Exceeded Multiplier = Exceed percent / 100 [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=275&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']275% as a decimal[/URL] = 2.75 We multiply as follows: Exceeded Attendance = Normal Attendance * Exceeded Multiplier Exceeded Attendance = 6600 * 2.75 Exceeded Attendance = [B]18,150[/B]

Before Barry Bonds, Mark McGwire, and Sammy Sosa, Roger Maris held the record for the most home runs in one season. Just behind Maris was Babe Ruth. The numbers of home runs hit by these two athletes in their record-breaking seasons form consecutive integers. Combined, the two athletes hit 121 home runs. Determine the number of home runs hit by Maris and Ruth in their record-breaking seasons. We want [URL='https://www.mathcelebrity.com/consecintwp.php?num=121&pl=Sum']the sum of 2 consecutive integers equals 121[/URL]. [B]We get Maris at 61 and Ruth at 60[/B]

Before you is a 3-quart container, a 5-quart container and a sink full of water. There are no markings on either container to show how many quarts are in each one. All you know is that when the 3-quart container is full, it contains three quarts. You also know that when the 5-quart container is full, it contains five quarts. Your task is to place exactly four quarts in the 5-quart container. How would you accomplish this task? [LIST=1] [*]Fill the 3-quart container and pour it into the 5-quart container [*]Fill the 3-quart container and pour as much as you can (2 quarts) into the 5-quart container. This will leave one quart left. [*]Empty the 5-quart container and pour the one quart into the 5-quart [*]Fill the 3-quart and pour it into the 5-quart. Now there are 4 quarts in the 5-quart container. [/LIST] [I]Note: This is the Die Hard 3 movie problem[/I]

Belen can make 15 necklaces in 3 1/2 hours. How many can she make in one hour? We set up a proportion of necklaces to time, where n is the number of necklaces Belen can make in 1 hour: 3 & 1/2 = 3.5, so we have: 15/3.5 = n/1 [SIZE=3][FONT=Helvetica][COLOR=rgb(34, 34, 34)] To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=n&den1=3.5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine and we ge[/URL]t: n = [B]4.29 hours[/B][/COLOR][/FONT][/SIZE]

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each pencil The cost per pencil is: 1560/30 = 52 Build revenue function: Revenue = Number of Pencils * Sales Price (s) Revenue = 30s The profit equation is: Profit = Revenue - Cost Given profit is 180 and cost is 1560, we have: 30s - 1560 = 180 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=30s-1560%3D180&pl=Solve']type this equation into our search engine[/URL] and we get: s = 58 This is sales for total profit. The question asks profit per pencil. Profit per pencil = Revenue per pencil - Cost per pencil Profit per pencil = 58 - 52 Profit per pencil = [B]6[/B]

Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects getting better each trial? Test the linear effect of trial for the data. A score trial B score trial 2 C Score trial 3 4 6 7 3 7 8 2 8 5 1 4 7 4 6 9 2 4 2 (a) Compute L for each subject using the contrast weights -1, 0, and 1. That is, compute (-1)(a) + (0)(b) + (1)(c) for each subject. (b) Compute a one-sample t-test on this column (with the L values for each subject) you created. Formula t = To computer a one-sample t-test first know the meaning of each letter (a) Each L column value is just -1(Column 1) + 0(Column2) + 1(Column 3) A score trial B score trial 2 C Score trial 3 L = (-1)(a) + (0)(b) + (1)(c) 4 6 7 3 3 7 8 5 2 8 5 3 1 4 7 6 4 6 9 5 2 4 2 0 (b) Mean = (3 + 5 + 3 + 6 + 5 + 0)/6 = 22/6 = 3.666666667 Standard Deviation = 2.160246899 Use 3 as our test mean (3.666667 - 3)/(2.160246899/sqrt(6)) = 0.755928946

Ben can write 153 letters in 3 minutes. At this rate, how many letters can he write in 10 minutes? We set up a proportion of letters to minutes where the number of letters in 10 minutes is l: 153/3 = l/10 We [URL='https://www.mathcelebrity.com/prop.php?num1=153&num2=l&den1=3&den2=10&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into a search engine[/URL] and we get: l =[B] 510[/B]

Ben has $4.50 in quarters(Q) and dimes(D). a)Write an equation expressing the total amount of money in terms of the number of quarters and dimes. b)Rearrange the equation to isolate for the number of dimes (D) a) The equation is: [B]0.1d + 0.25q = 4.5[/B] b) Isolate the equation for d. We subtract 0.25q from each side of the equation: 0.1d + 0.25q - 0.25q = 4.5 - 0.25q Cancel the 0.25q on the left side, and we get: 0.1d = 4.5 - 0.25q Divide each side of the equation by 0.1 to isolate d: 0.1d/0.1 = (4.5 - 0.25q)/0.1 d = [B]45 - 2.5q[/B]

Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan. Let b be Ben's age and i be Ishaan's age. We're given: [LIST=1] [*]b = 4i [*]b = i + 6 [/LIST] Set (1) and (2) equal to each other: 4i = i + 6 [URL='https://www.mathcelebrity.com/1unk.php?num=4i%3Di%2B6&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]i = 2[/B] Substitute this into equation (1): b = 4(2) [B]b = 8 [/B] [I]Therefore, Ishaan is 2 years old and Ben is 8 years old.[/I]

Ben visits the park every 2 days and goes to the library every 5 days. If Ben gets to do both of these today, how many days will pass before Ben gets to do them both on the same day again? To find this, we want the least common multiple (LCM) of 2 and 5. We [URL='https://www.mathcelebrity.com/gcflcm.php?num1=2&num2=5&num3=&pl=GCF+and+LCM']type LCM(2,5) into our search engine[/URL] and we get: [B]10 days [/B] We check our work: 2 days * 5 visits = 10 days 5 days * 2 visits = 10 days

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Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 47 cards left. How many cards did Benny start with? Let b be the number of baseball trading cards Benny started with. We have the following events: [LIST=1] [*]Benny buys 8 new cards, so we add 8 to get b + 8 [*]The dog ate half of his cards the next day, so Benny has (b + 8)/2 [*]We're told he has 47 cards left, so we set (b + 8)/2 equal to 47 [/LIST] (b + 8)/2 = 47 [B][U]Cross multiply:[/U][/B] b + 8 = 47 * 2 b + 8 = 94 [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B8%3D94&pl=Solve']Type this equation into the search engine[/URL], we get [B]b = 86[/B].

Benny bought a soft drink for 2 dollars and 7 candy bars. He spent a total of 27 dollars. How much did each candy bar cost? [U]Calculate the candy bar spend:[/U] Candy Bar Spend = Total Spend - Soft Drink Candy Bar Spend = 27 - 2 Candy Bar Spend = 25 [U]Calculate the cost of each candy bar:[/U] Cost of each candy bar = Candy Bar Spend / Total Candy Bars Cost of each candy bar = 25 / 7 Cost of each candy bar = [B]3.57[/B]

Benny had 119 dollars to spend on 9 books. After buying them he had 11 dollars. How much did each book cost ? Let each book cost "b". We have: 9b + 11 = 119 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=9b%2B11%3D119&pl=Solve']equation calculator[/URL], we get [B]b = 12[/B].

Benny had 90 dollars to spend on 7 books. After buying them he had 13 dollars. How much did each book cost? Let each book cost be b. We have: 7b + 13 = 90 [URL='https://www.mathcelebrity.com/1unk.php?num=7b%2B13%3D90&pl=Solve']Typing this equation into the search engine[/URL], and you get: [B]b = 11[/B]

Benny opened a bank account. He deposited $92.50 into his account every month for 10 months. He used $36.50 every month to pay for art lessons. After 10 months, he used 1/2 of the total money left in his account to go to a summer camp for artists. What is the total amount of money Benny spent to go to the summer camp? If Benny deposits $92.50 every month and withdraws $36.50 every month, his net deposit each month is: 92.50 - 36.50 = 56 Benny does this for 10 months, so his balance after 10 months is: 56 * 10 = 560 Half of this is: 560/2 = [B]280[/B]

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Besides 8 and 1, what is one factor of 8. Using our [URL='http://www.mathcelebrity.com/factoriz.php?num=8&pl=Show+Factorization']factor calculator[/URL], or entering the shortcut [B]Factor 8[/B], we get the following factors: 1, 2, 4, 8 Excluding 1 and 8, we have [B]2, 4[/B]

Beth is 5 years younger than celeste. Next year, their ages will have a sum equal to 57. How old is each now? Let b = Beth's age Let c = Celeste's age We are given: [LIST=1] [*]b = c - 5 [*]b + 1 + c + 1 = 57 [/LIST] Substitute (1) into (2) (c - 5) + 1 + c + 1 = 57 Group like terms: 2c - 3 = 57 [URL='https://www.mathcelebrity.com/1unk.php?num=2c-3%3D57&pl=Solve']Type 2c - 3 = 57 into our search engine[/URL], we get [B]c = 30[/B] Substitute c = 30 into Equation (1), we get: b = 30 - 5 [B]b = 25 [/B] Therefore, Beth is 25 and Celeste is 30.

Beth made a trip to the train station and back. On the trip there she traveled 45 km/h and on the return trip she went 30 km/h. How long did the trip there take if the return trip took six hours? We use the distance formula: D = rt where D = distance, r = rate, and t = time. Start with the return trip: D = 45(6) D = 270 The initial trip is: 270= 30t Divide each side by 30 [B]t = 9 hours[/B]

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Beverly has $50 to spend at an amusement park. She plans to spend $10 for food, and $15 for admission to the park. Each ride costs $1.50 to ride. Write an inequality to represent the possible number of rides she can ride? First, we subtract the food and admission cost from Beverly's starting balance of $50: Cost available for rides = Starting Balance - Food - Admission Cost available for rides = 50 - 10 - 15 Cost available for rides = 25 Now we set up an inequality for the number of rides (r) that Beverly can ride with the remaining balance: 1.50r <= 25 To solve for r, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.50r%3C%3D25&pl=Show+Interval+Notation']type this inequality into our search engine[/URL] and we get: [B]r <=[/B] [B]16.67[/B]

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Big John weighs 300 pounds and is going on a diet where he'll lose 3 pounds per week. Write an equation in slope-intercept form to represent this situation. [LIST] [*]The slope intercept form is y = mx + b [*]y is John's weight [*]x is the number of weeks [*]A 3 pound per week weight loss means -3 as the coefficient m [*]b = 300, John's starting weight [/LIST] [B]y = -3x + 300[/B]

Bike rental shop A charges $20 per kilometre travelled with no additional fee. Bike rental shop B charges only $8 per kilometre travelled, but has a starting charge of $35. If Bob plans to travel 7km by bike, which rental shop should he choose for a better price [U]Shop A Cost function C(k) where k is the number of kilometers used[/U] C(k) = Cost per kilometer * k + Starting Charge C(k) = 20k With k = 7, we have: C(7) = 20 * 7 C(7) = 140 [U]Shop B Cost function C(k) where k is the number of kilometers used[/U] C(k) = Cost per kilometer * k + Starting Charge C(k) = 8k + 35 With k = 7, we have: C(7) = 8 * 7 + 35 C(7) = 56 + 35 C(7) = 91 Bog should choose [B]Shop B[/B] since they have the better price for 7km

Bill and nine of his friends each have a lot of money in the bank. Bill has 10^10 dollars in his acc All nine of Bill's friends pooled together is: 9 * 10^9 Bill's 10^10 can be written as 10 * 10^9 So [B]Bill's is greater[/B]

Bill is q years old. How old will he in 6 years ? How old was he 4 years ago ? Start with q years old. In 6 years means we add since it's the future: [B]q + 6[/B] 4 years ago means we subtract since it's in the past: [B]q - 4[/B]

Bill raises the flag 15 feet above the ground. Then he lowers it 8 feet and raises it another 2 feet. how far above the ground is the flag now? We tally up the positives and negatives: Raise = +15 Lower = -8 Raise = +2 Total = +15 - 8 + 2 Total = [B]9 feet above the ground[/B]

Bills car rental charges a base fee of 50$ and then $0.20 per mile. Set up the cost function C(m) where m is the number of miles driven: [B]C(m) = 50 + 0.20m[/B]

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If a seed is planted, it has a 90% chance of growing into a healthy plant. If 12 seeds are planted, what is the probability that exactly 4 don't grow? Im seriously confused is it like u multiple the amount of the (0.90) and multiple (0.30) by power depends how any they r right?

You want the binomial distribution, where a "success" is that the plant [U]does not[/U] grow. So if the probability that the plant grows is 0.9, the probability it does not grow is 1 - 0.9 = 0.1. We have n = 12, p = 0.1 You want the probability that exactly 4 of 12 do not grow. Use our [URL='http://www.mathcelebrity.com/binomial.php?n=+12&p=+0.1&k=+4&t=+5&pl=P%28X+%3D+k%29']binomial distribution probability calculato[/URL]r to get P(X = 4) = [B]0.0213[/B]

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blair’s bank account was overdrawn by $40. she spent $30 at the grocery store. what is the balance in her account now? The word [I]overdrawn[/I] means a negative balance. So we start with: -40 Spending 30 at the grocery store means we subtract 30 from our initial balance: -40 - 30 = [B]-70 or $70 overdrawn[/B]

Blake and Tatsu are each assigned a paper for a class they share. Blake decides to write 4 pages at a time while Tatsu decides to write 7 pages at a time. If they end up writing the same number of pages, what is the smallest number of pages that the papers could have had? We want the least common multiple of 4 and 7, written as LCM(4, 7). Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=7&num3=&pl=LCM']LCM Calculator[/URL], we get: LCM(4, 7) = [B]28 pages[/B]

Blake writes 4 pages per hour. How many hours will Blake have to spend writing this week in order to have written a total of 16 pages? [U]Let x = the number of hours Blake needs to write[/U] 4 pages per hour * x hours = 16 [U]Divide each side by 4[/U] [B]x = 4 hours[/B]

Blanca works as a salesperson and earns a base salary of $72 per week plus a commission of 12% of all her sales. If Blanca had $75 in weekly sales, how much did she make? [U]Find the commission on her sales[/U] Commission = Sales * 12% Commission = 75 * 0.12 = 9 [U]Now add in her base salary[/U] Total Salary = Base Salary + Commission Total Salary = 72 + 9 Total Salary = [B]81[/B]

Blueberries are $4.99 a pound. Diego buys b pounds of blueberries and pays $14.95. Since price * quantity = cost, we have the equation: 4.99b = 14.95 To solve for b, [URL='https://www.mathcelebrity.com/1unk.php?num=4.99b%3D14.95&pl=Solve']we type this equation into our search engine[/URL] and we get: b = [B]$3.00[/B]

Bob bought 10 note books and 4 pens for 18$. Bill bought 6 notebooks and 4 pens for 12$. Find the price of one note book and one pen. Let the price of each notebook be n. Let the price of each pen be p. We're given two equations: [LIST=1] [*]10n + 4p = 18 [*]6n + 4p = 12 [/LIST] Since we have matching coefficients for p, we subtract equation 1 from equation 2: (10 - 6)n + (4 - 4)p = 18 - 12 Simplifying and cancelling, we get: 4n = 6 [URL='https://www.mathcelebrity.com/1unk.php?num=4n%3D6&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]n = 1.5[/B] Now, substitute this value for n into equation (2): 6(1.5) + 4p = 12 Multiply through: 9 + 4p = 12 [URL='https://www.mathcelebrity.com/1unk.php?num=9%2B4p%3D12&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]p = 0.75[/B]

Bob can complete 35 math problems in 5 minutes how many can he complete in 1 minute 35 math problems / 5 minutes Divide the top and bottom of the fraction by 5: 35 math problems / 5 minutes =[B] 7 math problems per minute[/B]

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 feet. Use the perimeter formula to find the width of the rectangular yard in inches: P = 2L + 2W. Plugging our numbers in for P = 22 and L = 5, we get: 22 = 2(5) + 2W 22 = 10 + 2w Rewritten, we have: 10 + 2w = 22 [URL='https://www.mathcelebrity.com/1unk.php?num=10%2B2w%3D22&pl=Solve']Plug this equation into the search engine[/URL], we get: [B]w = 6[/B]

Bob finished reading his book in x days. Each day, he read 4 pages. His book has 28 pages Our equation for this is found by multiplying pages per day times number of days; 4x = 28 To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3D28&pl=Solve']we type the equation into our search engine[/URL] and we get: x = [B]7[/B]

Bob has 1.5 pounds of nails. If there are 80 nails in a pound, how many nails does Bob have? 1.5 pounds x 80 nails per pound = [B]120 nails[/B].

Bob has 4/5 of a pound of fudge. He wants to share it with Sue. How much of a pound of fudge will both of them get? If Bob shares the fudge with Sue, we assume they split equal parts. This means: We take 4/5 total and divide into 2 for 2 people: 4/5/2 This is the same as 4/5 * 1/2 4/10 This fraction is not simplified. Factor of 4 = {1, [U]2[/U], 4} Factors of 10 = {1, [U]2[/U], 5, 10} In both of these lists, we see the greatest common factor is 2. So we divide top and bottom of 4/10 by 2: 4/2 / 10 / 2 [B]2/5 Bob gets 2/5 of a pound of fudge and Sue gets [B]2/5 of a pound of fudge[/B][/B]

Bob has a bookcase with 4 shelves. There are k books on each shelf. Using k, write an expression for the total number of books. Total Books = Bookcases * shelves per bookcase * books per shelf Total Books = 1 * 4 * k Total Books = [B]4k[/B]

Bob has half as many quarters as dimes. He has $3.60. How many of each coin does he have? Let q be the number of quarters. Let d be the number of dimes. We're given: [LIST=1] [*]q = 0.5d [*]0.25q + 0.10d = 3.60 [/LIST] Substitute (1) into (2): 0.25(0.5d) + 0.10d = 3.60 0.125d + 0.1d = 3.6 Combine like terms: 0.225d = 3.6 [URL='https://www.mathcelebrity.com/1unk.php?num=0.225d%3D3.6&pl=Solve']Typing this equation into our search engine[/URL], we're given: [B]d = 16[/B] Substitute d = 16 into Equation (1): q = 0.5(16) [B]q = 8[/B]

Bob is twice as old as Henry. The sum of their ages is 42. How old is Henry? Let Bob's age be b. Let Henry's age be h. We're given two equations: [LIST=1] [*]b = 2h [*]b + h = 42 [/LIST] Substitute b = 2h in equation 1 into equation 2 for b: 2h + h = 42 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2h%2Bh%3D42&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]14[/B]

Bob, Joe, Pete, Tom, Dick, and Tim share s sandwiches. How many sandwiches does each boy get? We have 6 boys, so they each get: [B]s/6 sandwiches[/B]

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Bonnita deposited $4,500 into a savings account paying 3% interest compounded continuously. She plans on leaving the account alone for 7 years. How much money will she have at that time? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=4500&int=3&t=7&pl=Continuous+Interest']compound interest calculator[/URL], we get: [B]$5551.55[/B]

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Boris baked 40 cookies. His family ate m of them If his family ate m, that mean we [I]subtract[/I] m from 40. So Boris has the remaining cookies: [B]40 - m[/B]

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Brad has $40 in a savings account. The interest rate is 5%, compounded annually. To the nearest cent, how much will he have in 3 years? [URL='https://www.mathcelebrity.com/compoundint.php?bal=40&nval=3&int=5&pl=Annually']Using our balance with interest calculator[/URL], we get [B]$46.31[/B].

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Brandon can shovel his sidewalk in 8 minutes, while his brother can shovel the walk in 12 minutes. If they work together, how long will it take them to shovel the sidewalk? Set up unit rates: [LIST] [*]Brandon can shovel 1/8 of a sidewalk per minute [*]His brother can shovel 1/12 of a sidewalk per minute [/LIST] Together, they can shovel: [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F8&frac2=1%2F12&pl=Add']1/8 + 1/12[/URL] = 5/24 of a sidewalk per minute 1 minute = 60 seconds 5/24 / 60 seconds = 1/x seconds 5/24 * 60 = 1/x 5/1440 = 1/x Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5&num2=1&den1=1440&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get: x = 288 288/60 = [B]4 minutes and 48 seconds[/B]

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Brenda has already knit 4 centimeters of scarf, and can knit 1 centimeter each night. After 43 nights of knitting, how many centimeters of scarf will Brenda have knit in total? 1 centimeter per night * 43 nights = 43 centimeters knitted. Add that to the 4 centimeters she started with, and we have: 43 + 4 = [B]47 centimeters[/B]

Brenda invests $1535 in a savings account with a fixed annual interest rate of 3% compounded continuously. What will the account balance be after 8 years Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=1535&int=3&t=8&pl=Continuous+Interest']continuous interest balance calculator[/URL], we get: [B]1,951.37 [MEDIA=youtube]vbYV6SYXtvs[/MEDIA][/B]

Brendan bought an aquarium originally priced at $50 but on sale for 50% off. After 12% sales tax, what was the total cost? 50% off of 50 means they pay half, or 1/2(50) = 25. Now, this gets taxed at 12%. So we multiply 25 * 1.12 Total Cost = 25(1.12) Total Cost = [B]$28[/B]

Brendan sells roses for $7.99 a bunch. at the end of the day he had collected $79.90. How many bunches did he sell? $79.90 / $7.99 = 10 bunches

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Brian's age is 3/4 of Marcus'. The sum of their ages is 14. How old are Marcus and Brian? Let Marcus's age be m. Then Brian's age = 3/4m The sum is: m + 3m/4 = 14 Combine like terms 7m/4 = 14 Cross multiply: 7m = 56 [URL='http://www.mathcelebrity.com/1unk.php?num=7m%3D56&pl=Solve']Plugging this into the search engine[/URL], we get m = 8. So Brian's age = 3(8)/4 = 24/4 = 6

Brice has 1200 in the bank. He wants to save a total of 3000 by depositing 40 per week from his paycheck. How many weeks will it take until he saves 3000? Remaining Savings = 3,000 - 1,200 = 1,800 40 per week * x weeks = 1,800 40x = 1800 Divide each side of the equation by 40 [B]x = 45 weeks[/B]

Bridget can grow 6 flowers with every seed packet. With 4 seed packets, how many total flowers can Bridget have in her garden? Set up a proportion of flowers to seed packets where f is the number of flowers for 4 seed packets. We have: 6/1 = f/4 Cross multiply: f(1) = 24 f = 24

Bridget deposited $4500 at 6 percent simple interest. How much money was in the account at the end of three years? Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=4500&int=6&t=3&pl=Simple+Interest']simple interest balance calculator[/URL], we get: $[B]5,310[/B]

Brighthouse charges $120 a month for their basic plan, plus $2.99 for each on demand movie you buy. Write and solve and inequality to find how many on demand movies could you buy if you want your bill to be less than $150 for the month. Let x equal to the number room movie rentals per month. Our inequality is: 120 + 2.99x < 150 To solve for the number of movies, Add 120 to each side 2.99x < 30 Divide each side by 2.99 x < 10.03, which means 10 since you cannot buy a fraction of a movie

Bruno is 3x years old and his son is x years old now. Their combined age is 40 years. How old is Bruno Combined age means we add, so we have: 3x + x = 40 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x%2Bx%3D40&pl=Solve']type it in our search engine[/URL] and we get: x = 10 This means Bruno is: 3(10) = [B]30[/B]

Bud makes $400 more per month than maxine If their total income is $3600 how much does bud earn per month Let Bud's earnings be b. Let Maxine's earnings be m. We're given two equations: [LIST=1] [*]b = m + 400 [*]b + m = 3600 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for b m + 400 + m = 3600 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B400%2Bm%3D3600&pl=Solve']type it in our search engine[/URL] and we get: m = 1600 To solve for b, we substitute m = 1600 into equation (1) above: b = 1600 + 400 b = [B]2200[/B]

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Price of x = P_x
Price of y = P_y

Building A is 150 feet shorter than Building B. The height of both building is 1530 feet. Find the height of both building A and B. Let a be the height of building A Let b be the height of building B We're given two equations: [LIST=1] [*]a = b - 150 [*]a + b = 1530 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for a: (b - 150) + b = 1530 To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b-150%2Bb%3D1530&pl=Solve']type it in our search engine[/URL] and we get: b = [B]840[/B] To solve for a, we substitute b = 840 into equation (1): a = 840 - 150 a = [B]690[/B]

by + 2/3 = c for y Subtract 2/3 from each side of the literal equation: by + 2/3 - 2/3 = c - 2/3 Cancel the 2/3 on the left side to get: by = c - 2/3 Divide each side by b to isolate y: by/b = (c - 2/3)/b Cancel the b's on the left side to get: y = [B](c - 2/3)/b[/B]

b^2 - 6 = 5an for a Divide each side of the equation by 5n to isolate a: (b^2 - 6)/5n = 5an/5n Cancel the 5n on the right side and we get: a = [B](b^2 - 6)/5n[/B]

C is the midpoint of BD then BC congruent CD [URL='https://www.mathcelebrity.com/proofs.php?num=cisthemidpointofbd&pl=Prove']True using this proof[/URL]

C times the product b and a [U]The product b and a:[/U] ab [U]c times the product:[/U] [B]abc[/B]

C varies directly as d use k as the constant of variation Direct variation means we multiply below: [B]C = kd[/B]

C varies directly as the cube of a and inversely as the 4th power of B The cube of a means we raise a to the 3rd power: a^3 The 4th power of B means we raise b to the 4th power: b^4 Varies directly means there exists a constant k such that: C = ka^3 Also, varies inversely means we divide by the 4th power of B C = [B]ka^3/b^4[/B] Varies [I]directly [/I]as means we multiply by the constant k. Varies [I]inversely [/I]means we divide k by the term which has inverse variation. [MEDIA=youtube]fSsG1OB3qdk[/MEDIA]

c varies jointly as the square of q and cube of p The square of q means we raise q to the 2nd power: q^2 The cube of p means we raise p to the rdd power: p^3 The phrase [I]varies jointly[/I] means there exists a constant k such that: [B]c = kp^3q^2[/B]

c/a=db/r for a Cross multiply the proportion: cr = adb Divide each side of the equation by db to isolate a: cr/db = adb/db Cancel the db terms on the left side and we get: a = [B]cr/db[/B]

c=59f-288 for f Add 288 to each side: c + 288 = 59f - 288 + 288 Cancel the 288 on the right side, we get: 59f = c + 288 Divide each side by 59 to isolate f: 59f/59 = (c + 288)/59 Cancel the 59 on the left side, we get: f = [B](c + 288)/59[/B]

Calculate the simple interest if the principal is 1500 at a rate of 7% for 3 years. Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=1500&int=7&t=3&pl=Simple+Interest']simple interest calculator[/URL], the total interest earned over 3 years is [B]$315[/B].

Calculate the value of an investment of $15,000 at 6% interest after 7 years. Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=15000&nval=7&int=6.5&pl=Annually']balance calculator[/URL], we get; [B]23,309.80[/B]

Caleb earns points on his credit card that he can use towards future purchases. He earns four points per dollar spent on flights, two points per dollar spent on hotels, and one point per dollar spent on all other purchases. Last year, he charged a total of $9,480 and earned 14,660 points. The amount of money spent on flights was $140 money than twice the amount of money spent on hotels. Find the amount of money spent on each type of purchase.

Let f = dollars spent on flights, h dollars spent on hotels, and p dollars spent on all other purchases. [U]Set up our equations:[/U] (1) 4f + 2h + p = 14660 (2) f + h + p = 9480 (3) f = 2h + 140 [U]First, substitute (3) into (2)[/U] (2h + 140) + h + p = 9480 3h + p + 140 = 9480 3h + p = 9340 [U]Subtract 3h to isolate p to form equation (4)[/U] (4) p = 9340 - 3h [U]Take (3) and (4), and substitute into (1)[/U] 4(2h + 140) + 2h + (9340 - h) = 14660 [U]Multiply through[/U] 8h + 560 + 2h + 9340 - 3h = 14660 [U]Combine h terms and constants[/U] (8 + 2 - 3)h + (560 + 9340) = 14660 7h + 9900 = 14660 [U]Subtract 9900 from both sides:[/U] 7h = 4760 [U]Divide each side by 7[/U] [B]h = 680[/B] [U]Substitute h = 680 into equation (3)[/U] f = 2(680) + 140 f = 1360 + 140 [B]f = 1,500[/B] [U] Substitute h = 680 and f = 1500 into equation (2)[/U] 1500 + 680 + p = 9480 p + 2180 = 9480 [U]Subtract 2180 from each side:[/U] [B]p = 7,300[/B]

Caleb has a complicated and difficult research paper due soon. What should he do to keep from feeling overwhelmed and procrastinating? A. work on the paper every day but save the bulk of the work for the night before it's due B. break down the paper into several small steps and start with the smallest one C. write down the deadline for the paper where he can see it every day so he doesn't forget D. work on the hardest parts of the paper first and take multiple breaks until he's finished Caleb wants to avoid both overwhelm and procrastination. Let's review each option: [LIST] [*]A is out because saving a majority of the work will cause overwhelm [U]and[/U] demonstrates procrastination [*]B is a good option as small steps reduce overwhelm [*]C looks nice on paper, but will he follow through with seeing the deadline everyday? [*]D is a good option as well. Finishing the tough parts first makes the rest of the journey seem like a downhill cruise [/LIST] Based on these, I'd take [B]B or D[/B]

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Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations. Let Cam's age be c. Let Lara's age be l. We're given two equations: [LIST=1] [*]c = l + 3 <-- older means we add [*]c + l = 63 <-- combined ages mean we add [/LIST] Substitute equation (1) into equation (2): l + 3 + l = 63 Combine like terms to simplify our equation: 2l + 3 = 63 To solve for l, [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B3%3D63&pl=Solve']we type this equation into our search engine[/URL] and we get: l = [B]30[/B] Now, we plug l = 30 into equation (1) to solve for c: c = 30 + 3 c = [B]33[/B]

Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations. Let Cam's age be c. Let Lara's age be l. We're given two equations: [LIST=1] [*]c = l + 3 (Since older means we add) [*]c + l = 63 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for c: l + 3 + l = 63 To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l%2B3%2Bl%3D63&pl=Solve']type it in our search engine [/URL]and we get: l = [B]30 [/B] Now, we take l = 30 and substitute it in equation (1) to solve for c: c = 30 + 3 c = [B]33[/B]

camille has 7 blouses,2 skirts,3 pair of short pants and 5 pair of jeans.how many different outfits can he wear,assuming that he always wear a belt. Using the fundamental rule of counting, we find total amount of different outfits as follows: 7 blouses * 2 skirts * 3 pair of short pants * 5 pair of jeans = [B]210 outfits[/B].

can 0.2 be the probability of an outcome in a sample space? Yes. Any probability p is a valid sample space outcome if: [B]0 <= p <= 1[/B]

Can a coefficient of determination be negative? Why or why not? [B]Yes, reasons below[/B] [LIST] [*] predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data [*] where linear regression is conducted without including an intercept [*] Yes, negative values of R2 may occur when fitting non-linear functions to data [/LIST]

Consider a paper cone, pointing down, with the height 6 cm and the radius 3 cm; there is currently 9/4 (pie) cubic cm of water in the cone, and the cone is leaking at a rate of 2 cubic centimeters of water per second. How fast is the water level changing, in cm per second?

Have you tried the rate of change formula?

can you continue this pattern 1,5,13,29 Looking at the numbers, we see a pattern of the next number as the prior number * 2 and then add 3 With each term as t(n), we find t(n + 1) as: t(n + 1) = [B]2*t(n) + 3[/B] t(2) = 2(1) + 3 = 2 + 3 = 5 t(3) = 2(5) + 3 = 10 + 3 = 13 t(4) = 2(13) + 3 = 26 + 3 = 29 t(5) = 2(29) + 3 = 58 + 3 = [B]61[/B]

Can you solve this word problem? The Wildgrove Middle School cafeteria goes through a lot of peanut butter. Currently, they have 120 ounces of regular peanut butter in stock. They also have 319 ounces of crunchy peanut butter. How many ounces do they have in total? [U]Calculate Total Peanut Butter Ounces[/U] Total Peanut Butter Ounces = Regular Peanut Butter Ounces + Crunch Peanut Butter Ounces Total Peanut Butter Ounces = 120 + 319 Total Peanut Butter Ounces = [B]439 ounces[/B]

Free Cardioid Calculator - Shows you the area, arc length, polar equation of the horizontal cardioid, and the polar equation of the vertical cardioid

Cards in a pack are either orange or purple. 80% of the cards are orange. Write the ratio of orange cards to purple cards. [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=80&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']80% as a fraction [/URL]is 4/5. Fractions to ratios can be written as numerator : denominator, so we have: [B]4:5[/B]

Carl is taking a math test. There are 10 questions which take 30 seconds each; 15 questions which take 40 seconds each; and 12 questions which take 2 minutes each. Carl pauses for 5 seconds between questions. In addition, he sharpens his pencil twice, which takes 20 seconds each time. The test begins promptly at 10:00 am. When Carl hands in his completed test, what time is it? [U]10 Questions:[/U] [LIST] [*]30 seconds each x 10 questions = 5 minutes [*]10 pauses between questions x 5 seconds per question = 50 seconds [/LIST] [U]15 Questions[/U] [LIST] [*]40 seconds each x 15 questions = 600 seconds, or 10 minutes [*]15 pauses between questions x 5 seconds per question = 75 seconds, or 1 minute, 15 seconds [/LIST] [U]12 Questions[/U] [LIST] [*]2 minutes x 12 questions = 24 minutes [*]12 pauses x 5 seconds per question = 60 seconds, or 1 minute [/LIST] [U]2 Pencil Sharpenings[/U] [LIST] [*]2 pencil sharpening x 20 seconds each = 40 seconds [/LIST] [U]Total Time[/U] 5 minutes, 50 seconds 11 minutes, 15 seconds 25 minutes 40 seconds 41 minutes and 105 seconds But 105 seconds is 1 minute, 45 seconds. So we have 41 minutes, 45 seconds Therefore, it's [B]10:41[/B]

Carlos age increased by is 16 is 62. Let a be Carlos's age. Increased by 16 means we add 16 a + 16 Now the phrase [I]is[/I] means equal to, so we set [B]a + 16 = 62[/B]

Carlos was asked to write an equivalent equation to 2x/5 = 1 - x. he wrote it as 2x = 1 - 5x. do you agree with his conclusion? explain your answer for x Cross multiply 2x/5 = 1 - x 2x = 5(1 - x) 2x = 5 - 5x I disagree with his conclusion. He forgot to multiply the 5 through to [B]both terms[/B]

Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly have in her backyard? Solve using unit rates. Set up a proportion of plants per seed packets where p is the number of plants per 37 seed packets. 50/25 = p/37 Copying and pasting this problem [URL='http://www.mathcelebrity.com/prop.php?num1=50&num2=p&den1=25&den2=37&propsign=%3D&pl=Calculate+missing+proportion+value']into our search engine[/URL], we get [B]p = 74[/B].

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months. Let m be the number of months. We have the pages written function P(m) as: P(m) = 12m + 35 The problem asks for P(5): P(5) = 12(5) + 35 P(5) = 60 + 35 P(5) = [B]95[/B]

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months. Set up the equation where m is the number of months: pages per month * m + pages written already 12m + 35 The problems asks for m = 5: 12(5) + 35 60 + 35 [B]95 pages[/B]

Carmen has $30 in store bucks and a 25% discount coupon for a local department store. What maximum dollar amount can Carmen purchase so that after her store bucks and discount are applied, her total is no more than $60 before sales tax Let the original price be p. p Apply 25% discount first, which is the same as subtracting 0.25: p(1 - 0.25) Subtract 30 for in store buck p(1 - 0.25) - 30 The phrase [I]no more than[/I] means an inequality using less than or equal to: p(1 - 0.25) - 30 <= 60 To solve this inequality for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=p%281-0.25%29-30%3C%3D60&pl=Solve']type it in our math engine[/URL] and we get: [B]p <= 120[/B]

Carmen is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Carmen wants the total calorie count from the french fries and chicken wings to be less than 500 calories. Using the values and variables given, write an inequality describing this. We have: 25f + 100c < 50 Note: We use < and not <= because it states less than in the problem.

Carol bought a pair of jeans for $12.95 and a belt for $3.79. The sales tax is $1.01. Carol gave the store clerk a $20.00 bill. How much change should she get back? Calculate total cost: Total cost = Jeans + Belt + Sales Tax Total cost = $12.95 + $3.79 + $1.01 Total cost = $17.75 Calculate Change Change = Carol's payment - Total cost Change = $20 - $17.75 Change = [B]$2.25[/B]

Carol gets 5 each week for allowance. She saves 1 of her allowance. What percent of her allowance does carol save? [U]Calculate the decimal:[/U] 1/5 = 0.2 [U]Convert the decimal to a percentage[/U] Percentage = Decimal * 100 Percentage = 100 * 0.2 [B]20%[/B]

Carrie had $32 when she got to the carnival. After riding 6 rides, she had $20 left. What was the price for each ride? If Carrie had $20 left, then the rides cost: $32 - $20 = 12 Price per ride = Cost per all rides / Total Rides Price per ride = 12/6 Price per ride = [B]2[/B]

Cars and trucks are the most popular vehicles. last year, the number of cars sold was 39,000 more than 3 times the number of trucks sold. There were 216,000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year. Let c be the number of cars. Let t be the number of trucks. We're given two equations: [LIST=1] [*]c = 3t + 39000 [*]c + t = 216000 [/LIST] Substitute equation (1) into equation (2) for c: 3t + 39000 + t = 216000 To solve this equation for t, [URL='https://www.mathcelebrity.com/1unk.php?num=3t%2B39000%2Bt%3D216000&pl=Solve']we type it in our math engine [/URL]and we get: t = [B]44,250[/B]

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Casey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double her daughter's age Declare variables for each age: [LIST] [*]Let Casey's age be c [*]Let her daughter's age be d [*]Let n be the number of years from now where Casey will be double her daughter's age [/LIST] We're told that: 26 + n = 2(4 + n) 26 + n = 8 + 2n Solve for [I]n[/I] in the equation 26 + n = 8 + 2n [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables n and 2n. To do that, we subtract 2n from both sides n + 26 - 2n = 2n + 8 - 2n [SIZE=5][B]Step 2: Cancel 2n on the right side:[/B][/SIZE] -n + 26 = 8 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 26 and 8. To do that, we subtract 26 from both sides -n + 26 - 26 = 8 - 26 [SIZE=5][B]Step 4: Cancel 26 on the left side:[/B][/SIZE] -n = -18 [SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE] -1n/-1 = -18/-1 n = [B]18[/B] Check our work for n = 18: 26 + 18 ? 8 + 2(18) 44 ? 8 + 36 44 = 44

Cassidy is renting a bicycle on the boardwalk. The rental costs a flat fee of $10 plus an additional $7 per hour. Cassidy paid $45 to rent a bicycle. We set up the cost equation C(h) where h is the number of hours of rental: C(h) = hourly rental rate * h + Flat Fee C(h) = 7h + 10 We're told that Cassidy paid 45 to rent a bicycle, so we set C(h) = 45 7h + 10 = 45 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=7h%2B10%3D45&pl=Solve']type this equation into our math engine[/URL] and we get: h = [B]5[/B]

Catherine has $400 in her checking account. She writes a check for $600. What is the balance in her account? Writing a check decreases the bank balance. So we have: $400 - $600 = [B]-$200[/B]

Cathy wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another gym has no joining fee and costs $60 per month. a. In how many months will both gym memberships cost the same? What will that cost be? Set up cost equations where m is the number of months enrolled: [LIST=1] [*]C(m) = 35m + 150 [*]C(m) = 60m [/LIST] Set them equal to each other: 35m + 150 = 60m [URL='http://www.mathcelebrity.com/1unk.php?num=35m%2B150%3D60m&pl=Solve']Pasting the equation above into our search engine[/URL], we get [B]m = 6[/B].

CCP Stat Club is sending a delegate of 2 members to attend the 2015 Joint Statistical Meeting in Seattle. There are 10 qualified candidates. How many different ways can the delegate be selected? 10C2 = [B]45[/B] shown on our [URL='http://www.mathcelebrity.com/permutation.php?num=10&den=2&pl=Combinations']Combinations Calculator[/URL]

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center (3, -2), radius = 4 To see the general form or standard form, you can check out this link: [URL='http://Circle Equations']https://www.mathcelebrity.com/eqcircle.php?h=3&k=-2&r=4&d1=1&d2=1&d3=2&d4=4&calc=1&ceq=&pl=Calculate[/URL]

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cereal is on sale for 3.60 for a 9-ounce box. what is the price per ounce? price per ounce = Total cost / ounces price per ounce = 3.60/9 price per ounce = [B]$0.40[/B]

Free Cevian Triangle Relations Calculator - Given a triangle with a cevian, this will solve for the cevian or segments or sides based on inputs

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Chance has 3/4 hour left to finish 5 math problems on the test. How much time does she have to spend on each problem? 3/4 of an hour in minutes is: 3/4 * 60 = 45 minutes 45 minutes / 5 math problems = [B]9 minutes per problem[/B]

Chang is serving his child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Chang wants the total calorie count from the french fries and chicken wings to be less than 600 calories. Using the values and variables given, write an inequality describing this. We have [B]25f + 100c < 600[/B] as our inequality.

Change 1/9 to a decimal This is the same as 100/9 = 11.1111% or [B]0.1111[/B]

Free Change Counting Calculator - This shows you how to make change using the least amount of bills/coins by taking a bill amount and a cash tendered amount from a customer and figuring out the fastest way to make change. Maximum denomination is $100

Change the base 10 number 100 into base 5 Using our [URL='https://www.mathcelebrity.com/binary.php?num=100&check1=7&bchoice=5&pl=Convert']base change calculator[/URL], we get: 100 = [B]400 (Base 5)[/B]

Change the base 2 number 1000 into base 10 1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 0 * 2^0 8 + 0 + 0 + 0 = [B]8[/B]

Charlene wants to invest $10,000 long enough for it to grow to at least $20,000. The compound interest rate is 6% p.a. How many whole number of years does she need to invest the money for so that it grows to her $20,000 target? We want 10,000(1.06)^n = 20,000. But what the problem asks for is how long it will take money to double. We can use a shortcut called the Rule of 72. [URL='https://www.mathcelebrity.com/rule72.php?num=6&pl=Calculate']Using the Rule of 72 at 6%[/URL], we get [B]12 years[/B].

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V1 ÷ T1 = V2 ÷ T2

Charlie buys a 40 pound bag of cat food. His cat eats a 1/2 pound of food per day. Set up an equation: 1/2x = 40 where x is the number of days Multiply through by 2 [B]x = 80[/B]

Charlie has $2700 in his bank account. He spends $150 a week. How many weeks will have passed when Charlie has $600 in his bank account? Let w be the weeks that pass. We have the following equation for Charlie's balance: 2700 - 150w = 600 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=2700-150w%3D600&pl=Solve']type this equation into our math engine[/URL] and we get: w = [B]14[/B]

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the tank has at least 58 liters. What are the possible numbers of minutes Charmaine could add water? This is an algebraic inequality. The phrase [I]at least[/I] means greater than or equal to. So we have: 6m + 16 >= 58 <-- This is our algebraic expression/inequality. To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=6m%2B16%3E%3D58&pl=Solve']we type this into our search engine [/URL]and we get: [B]m >= 7[/B]

Charrie found a piece of 8 meters rope. She cuts it into equal length. She made three cuts. How long is each piece of the rope? Equal length means we divide the length of the rope by the number of equal cuts [B]8/3 or 2 & 2/3 meters[/B]

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Probability that random variable X is within k standard deviations of the mean.
How many k standard deviations within the mean given a P(X) value.

CHEBYSHEVS THEOREM TELLS US THAT WHAT PERCENTAGE LIES BETWEEN 2.25 STANDARD DEVIATIONS? Using our [URL='http://www.mathcelebrity.com/chebyshev.php?pl=probability&k=2.25&probk=0.75']Chebyshevs Theorem calculator[/URL], we get: P(X - u| < k?) >= [B]0.802469[/B]

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cheryl scores 68 out of 80 on her science test, nadia scores 86 out of 120 on her science test and ali scores 120 out of 150 on her science test. who preforms the best in his/her science test Cheryl: [URL='https://www.mathcelebrity.com/perc.php?num=68&den=80&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']68/80[/URL] = 85% Nadia: [URL='https://www.mathcelebrity.com/perc.php?num=86&den=120&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pof1=&pof2=&pl=Calculate']86/120[/URL] = 71.67% Ali: [URL='https://www.mathcelebrity.com/perc.php?num=+120&den=+150&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pof1=&pof2=&pl=Calculate']120/150[/URL] = 80% [B]Cheryl[/B] has the highest percentage, so she did the best on her test.

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Chicken is on sale for $3.90 per pound. If Ms.Gelllar buys 2.25 pounds of chicken, how much will she spend? round to the nearest penny and show your work Total spend = Cost per pound * Number of pounds Total spend = $3.90 * 2.25 pounds Total spend = [B]$8.78[/B] (rounded to 2 digits)

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x ≡ a mod b
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the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.
Given that the n_i portions are not pairwise coprime and you entered two modulo equations, then the calculator will attempt to solve using the Method of Successive Subsitution

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Choose the best inequality for this scenario. Casey bought a sandwich and a drink for $3.75. If she has $6.00 to spend, what is the most she can spend on dessert? Let dessert spend be d. We have: d <= $6.00 - $3.75 [B]d <= $2.25[/B]

Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to 4x + y = 8 through (4, 3). Step 1: Find the slope of the line 4x + y = 8. In y = mx + b form, we have y = -4x + 8. The slope is -4. To be perpendicular to a line, the slope must be a negative reciprocal of the line it intersects with. Reciprocal of -4 = -1/4 Negative of this = -1(-1/4) = 1/4 Using our [URL='https://www.mathcelebrity.com/slope.php?xone=4&yone=3&slope=+0.25&xtwo=3&ytwo=2&bvalue=+&pl=You+entered+1+point+and+the+slope']slope calculator[/URL], we get [B]y = 1/4x + 2[/B]

Choosing coffee or tea; with cream, milk, or honey; served in a glass or plastic cup Using the fundamental rule of counting: 2 drink types * 3 sweetness * 2 cups = [B]12 possible choices[/B]

Free Chord Calculator - Solves for any of the 3 items in the Chord of a Circle equation, Chord Length (c), Radius (r), and center to chord midpoint (t).

Chris has 6 cds that he is going to give away. He let his best friend choose 2 of the 6 cds. How many different groups of 2cds are possible? We want 6 choose 2 using combinations. We use combinations because the problem states the word [I]different[/I]. [URL='https://www.mathcelebrity.com/permutation.php?num=6&den=2&pl=Combinations']6 C 2[/URL] using our calculator is [B]15[/B].

Chris walks 12 blocks north and then 16 blocks East. How far is his home from the park We've got a right triangle. If we divide 12 and 16 by 4, we get: 12/4 = 3 16/4 = 4 Since the hypotenuse is the distance from the home to the park, we have a classic 3-4-5 right triangle. So our hypotenuse is 5*4 = [B]20[/B]

Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse is 6 years older than Alex. The sum of their ages is 31 years. How old is each one of them? Set up the relational equations where a = Alex's age, c = Chris's aged and j = Jesse's age [LIST=1] [*]a = c + 5 [*]j = a + 6 [*]a + c + j = 31 [*]Rearrange (1) in terms of c: c = a - 5 [/LIST] [U]Plug in (4) and (2) into (3)[/U] a + (a - 5) + (a + 6) = 31 [U]Combine like terms:[/U] 3a + 1 = 31 [U]Subtract 1 from each side[/U] 3a = 30 [U]Divide each side by 3[/U] [B]a = 10[/B] [U]Plug in 1 = 10 into Equation (4)[/U] c = 10 - 5 [B]c = 5[/B] Now plug 1 = 10 into equation (2) j = 10 + 6 [B]j = 16[/B]

Christopher has $25 000 to invest. He finds a bank who will pay an interest rate of 5.65% p.a compounded annually. What will the total balance be after 6 years? Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=25000&nval=6&int=5.65&pl=Annually']compound interest balance calculator[/URL], we get: [B]34,766.18[/B]

Chuck-a-luck is an old game, played mostly in carnivals and county fairs. To play chuck-a-luck you place a bet, say $1, on one of the numbers 1 through 6. Say that you bet on the number 4. You then roll three dice (presumably honest). If you roll three 4’s, you win $3.00; If you roll just two 4’s, you win $2; if you roll just one 4, you win $1 (and, in all of these cases you get your original $1 back). If you roll no 4’s, you lose your $1. Compute the expected payoff for chuck-a-luck. Expected payoff for each event = Event Probability * Event Payoff Expected payoff for 3 matches: 3(1/6 * 1/6 * 1/6) = 3/216 = 1/72 Expected payoff for 2 matches: 2(1/6 * 1/6 * 5/6) = 10/216 = 5/108 Expected payoff for 1 match: 1(1/6 * 5/6 * 5/6) = 25/216 Expected payoff for 0 matches: -1(5/6 * 5/6 * 5/6) = 125/216 Add all these up: (3 + 10 + 25 - 125)/216 -87/216 ~ [B]-0.40[/B]