$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]

$300 for 13 years at 8% compounded semiannually. P=principle = original funds, r=rate, in percent, written as a decimal (1%=.01, 2%=.02,etc) , n=number of times per year, t= number of years So we have: [LIST] [*]$300 principal [*]13 * 2 = 26 periods for n [*]Rate r for a semiannual compound is 8%/2 = 4% per 6 month period [/LIST] Using our [URL='https://www.mathcelebrity.com/simpint.php?av=&p=300&int=4&t=26&pl=Compound+Interest']compound interest with balance calculator[/URL], we get: [B]$831.74[/B]

(n^2)^3 without exponents This expression evaluates to: n^(2 *3) n^6 To write this without exponents, we expand n times itself 6 times: [B]n * n * n * n * n * n [MEDIA=youtube]zVAlzX9oHOQ[/MEDIA][/B]

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

-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]

-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]

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 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 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]

1/3 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 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]

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

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]

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]

11 combination of 3 times 6 combination of 3 [URL='https://www.mathcelebrity.com/permutation.php?num=11&den=3&pl=Combinations']11 combination of 3[/URL] = 165 [URL='https://www.mathcelebrity.com/permutation.php?num=6&den=3&pl=Combinations']6 combination of 3[/URL] = 20 11 combination of 3 times 6 combination of 3 = 165 * 20 11 combination of 3 times 6 combination of 3 = [B]3300[/B]

Free 12 Hour Clock Conversion Calculator - This calculator performs the following two conversions:
1) Takes a time in 24 hour clock (military time) format and converts it to a 12 hour clock format (AM/PM)
2) Takes a time in 12 hour clock format and converts it to military time (12 hour clock format)

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]

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]

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 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]

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]

Using our [URL='http://www.mathcelebrity.com/linearcon.php?quant=165&pl=Calculate&type=centimeter#foot']linear conversion calculator[/URL], we get: [B]5.41339 feet[/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]

18 seconds faster than Tina’s time Let Tina's time be t. Speaking in terms of time, faster means less. So we have an algebraic expression of: [B]t - 18[/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 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 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]

A number is represented by an arbitrary variable, let's call it x. 7 times x means we multiply 7 times x. 7x 2 minus 7x is written: 2 - 7x

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 itself Itself means we multiply 2 by 2: 2 * 2 [B]4[/B]

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 times x divided by 4 times y 2 times x: 2x 4 times y: 4y 2 times x divided by 4 times y [B]2x/4y[/B]

2 times x squared minus 4 times x 2x^2 - 4x

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]

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]

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]

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]

26 increased by 12 times a number A number is represented by an arbitrary variable, let's call it x 12 times a number is written as 12x 26 increased by 12 times a number means we add: [B]26 + 12x[/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)

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]

2^46 is how many times as many as 2^42 We can break this apart as follows: 2^46 = 2^42 * [B]2^4 2^4= 16 times as many [MEDIA=youtube]lHbA_DGO-CE[/MEDIA][/B]

3 decreased by 7 times a number A number signifies an arbitrary variable, let's call it x. 7 times a number: 7x 3 decreased by this means we subtract 7x [B]3 - 7x[/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]

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 times x squared minus 4 times x [U]x squared[/U] x^2 [U]3 times x squared:[/U] 3x^2 [U]4 times x:[/U] 4x [U]3 times x squared minus 4 times x[/U] [B]3x^2 - 4x[/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]

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]

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.

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

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]

346 times w, decreased by 79 equals w 346 times w 346w Decreased by 79 346w - 79 Equals w [B]346w - 79 = w[/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]

[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]

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]

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]

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

A number means an arbitrary variable, let's call it "x". 4 times a number is 4x. Plus 9 means we add: 4x + 9

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]

4 times x plus 2 is at most 10 4 times x 4x Plus 2 4x + 2 At most means less than or equal to, so we have: [B]4x + 2 <= 10[/B]

4 times x times y increase by 9 4 times x times y: 4xy Increase this by 9: [B]4xy + 9[/B]

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]

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]

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].

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 13 A number is denoted as an arbitrary variable, let's call it x x 5 times that number 5x Increased by 13 means we add 5x + 13

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 quantity n minus 3 quantity n minus 3 (n - 3) 5 times quantity n minus 3 [B]5(n - 3)[/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 times x 5x Divided by 7 5x/7

5 times y 5y Divided by 8 5y/8

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]

50 is how many times as big as 20 50/20 = [B]2.5[/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 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]

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]

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

We have 15 cents times 7 bananas = $1.05

-2 times a number x is written as -2x. Less means subtract, so we have 7 less than this is -2x - 7. Finally, greater than or equal to is >=, so our expression becomes: -2x - 7 >= 41

-2 times a number x is denoted as -2x. 7 less than that means we subtract 7: -2x - 7 Finally, that entire expression is greater than or equal to 41 -2x - 7 >= 41

-2 times a number x is denoted as -2x. 7 less means we subtract, so 7 less than that is -2x - 7. Finally, that entire expression is greater than or equal to 41 -2x - 7 >= 41

7 less than -2 times a number x is greater than or equal to 41 -2 times a number x -2x 7 less than this -2x - 7 Now we set this expressions greater than or equal to 41 [B]-2x - 7 >= 41[/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]

74 increased by 3 times y [U]3 times y[/U] 3y [U]74 increased by 3 times y[/U] [B]74 + 3y[/B]

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

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 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]

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 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 times x squared times y times z x squared: x^2 x squared times y times z x^2yz 9 times x squared times y times z 9x^2yz

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 1.5 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 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-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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 cheetah can maintain it's maximum speed of 28 m/s for 30 seconds. how far does it go in this amount of time? Distance = rate * time Distance = 28 m/s * 30 s Distance = [B]840m[/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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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]

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 $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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 shop tech earns a base PayPal $15.68 per hour, plus "time-and-a-half" for overtime (time exceeding 40 hours). If he work 44.5 hours during a particular week, what is his gross pay? Gross pay = Regular Pay + Overtime Pay Calculate regular pay: Regular Pay = 40 hours * $15.68 = $627.20 Calculate overtime pay Overtime pay = (44.5 - 40) * 1.5 * $15.68 Overtime Pay = 4.5 * 1.5 * $15.68 Overtime Pay = $105.84 Gross pay = $627.20 + $105.84 Gross pay = [B]$733.04[/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 street sign is 85 inches tall. How tall is it in feet and inches? Since 12 inches is a foot, we have: 12 goes into 85 7 times remainder 1 So we have [B]7 feet, 1 inch[/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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 ^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]

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]

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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]

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, 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]

[U]2 times c[/U] 2c [U]Add 6[/U] [B]2c + 6[/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]

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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]

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?

Thank you, but I'm going to have to talk to my teacher about how someone can't be 9 times older than nothing....

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

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

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]

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]

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y. If Alberto's salary is x and Nick's salary is y, we have: [B]x = 4y + 2000[/B]

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y. Let Alberto's salary be x, and Nick's salary be y. We have: [B]x = 4y + 2000[/B]

Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y. If Alberto's salary is x and Nick's is y, we have: [B]x = 4y + 2000 [/B](since greater than means we add)

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.

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

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]

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.

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]

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.

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 flies at 250 mph. How far will it travel in 5 h at that rate of speed? Distance = Rate x Time Distance = 250mph x 5h Distance = [B]1,250 miles[/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 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 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 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 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 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 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 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]

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]

Angelo is paid double time for each hour he works over 40 hours in a week. Last week he worked 46 hours and earned $624. What is his normal hourly rate? Let h be Angelo's hourly rate. We have: 40h + (46 - 40) * 2 * h = 624 40h + 6 * 2 * h = 624 40h + 12h = 624 Combine like terms: 52h = 624 [URL='https://www.mathcelebrity.com/1unk.php?num=52h%3D624&pl=Solve']Typing this equation into our search engine[/URL], we get [B]h = 12[/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]

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 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].

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]

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 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 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 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 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]

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]

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]

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]

Ben is 3 times as old as Daniel and is also 4 years older than Daniel. Let Ben's age be b, let Daniel's age by d. We're given: [LIST=1] [*]b = 3d [*]b = d + 4 [/LIST] Substitute (1) into (2) 3d = d + 4 [URL='https://www.mathcelebrity.com/1unk.php?num=3d%3Dd%2B4&pl=Solve']Type this equation into our search engine[/URL], and we get [B]d = 2[/B]. Substitute this into equation (1), and we get: b = 3(2) [B]b = 6 [/B] So Daniel is 2 years old and Ben is 6 years old.

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]

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]

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]

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]

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]

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]

C times the product b and a [U]The product b and a:[/U] ab [U]c times the product:[/U] [B]abc[/B]

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?

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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]

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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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]

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Committees of 4 men 5 women form a group of 11 men and 11 women. We want combinations. 4 men from 11 men is the combination 11C4. [URL='https://www.mathcelebrity.com/permutation.php?num=11&den=4&pl=Combinations']Using our combinations calculator[/URL], we get: 11C4 = 330 5 women from 11 women is the combination 11C5. [URL='https://www.mathcelebrity.com/permutation.php?num=11&den=5&pl=Combinations']Using our combinations calculator[/URL], we get: 11C5 = 462 We multiply the committee of men times the committee of women: 11C4 * 11C5 = 330 * 432 11C4 * 11C5 = [B]142,560[/B]

Free Compound Interest and Annuity Table Calculator - Given an interest rate (i), number of periods to display (n), and number of digits to round (r), this calculator produces a compound interest table. It shows the values for the following 4 compound interest annuity functions from time 1 to (n) rounded to (r) digits:
vⁿ
d
(1 + i)ⁿ
a_n|
s_n|
ä_n|i
s_n|i
Force of Interest δⁿ

Consider the case of a manufacturer who has an automatic machine that produces an important part. Past records indicate that at the beginning of the data the machine is set up correctly 70 percent of the time. Past experience also shows that if the machine is set up correctly it will produce good parts 90 percent of the time. If it is set up incorrectly, it will produce good parts 40 percent of the time. Since the machine will produce 60 percent bad parts, the manufacturer is considering using a testing procedure. If the machine is set up and produces a good part, what is the revised probability that it is set up correctly? [U]Determine our events:[/U] [LIST] [*]C = Correctly Set Machine = 0.7 [*]C|G = Correctly Set Machine And Good Part = 0.9 [*]I = Incorrectly Set Machine = 1 - 0.7 = 0.3 [*]I|G = Incorrectly Set Machine And Good Part = 0.4 [*]B< = BAD PARTS = 0.60 [/LIST] P[correctly set & part ok] = P(C) * P(C|G) P[correctly set & part ok] = 70% * 90% = 63% P[correctly set & part ok] = P(I) * P(I|G) P[incorrectly set & part ok] = 30% *40% = 12% P[correctly set | part ok] = P[correctly set & part ok]/(P[correctly set & part ok] + P[incorrectly set & part ok]) P[correctly set | part ok] = 63/(63+12) = [B]0.84 or 84%[/B]

Consider the following 15 numbers 1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20 - The mean of the last 10 numbers is TWICE the mean of the first 10 numbers - The sum of the last 2 numbers is FIVE times the sum of the first 3 numbers (i) Calculate the values of x and y We're given two equations: [LIST=1] [*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = 2(1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/10 [*]3x - 20 = 5(1 + 2 + y - 4) [/LIST] Let's evaluate and simplify: [LIST=1] [*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = (1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5 [*]3x - 20 = 5(y - 1) [/LIST] Simplify some more: [URL='https://www.mathcelebrity.com/polynomial.php?num=x%2B6%2B7%2B8%2By%2B9%2B10%2B12%2B3x%2B20&pl=Evaluate'](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10[/URL] = (4x + y + 72)/10 [URL='https://www.mathcelebrity.com/polynomial.php?num=1%2B2%2By-4%2B4%2B5%2Bx%2B6%2B7%2B8%2By&pl=Evaluate'](1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5[/URL] = (2y + x + 29)/5 5(y - 1) = 5y - 5 So we're left with: [LIST=1] [*](4x + y + 72)/10 = (2y + x + 29)/5 [*]3x - 20 = 5y - 5 [/LIST] Cross multiply equations in 1, we have: 5(4x + y + 72) = 10(2y + x + 29) 20x + 5y + 360 = 20y + 10x + 290 We have: [LIST=1] [*]20x + 5y + 360 = 20y + 10x + 290 [*]3x - 20 = 5y - 5 [/LIST] Combining like terms: [LIST=1] [*]10x - 15y = -70 [*]3x - 5y = 15 [/LIST] Now we have a system of equations which we can solve any of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: (x, y) = [B](-115, -72)[/B]

Corvettes are known as sporty cars that can travel at high rates of speed. It is therefore assumed that they are much more dangerous than minivans. An owner of a Corvette points out that when statistics are studied, there are far more deaths each year from crashes that involve minivans than crashes that involve Corvettes, so Corvettes, so Corvettes must be safer than minivans. The statistics the Covert owner sites are correct. Is his logic faulty? Why or why not? [B]Faulty.[/B] There are hundreds of times more minivans on the road than Corvettes, so we expect more deaths even if they are the safest car on the road.

Country A produces about 7 times the amount of diamonds in carats produce in Country B. If the total produced in both countries is 40,000,000 carats, find the amount produced in each country. Set up our two given equations: [LIST=1] [*]A = 7B [*]A + B = 40,000,000 [/LIST] Substitute (1) into (2) (7B) + B = 40,000,000 Combine like terms 8B = 40,000,000 Divide each side by 8 [B]B = 5,000,000[/B] Substitute this into (1) A = 7(5,000,000) [B]A = 35,000,000[/B]

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I'd like to warn our fans about a crypto scam going around. The site is [URL]https://crypto-fortress.com[/URL]. The scam runs like this... [LIST] [*]You're asked to deposit money, a minimum of $1,000 in BTC. [*]You're given credits on the money from their mining/aribtrage plan. [*]However, when it comes time to cash out after a week, they suddenly tell you, their is some magical agreement (which you never signed nor is on their website) where you now have to pay 25% of your profits to them and you'll get a withdrawal code for the rest. [*]When you press them on how they pay 75% of your profits from a 25% deposit which makes no sense, they tell you that it's how things work. [/LIST]

Currently 16 out of every 25 American adults drink coffee every day. In a town with a population of 7900 adults, how many of these adults would you expect to drink coffee ever We'd multiply 16/25 times 7900: Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=7900&frac2=16/25&pl=Multiply']fraction multiplication calculator by type 16/25 of 7900[/URL], we get: [B]5056[/B]

Customers arrive at the claims counter at the rate of 20 per hour (Poisson distributed). What is the probability that the arrival time between consecutive customers is less than five minutes? Use the [I]exponential distribution[/I] 20 per 60 minutes is 1 every 3 minutes 1/λ = 3 so λ = 0.333333333 Using the [URL='http://www.mathcelebrity.com/expodist.php?x=+5&l=0.333333333&pl=CDF']exponential distribution calculator[/URL], we get F(5,0.333333333) = [B]0.811124396848[/B]

Dale has a box that contains 20 American quarters and 20 Canadian quarters. If he takes them from the box one at a time, how many must he remove before he is guaranteed to have 5 quarters from the same country? Worst case scenario, Dale picks 4 American and 4 Canadian quarters which guarantees his next pick would be a 5th of either quarter. So the answer is 4 + 4 + 1 = [B]9[/B]

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Dave paints a fence in 4 hours while Sara paints the same fence in 2 hours. If they work together, how long will it take them to paint the fence? Set up unit rates: [LIST] [*]Dave paints 1/4 of the fence in 1 hour [*]Sara will paint 1/2 of the fence in 1 hour [/LIST] So together, they paint 1/2 + 1/4 = 2/4 + 14 = 3/4 of the fence in one hour. 1 hour = 60 minutes, so we set up a proportion of time to minutes where m is the time in minutes needed to complete 1 full fence: 3/4/60 = 1/m 3/240 = 1/m [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3&num2=1&den1=240&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion in our math engine[/URL], we get: m = [B]80 minutes[/B] [B]80 minutes is also 1 hour and 20 minutes.[/B]

David has b dollars in his bank account; Claire has three times as much money as David. The sum of their money is $240. How much money does Claire have? David has b Claire has 3b since three times as much means we multiply b by 3 The sum of their money is found by adding David's bank balance to Claire's bank balance to get the equation: 3b + b = 240 To solve for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b%2Bb%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get: b = 60 So David has 60 dollars in his bank account. Therefore, Claire has: 3(60) = [B]180[/B]

David roller skates for 3 1/3 hours with a constant speed of 24 km/h and then for another 1 hour 10 minutes with constant speed of 12 km/h. What distance did he go? Distance = Rate x Time [U]Part 1 of his trip:[/U] D1 = R1 x T1 D1 = 3 & 1/3 hours * 24 km/h D1 = 80 km [U]Part 2 of his trip:[/U] D2 = R2 x T2 D2 = 1 & 1/6 hours * 12 km/h (Note, 10 minutes = 1/6 of an hour) D2 = 14 km [U]Calculate Total Distance (D)[/U] D = D1 + D2 D = 80 + 14 D = [B]94 km[/B]

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devaughn,sageis2timessydneysage,thesumoftheiragesis78,whatissydneysage Let d be Devaughn's age. Let s be Sydney's age. We have two equations: [LIST=1] [*]d = 2s [*]d + s = 78 [/LIST] Substitute (1) into (2) 2s + s = 78 3s = 78 Entering [URL='http://www.mathcelebrity.com/1unk.php?num=3s%3D78&pl=Solve']3x = 78 into the search engine[/URL], we get [B]s = 26[/B].

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12. Our givens are: [LIST] [*]I = 450 [*]P = 3000 [*]t = 3 [*]We want r [/LIST] 450 = 3000(r)(3) 450 = 9000r Divide each side by 9000 [B]r = 0.05[/B]

Let d be distance and h be hours in time. Set up our function. [LIST] [*]f(h) = d [*][B]f(h) = 5h[/B] [/LIST] Read this out, it says, for every hour Diego jogs, multiply that by 5 to get the distance he jogs.

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During a performance, a juggler tosses one ball straight upward while continuing to juggle three others. The height f(t), in feet, of the ball is given by the polynomial function f(t) = ?16t^2 + 26t + 3, where t is the time in seconds since the ball was thrown. Find the height of the ball 1 second after it is tossed upward. We want f(1): f(1) = ?16(1)^2 + 26(1) + 3 f(1) = -16(1) + 26 + 3 f(1) = -16 + 26 + 3 f(1) = [B]13[/B]

Dylans mother tells Dylan he must spend less time playing electronic games. On the weekends he spends 9.5 hours playing electronic games. If he plays between 13 and 19 hours each week, how many hours does he play games on weekdays? Let x equal the number of hours Dylan plays electronic games per week. [U]Set up our inequality:[/U] 13 <= x <= 19 [U]To see how much he plays during weekdays, subtract off the weekend time[/U] 13 - 9.5 <= x <= 19 - 9.5 [B]3.5 <= x <= 9.5[/B]

the quantity y plus two y + 2 the quantity y plus two divided by four (y +2)/4 Eight times the quantity y plus two divided by four 8(y +2)/4 8/4 = 2, so we have: [B]2(y +2) or 2y + 4 [MEDIA=youtube]xzwaXi6N1uI[/MEDIA][/B]

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 difference of a number and ten x - 10 Eighteen times the difference of a number and ten [B]18(x - 10)[/B]

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Erin has 72 stamps in her stamp drawer along with a quarter, two dimes and seven pennies. She has 3 times as many 3-cent stamps as 37-cent stamps and half the number of 5-cent stamps as 37-cent stamps. The value of the stamps and coins is $8.28. How many 37-cent stamps does Erin have? Number of stamps: [LIST] [*]Number of 37 cent stamps = s [*]Number of 3-cent stamps = 3s [*]Number of 5-cent stamps = 0.5s [/LIST] Value of stamps and coins: [LIST] [*]37 cent stamps = 0.37s [*]3-cent stamps = 3 * 0.03 = 0.09s [*]5-cent stamps = 0.5 * 0.05s = 0.025s [*]Quarter, 2 dime, 7 pennies = 0.52 [/LIST] Add them up: 0.37s + 0.09s + 0.025s + 0.52 = 8.28 Solve for [I]s[/I] in the equation 0.37s + 0.09s + 0.025s + 0.52 = 8.28 [SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE] (0.37 + 0.09 + 0.025)s = 0.485s [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 0.485s + 0.52 = + 8.28 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 0.52 and 8.28. To do that, we subtract 0.52 from both sides 0.485s + 0.52 - 0.52 = 8.28 - 0.52 [SIZE=5][B]Step 4: Cancel 0.52 on the left side:[/B][/SIZE] 0.485s = 7.76 [SIZE=5][B]Step 5: Divide each side of the equation by 0.485[/B][/SIZE] 0.485s/0.485 = 7.76/0.485 s = [B]16[/B] [URL='https://www.mathcelebrity.com/1unk.php?num=0.37s%2B0.09s%2B0.025s%2B0.52%3D8.28&pl=Solve']Source[/URL]

Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, whereas Kurt is contributing $1 per day. Eventually, the two accounts will contain the same amount. What balance will each account have? How long will that take? Set up account equations A(d) where d is the number of days since time 0 for each account. Ethan A(d): 9079 + 19d Kurt A(d): 9259 + d The problems asks for when they are equal, and how much money they have in them. So set each account equation equal to each other: 9079 + 19d = 9259 + d [URL='https://www.mathcelebrity.com/1unk.php?num=9079%2B19d%3D9259%2Bd&pl=Solve']Typing this equation into our search engine[/URL], we get [B]d = 10[/B]. So in 10 days, both accounts will have equal amounts in them. Now, pick one of the account equations, either Ethan or Kurt, and plug in d = 10. Let's choose Kurt's since we have a simpler equation: A(10) = 9259 + 10 A(10) = $[B]9,269 [/B] After 10 days, both accounts have $9,269 in them.

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Find 2 consecutive numbers such that the sum of twice the smaller number and 3 times the larger number is 73. Let x be the smaller number and y be the larger number. We are given: 2x + 3y = 73 Since the numbers are consecutive, we know that y = x + 1. Substitute this into our given equation: 2x + 3(x + 1) = 73 Multiply through: 2x + 3x + 3 = 73 Group like terms: 5x + 3 = 73 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3%3D73&pl=Solve']Type 5x + 3 = 73 into the search engine[/URL], and we get [B]x = 14[/B]. Our larger number is 14 + 1 = [B]15 [/B] Therefore, our consecutive numbers are[B] (14, 15)[/B]

Find 3 consecutive integers such that the sum of twice the smallest and 3 times the largest is 126. Let the first integer be n, the second integer be n + 1, and the third integer be n + 2. We have: Sum of the smallest and 3 times the largest is 126: n + 3(n + 2) = 126 Multiply through: n + 3n + 6 = 126 Group like terms: 4n + 6 = 126 [URL='https://www.mathcelebrity.com/1unk.php?num=4n%2B6%3D126&pl=Solve']Type 4n + 6 = 126 into our calculator[/URL], we get n = 30. Which means the next two integers are 31 and 32. [B]{30, 31, 32}[/B]

Find the largest of three consecutive even integers when six times the first integers is equal to five times the middle integer. Let the first of the 3 consecutive even integers be n. The second consecutive even integer is n + 2. The third (largest) consecutive even integer is n + 4. We are given 6n = 5(n + 2). Multiply through on the right side, and we get: 6n = 5n + 10 [URL='https://www.mathcelebrity.com/1unk.php?num=6n%3D5n%2B10&pl=Solve']Typing 6n = 5n + 10 into the search engine[/URL], we get n = 10. Remember, n was our smallest of 3 consecutive even integers. So the largest is: n + 4 10 + 4 [B]14[/B]

Find the number of combinations and the number of permutations for 10 objects taken 6 at a time [LIST] [*]Combinations is written as 10 C 6. Using our [URL='http://www.mathcelebrity.com/permutation.php?num=10&den=6&pl=Combinations']combinations calculator[/URL], we get [B]210[/B]. [*]Permutations is written as 10 P 6. Using our [URL='http://www.mathcelebrity.com/permutation.php?num=10&den=6&pl=Permutations']permutations calculator[/URL], we get [B]151,200[/B]. [/LIST]

Finn has 8 toy cars. Dirk has t times as many toy cars as Finn The phrase [I]times as many [/I]means we multiply: [B]8t[/B]

Five times Kim's age plus 13 equals 58. How old is Kim? Let Kim's age be a. We have: Five times Kim's age: 5a Plus 13 means we add 13 5a + 13 Equals 58 means we set the expression 5a + 13 equal to 58 5a + 13 = 58 <-- This is our algebraic expression To solve this equation for a, [URL='https://www.mathcelebrity.com/1unk.php?num=5a%2B13%3D58&pl=Solve']we type it into our search engine[/URL] and get: a = [B]9[/B]

For the first 10 seconds of the ride, the height of the coaster can be determined by h(t) = 0.3t^3 - 5t^2 + 21t, where t is the time in seconds and h is the height in feet. classify this polynomial by degree and by number of terms. [URL='http://www.mathcelebrity.com/polynomial.php?num=0.3t%5E3-5t%5E2%2B21t&pl=Evaluate']Using our polynomial calculator, we determine[/URL]: [LIST] [*]The degree of the polynomial is 3 [*]There are 3 terms [/LIST]

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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. 5 times a number: 5x Four less means we subtract 4 from 5x: [B]5x - 4[/B]

Three times y: 3y Four less than three times y means we subtract 4 from3y: [B]3y - 4[/B]

six plus two: 6 + 2 Four times the quantity six plus two [B]4(6 + 2) [/B]<-- This is our algebraic expression If we need to evaluate this, we have: 4(8) [B]32[/B]

Free Frequency and Wavelength and Photon Energy Calculator - Provides the following 3 items using the speed of light and Plancks constant (h):
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g equals 232 subtracted from the quantity 377 times g 377 times g: 377g 232 subtracted from 377 times g: 377g - 232 We set the variable g equal to this expression: [B]g = 377g - 232[/B]

g times by 5 then add 3 The phrase [I]times by [/I]means times or multiplied by: 5g Then add 3 means we add 3 to 5g: [B]5g + 3 [MEDIA=youtube]7KeEWSY1WMg[/MEDIA][/B]

George and William both ran a one mile race. William won the race with a time of 4 minutes and 30 seconds. If George was 480 feet behind William when the race finished, how long did it take George to run the entire mile? (George continued to run at the same pace.) When the race was done, George completed: 5280 feet in a mile - 480 feet = 4800 feet set up a proportion of distance traveled to time where n is the time needed to run the mile 4800/4.5 = 5280/n Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=4800&num2=5280&den1=4.5&den2=n&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get: n = 4.95 5280/4800 = 1.1 Setup another proportion with the 1.1 factor of distance to time: 4800 * 1.1/4.5 * 1.1 = 5280/4.95 4.95 = 4 minutes and .95*60 seconds 4.95 = [B]4 minutes and 57 seconds[/B]

George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a total of 25 apples. Let George's apples be g. Let Sarah's apples be s. We're give two equations: [LIST=1] [*]s = 4g [*]g + s = 25 [/LIST] Substitute equation (1) into equation (2) for s: g + 4g = 25 If [URL='https://www.mathcelebrity.com/1unk.php?num=g%2B4g%3D25&pl=Solve']we plug this equation into our search engine[/URL] and solve for g, we get: g = [B]5[/B] Now substitute this into equation 1 for g = 5: s = 4(5) s = [B]20[/B] [B]So George has 5 apples and Sarah has 20 apples[/B]

Greg runs 120 m in 20 seconds. How far can he run in one minute? We want to compare seconds to seconds. [URL='https://www.mathcelebrity.com/timecon.php?quant=1&pl=Calculate&type=minute']1 minute[/URL] = 60 seconds Set up a proportion of meters to seconds where m is the meters ran in 60 seconds: 120/20 = m/60 To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=120&num2=m&den1=20&den2=60&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: m. = [B]360 meters[/B]

Guadalupe left the restaurant traveling 12 mph. Then, 3 hours later, Lauren left traveling the same direction at 24 mph. How long will Lauren travel before catching up with Guadalupe? Distance = Rate x Time Guadulupe will meet Lauren at the following distance: 12t = 24(t - 3) 12t = 24t - 72 [URL='https://www.mathcelebrity.com/1unk.php?num=12t%3D24t-72&pl=Solve']Typing that equation into our search engine[/URL], we get: t = 6

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Hanna cooked 5 pizzas. She sliced each pizza into eighths. How many slices of pizza does she have in total? 5 pizzas times 8 slices per pizza = [B]40 slices[/B]

[CENTER][B]The Sum of three times a number and 18 is -39. Find the number.[/B][/CENTER] I was always confused with these problems and never understood them. Any help would be much appreciated!! Thank you!

The phrase a number means an arbitrary variable, let's call it x. Three times a number: 3x And 18 means we add 18 3x + 18 The word is means equal to, so we set 3x + 18 equal to -39 3x + 18 = -39 This is your algebraic expression. If you want to solve for x, plug it into the [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']search engine[/URL] and you get x = -19

Hong is riding his bicycle. He rides for 22.5 kilometers at a speed of 9 kilometers per hour. For how many hours does he ride? Distance = Rate * Time The problem asks for time. [URL='https://www.mathcelebrity.com/drt.php?d=+22.5&r=+9&t=&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator[/URL], we get: t = [B]2.5 hours[/B]

Hose A can fill a pool in 4 hours. Hose B can fill the pool in 2 hours. If both hoses are turned on at the same time how long will it take to fill the pool? [LIST] [*]Hose A can fill the pool in 1/4 of the pool an hour [*]Hose B can fill the pool in 1/2 of the pool an hour [/LIST] In one hour using combined effort, we have: [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F2&frac2=1%2F4&pl=Add']1/2 + 1/4[/URL] = 3/4 of the pool will be filled. 3/4 of the pool gets filled in 60 minutes. We set up a proportion of proportion filled to time where t is the time to fill the full pool: 3/4/60 = 1/t 3/240 = 1/t Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3&num2=1&den1=240&den2=t&propsign=%3D&pl=Calculate+missing+proportion+value']proportion solver[/URL], we get: t = [B]80 minutes or 1 hour and 20 minutes[/B]

Free Hour and Minute Conversion Calculator - Converts Hours and Minutes to Hours for things like timecards and such.

How many days are there in 12 weeks? Use the following information to convert this time to days 12 weeks * 7 days / week = [B]84 days[/B]

How many times bigger is 3^9 than 3^3 Using exponent rules, we see that: 3^9 = 3^3 * 3^6 So our answer is [B]3^6 times bigger[/B]

How old am I if 400 reduced by 2 times my age is 244? Let my age be a. We're given: 400 - 2a = 244 To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D244&pl=Solve']type this equation into our search engine [/URL]and we get: a = [B]78[/B]

How old am I if 400 reduced by 3 times my age is 124? Let my age be a. We're given an algebraic expression: [LIST] [*]3 times my age means we multiply a by 3: 3a [*]400 reduced by 3 times my age means we subtract 3a from 400: [*]400 - 3a [*]The word [I]is[/I] mean an equation, so we set 400 - 3a equal to 124 [/LIST] 400 - 3a = 124 To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D124&pl=Solve']we type this equation into our search engine[/URL] and we get: a = [B]92[/B]

How old am I if: 210 reduced by 3 times my current age is 4 times my current age? Let your current age be a. We're given: [LIST] [*]210 reduced by 3 times current age = 210 - 3a [*]4 times current age = 4a [*]The word [I]is[/I] means equal to. So we set 210 - 3a equal to 4a [/LIST] 210 - 3a = 4a To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=210-3a%3D4a&pl=Solve']type this equation into our search engine [/URL]and we get: a = [B]30[/B]

How old am I of 400 reduced by 2 times my age is 224 [LIST=1] [*]Let my age be a. [*]2 times my age: 2a [*]400 reduced by 2 times my age: 400 - 2a [*]The phrase [I]is [/I]means an equation. So we set 400 - 2a equal to 224 for our algebraic expression [/LIST] [B]400 - 2a = 224 [/B] If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D224&pl=Solve']type this equation into our search engine[/URL] and we get: a = [B]88[/B]

I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13 and subtract 13.What is my number? Take a number (n): The first operation is multiply 5 times n, and then add 39: 5n + 139 The second operation is multiply 13 times n and subtract 13: 13n - 13 Set both operations equal to each other since they result in [I]the same number[/I] 5n + 139 = 13n - 13 [URL='https://www.mathcelebrity.com/1unk.php?num=5n%2B139%3D13n-13&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]n = 19[/B]

If 100 people are required to introduce themselves to each other and shake hands with each person one time, how many handshakes will take place? We want 100 choose 2 since we have 2 people per handshake: [URL='https://www.mathcelebrity.com/permutation.php?num=100&den=2&pl=Combinations']100C2[/URL] = [B]4950[/B]

If 11 times a number is added to twice the number, the result is 104 Let [I]the number[/I] be an arbitrary variable we call x. 11 times a number: 11x Twice the number (means we multiply x by 2): 2x The phrase [I]is added to[/I] means we add 2x to 11x: 11x + 2x Simplify by grouping like terms: (11 + 2)x = 13x The phrase [I]the result is[/I] means an equation, so we set 13x equal to 104: 13x = 104 <-- This is our algebraic expression To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=13x%3D104&pl=Solve']we type it in our search engine[/URL] and we get: x = [B]8[/B]

If 12 times a number is added to twice the number, the result is 112. Let the number be n, so we have: 12n + 2n = 112 Combine like terms 14n = 112 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=14n%3D112&pl=Solve']equation solver[/URL], we get [B]n = 8[/B].

If 2 inches is about 5 centimeters, how many inches are in 25 centimeters? Choose the proportions that accurately represent this scenario. We set up a proportion of inches to centimeters where i is the number of inches in 25 centimeters: 2/5 = i/25 To solve this proportion for i, we [URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=i&den1=5&den2=25&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get: i = [B]10[/B]

If 2 times an integer x is increased by 5 2 times an integer x: 2x The phrase [I]increased by[/I] means we add, so we add 5 to 2x: [B]2x + 5[/B]

If 200 bacteria triple every 1/2 hour, how much bacteria in 3 hours Set up the exponential function B(t) where t is the number of tripling times: B(d) = 200 * (3^t) 3 hours = 6 (1/2 hour) periods, so we have 6 tripling times. We want to know B(6): B(6) = 200 * (3^6) B(6) = 200 * 729 B(6) = [B]145,800[/B]

If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3 Take this in pieces, where "a number" means an arbitrary variable, let's call it "x". [LIST=1] [*]3 times a number --> 3x [*]3 times a number added to 2 --> 3x + 2 [*]The number plus 4 --> x + 4 [*]is divided by --> (3x + 2)/(x + 4) [*]the result is 4/3 --> (3x + 2)/(x + 4) = 4/3 [/LIST]

If 4 times a number is added to 9, the result is 49. [I]A number[/I] means an arbitrary variable, let's call it x. 4 [I]times a number[/I] means we multiply x by 4 4x [I]Added to[/I] 9 means we add 9 to 4x 4x + 9 [I]The result is[/I] means we have an equation, so we set 4x + 9 equal to 49 [B]4x + 9 = 49[/B] <-- This is our algebraic expression To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D49&pl=Solve']we type it in the search engine[/URL] and get x = 10

If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integer. [LIST] [*]Let the integer be "x". [*]Square the integer: x^2 [*]7 times the square: 7x^2 [*]5 times the integer: 5x [*]Add them together: 7x^2 + 5x [*][I]The result is[/I] means an equation, so we set 7x^2 + 5x equal to 2 [/LIST] 7x^2 + 5x = 2 [U]This is a quadratic equation. To get it into standard form, we subtract 2 from each side:[/U] 7x^2 + 5x - 2 = 2 - 2 7x^2 + 5x - 2 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=7x%5E2%2B5x-2%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get two solutions: [LIST=1] [*]x = 2/7 [*]x= -1 [/LIST] The problem asks for an integer, so our answer is x[B] = -1[/B]. [U]Let's check our work by plugging x = -1 into the quadratic:[/U] 7x^2 + 5x - 2 = 0 7(-1)^2 + 5(-1) - 2 ? 0 7(1) - 5 - 2 ? 0 0 = 0 So we verified our answer, [B]x = -1[/B].

If 72 is added to a number it will be 4 times as large as it was originally The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. x 72 added to a number: x + 72 4 times as large as it was originally means we take the original number x and multiply it by 4: 4x Now, the phrase [I]it will be[/I] means an equation, so we set x + 72 equal to 4x to get our final algebraic expression: [B]x + 72 = 4x[/B] [B][/B] If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B72%3D4x&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]24[/B]

if 9 times a number is decreased by 6, the result is 111 A number means an arbitrary variable, let's call it x. 9 times a number: 9x Decreased by 6 9x - 6 The result is 11, this means we set 9x - 6 equal to 11 [B]9x - 6 = 11 [/B] To solve this equation for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=9x-6%3D11&pl=Solve']equation calculator[/URL]

if a teachers salary grows by 4% each year. How many years will it take to double. We can use the[URL='https://www.mathcelebrity.com/rule72.php?num=4&pl=Calculate+Rule+of+72+Time'] Rule of 72 at 4%[/URL] to get [B]18 years[/B]

if a train travels at 80 mph for 15 mins, what is the distance traveled? Let d = distance, r = rate, and t = time, we have the distance equation: D = rt Plugging in our values for r and t, we have: D = 80mph * 15 min Remember our speed is in miles per hour, so 15 min equal 1/4 of an hour D = 80mph * 1/4 D = [B]20 miles[/B]

If Distance equals Speed times Time (D = S x T), then what does time equal in terms of speed and distance? Divide each side by S to isolate T: D/S = S x T/S Cancel the S's on the right side: [B]T = D/S[/B]

if flip a coin 4 times, what is the probability of getting all 4 tails. P(Tails) = 1/2 Each flip is independent, so we have: [URL='https://www.mathcelebrity.com/cointoss.php?hts=TTTT&hct=+2&tct=+1&fct=+5>=no+more+than&nmnl=+2&htpick=tails&calc=1&montect=500&pl=Calculate+Probability']P(TTTT)[/URL] = [B]1/16[/B]

If I have a reading average of 2 hours 30 minutes 0 seconds per 93.25 pages, how long would it take me to read 58 pgs? Set up a proportion, of reading time to pages where m is the number of minutes it takes you to read 58 pages. 2 hours and 30 minutes is: 60(2) + 30 120 + 30 150 minutes Our proportion is: 150/93.25 = m/58 [URL='https://www.mathcelebrity.com/prop.php?num1=150&num2=m&den1=93.25&den2=58&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get: [B]m = 93.3 minutes, or about 1 hour, 33 minutes[/B]

If Mr hernandez has 5 times as many students as Mr daniels and together they have 150 students how many students do each have? Let h = Mr. Hernandez's students and d = Mr. Daniels students. We are given two equations: (1) h = 5d (2) d + h = 150 Substitute equation (1) into equation (2) d + (5d) = 150 Combine like terms: 6d = 150 Divide each side of the equation by 6 to isolate d d = 25 <-- Mr. Daniels Students Now, plug the value for d into equation (1) h = 5(25) h = 125 <-- Mr. Hernandez students

if p=2x is even, then p^2 is also even p^2 = 2 * 2 * x^2 p^2 = 4x^2 This is [B]true [/B]because: [LIST] [*]If x is even, then x^2 is even since two evens multiplied by each other is even and 4x^2 is even [*]If x is odd, the x^2 is odd, but 4 times the odd number is always even since even times odd is even [/LIST]

If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how many of each coin does he have? Using q for quarters and n for nickels, and using 525 cents as $5.25, we're given two equations: [LIST=1] [*]q = 4n [*]0.25q + 0.05n = 5.25 [/LIST] Substitute equation (1) into equation (2) for q: 0.25(4n) + 0.05n = 5.25 Multiply through and simplify: n + 0.05n = 5.25 To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B0.05n%3D5.25&pl=Solve']type it in our search engine[/URL] and we get: n = [B]5 [/B] To get q, we plug in n = 5 into equation (1) above: q = 4(5) q = [B]20[/B]

If the max time that John can spend on Client A ($20/hr) in one week is 32 hours, and the min time is 8 hours, while the max time on Client B ($14/hr) is 8 hours and the min 5 hours, what is the RANGE (max, min) of total pay he can earn in one week (40 hours) [LIST] [*]Client A Minimum = 20 x 8 hours = $160 [*]Client A Maximum = 20 x 32 hours = $640 [*]Client B Minimum = 14 x 5 hours = $70 [*]Client B Maximum = 14 x 8 hours = $112 [/LIST] [U]The Total Maximum Pay is found by adding Client A Maximum and Client B Maximum[/U] Total Maximum = Client A Maximum + Client B Maximum Total Maximum = 640 + 112 Total Maximum = 752 [U]The Total Minimum Pay is found by adding Client A Minimum and Client B Minimum[/U] Total Minimum = Client A Minimum + Client B Minimum Total Minimum = 160 + 70 Total Minimum = 230 [U]The Range is the difference between the Total maximum and the Total minimum[/U] Range(Total Maximum, Total Minimum) = Total Maximum - Total Minimum Range(752, 230) = 752 - 230 Range(752, 230) = [B]522[/B]

If the number of professors in a college is P and the number is students S, and there are 14 times as many students as professors 14 times as many means we multiply: [B]S = 14P[/B]

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find the time taken by aeroplane to cover 1200m initially. We know from the distance formula (d) using rate (r) and time (t) that: d = rt Regular speed: 1200 = rt Divide each side by t, we get: r = 1200/t Reduced speed. 20 minutes = 60/20 = 1/3 of an hour. So we multiply 1,200 by 3 3600 = (r - 40)(t + 1/3) If we multiply 3 by (t + 1/3), we get: 3t + 1 So we have: 3600 = (r - 40)(3t + 1) Substitute r = 1200/t into the reduced speed equation: 3600 = (1200/t - 40)(3t + 1) Multiply through and we get: 3600 = 3600 - 120t + 1200/t - 40 Subtract 3,600 from each side 3600 - 3600 = 3600 - 3600 - 120t + 1200/t - 40 The 3600's cancel, so we get: - 120t + 1200/t - 40 = 0 Multiply each side by t: -120t^2 - 40t + 1200 = 0 We've got a quadratic equation. To solve for t, [URL='https://www.mathcelebrity.com/quadratic.php?num=-120t%5E2-40t%2B1200%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this in our search engine[/URL] and we get: t = -10/3 or t = 3. Since time [I]cannot[/I] be negative, our final answer is: [B]t = 3[/B]

If there are 10^30 grains of sand on Beach A, how many grains of sand are there on a beach the has 10 times the sand as Beach A? (Express your answer using exponents.) 10^30 * 10 = 10^(30 + 1) = [B]10^31[/B]

If you are running 6 miles per hour, then it takes you 10 minutes to run 1 mile. If you are running 8 miles per hour, it takes you 7.5 minutes to run a mile. What does your speed have to be for your speed in miles per hour to be equal to your mile time in minutes? From above, we have: [LIST] [*]6mph x 10 minutes = 1 mile [*]8mph x 7.5 minutes = 1 mile [/LIST] Notice that mph x minutes = 60 since there are 60 minutes in 1 hour? So we have x mph x y minutes = 60. Since we want mph and y (minutes) = x (mph), we have x^2 = 60 x = sqrt(60) [B]x = 7.746 mph[/B]

If you arrived at your preschool classroom at 7:35 am and stayed until 10:24 am how much time did you spend in the classroom? Using our [URL='https://www.mathcelebrity.com/elaptime.php?num1=7%3A35&check1=1&num2=10%3A24&check2=1&pl=Calculate+Elapsed+Time']elapsed time calculator[/URL], we get: [B]2 hours and 49 minutes[/B]

If you buy a computer directly from the manufacturer for $3,509 and agree to repay it in 36 equal installments at 1.73% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid? [U]Determine the monthly payment[/U] The monthly payment is [B]$114.87[/B] using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=3059&av=&pmt=&n=36&i=1.73&check1=1&pl=Calculate']annuity calculator[/URL] [U]Determine the total payments made[/U] Total payment is 36 times $114.87 = $4,135.37 [U]Now determine the total interest paid[/U] Take the total payments of $4,135.37 and subtract the original loan of $3,059 to get interest paid of [B]$1,076.37[/B]

If you throw a die for two times, what is the probability that you will get a one on the first throw or a one on the second throw (or both)? [LIST] [*]P(1) on first roll and P(anything on second roll) = 1/6 * 1 = 1/6 [*]P(anything on first roll) and P(1) on second roll = 1 * 1/6 = 1/6 [*]Add those together: 1/6 + 1/6 = 2/6 = [B]1/3[/B] [/LIST]

If you toss a fair coin 6 times, what is the probability of getting all tails? We [URL='https://www.mathcelebrity.com/cointoss.php?hts=TTTTTT&hct=+2&tct=+1&fct=+5>=no+more+than&nmnl=+2&htpick=tails&calc=1&montect=500&pl=Calculate+Probability']type in our search engine [I]TTTTTT [/I]and we get[/URL]: P(TTTTTT) = [B]1/64 or 0.015625[/B]

Imagine a researcher wanted to test the effect of the new drug on reducing blood pressure. In this study, there were 50 participants. The researcher measured the participants' blood pressure before and after the drug intake. If we want to compare the mean blood pressure from the two time periods with a two-tailed t test, how many degrees of freedom are there? a. 49 b. 50 c. 99 d. 100 [B]a. 49[/B] Degrees of Freedom = n - 1 Degrees of Freedom = 50 - 1 Degrees of Freedom = 49

In 1 year, a baseball player got 195 hits in 600 times. What is his batting average? Batting Average = Hits / Times at Bat Batting Average = 195 / 600 [URL='https://www.mathcelebrity.com/perc.php?num=196&den=600&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']Batting Average[/URL] = [B]0.327[/B]

In 16 years, Ben will be 3 times as old as he is right now. Let Ben's age today be a. We're given: a + 16 = 3a [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B16%3D3a&pl=Solve']Type this equation into the search engine[/URL], and we get: a = [B]8[/B]

In 16 years, Ben will be 3 times as old as he is right now. Let Ben's age right now be b. We have, in 16 years, Ben's age will be 3 times what his age is now: b + 16 = 3b Subtract b from each side: 2b = 16 Divide each side by 2 [B]b = 8[/B] Check our work: 16 years from now, Ben's age is 8 + 16 = 24 And, 8 x 3 = 24

In 1996 Ato Boldon of UCLA ran the 100-meter dash in 9.92 seconds. In 1969 John Carlos of San Jose State ran the 100-yard dash in 9.1 seconds. Which runner had the faster average speed? We [URL='https://www.mathcelebrity.com/linearcon.php?quant=100&type=yard&pl=Calculate']convert yards to meters using our conversion calculator[/URL] and we get: 100 yards = 91.44 meters Now we set up a proportion of time per meter: [LIST] [*]Ato Boldon: 9.92/100 = 0.992 per meter [*]John Carlos: 9.1/91.44 = 0.995 per meter [/LIST] [B]Since Ato Boldon's time was [I]less per meter[/I], he had the faster average speed[/B]

In 20 years charles will be 3 times as old as he is now. How old is he now? Let Charles's age be a today. We're given: a + 20 = 3a [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B20%3D3a&pl=Solve']If we type this equation into our search engine[/URL], we get: [B]a = 10 [/B] Let's check our work in our given equation: 10 + 20 ? 3(10) 30 = 30 <-- Checks out!

In 45 years, Gabriela will be 4 times as old as she is right now. Let a be Gabriela's age. we have: a + 45 = 4a Subtract a from each side: 3a = 45 Divide each side by a [B]a = 15[/B]

In 56 years, Stella will be 5 times as old as she is right now. Let Stella's age be s. We're given: s + 56 = 5s [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B56%3D5s&pl=Solve']Type this equation into our search engine[/URL], and we get: [B]s = 14[/B]

In a hurricane the wind pressure varies directly as the square of the wind velocity. If a wind pressure is a measure of a hurricane's destruction capacity, what happens to this destructive power when the wind speed doubles? Let P = pressure and v = velocity (wind speed) We are given p = v^2 Double velocity, so we have a new pressure P2: P2 = (2v)^2 P2 = 4v^2 Compare the 2: p = v^2 p = 4v^2 Doubling the wind speed [B]quadruples, or 4 times[/B] the pressure.

In the year 1989, Luke's age was 3 times Rachel's age and Rachel's age was 3 times Dan's age. If Dan's age was n, how old were Rachel and Luke? Rachel's age = 3 * Dan's age Rachel's age = 3n Luke's age = 3 times Rachel's age Luke's age = 3(3n) Luke's age = [B]9n[/B]

In x years time, Peter will be 23 years old. How old is he now? Let Peter's current age be a. In x years time means we add x to a, so we're given: a + x = 23 We want to find a, s we subtract x from each side to get: a + x - x = 23 - x Cancel the x terms on the left side and we get: a = [B]23 - x[/B]

I read that as 10% times 50 plus 50

Isabel earns $7.50 per hour on the weekends. Write and solve an inequality to find how many hours she needs to work to earn at least $120. A few things to note: [LIST] [*]Earnings = Rate * time [*]Let h be the number of hours worked [*]The phrase [I]at least[/I] means greater than or equal to, so we have the following inequality. [/LIST] We represent this with the following inequality: 7.5h < 120 To solve this inequality for h, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=7.5h%3C120&pl=Show+Interval+Notation']type it into our math engine[/URL] and we get: [B]h < 16[/B]

[SIZE=4]Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only 5 times as old as William? [U]Express Ishaan and William's age since today where y is the number of years since today, we have:[/U] i = 72+y w = 4+y [U]We want the time for Ishaan age will be 5 times William's age:[/U] i = 5w 72 + y = 5(4 + y) We [URL='https://www.mathcelebrity.com/1unk.php?num=72%2By%3D5%284%2By%29&pl=Solve']plug this equation into our search engine [/URL]and get: y = [B]13[/B] [/SIZE]

It takes 3/4 of an hour to complete a puzzle. How many puzzles can Cindy finish in 3 hours? We setup a proportion of time to puzzles where p is the number of puzzles Cindy can complete in 3 hours: 3/4/1 = 3/p Dividing by 1 means the same as the original fraction, so we have: 3/4 = 3/p [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=3&den1=4&den2=p&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into the search engine[/URL], we get: p = [B]4[/B]

It takes 60 minutes for 7 people to paint 5 walls. How many minutes does it take 10 people to paint 10 walls? Rate * Time = Output Let "Rate" (r) be the rate at which [B]one person[/B] works. So we have: 7r * 60 = 5 Multiply through and simplify: 420r = 5 Divide each side by 5 to isolate r: r = 1/84 So now we want to find out how many minutes it takes 10 people to paint 10 walls using this rate: 10rt = 10 With r = 1/84, we have: 10t/84 = 10 Cross multiply: 10t = 840 To solve for t, we t[URL='https://www.mathcelebrity.com/1unk.php?num=10t%3D840&pl=Solve']ype this equation into our search engine[/URL] and we get: t = [B]84 minutes[/B]

It takes Spot 2 hours to paint a fence and Steven 4 hours to paint the same fence. If they work together, how long will it take them to paint the fence? Spot paints 1/2 of a fence in an hour Steven paints 1/4 of a fence in an hour Together, in an hour, they paint 1/2 + 1/4 of a fence in an hour 1/2 = 2/4, so we have 2/4 + 1/4 = 3/4 of a fence in an hour Meaning they take another 20 minutes to pain the last 1/4 of the fence [B]1 hour + 20 minutes[/B] is the total time it takes

Jack and Jill have a magic pail of beans. The number of beans in the pail doubles every second. If the pail is full after 10 seconds, when was the pail half full? Explain your answer. [LIST] [*]At time 0, we have n beans [*]At time 1, we have 2n beans [*]At time 2, we have 4n beans [*]At time 3, we have 8n beans [*]At time 4, we have 16n beans [*]At time 5, we have 32n beans [*]At time 6, we have 64n beans [*]At time 7, we have 128n beans [*]At time 8, we have 256n beans [*]At time 9, we have 512n beans [*]At time 10, we have 1024n beans [/LIST] 1/2 of 1024 is 512, so at [B]Time 9[/B], the pail is half full.

Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episode airs, Jake receives a bunch of fan mail. He splits all the letters into 3 equal stacks to open with his mom and his sister. Each stack contains 21 letters. Which equation can you use to find the number of letters n Jake receives? The number of letters n is represented by number of stacks (s) times letter per stack (l). We're given s = 3 and l = 21, so we have: n = 21(3) n = [B]63[/B]

James is four time as old as peter if their combined age is 30 how old is James. Let j be Jame's age. Let p be Peter's age. We're given: [LIST=1] [*]j = 4p [*]j + p = 30 [/LIST] Substitute (1) into (2) 4p + p = 30 Combine like terms: 5p = 30 [URL='https://www.mathcelebrity.com/1unk.php?num=5p%3D30&pl=Solve']Type 5p = 30 into our search engine[/URL], and we get p = 6. Plug p = 6 into equation (1) to get James's age, we get: j = 4(6) j = [B]24[/B]

Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling? Distance = Rate * Time We're given D = 395 and t = 5 We want Rate. We divide each side of the equation by time: Distance / Time = Rate * Time / Time Cancel the Time's on each side and we get: Rate = Distance / Time Plugging our numbers in, we get: Rate = 395/5 Rate = [B]79 kilometers[/B]

Jenny makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours. Since Jenny makes 9 dollars for each hour of work, then her total pay (p) is her hourly rate times the number of hours worked: [B]p = 9h[/B]

Jerry rolls a dice 300 times what is the estimated numbers the dice rolls on 6 Expected Value = Rolls * Probability Since a 6 has a probability of 1/6, we have: Expected Value = 300 * 1/6 Expected Value = [B]50[/B]

Jill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes for $34. Jack buys 10 carrots and 7 tomatoes for $29. How much does each carrot and each tomato cost? Let the cost of carrots be c and the cost of tomatoes be t. Since the total cost is price times quantity, We're given two equations: [LIST=1] [*]12c + 8t = 34 <-- Jill [*]10c + 7t = 29 <-- Jack [/LIST] We have a system of equations. We can solve this one of three ways: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [LIST] [*][B]t = 2[/B] [*][B]c = 1.5[/B] [/LIST]

Jim and his family are touring Chicago. They want to visit the Willis Tower, hang out at Navy Pier, and shop on Michigan Avenue before their dinner reservations at 4:15 P.M. They plan to spend 1 hour and 25 minutes at the Willis Tower, 1 hour and 40 minutes at Navy Pier, and 1 hour and 40 minutes shopping. What is the latest time Jim's family can start their tour of Chicago and still make it to dinner on time? First thing we want is how much time is Jim's family spending on pre-dinner activities [LIST=1] [*]1 hour and 25 minutes at Willis Tower [*]1 hour and 40 minutes at Navy Pier [*]1 hour and 40 minutes shopping [/LIST] Add these all up and we get: 3 hours and 105 minutes 105 minutes = 60 + 45 3 + 1 hours = 4 hours and 45 minutes IF dinner reservations start at 4:15, the latest Jim's family can start their tour is: 4:15 pm and go back 4 hours and 45 minutes We go back 5 hours and we get 11:15 am and add 15 minutes to get [B]11:30 AM [/B] 4:15 pm and go back 4 hours to get 12:15 pm Now go back another 45 minutes and we get 11:30 am

Jim has $440 in his savings account and adds $12 per week to the account. At the same time, Rhonda has $260 in her savings account and adds $18 per week to the account. How long will it take Rhonda to have the same amount in her account as Jim? [U]Set up Jim's savings function S(w) where w is the number of weeks of savings:[/U] S(w) = Savings per week * w + Initial Savings S(w) = 12w + 440 [U]Set up Rhonda's savings function S(w) where w is the number of weeks of savings:[/U] S(w) = Savings per week * w + Initial Savings S(w) = 18w + 260 The problems asks for w where both savings functions equal each other: 12w + 440 = 18w + 260 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=12w%2B440%3D18w%2B260&pl=Solve']type this equation into our math engine[/URL] and we get: w = [B]30[/B]

3 cars times $9,876 for each car = $29,628

Joanie multiplied 0.78 times 0.34 and got the product 26.52. What error did she make [B]She didn't move the decimal point over 2 spots[/B]: 0.78 * 0.34 = 0.2652

John is n years old now. How old was he 10 years ago? What will be his age in 20 years time? 10 years ago means we [I]subtract[/I] 10 from n: [B]n - 10[/B] 20 years time or 20 years from now means we [I]add[/I] 20 to n: [B]n + 20[/B]

Johnny Rocket can run 300 meters in 90 seconds. If his speed remains constant, how far could he run in 500 seconds? Round to one decimal place. Set up the distance equation: Distance = Rate * Time 300 = 90r Solving this equation for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=300%3D90r&pl=Solve']type it in our search engine[/URL] and we get: r = 3.333 For 500 seconds, we set up our distance equation again: Distance = 500 * 3.333333 Distance = [B]1666.7 meters[/B]

Juliana answered 42 times correctly on an 80-item quiz, while her sister Angela answered 21 items correctly on a 40-item quiz. Do they have the same portion of correct answers? Let's compare based on correct answers to questions: Juliana = 42/80 = 0.525 Angela = 21/40 = 0.525 So yes, they do have the same portion of correct answers. But there's another way to solve this: [LIST=1] [*]Divide Juliana's the top and bottom of Juliana's fraction by 2. [*]We picked 2 as a GCF shown in our calculator. [*]Type [URL='https://www.mathcelebrity.com/gcflcm.php?num1=42&num2=80&num3=&pl=GCF']GCF of 42 and 80[/URL]. [/LIST] Divide top and bottom of Juliana's fraction by the GCF of 2 42/2 = 80/2 = 21/40 This ratio equals Angela's.

Julie has $300 to plan a dance. There is a one-time fee of $75 to reserve a room. It also costs $1.50 per person for food and drinks. What is the maximum number of people that can come to the dance? Let each person be p. We have the following relationship for cost: 1.50p + 75 <=300 We use the <= sign since we cannot go over the $300 budget. [URL='https://www.mathcelebrity.com/1unk.php?num=1.50p%2B75%3C%3D300&pl=Solve']We type this inequality into our search engine[/URL], and we get: p <= 150 Since we have the equal sign within the inequality, the maximum number of people that can come to the dance is [B]150.[/B]

Julio had a coin box that consisted of only quarters and dimes. The number of quarters was three times the number of dimes. If the number of dimes is n, what is the value of coins in the coin box? Set up monetary value: [LIST] [*]Value of the dimes = 0.1n [*]Value of the quarters = 0.25 * 3n = 0.75n [/LIST] Add them together [B]0.85n[/B]

Julius Caesar was born and 100 BC and was 66 years old when he died in which year did he die? BC means "Before Christ". On a timeline, it represents a negative number, where year 0 is the birth of Christ. So we have -100 + 66 = -34 -34 means [B]34 BC[/B].

July has 31 days how many seconds are there in July Using our [URL='https://www.mathcelebrity.com/timecon.php?quant=31&pl=Calculate&type=day']time conversion calculator[/URL], we get: 31 days = [B]2,678,400 seconds[/B]

Karin has 3 to spend in the arcade. The game she likes costs 50c per play. What are the possible numbers of times that she can play? [U]Let x = the number of games Karin can play with her money[/U] 0.5x = 3 [U]Divide each side by 0.5[/U] [B]x = 6[/B]

Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slacks and paid11.45. Then she brought 5 shirts, 3 pairs of slacks, and 1 sports coat and paid 27.41. Finally, she brought 5 shirts and 1 sports coat and paid 16.94. How much was she charged for each shirt, each pair of slacks, and each sports coat? Let s be the cost of shirts, p be the cost of slacks, and c be the cost of sports coats. We're given: [LIST=1] [*]4s + p = 11.45 [*]5s + 3p + c = 27.41 [*]5s + c = 16.94 [/LIST] Rearrange (1) by subtracting 4s from each side: p = 11.45 - 4s Rearrange (3)by subtracting 5s from each side: c = 16.94 - 5s Take those rearranged equations, and plug them into (2): 5s + 3(11.45 - 4s) + (16.94 - 5s) = 27.41 Multiply through: 5s + 34.35 - 12s + 16.94 - 5s = 27.41 [URL='https://www.mathcelebrity.com/1unk.php?num=5s%2B34.35-12s%2B16.94-5s%3D27.41&pl=Solve']Group like terms using our equation calculator [/URL]and we get: [B]s = 1.99 [/B] <-- Shirt Cost Plug s = 1.99 into modified equation (1): p = 11.45 - 4(1.99) p = 11.45 - 7.96 [B]p = 3.49[/B] <-- Slacks Cost Plug s = 1.99 into modified equation (3): c = 16.94 - 5(1.99) c = 16.94 - 9.95 [B]c = 6.99[/B] <-- Sports Coat cost

Kevin is 4 times old as Daniel and is also 6 years older than Daniel. Let k be Kevin's age and d be Daniel's age. We have 2 equations: [LIST=1] [*]k = 4d [*]k = d + 6 [/LIST] Plug (1) into (2): 4d = d + 6 Subtract d from each side: 4d - d = d - d + 6 Cancel the d terms on the right side and simplify: 3d = 6 Divide each side by 3: 3d/3 = 6/3 Cancel the 3 on the left side: d = 2 Plug this back into equation (1): k = 4(2) k = 8 So Daniel is 2 years old and Kevin is 8 years old

Kiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. What is their present age? Let k be Kiko's present age Let s be Kiko's sisters age. We're given two equations: [LIST=1] [*]k = 6s [*]k + 6 = 3(s + 6) [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for k: 6s + 6 = 3(s + 6) [URL='https://www.mathcelebrity.com/1unk.php?num=6s%2B6%3D3%28s%2B6%29&pl=Solve']Typing this equation into our math engine[/URL] to solve for s, we get: s = [B]4[/B] To solve for k, we substitute s = 4 into equation (1) above: k = 6 * 4 k = [B]24[/B]

kim and jason just had business cards made. kim’s printing company charged a one time setup fee of $8 and then $20 per box of cards. jason,meanwhile ordered his online. they cost $8 per box. there was no setup fee, but he had to pay $20 to have his order shipped to his house. by coincidence, kim and jason ended up spending the same amount on their business cards. how many boxes did each buy? how much did each spend? Set up Kim's cost function C(b) where b is the number of boxes: C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee C(b) = 20c + 8 + 0 Set up Jason's cost function C(b) where b is the number of boxes: C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee C(b) = 8c + 0 + 20 Since Kim and Jason spent the same amount, set both cost equations equal to each other: 20c + 8 = 8c + 20 [URL='https://www.mathcelebrity.com/1unk.php?num=20c%2B8%3D8c%2B20&pl=Solve']Type this equation into our search engine[/URL] to solve for c, and we get: c = 1 How much did they spend? We pick either Kim's or Jason's cost equation since they spent the same, and plug in c = 1: Kim: C(1) = 20(1) + 8 C(1) = 20 + 8 C(1) = [B]28 [/B] Jason: C(1) = 8(1) + 20 C(1) = 8 + 20 C(1) = [B]28[/B]

Kimberly is taking three online classes during the summer. She spends 10 hours each week studying for her marketing class, 12 hours studying for her statistics class, and 8 hours studying for her business law class. What percent of her study time does she spend for her statistics class? The percentage equals hours spent on statistics divided by total hours spent studying for everything. [U]Calculate total study hours:[/U] Total Study Hours = Marketing Class Study Hours + Statistics Class Study Hours + Business Law Study Hours Total Study Hours = 10 + 8 + 12 Total Study Hours = [B]30[/B] [U]Calculate Statistics Study Hours Percentage:[/U] Statistics Study Hours Percentage = Statistics Class Study Hours / Total Study Hours Statistics Class Study Hours = 8/30 Using our [URL='https://www.mathcelebrity.com/perc.php?num=8&den=30&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']fraction to decimal calculator[/URL], we get Statistics Class Study Hours = [B]26.67%[/B]

Kimberly takes 4 pages of notes during each hour of class. Write an equation that shows the relationship between the time in class x and the number of pages y. With x hours and y pages, our equation is: [B]y = 4x [/B]

Larry is buying new clothes for his return to school. He is buying shoes for $57 and shirts cost $15 each. He has $105 to spend. Which of the following can be solved to find the number of shirts he can afford? Let s be the number of shirts. Since shoes are a one-time fixed cost, we have: 15s + 57 = 105 We want to solve this equation for s. We [URL='https://www.mathcelebrity.com/1unk.php?num=15s%2B57%3D105&pl=Solve']type it in our math engine[/URL] and we get: s = [B]3.2 or 3 whole shirts[/B]

Last week, a man worked 47 hours at Starbucks. Find his gross earnings for the week if he is paid $7.80 per hour and earns time-and-a-half for all hours over 40. [U]Step 1: Calculate regular time pay up to 40 hours:[/U] Regular Pay = Hourly Wage * Hours up to 40 Regular Pay = $7.80 * 40 Regular Pay = $312 [U]Step 2: Calculate overtime hours above 40 hours:[/U] Overtime Hours = Hours Worked - 40 hours Overtime Hours = 47 - 40 Overtime Hours = 7 [U]Step 3: Calculate overtime pay above 40 hours:[/U] Overtime Pay = 1.5 * Hourly Rate * Overtime Hours Overtime Pay = 1.5 * $7.80 * 7 Overtime Pay = $81.90 [U]Step 4: Calculate Gross Earnings[/U] Gross Earnings = Regular Pay + Overtime Pay Gross Earnings = $312 + $81.90 = [B]$393.90 [URL='https://www.facebook.com/MathCelebrity/videos/10156751976078291/']FB Live Session[/URL][/B]

Liam, a 19th century cowboy, carries an 1847 Colt single action 6 shooter revolver. So proficient is he with this weapon that when he fires all 6 shots in a row, the time between the first bullet and the last is 40 seconds. How long would it take him to fire 4 shots? We set up a proportion of shots to seconds where s is the number of seconds it takes to fire 4 shots: 6/40 = 4/s Using our [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=4&den1=40&den2=s&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get: s = [B]26.67[/B]

Linda can run about 6 yards in one second. About how far can she run in 12 seconds? Distance = Rate * Time Distance = 6 yds/ second * 12 seconds Distance = [B]72 yards[/B]

Free Linear Conversions Calculator - Converts to and from the following linear measurements for a given quantity:
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Free Littles Law Calculator - Given two out of the three inputs for Littles Law, Throughput (TH), Cycle Time (CT, and WIP, this solves for the third item.

Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nephew? Let the age of Logan's nephew be n. We're given: 4n + 8 = 32 (Since [I]older[/I] means we add) To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=4n%2B8%3D32&pl=Solve']type it into our search engine[/URL] and we get: [B]n = 6[/B]

Luke and Dan's total debt is $72. If Luke's debt is three times Dan's debt, what is Dan's debt? Let Dan's debt be d. Let Luke's debt be l. We're given two equations: [LIST=1] [*]d + l = 72 [*]l = 3d [/LIST] Substitute equation (2) for l into equation (1): d + 3d = 72 Solve for [I]d[/I] in the equation d + 3d = 72 [SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE] (1 + 3)d = 4d [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 4d = + 72 [SIZE=5][B]Step 3: Divide each side of the equation by 4[/B][/SIZE] 4d/4 = 72/4 d = [B]18[/B]

Luke drove for n hours at 55 miles per hour. Luke's mother drove for n hours at a speed of 60 miles per hour. How much farther than Luke did his mother drive? Distance = Rate * Time [LIST] [*]Luke drove: 55n [*]Mom drove 60n [/LIST] Distance difference = 60n - 55n = [B]5n[/B]

m times the difference of 2p and 4r The difference of 2p and 4r: 2p - 4r m times the difference: [B]m(2p - 4r)[/B]

Sum of n and 5 n + 5 m times that sum m(n + 5)

Free MAPE - MPE - MAPD Calculator - Given a time series of actual and forecasted values, this determines the following:
* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)
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Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of weeks x and the total number of quizzes y. Write your answer as an equation with y first, followed by an equals sign. Our total quizzes equal 2 times the number of weeks (x): [B]y = 2x[/B]

Maria runs each lap in 5 minutes. She will run less than 7 laps today. What are the possible numbers of minutes she will run today? Total Time < Laps * minutes per laps Total Time < 7 * 5 [B]Total Time < 35[/B]

Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than 11. What is the youngest age Warren can be? Let m be Marty's age and w be Warren's age. We have two equations: (1) m = 6w - 3 (2) m + w > 11 Plug (1) into (2) 6w - 3 + w > 11 Combine w terms 7w - 3 > 11 Add 3 to each side 7w > 14 Divide each side by 7 w > 2 which means [B]w = 3[/B] as the youngest age.

Mary owns a store that sells computers. Her profit in dollars is represented by the function P(x) = x^3 - 22x^2 - 240x, where x is the number of computers sold. Mary hopes to make a profit of at least $10,000 by the time she sells 36 computers. Explain whether Mary will meet her goal. Justify your reasoning. Calculate P(10): P(10) = 10^3 - 22(10)^2 - 240(10) P(10) = 1000 - 2200 - 2400 P(10) = -3600 Mary will [B]not[/B] meet her goal of making a profit of at least $10,000 when she sells 36 computers because her profit is in the negative.

Match each variable with a variable by placing the correct letter on each line. a) principal b) interest c) interest rate d) term/time 2 years 1.5% $995 $29.85 [B]Principal is $995 Interest is $29.85 since 995 * .0.15 * 2 = 29.85 Interest rate is 1.5% Term/time is 2 year[/B]s

The truck bed is 80 inches long, 69 inches wide, and 20 inches tall. So the total volume the truck can carry is: 80 x 69 x 20 = 110,400 cubic inches can be carried each time. Find out how many gallons in a full tank for the 2003 Ford F150. Then you calculate the amount of miles you can drive on a full trip.

Matthew works 45 hours at $22.10 per hour and 3 hours overtime at double time. Calculate his total earnings per week. If Matthew gets 3 hours overtime, then his regular time is 45 - 3 = 42 [U]Calculate regular hours earnings:[/U] Regular hours earnings = Hourly Rate * Regular hours worked Regular hours earnings = 22.10 * 42 Regular hours earnings = 928.20 [U]Calculate overtime hours earnings:[/U] Double time = twice the regular hourly ratre Overtime hours earnings = Hourly Rate * 2 * Overtime hours worked Overtime hours earnings = 22.10 * 2 * 3 Overtime hours earnings = 132.60 [U]Calculate total earnings:[/U] Total earnings = Regular hours earnings + Overtime hours earnings Total earnings = 928.20 + 132.60 Total earnings = [B]$1,060.80[/B]

Max sneezes every 5 minutes, Lina coughs every 6 minutes, and their dog barks every 3 minutes. If there was sneezing, barking, and coughing at 3:15 PM, when is the next time that these three sounds will happen simultaneously? To find the next time the sounds happen simultaneously, we want to find the Least Common Multiple (LCM). [URL='https://www.mathcelebrity.com/gcflcm.php?num1=3&num2=5&num3=6&pl=LCM']Using our LCM Calculator[/URL], we find the least common multiple of 3, 5, and 6 is 30. The least common multiple gives us a common time where each sound reaches a "cycle". [LIST] [*]Dog: A bark every e minutes means the dog has 10 barks, with the 10th bark at 30 minutes after 3:15 [*]Max: A sneeze every 5 minutes means he has 6 sneezes, with the 6th sneeze at 30 minutes after 3:15 [*]Lisa: A cough every 6 minutes means she has 5 coughs, with the 5th cough at 30 minutes after 3:15 [/LIST] 30 minutes after 3:15 means we have: 3:15 + 30 = [B]3:45 PM[/B]

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Michael invited 30 of his friends to his part and a third of guest arrived late how many arrived on time If 1/3 arrived late, then [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=1%2F3&pl=Subtract']1 - 1/3[/URL] = 2/3 arrived on time Guests who arrived on time = 2/3 of 30 [URL='https://www.mathcelebrity.com/fraction.php?frac1=30&frac2=2/3&pl=Multiply']Guests who arrived on time[/URL] = [B]20[/B]

Mike received a penny on December 1st. On December 2nd he received 2 cents. December 3rd another 4 cents and December 4th he received 8 cents. If his money continues to double, how much will he earn on December 25th? We have 24 doubling times starting December 2 to December 25 0.01 * 2^24 0.01 * 16,777,216 [B]167,772.16[/B]

Milan plans to watch 2 movies each month. Write an equation to represent the total number of movies n that he will watch in m months. Number of movies equals movies per month times the number of months. So we have: [B]n = 2m[/B]

Mimi just started her tennis class three weeks ago. On average, she is able to return 20% of her opponent's serves. Assume her opponent serves 8 times. Show all work. Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomial probability distribution. a) What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively? b) Find the probability that that she returns at least 1 of the 8 serves from her opponent. (c) How many serves can she expect to return? a) [B]n = 8 p = 0.2[/B] q = 1 - p q = 1 - 0.2 [B]q = 0.8 [/B] b) [B]0.4967[/B] on our [URL='http://www.mathcelebrity.com/binomial.php?n=+8&p=0.2&k=1&t=+5&pl=P%28X+>+k%29']binomial calculator[/URL] c) np = 8(0.2) = 1.6 ~ [B]2[/B] using the link above

Mimis math class starts at 9:00 A.M. and lasts for 1 hour and 55 minutes. After math class, Mimi has recess for 15 minutes. What time does Mimis recess end? [LIST=1] [*]Start at 9:00 AM [*]1 hour and 55 minutes of class puts us at 10:55 AM [*]Recess for 15 minutes puts us at [B]11:10 AM[/B] [/LIST] [B][/B] [LIST=1] [*]Another way to do this is work in whole hours and minute blocks [*]9:00 AM, add 1 hour that is 10:00 AM [*]55 minutes is 5 minutes less than 1 hour [*]So add another hour to 10:00 AM which is 11:00 AM [*]Subtract the 5 minutes is 10:55 AM [*]15 minutes is 5 minutes + 10 minutes [*]Add 5 minutes to 10:55AM is 11:00 [*]10 minutes added to this is [B]11:10 AM[/B] [/LIST]

Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water as juice. How many ounces of strawberry juice and how many ounces of water does she need to make 40 ounces of strawberry infused water? Let j be the ounces of strawberry juice and w be the ounces of water. We're given: [LIST=1] [*]j + w = 40 [*]w = 3j [/LIST] Substitute (2) into (1): j + 3j = 40 Combine like terms: 4j = 40 [URL='https://www.mathcelebrity.com/1unk.php?num=4j%3D40&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]j = 10[/B] From equation (2), we substitute j = 2: w = 3(10) [B]w = 30 [/B] This means we have [B]10 ounces of juice[/B] and [B]30 ounces of water[/B] for a 40 ounce mix.

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Mr turner sent his car to the workshop for repair work as well as to change 4 tires. Mr turner paid $1035 in all. The repair work cost 5 times the price of each tire. The mechanic told Mr. turner that the repair work cost $500. Explain the mechanic’s mistake Let the cost for work be w. Let the cost for each tire be t. We're given; [LIST=1] [*]w = 5t [*]w + 4t = 1035 [/LIST] Substitute equation 1 into equation 2: (5t) + 4t = 1035 [URL='https://www.mathcelebrity.com/1unk.php?num=%285t%29%2B4t%3D1035&pl=Solve']Type this equation into our search engine[/URL], and we get: t = 115 Substitute this into equation (1): w = 5(115) w = [B]575[/B] The mechanic underestimated the work cost.

Mrs diaz works 40 hours per week regularly at a rate of $15.15 per hour.When she works overtime , her rate is time and a half of her regular rate. What is Mrs. Diaz overtime rate? Time and a half means your hourly rate plus 50% or 1/2 of your hourly rate: 15.15 * 1.5 = $[B]22.73[/B]

n increased by the difference between 10 times n and 9 Take this algebraic expression in pieces: [LIST] [*]10 times n: 10n [*]The difference between 10 times n and 9: 10n - 9 [*]n increased by the difference...: [B]n + (10n - 9)[/B] [/LIST]

n is equal to 135 less than the quantity 61 times n 61 times n: 61n 135 less than the quantity 61 times n 61n - 135 We set n equal to this expression: [B]n = 61n - 135[/B]

n times 146, reduced by 94 is the same as h n time 146 146n Reduced by 94 146n - 94 Is the same as h means an equation: [B]146n - 94 = h[/B]

Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daughter? Declare variables for each age: [LIST] [*]Let Nancy's age be n [*]Let her daughter's age be d [/LIST] We're given two equations: [LIST=1] [*]n = 3d - 10 [*]n = 41 [/LIST] We set 3d - 10 = 41 and solve for d: Solve for [I]d[/I] in the equation 3d - 10 = 41 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -10 and 41. To do that, we add 10 to both sides 3d - 10 + 10 = 41 + 10 [SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE] 3d = 51 [SIZE=5][B]Step 3: Divide each side of the equation by 3[/B][/SIZE] 3d/3 = 51/3 d = [B]17[/B]

[SIZE=5]Nervous Speaker #1 says the word "um" 8 times each minute. Nervous Speaker #2 says the word "um" 10 times each minute. Working together, how many minutes will it take them to say the word "um" 270 times? [/SIZE] [SIZE=4]In one minute, Nervous speaker 1 and 2 say "um" 8 + 10 = 18 times per minute. We want to know how many minutes it takes for both of them to say 270 "um"s. We divide 270/18 to get [B]15 minutes[/B][/SIZE]

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Nia is trying to decide between two possible jobs. Job A pays $2000 a month with a 2% annual raise. Job B pays 24,000 a year with a $500 annual raise. Write a function to represent the annual salary for Job A after x years. Write a function to represent the annual salary for Job B after x years. After how many years would Nia have a greater salary at Job A? Nia Job A salary at time t: S(t) $2,000 per month equals $24,000 per year. So we have S(t) = 24,000(1.o2)^t Nia Job B salary at time t: S(t) $24,000 per year. So we have S(t) = 24,000 + 500t We want to know t when Job A salary is greater than Job B Salary: 24,000(1.o2)^t > 24,000 + 500t Time | A | B 0 | 24000 | 24000 1 | 24480 | 24500 2 | 24969.6 | 25000 3 | 25468.99 | 25500 4 | 25978.37 | 26000 5 | 26497.94 | 26500 6 | 27027.9 | 27000 7 | 27568.46 | 27500 8 | 28119.83 | 28000 9 | 28682.22 | 28500 10 | 29255.87 | 29000 11 | 29840.98 | 29500 12 | 30437.8 | 30000 13 | 31046.56 | 30500

Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 complete this equation to find his brothers age Let b be the brother's age and s be the sister's age. We're given two equations: [LIST=1] [*]s =4b [*]b + s = 20 [/LIST] Plug (1) into (2): b + 4b = 20 [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B4b%3D20&pl=Solve']Type this equation into the search engine[/URL], and we get: [B]b = 4[/B]

Nine times the sum of a number and 6 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The sum of a number and 6 means we add 6 to x: x + 6 9 times the sum: [B]9(x + 6)[/B]

nine times x is twice the sum of x and five Take this algebraic expression in 4 pieces: [U]Step 1: nine time x:[/U] 9x [U]Step 2: The sum of x and five means we add 5 to x:[/U] x + 5 [U]Step 3: The word [I]twice[/I] means we multiply the sum x + 5 by 2:[/U] 2(x + 5) [U]Step 4: The word [I]is[/I] means equal to, so we set 9x equal to 2(x + 5) to get our final algebraic expression of:[/U] [B]9x = 2(x + 5)[/B]

Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend? Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (?2.71828), r is the interest rate expressed as a decimal, and t is the time in years. Round your answer to the nearest cent. [URL='https://www.mathcelebrity.com/simpint.php?av=&p=1000&int=3&t=14&pl=Continuous+Interest']Using our continuous interest calculator[/URL], we get: A = [B]1,521.96[/B]

One number is 3 times another. Their sum is 44. Let the first number be x, and the second number be y. We're given: [LIST=1] [*]x = 3y [*]x + y = 44 [/LIST] Substitute (1) into (2): 3y + y = 44 [URL='https://www.mathcelebrity.com/1unk.php?num=3y%2By%3D44&pl=Solve']Type this equation into the search engine[/URL], and we get: [B]y = 11[/B] Plug this into equation (1): x = 3(11) [B]x = 33[/B]

one number is 3 times as large as another. Their sum is 48. Find the numbers Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x = 3y [*]x + y = 48 [/LIST] Substitute equation (1) into equation (2): 3y + y = 48 To solve for y, [URL='https://www.mathcelebrity.com/1unk.php?num=3y%2By%3D48&pl=Solve']we type this equation into the search engine[/URL] and we get: [B]y = 12[/B] Now, plug y = 12 into equation (1) to solve for x: x = 3(12) [B]x = 36[/B]

One number is 8 times another number. The numbers are both positive and have a difference of 70. Let the first number be x, the second number be y. We're given: [LIST=1] [*]x = 8y [*]x - y = 70 [/LIST] Substitute(1) into (2) 8y - y = 70 [URL='https://www.mathcelebrity.com/1unk.php?num=8y-y%3D70&pl=Solve']Plugging this equation into our search engine[/URL], we get: [B]y = 10[/B] <-- This is the smaller number Plug this into Equation (1), we get: x = 8(10) [B]x = 80 [/B] <-- This is the larger number

One thousand people in. room decide to shake hands with every other person in the room. Instead of one handshake per couple, each person must shake both of the hands of every person in the room with both his right and his left hand. (Tom will use his right hand to shake Dave's right hand and then Dave's left hand. Tom will then use his left hand to shake Dave's right hand and then Dave's left hand.) How many total handshakes will take place? 1000 people taken 2 at a time: [URL='https://www.mathcelebrity.com/permutation.php?num=1000&den=2&pl=Combinations']1000C2[/URL] = 499,500 But each group of 2 makes 4 unique handshakes: 499,500 * 4 = [B]1,998,000[/B]

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. One-half a number means we multiply x by 1/2: x/2 Times fifteen means we multiply: [B]15x/2[/B]

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output is 3 times the input x Let output be y. We have: [B]y = 3x[/B]

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p is equal to r plus 2 times q 2 times q: 2q r plus 2 times q: r + 2q is equal to means we set p equal to r + 2q [B]p = r + 2q[/B]

Pam has two part-time jobs. At one job, she works as a cashier and makes $8 per hour. At the second job, she works as a tutor and makes$12 per hour. One week she worked 30 hours and made$268 . How many hours did she spend at each job? Let the cashier hours be c. Let the tutor hours be t. We're given 2 equations: [LIST=1] [*]c + t = 30 [*]8c + 12t = 268 [/LIST] To solve this system of equations, we can use 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we use, we get the same answer: [LIST] [*]c = [B]23[/B] [*]t = [B]7[/B] [/LIST]

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Distance = Rate x Time 6.4 meters = 4 meters/minute * t Divide each side by 4 [B]t = 1.6 minutes[/B]

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 105 miles per hour. The westbound train travels at 85 miles per hour. How long will it take for the two trains to be 494 miles apart?

Time 1, distance apart is 105 + 85 = 190 So every hour, the distance between them is 190 * t where t is the number of hours. Set up our distance function: D(t) = 190t We want D(t) = 494 190t = 494 Divide each side by 190 [B]t = 2.6 hours[/B]

The sum of three numbers is 105 . The first number is 5 less than the second. The third number is 3 times the second. What are the numbers?

A Web music store offers two versions of a popular song. The size of the standard version is 2.7 megabytes (MB). The size of the high-quality version is 4.7 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 4200 MB. How many downloads of the standard version were there?

A Web music store offers two versions of a popular song. The size of the standard version is 2.7 megabytes (MB). The size of the high-quality version is 4.7 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 4200 MB. How many downloads of the standard version were there? Let s be the standard version downloads and h be the high quality downloads. We have two equations: [LIST=1] [*]h = 3s [*]2.7s + 4.7h = 4200 [/LIST] Substitute (1) into (2) 2.7s + 4.7(3s) = 4200 2.7s + 14.1s = 4200 Combine like terms: 16.8s = 4200 Divide each side by 16.8 [B]s = 250[/B]

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Im not really good with proportion and rates word problems and I need some help with it in my homework If Leah walks 5 miles in 60 minutes, then Leah will walk how far in 110 minutes if she walks at the same speed the whole time? If necessary, round your answer to the nearest tenth of a mile. I wanna know how i get this answer and copy the formula. Please help me thank you.

principal $3000, actual interest rate 5.6%, time 3 years. what is the balance after 3 years [URL='https://www.mathcelebrity.com/compoundint.php?bal=3000&nval=3&int=5.6&pl=Annually']Using our compound interest calculator[/URL], we get a final balance of: [B]$3,532.75[/B]

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Take two arbitrary integers, x and y We can express the odd integer x as 2a + 1 for some integer a We can express the odd integer y as 2b + 1 for some integer b x + y = 2a + 1 + 2b + 1 x + y = 2a + 2b + 2 Factor out a 2: x + y = 2(a + b + 1) Since 2 times any integer even or odd is always even, then [B]x + y by definition is even[/B]. [MEDIA=youtube]9A-qe4yZXYw[/MEDIA]

q increased by the difference between 18 times q and 5 Take this algebraic expression in parts. 18 times q: 18q The difference between 18 times q and 5 means we subtract 5 from 18q: 18q - 5 q increased by the difference between 18 times q and 5 means we add 18q - 5 to q: q + (18q - 5) [B]q + 18q - 5[/B] IF we want to simplify, we group like terms: [B]19q - 5[/B]

q is equal to 207 subtracted from the quantity 4 times q 4 time q 4q 207 subtracted from 4 times q: 4q - 207 Set this equal to q: [B]4q - 207 = q [/B]<-- This is our algebraic expression To solve for q, [URL='https://www.mathcelebrity.com/1unk.php?num=4q-207%3Dq&pl=Solve']type this equation into the search engine[/URL]. We get: [B]q = 69[/B]

Rachel borrowed 8000 at a rate of 10.5%, compounded monthly. Assuming she makes no payments, how much will she owe after 4 years? [U]Convert annual amounts to monthly[/U] 4 years = 12 * 4 = 48 months i = .105/12 = 0.00875 monthly [U]Build our accumulation function A(t) where t is the time in months[/U] A(48) = 8,000 * (1.00875)^48 A(48) = 8,000 * 1.5192 A(48) = [B]12,153.60 [/B] [URL='http://www.mathcelebrity.com/compoundint.php?bal=8000&nval=48&int=10.5&pl=Monthly']You can also use the balance calculator[/URL]

Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will he be paid in the first 4 years? The formula for [U]interest[/U] using simple interest is: I = Prt where P = Principal, r = interest, and t = time. We're given P = 500, r =0.04, and t = 4. So we plug this in and get: I = 500(0.04)(4) I = [B]80[/B]

Reece made a deposite into an account that earns 8% simple interest. After 8 years Reece has earned 400 dollars. How much was Reece's initial deposit? Simple interest formula: A = P(1 + it) where P is the amount of principal to be invested, i is the interest rate, t is the time, and A is the amount accumulated with interest. Plugging in our numbers, we get: 400 = P(1 + 0.08(8)) 400 = P(1 + 0.64) 400 = 1.64P 1.64P = 400 [URL='https://www.mathcelebrity.com/1unk.php?num=1.64p%3D400&pl=Solve']Typing this problem into our search engine[/URL], we get: P = [B]$243.90[/B]

Let x be the price of one t-shirt. Set up an equation: 6 times the number of t-shirts plus 7 dollars left over get him to a total of 45 6x = 45 - 7 6x = 38 Divide each side by 6 [B]x = 6.33[/B]

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Sadie and Connor both play soccer. Connor scored 2 times as many goals as Sadie. Together they scored 9 goals. Could Sadie have scored 4 goals? Why or why not? [U]Assumptions:[/U] [LIST] [*]Let Connor's goals be c [*]Let Sadie's goals be s [/LIST] We're given the following simultaneous equations: [LIST=1] [*]c = 2s [*]c + s = 9 [/LIST] We substitute equation (1) into equation (2) for c: 2s + s = 9 To solve the equation for s, we type it in our search equation and we get: s = [B]3[/B] So [U][B]no[/B][/U], Sadie could not have scored 4 goals since s = 3

Sally can paint a room in 7 hours while it takes Steve 6 hours to paint the same room. How long would it take them to paint the room if they worked together? [URL='http://www.mathcelebrity.com/workcombine.php?w1=+7&w2=+6&pl=Calculate+Combined+Work+Time']Use our work word problem calculator[/URL] [B]3 hours and 13 minutes[/B]

Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64. Let Sally's age be s. Let Mark's age be m. We're given two equations: [LIST=1] [*]s = m + 4 [*]2s + 5m = 64 <-- [I]Since Twice means we multiply by 2[/I] [/LIST] Substitute equation (1) into equation (2): 2(m + 4) + 5m = 64 Multiply through: 2m + 8 + 5m = 64 Group like terms: (2 + 5)m + 8 = 64 7m + 8 = 64 [URL='https://www.mathcelebrity.com/1unk.php?num=7m%2B8%3D64&pl=Solve']Type this equation into the search engine[/URL] and we get: m = [B]8[/B]

Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John Let John's age be j. We're given the following equation: 3j - 20 = 52 ([I]Less than[/I] means we subtract) To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=3j-20%3D52&pl=Solve']type this equation into our search engine[/URL] and we get: j = [B]24[/B]

sample space for flipping a coin 3 times Each flip gives us 2 possible outcomes, heads or tails. So we have: 2 * 2 * 2 = 8 possible outcomes [LIST=1] [*]HHH [*]HHT [*]HTH [*]HTT [*]THH [*]THT [*]TTH [*]TTT [/LIST]

Scientists are studying a cell that divides in half every 15 minutes. How many cells will there by after 2.5 hours? Divide 2.5 hours into 15 minute blocks. 2.5 hours = 2(60) + 0.5(60) minutes 2.5 hours = 120 + 30 minutes 2.5 hours = 150 minutes Now determine the amount of 15 minute blocks 150 minutes/15 minutes = 10 blocks or divisions [LIST] [*]We start with 1 cell at time 0, and double it every 15 minutes [*]We have A(0) = 1, we want A(10). [*]Our accumulation function is A(t) = A(0) * 2^t [/LIST] A(10) = 1 * 2^10 A(10) = [B]1024[/B]

Scott and Dylan both leave the park at the same time, but in opposite directions. If Scott travels 12 mph and Dylan travels 19 mph, how long until they are 186 miles apart? Hour 1, they are 19 + 12 = 31 miles apart. So each hour, they get 31 miles more apart. When they are [URL='https://www.mathcelebrity.com/fraction.php?frac1=186%2F31&frac2=3%2F8&pl=Simplify']186 miles apart[/URL], we divide this by 31 miles apart per hour: 186/31 = [B]6 hours[/B]

Sergeant U has 360 rounds of ammunition to distribute to Lance Corporal (LCpl) F, Lance Corporal (LCpl) M and Lance Corporal (LCpl) Z in the ratio 3:5:7. How many rounds did Lance Corporal (LCpl) M receive? Our ratio denominator is: 3 + 5 + 7 = 15 Lance Corporal (LCpl) M gets 5:15 of the ammunition. [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F15&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we see that 5/15 = 1/3 So we take 360 rounds of ammunition times 1/3: 360/3 = [B]120[/B]

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants it to be 5 times as long as it is wide. What dimensions should the play area be? Sheila wants: [LIST=1] [*]l =5w [*]2l + 2w = 100 <-- Perimeter [/LIST] Substitute (1) into (2) 2(5w) + 2w = 100 10w + 2w = 100 12w = 100 Divide each side by 12 [B]w = 8.3333[/B] Which means l = 5(8.3333) -->[B] l = 41.6667[/B]

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Six Less than the total of three times a number and negative eight. Let's take this in pieces: Three times a number = 3x The total of this and negative eight means we subtract eight 3x - 8 Six Less than this total means we subtract 6 3x - 8 - 6 Simplify by combining like terms: [B]3x - 14[/B]

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. 5 times a number 5x Sixteen subtracted from five times a number 5x - 16 the number plus 4: x + 4 Equals means we set 5x - 16 equals to x + 4 for our algebraic expression: [B]5x - 16 = x + 4[/B] [B][/B] If you have to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-16%3Dx%2B4&pl=Solve']type this expression into our math solver[/URL] and we get: x = [B]5[/B]

Some scientists believe that there are 10^87 atoms in the entire universe. The number googolplex is a 1 followed by a googol of zeros. If each atom in the universe is used as a zero, how many universes would you need in order to have enough zeros to write out completely the number googolplex? 10^100 zeros in the entire googolplex and 10^87 atoms in the universe 10^100 / 10^87 = [B]10^13 times as many zeros in the googolplex as there are atoms in the universe[/B]

Sonia visited a park in California that had redwood trees. When Sonia asked how tall a certain large redwood tree was, the ranger said that he wouldn't tell its height, but would give Sonia a clue. How tall is the redwood tree Sonia asked about? Sonia said the tree is 64 times my height. The tree is also 112 feet taller than the tree next to it. The two trees plus my height total 597.5 feet. [LIST] [*]Rangers's height = n [*]Tree height = 64n [*]Smaller tree height = 64n - 112 [*]Total height = 64n - 112 + 64n = 597.5 [/LIST] Solve for [I]n[/I] in the equation 64n - 112 + 64n = 597.5 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (64 + 64)n = 128n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 128n - 112 = + 597.5 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -112 and 597.5. To do that, we add 112 to both sides 128n - 112 + 112 = 597.5 + 112 [SIZE=5][B]Step 4: Cancel 112 on the left side:[/B][/SIZE] 128n = 709.5 [SIZE=5][B]Step 5: Divide each side of the equation by 128[/B][/SIZE] 128n/128 = 709.5/128 n = 5.54296875 Tree height = 64 * ranger height Tree height = 64 * 5.54296875 Tree height = [B]354.75 feet[/B]

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square root of x times the square root of y square root of x: sqrt(x) square root of y: sqrt(y) square root of x times the square root of y [B]sqrt(x) * sqrt(y)[/B]

Squaring a number equals 5 times that number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Squaring this number: x^2 5 times this number means we multiply by 5: 5x The phrase [I]equals[/I] means we set both expressions equal to each other: [B]x^2 = 5x [/B] <-- This is our algebraic expression If you want to solve for x, then we subtract 5x from each side: x^2 - 5x = 5x - 5x Cancel the 5x on the right side, leaving us with 0: x^2 - 5x = 0 Factor out x: x(x - 5) So we get x = 0 or [B]x = 5[/B]

Stacy and Travis are rock climbing. Stacys rope is 4 feet shorter than 3 times the length of Travis rope. Stacys rope is 23 feet long. Write and solve an equation to find the length t of Travis rope. Let Stacy's rope be s. Travis's rope be t. We have: s = 3t - 4 s = 23 So [B]3t - 4 = 23 [/B] [URL='http://www.mathcelebrity.com/1unk.php?num=3t-4%3D23&pl=Solve']Paste this equation into our search engine[/URL] to get [B]t = 9[/B].

Start with x , subtract 6, then times by 3. We start with x: x Subtract 6: x - 6 The phrase [I]times by[/I] means we multiply (x - 6) by 3 [B]3(x - 6) [/B] <-- This is our algebraic expression If the problem asks you to multiply through, then you'd have: 3x - 18

Free Straight Line Depreciation Calculator - Solves for Depreciation Charge, Asset Value, Salvage Value, Time, N, and Book Value using the Straight Line Method.

Stuart traveled n miles at a speed of 72 miles per hour. How many seconds did it take Stuart to travel the n miles? Distance = Rate * Time Time = Distance/Rate Time = n/72 hours 3600 seconds per hour so we have: 3600n/72 [B]50n[/B]

Subtract 6 from 7 times s 7 times s 7s Subtract 6 from that [B]7s - 6[/B]

sum of 5 times h and twice g is equal to 23 Take this [U]algebraic expressions[/U] problem in pieces. Step 1: 5 times h: 5h Step 2: Twice g means we multiply g by 2: 2g Step 3: sum of 5 times h and twice g means we add 2g to 5h 5h + 2g Step 4: The phrase [I]is equal to[/I] means an equation, so we set 5h + 2g equal to 23: [B]5h + 2g = 23[/B]

sum of twice w and 3 times l Twice w means we multiply w by 2: 2w 3 times l: 3l When we see the phrase [I]sum of[/I], we add: [B]2w + 3l[/B]

SuperFit Gym charges $14 per month, as well as a one-time membership fee of $25 to join. After how many months will I spend a total of $165? [U]Let the number of months be m. We have a total spend T of:[/U] cost per month * m + one-time membership fee = T [U]Plugging in our numbers, we get:[/U] 14m + 25 = 165 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=14m%2B25%3D165&pl=Solve']type it in our search engine[/URL] and we get: m = [B]10[/B]

Suppose a firm producing light bulbs wants to know if it can claim that its light bulbs it produces last 1,000 burning hours (u). To do this, the firm takes a random sample of 100 bulbs and find its average life time (X=980 hrs) and the sample standard deviation s = 80 hrs. If the firm wants to conduct the test at the 1% of significance, what's you final suggestion? (i..e, Should the producer accept the Ho that its light bulbs have a 1,000 burning hrs. at the 1% level of significance?) Ho: u = 1,000 hours. Ha: u <> 1,000 hours. [URL='http://www.mathcelebrity.com/mean_hypothesis.php?xbar=+980&n=+100&stdev=+80&ptype==&mean=+1000&alpha=+0.01&pl=Mean+Hypothesis+Testing']Perform a hypothesis test of the mean[/URL] [B]Yes, accept null hypothesis[/B]

Suppose Rocky Mountain have 72 centimeters of snow. Warmer weather is melting at the rate of 5.8 centimeters a day. If snow continues to melt at this rate, after seven days of warm weather, how much snow will be left? Snow remaining = Starting snow - melt rate * days Snow remaining = 72 - 5.8(7) Snow remaining = 72 - 40.6 Snow remaining = [B]31.4 cm[/B]

Suppose that you have just purchased a car for $40,000. Historically, the car depreciates by 8% each year, so that next year the car is worth $40000(.92). What will the value of the car be after you have owned it for three years? Book Value B(t) at time t is B(t) = 40,000(1-0.08)^t or B(t) = 40,000(0.92)^t At t = 3 we have: B(3) = 40,000(0.92)^3 B(3) = 40,000 * 0.778688 B(3) = [B]31,147.52[/B]

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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. Twice a number means we multiply x by 2: 2x The sum of twice a number and 6: 2x + 6 Ten times the sum of twice a number and six [B]10(2x + 6)[/B]

Terry recorded the temperature every hour from 8 AM to 1 PM. The temperature at 8 AM was 19?. The temperature dropped 4? every hour. What was the temperature at 1 PM? Group of answer choices 1 degree Set up our temperature function T(h) where h is the number of hours since 8 AM: T(h) = 19 - 4h <-- We subtract 4h since each hour, the temperature drops 4 degrees The questions asks for the temperature at 1PM. We need to figure out how many hours pass since 8 AM: 8 AM to 12 PM is 4 hours 12 PM to 1 PM is 1 hour Total time is 5 hours So we want T(5): T(5) = 19 - 4(5) T(5) = 19 - 20 T(5) = [B]-1?[/B]

The 4/7 part of a number is 84 . What is the number? We multiply 4/7 * 84. 7 goes into 84 12 times, so we have: 4 * 12 = [B]48[/B]

The anti-inflammation drug Advil has a half-life of 2 hours. That is, the amount of the drug present in the body is halved every two hours. What fraction of the initial amount of the drug will be left in the body after 4 hours? [LIST] [*]At time 0, we have 100% [*]At time 2, we have 100% * 1/2 = 50% or 1/2 [*]At time 4, we have 1/2 * 1/2 = [B]1/4[/B] [/LIST]

The area of a desert in Africa is 12 times the area of a desert in Asia. If the area of a desert in Asia is Y square miles, express the area of a desert in Africa as an algebraic expression in Y. [B]Africa Area = 12Y[/B]

The cost of a gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a gallon of milk cost 3.75, what is the cost of a gallon of water? We're given: m = 5w + 0.50 m = $3.75 Set them equal to each other: 5w + 0.50 = 3.75 [URL='https://www.mathcelebrity.com/1unk.php?num=5w%2B0.50%3D3.75&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 0.65[/B]

The cube of the difference of 5 times the square of y and 7 divided by the square of 2 times y Take this in algebraic expression in parts: [U]Term 1[/U] [LIST] [*]The square of y means we raise y to the 2nd power: y^2 [*]5 times the square of y: 5y^2 [/LIST] [U]Term 2[/U] [LIST] [*]2 times y: 2y [*]The square of 2 times y: (2y)^2 = 4y^2 [*]7 divide by the square of 2 times y: 7/4y^2 [/LIST] [U]The difference of these terms is written as Term 1 minus Term 2:[/U] [LIST] [*]5y^2/4y^2 [/LIST] [U]The cube of the difference means we raise the difference to the power of 3:[/U] [B](5y^2/4y^2)^3[/B]

the cube of the difference of 5 times x and 4 Take this algebraic expression in pieces: 5 times x: 5x The difference of 5x and 4 means we subtract 4 from 5x: 5x - 4 We want to cube this difference, which means we raise the difference to the power of 3. [B](5x - 4)^3[/B]

The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. What are the numbers? Let the smaller number be x. Let the larger number be y. We're given: [LIST=1] [*]y - x = 108 [*]6x = y + 2 [/LIST] Rearrange (1) by adding x to each side: [LIST=1] [*]y = x + 108 [/LIST] Substitute this into (2): 6x = x + 108 + 2 Combine like terms 6x = x +110 Subtract x from each side: 5x = 110 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D110&pl=Solve']Plugging this equation into our search engine[/URL], we get: x = [B]22[/B]

[U]3 times x:[/U] 3x [U]The difference between 3x and 4 means we subtract:[/U] 3x - 4

the difference between 7 times a number and 9 less than a number 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 9 less than a number means we subtract 9 from x x - 9 The difference between the two expressions means we subtract (x - 9) from 7x 7x - (x - 9) Simplifying this, we have: 7x - x + 9 Grouping like terms, we get: [B]6x + 9[/B]

The difference between two numbers is 96. One number is 9 times the other. What are the numbers? Let x be the first number Let y be the second number We're given two equations: [LIST=1] [*]x - y = 96 [*]x = 9y [/LIST] Substitute equation (2) into equation (1) for x 9y - y = 96 [URL='https://www.mathcelebrity.com/1unk.php?num=9y-y%3D96&pl=Solve']Plugging this equation into our math engine[/URL], we get: y = [B]12 [/B] If y = 12, then we plug this into equation 2: x = 9(12) x = [B]108[/B]

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number? We have two expressions: [U]Expression 1: [I]The difference of a number and 6[/I][/U] The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The difference of a number and 6 means we subtract 6 from x: x - 6 [U]Expression 2: [I]5 times the sum of the number and 2[/I][/U] The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The sum of a number and 2 means we add 2 to x: x + 2 5 times the sum means we multiply x + 2 by 5 5(x + 2) [U]For the last step, we evaluate the expression [I]is the same as[/I][/U] This means equal to, so we set x - 6 equal to 5(x + 2) [B]x - 6 = 5(x + 2)[/B]

The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown number. The phrase a number uses the variable w. 3 times w is written as 3w The difference of 3w and 6 is written as 3w - 6 Set this equal to 7 [B]3w - 6 = 7 [/B] This is our algebraic expression. To solve this equation for w, we [URL='http://www.mathcelebrity.com/1unk.php?num=3w-6%3D7&pl=Solve']type the algebraic expression into our search engine[/URL].

the difference of x and 5 is 2 times of x The difference of x and 5 means we subtract 5 from x x - 5 The word [I]is[/I] means an equation, so we set x - 5 equal to 2 times x [B]x - 5 = 2x[/B]

The distance traveled in t hours by a car traveling at 65 miles per hour. Distance = Rate * Time Distance = 65 mph * t hours Distance = [B]65t[/B]

The doctor told Anna that tomorrow she will have to check her blood pressure every 15 minutes from 10:00 AM to 4:00 PM. How many times does she have to take her blood pressure? 10:00 A.M. to 4:00 P.M. is 6 hours. Each hour is 60 minutes 60 minutes divided by 15 minutes equals 4 blood pressure checks per hour. 4 blood pressure checks per hour * 6 hours = [B]24 blood pressure checks[/B]

The doubling time of a population of flies is 8 hours. a) By what factor does a population increase in 24 hours? b) By what factor does the population increase in 2 weeks? a) If the population doubles every 8 hours, then it doubles 3 times in 24 hours, since 24/8 = 3. So 2 * 3 = 6. The increase factor is [B]6[/B] b) Since a) is one full day, we now need to know how much it doubles in 14 days, which is 2 weeks. We take our factor of 6 for each day, and multiply it by 14: 14 * 6 = [B]84[/B]

The earth makes a full rotation in 24 hours. Jupiter takes approximately 58 days, 15 h, and 30 min to complete a full rotation. How many hours does it take Jupiter to complete a full rotation? Show your work using the correct conversion factors. Convert 58 days, 15 h, and 30 min to hours. [LIST=1] [*]Type [URL='https://www.mathcelebrity.com/timecon.php?quant=58&pl=Calculate&type=day']58 days[/URL] into the search engine to get 1,392 hours. [*]Add 15 hours to get 1,392 + 15 = 2,007 hours [*]Now convert the 30 min to hours. [URL='https://www.mathcelebrity.com/timecon.php?quant=30&pl=Calculate&type=minute']Type 30 minutes into the search engine[/URL] to get 0.5 hours [*]Add up (1), (2), and (3) to get 1,392 + 15 + 0.5 = [B]2007.5[/B] hours for a full rotation. [/LIST]

The famous Concorde jet travelled at a speed of 2000km/h for two and a half hours. Do you think it could make it to its destination which is 5500km away on time Calculate the total distance traveled @ 2000km/h for 2.5 hours: d = rt d = 2000 * 2.5 d = 5,000 km The answer is [B]no, it cannot make the destination[/B].

The famous mathematician Pythagoras founded the Mathematical Brotherhood in 530 BC. About how many years ago did this happen? BC means before year 0. So we take the current year, which at the time of this post, is 2021. We [U]add[/U] 530 years to that since BC is before year 0, and we get: 2021 + 530 = [B]2551 years ago[/B]

The fastest student in gym class runs 50 meters in 7.4 seconds. The slowest time in the class was 4.36 seconds slower than the fastest time. Slowest time = 7.4 - 4.36 Slowest time = [B]3.04[/B]

the grass in jamie’s yard grew 16 centimeters in 10 days. how many days did it take for the grass to grow 1 centimeter We set up a proportion of centimeters to days where d is the number of days it takes for the grass to grow 1 centimeter: 16/10 = 1/d To solve this proportion for d, [URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=1&den1=10&den2=d&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get: d = [B]0.625 or 5/8[/B]

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +300. Find the average velocity of the object during the first 3 seconds? (b) Use the Mean value Theorem to verify that at some time during the first 3 seconds of the fall the instantaneous velocity equals the average velocity. Find that time. Average Velocity: [ f(3) - f(0) ] / ( 3 - 0 ) Calculate f(3): f(3) = -4.9(3^2) + 300 f(3) = -4.9(9) + 300 f(3) = -44.1 + 300 f(3) = 255.9 Calculate f(0): f(0) = -4.9(0^2) + 300 f(0) = 0 + 300 f(0) = 300 So we have average velocity: Average velocity = (255.9 - 300)/(3 - 0) Average velocity = -44.1/3 Average velocity = -[B]14.7 [/B] Velocity is the first derivative of position s(t)=-4.9t^2 +300 s'(t) = -9.8t So we set velocity equal to average velocity: -9.8t = -14.7 Divide each side by -9.8 to solve for t, we get [B]t = 1.5[/B]

The larger of 2 numbers is 1 more than 3 times the smaller number. Let the larger number be l. Let the smaller number be s. The algebraic expression is: 3 times the smaller number is written as: 3s 1 more than that means we add 1 3s + 1 Our final algebraic expression uses the word [I]is[/I] meaning an equation. So we set l equal to 3s + 1 [B]l = 3s + 1[/B]

The length of a rectangle is three times its width.If the perimeter is 80 feet, what are the dimensions? We're given 2 equations: [LIST=1] [*]l = 3w [*]P = 80 = 2l + 2w = 80 [/LIST] Substitute (1) into (2) for l: 2(3w) + 2w = 80 6w + 2w = 80 8w = 80 Divide each side by 8: 8w/8 = 80/8 w = [B]10 [/B] Substitute w = 10 into (1) l = 3(10) l = [B]30[/B]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building. P = 2l + 2w Since P = 120, we have: (1) 2l + 2w = 120 We are also given: (2) l = 3w - 6 Substitute equation (2) into equation (1) 2(3w - 6) + 2w = 120 Multiply through: 6w - 12 + 2w = 120 Combine like terms: 8w - 12 = 120 Add 12 to each side: 8w = 132 Divide each side by 8 to isolate w: w =16.5 Now substitute w into equation (2) l = 3(16.5) - 6 l = 49.5 - 6 l = 43.5 So (l, w) = (43.5, 16.5)

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building. Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangular word problem calculator[/URL], we have: [LIST] [*][B]l = 43.5[/B] [*][B]w = 16.5[/B] [/LIST]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building. Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangle word problem calculator[/URL], we get: [LIST] [*][B]w = 16.5[/B] [*][B]l = 43.5[/B] [/LIST]

The length of a train car is 50.6 feet. This is 5.8 feet less than 6 times the width. What is the width? 5.8 feet less than 6 times the width is an algebraic expression: 6w - 5.8 We set this equal to the length of 50.6 6w - 5.8 = 50.6 Add 5.8 to each side: 6w - 5.8 + 5.8 = 50.6 + 5.8 Cancel the 5.8 on the left side: 6w = 56.4 Divide each side by 6: 6w/6 = 56.4/6 [URL='http://www.mathcelebrity.com/1unk.php?num=6w-5.8%3D50.6&pl=Solve']Typing this problem into the search engine[/URL], we get [B]w = 9.4[/B]. [MEDIA=youtube]gfM-d_Ej728[/MEDIA]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. Find the dimensions of Sally’s garden. Gardens have a rectangle shape. Perimeter of a rectangle is 2l + 2w. We're given: [LIST=1] [*]l = 3w + 4 [I](3 times the width Plus 4 since greater means add)[/I] [*]2l + 2w = 72 [/LIST] We substitute equation (1) into equation (2) for l: 2(3w + 4) + 2w = 72 Multiply through and simplify: 6w + 8 + 2w = 72 (6 +2)w + 8 = 72 8w + 8 = 72 To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B8%3D72&pl=Solve']type it in our search engine[/URL] and we get: w = [B]8 [/B] To solve for l, we substitute w = 8 above into Equation (1): l = 3(8) + 4 l = 24 + 4 l = [B]28[/B]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters A garden is a rectangle, which has perimeter P of: P = 2l + 2w With P = 72, we have: 2l + 2w = 72 We're also given: l = 3w + 4 We substitute this into the perimeter equation for l: 2(3w + 4) + 2w = 72 6w + 8 + 2w = 72 To solve this equation for w, we t[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B8%2B2w%3D72&pl=Solve']ype it in our search engine[/URL] and we get: w =[B] 8[/B] Now, to solve for l, we substitute w = 8 into our length equation above: l = 3(8) + 4 l = 24 + 4 l = [B]28[/B]

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length and width. A flag is a rectangle shape. So we have the following equations Since P = 2l + 2w, we have 2l + 2w = 60 l = 7w - 2 Substitute Equation 1 into Equation 2: 2(7w -2) + 2w = 60 14w - 4 + 2w = 60 16w - 4 = 60 Add 4 to each side 16w = 64 Divide each side by 16 to isolate w w = 4 Which means l = 7(4) - 2 = 28 - 2 = 26

The negative of the sum of C and D is equal to the difference of the negative of C and D The negative of the sum of C and D means -1 times the sum of C and D -(C + D) Distribute the negative sign: -C - D the difference of the negative of C and D means we subtract D from negative C -C - D So this statement is [B]true[/B] since -C - D = -C - D

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days. What is the median recovery time? a. 2.7 b. 5.3 c. 7.4 d. 2.1 [B]b. 5.3 (mean, median, and mode are all the same in a normal distribution)[/B]

The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Find the length and the width of the rectangle. l = 4w - 15 Perimeter = 2l + 2w Substitute, we get: 400 = 2(4w - 15) + 2w 400 = 8w - 30 + 2w 10w - 30 = 400 Add 30 to each side 10w = 370 Divide each side by 10 to isolate w w = 37 Plug that back into our original equation to find l l = 4(37) - 15 l = 148 - 15 l = 133 So we have (l, w) = (37, 133)

The population of a town doubles every 12 years. If the population in 1945 was 11,005 people, what was the population in 1981? Calculate the difference in years: Difference = 1981 - 1945 Difference = 36 Calculate doubling periods: Doubling periods = Total years / Doubling time Doubling periods = 36/12 Doubling periods = 3 Population = Initial Population * 2^doubling periods Population = 11005 * 2^3 Population = 11005 * 8 Population = [B]88,040[/B]

The population of goats on a particular nature reserve t years after the initial population was settled is modeled by p(t) = 4000 - 3000e^-0.2t. How many goats were initially present? [U]Initially present means at time 0. Substituting t = 0, p(0), we get:[/U] p(0) = 4000 - 3000e^-0.2(0) p(0) = 4000 - 3000e^0 p(0) = 4000 - 3000(1) p(0) = 4000 - 3000 [B]p(0) = 1000[/B]

the product of k and 70, minus 15 Take this algebraic expression in pieces: The product of k and 70 means we multiply 70 times k 70k The word [I]minus[/I] means we subtract 15 from 70k [B]70k - 15[/B]

the reciprocal of the product a and b Take this algebraic expression in pieces: The product a and b means we multiply a times b ab The [I]reciprocal[/I] means we take 1 over ab [B]1/ab[/B]

The relief time provided by a standard dose of a popular children’s allergy medicine averages 7.9 hours with a standard deviation of 2.2 hours. Use Table 1. a. Determine the percentage of children who experience relief for less than 6.4 hours if the relief time follows a normal distribution. (Round your answer to 2 decimal places.) Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=6.4&mean=7.9&stdev=2.2&n=1&pl=P%28X+%3C+Z%29']normal distribution calculator[/URL], we get Answer = [B]0.25[/B]

The singular form of the word "dice" is "die". Tom was throwing a six-sided die. The first time he threw, he got a three; the second time he threw, he got a three again. What's the probability of getting a three at the third time? Since all trials are independent: 1/6 * 1/6 * 1/6 = [B]1/216[/B]

The square of a number is always nonnegative. This is true, and here is why: Suppose you have a positive number n. n^2 = n * n A positive times a positive is a positive Suppose you have a negative number -n (-n)^2 = -n * -n = n^2 A negative times a negative is a positive.

The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers? Let the first number be x. And the second number be y. We're given: [LIST=1] [*]y = x + 1 [*]x + y = 3x - 3 (less 3 means subtract 3) [/LIST] Substitute (1) into (2): x + x + 1 = 3x - 3 Combine like terms: 2x + 1 = 3x - 3 [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B1%3D3x-3&pl=Solve']Type this equation into the search engine[/URL], we get: x = 4 Substituting x = 4 into equation 1: y = 4 + 1 y = 5 So (x, y) = [B](4, 5)[/B]

The sum of 2 numbers is 18. 3 times the greater number exceeds 4 times the smaller number by 5. Find the numbers. Let the first number be x. The second number is y. We have: [LIST=1] [*]x + y = 18 [*]3x = 4y + 5 [/LIST] Rearrange (2), by subtracting 4y from each side: 3x - 4y = 5 So we have a system of equations: [LIST=1] [*]x + y = 18 [*]3x - 4y = 5 [/LIST] Using our [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y+%3D+18&term2=3x+-+4y+%3D+5&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: [B]x = 11 y = 7[/B]

the sum of 2 numbers is 5. 5 times the larger number plus 4 times the smaller number is 37. Find the numbers Let the first small number be x. Let the second larger number be y. We're given: [LIST=1] [*]x + y = 5 [*]5y + 4x = 37 [/LIST] We can solve this 3 ways, using the following methods: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [B]x = -12 y = 17 [/B] Let's check our work using equation 1: -12 + 17 ? 5 5 = 5 <-- Check Let's check our work using equation 2: 5(17) + 4(-12) ? 37 85 - 48 ? 37 37 = 37 <-- Check

the sum of 2 times a number and -2, added to 4 times a number. The phrase, [I]a number[/I], means an arbitrary variable, let's call it x. 2 times a number 2x The sum of means add, so we add -2, which is the same as subtracting 2 2x - 2 Now, we add 4 times x 2x - 2 + 4x Combining like terms, we have: (2 + 4)x - 2 [B]6x - 2[/B]

the sum of 2 times x and 3 times y diminished by 12 2 times x: 2x 3 times y: 3y the sum of 2 times x and 3 times y 2x + 3y the sum of 2 times x and 3 times y diminished by 12 [B]2x + 3y - 12[/B]

The sum of 2 times x and 5 times y is 7 2 times x: 2x 5 times y: 5y The sum of 2 times x and 5 times y: 2x + 5y The word [I]is[/I] means equal to, so we set 2x + 5y equal to 7: [B]2x + 5y = 7[/B]

The sum of 3 times the square of a number and negative 7 [U]The phrase [I]a number[/I] means an arbitrary variable, let's call it x:[/U] x [U]The square of a number means we raise x to the power of 2:[/U] x^2 [U]3 times the square of a number:[/U] 3x^2 [U]The sum of 3 times the square of a number and negative 7[/U] [B]3x^2 - 7[/B]

the sum of 5 times p and 10 5 times p 5p and 10 means add 10 [B]5p + 10[/B]

the sum of 6 and 7, plus 5 times a number, is -12 The sum of 6 and 7 means we add the two numbers: 6 + 7 This evaluates to 13 Next, we take 5 times a number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So we multiply x by 5: 5x The first two words say [I]the sum[/I], so we add 13 and 5x 13 + 5x The word [I]is[/I] means an equation, so we set 13 + 5x equal to -12 [B]13 + 5x = -12[/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=13%2B5x%3D-12&pl=Solve']type this algebraic expression into our search engine[/URL] and you get: [B]x = -5[/B]

The sum of 6 times a number and -8, added to 3 times a number The phrase "a number", means an arbitrary variable, let's call it x. 6 times a number: 6x And means we add, so we have 6x - 8 Added to 3 times a number 6x - 8 + 3x Combine like terms: [B]9x - 8[/B]

the sum of 7 times y and 3 is equal to 2 7 times y: 7y The sum of 7 times y and 3 means we add 3 to 7y 7y + 3 The phrase [I]is equal to[/I] means an equation, so we set 7y + 3 equal to 2 [B]7y + 3 = 2[/B]

The sum of a number and 34 times the number The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. x 34 times the number: 34x The sum of a number and 34 times the number means we add both terms together: x + 34x

the sum of a number times 3 and 30 is less than 17 A number is denoted as an arbitrary variable, let's call it x. x Times 3 means we multiply x by 3: 3x The sum of a number times 3 and 30 means we add 30 to 3x above 3x + 30 Is less than 17 means we have an inequality, so we set 3x + 30 less than 17 3x + 30 < 17 To solve for x and see the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B30%3C17&pl=Solve']our calculator[/URL]:

The sum of six times a number and 1 is equal to five times the number. Find 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 the sum of six times a number and 1 is written as: 6x + 1 Five times the number is written as: 5x The phrase [I]is equal to[/I] means an equation, so we set 6x + 1 equal to 5x: 6x + 1 = 5x [URL='https://www.mathcelebrity.com/1unk.php?num=6x%2B1%3D5x&pl=Solve']Plugging this into our search engine[/URL], we get: x = [B]-1[/B]

The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now? Let Levi's current age be l. Let Renee's current age be r. Were given two equations: [LIST=1] [*]l + r = 89 [*]l - 7 = 4(r - 7) [/LIST] Simplify equation 2 by multiplying through: [LIST=1] [*]l + r = 89 [*]l - 7 = 4r - 28 [/LIST] Rearrange equation 1 to solve for r and isolate l by subtracting l from each side: [LIST=1] [*]r = 89 - l [*]l - 7 = 4r - 28 [/LIST] Now substitute equation (1) into equation (2): l - 7 = 4(89 - l) - 28 l - 7 = 356 - 4l - 28 l - 7 = 328 - 4l To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l-7%3D328-4l&pl=Solve']type the equation into our search engine[/URL] and we get: l = [B]67[/B]

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times the unit digit. Find the number. Let the digits be (x)(y) where t is the tens digit, and o is the ones digit. We're given: [LIST=1] [*]x + y = 10 [*]10x+ y = 15y + 4 [/LIST] Simplifying Equation (2) by subtracting y from each side, we get: 10x = 14y + 4 Rearranging equation (1), we get: x = 10 - y Substitute this into simplified equation (2): 10(10 - y) = 14y + 4 100 - 10y = 14y + 4 [URL='https://www.mathcelebrity.com/1unk.php?num=100-10y%3D14y%2B4&pl=Solve']Typing this equation into our search engine[/URL], we get: y = 4 Plug this into rearranged equation (1), we get: x = 10 - 4 x = 6 So our number xy is [B]64[/B]. Let's check our work against equation (1): 6 + 4 ? 10 10 = 10 Let's check our work against equation (2): 10(6)+ 4 ? 15(4) + 4 60 + 4 ? 60 + 4 64 = 64

The sum of the square of a number and 7 times a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x Square the number: x^2 7 times the number means we multiply x by 7: 7x The sum means we add x^2 and 7x [B]x^2 + 7x[/B]

The Sum of three times a number and 18 is -39. Find the number. A number means an arbitrary variable, let us call it x. Three times x: 3x The sum of this and 18: 3x + 18 Is means equal to, so we set 3x + 18 = -39 3x + 18 = -39 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']equation solver[/URL], we get [B]x = -19[/B]

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. 3 times a number: 3x The sum of three times a number and twelve means we add 12 to 3x: [B]3x + 12[/B]

The sum of twice an integer and 3 times the next consecutive integer is 48 Let the first integer be n This means the next consecutive integer is n + 1 Twice an integer means we multiply n by 2: 2n 3 times the next consecutive integer means we multiply (n + 1) by 3 3(n + 1) The sum of these is: 2n + 3(n + 1) The word [I]is[/I] means equal to, so we set 2n + 3(n + 1) equal to 48: 2n + 3(n + 1) = 48 Solve for [I]n[/I] in the equation 2n + 3(n + 1) = 48 We first need to simplify the expression removing parentheses Simplify 3(n + 1): Distribute the 3 to each term in (n+1) 3 * n = (3 * 1)n = 3n 3 * 1 = (3 * 1) = 3 Our Total expanded term is 3n + 3 Our updated term to work with is 2n + 3n + 3 = 48 We first need to simplify the expression removing parentheses Our updated term to work with is 2n + 3n + 3 = 48 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (2 + 3)n = 5n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 5n + 3 = + 48 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 3 and 48. To do that, we subtract 3 from both sides 5n + 3 - 3 = 48 - 3 [SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE] 5n = 45 [SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE] 5n/5 = 45/5 Cancel the 5's on the left side and we get: n = [B]9[/B]

The sum of x and 10 equals the sum of 2 times x and 12 The sum of x and 10 means we add 10 to x: x + 10 2 times x means we multiply x by 2: 2x the sum of 2 times x and 12 means we add 12 to 2x: 2x + 12 The sum of x and 10 equals the sum of 2 times x and 12: x + 10 + (2x + 12) Distribute the parentheses, and we get: x + 10 + 2x + 12 Group like terms: (1 + 2)x + 10 + 12 [B]3x + 22[/B]

The temperature when Spencer arrived at school was a very chilly – 4°F. By the time school got out, the temperature had risen 13°F. What was the temperature when school got out? -4 + 13 = [B]9 degrees[/B]

The top part of the tree is 3 times as long as the trunk which equation can tulia use to find t the length of the trunk Let p be the top part of the tree. We have p = 3t. Divide by 3, we get t = [B]p/3[/B]

the total of 3 times the cube of u and the square of u [U]The cube of u means we raise u to the power of 3:[/U] u^3 [U]The square of u means we raise u to the power of 2:[/U] u^2 The total of both of these is found by adding them together: [B]u^3 + u^2[/B]

The value of 3 times the quantity of 4 + x is greater than 6 less than x. 3 times the quantity 4 + x 3(4 + x) 6 less than x x - 6 3 times the quantity 4 + x is greater than x - 6 [B]3(4 + x) > x - 6[/B]

The value of a company van is $15,000 and decreased at a rate of 4% each year. Approximate how much the van will be worth in 7 years. Each year, the van is worth 100% - 4% = 96%, or 0.96. We have the Book value equation: B(t) = 15000(0.96)^t where t is the time in years from now. The problem asks for B(7): B(7) = 15000(0.96)^7 B(7) = 15000(0.7514474781) B(7) = [B]11,271.71[/B]

The world record for the mile in the year 1865 was held by Richard Webster of England when he completed a mile in 4 minutes and 36.5 seconds. The world record in 1999 was set by Hicham El Guerrouj when he ran a mile in 3 minutes and 43.13 seconds. If both men ran the mile together, how many feet behind would Richard Webster be when Hichem El Guerrouj crossed the finish line? Change times to seconds: [LIST] [*]4 minutes and 36.5 seconds = 4*60 + 36.5 = 240 + 36.5 = 276.5 seconds [*]3 minute and 43.13 seconds = 3*60 + 43.13 = 180 + 43.13 = 223.13 seconds [/LIST] Now, find the distance Richard Webster travelled in 3 minutes and 43.13 seconds which is when Hiram El Guerrouj crossed the finish line. 1 mile = 5280 feet: Set up a proportion of distance in feet to seconds where n is the distance Richard Webster travelled 5280/276.5 = n/223.13 Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5280&num2=n&den1=276.5&den2=223.13&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get: n = 4260.85 feet Distance difference = 5280 - 4260.85 = [B]1019.15 feet[/B]

There are 10 true or false questions on a test. You do not know the answer to 4 of the questions, so you guess. What is the probability that you will get all 4 answers right? Probability you guess right is 1/2 or 0.5. Since each event is independent of the other events, we multiply 1/2 4 times: 1/2 * 1/2 * 1/2 * 1/2 = [B]1/16[/B]

There are 15 houses in a neighborhood. Nine of the houses have 6 people in them. The remaining houses have 4 people in them. How many people are in a neighborhood. 9 houses * 6 people per house = 54 people The remaining houses equal 15 total houses - 9 houses = 6 houses 6 houses remaining times 4 people in each house = 24 people 54 people + 24 people = [B]78 people in the neighborhood[/B]

There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much time should we spend sleeping? Multiply 24 hours per day * 3/8 day Since 24/8 = 3, we have: 3 * 3 = [B]9 hours of sleep[/B].

There are 24 hours in a day and scientists tell us that we should sleep for 3/8 of the day. How much time should we spend sleeping? 3/8 of the day means we take 3/8 of 24 also written as: 3/8 * 24 We [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F8&frac2=24&pl=Multiply']type this expression into our search engine [/URL]and get: [B]9 hours[/B]

There are 30 students in a classroom. Eighteen students read [I]A Wrinkle in Time[/I] while 22 children read [I]The Hobbit[/I]. If all children read at least one of the books, how many read both books? 30 - 18 = 12 students read the Hobbit only 30 - (12 + 8) = [B]10 students who read both[/B]

There are 480 calories per hour. An officer swims 1.5 hours for 30 days. How many calories is that? 1.5 hours per day times 30 days = 45 total hours. 480 calories per hour times 45 total hours = [B]21,600 total calories[/B].

There are two bells in the school. Bell A rings every 2 minutes. Bell B rings every 3 minutes. If both bells ring together at 8.02 p.m., when will they ring together again? Using our[URL='http://www.mathcelebrity.com/gcflcm.php?num1=2&num2=3&num3=&pl=LCM'] least common multiple calculator,[/URL] we find the LCM(2, 3) = 6. Which means the next time both bells ring together is 6 minutes from now. 8:02 p.m. + 6 minutes = [B]8:08 p.m.[/B]

There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The difference between 2 times the first number and 3 times the second number is 24. Find the two numbers. Let the first number be x and the second number be y. We have 2 equations: [LIST=1] [*]4x + 3y = 24 [*]2x - 3y = 24 [/LIST] Without doing anything else, we can add the 2 equations together to eliminate the y term: (4x + 2x) + (3y - 3y) = (24 + 24) 6x = 48 Divide each side by 6: [B]x = 8 [/B] Substitute this into equation (1) 4(8) + 3y = 24 32 + 3y = 24 [URL='https://www.mathcelebrity.com/1unk.php?num=32%2B3y%3D24&pl=Solve']Type 32 + 3y = 24 into our search engine[/URL] and we get [B]y = 2.6667[/B].

There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 blue? Find the total number of marbles in the bag: Total marbles = 5 blue + 6 red + 2 green Total marbles = 13 The problem asks for exactly one blue in 2 draws [I]with replacement[/I]. Which means you could draw as follows: Blue, Not Blue Not Blue, Blue The probability of drawing a blue is 5/13, since we replace the marbles in the bag each time. The probability of not drawing a blue is (6 + 2)/13 = 8/13 And since each of the 2 draws are independent of each other, we multiply the probability of each draw: Blue, Not Blue = 5/13 * 8/13 =40/169 Not Blue, Blue = 8/13 * 5/13 = 40/169 We add both probabilities since they both count under our scenario: 40/169 + 40/169 = 80/169 Checking our [URL='https://www.mathcelebrity.com/fraction.php?frac1=80%2F169&frac2=3%2F8&pl=Simplify']fraction simplification calculator[/URL], we see you cannot simplify this fraction anymore. So our probability stated in terms of a fraction is 80/169 [URL='https://www.mathcelebrity.com/perc.php?num=80&den=169&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']Stated in terms of a decimal[/URL], it's 0.4734

Three tennis balls each have a radius of 2 inches. They are put into a 12 inch high cylinder with a 4 inch diameter. What is the volume of the space remaining in the cylinder? Volume of each ball is 4/3 ?r^3 V = 4/3 * 3.1415 * 2^3 V = 1.33 * 3.1415 * 8 = 33.41 cubic inches The volume of 3 balls is: V = 3(33.41) V = 100.23 Volume of the cylinder is area of circle times height: V = 3.14 * 2 * 2 * 1 = 150.72 Volume of remaining space is: V = Volume of cylinder - Volume of 3 balls V = 150.72 - 100.23 V = [B]50.49[/B]

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Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli department at least 260 person-hours per week. Tom has one part-time employeewho works 20 hours per week. Each full-time employee works 40 hours per week. Write an inequality to determine n, the number of full-time employees Tom must schedule, so that his employees will work at least 260 person-hours per week. Set up the inequality: [LIST] [*]Add the part-timer's hours of 20 [*]Full time hours is 40 times n employees [*]At least means greater than or equal to, so we use the >= sign [/LIST] [B]40n + 20 >= 260[/B]

Translate and solve: 30 times m is greater than ?330. (Write your solution in interval notation.) 30 times m: 30m is greater than -330 30m > -330 Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=30m%3E-330&pl=Show+Interval+Notation']equation and interval solver[/URL], we get: m > -11

Twelve friends went to a movie theater. Because the movie was boring, they decided to figure out how many different ways they could sit in the 12 seats. How many different permutations are there for these 12 friends? 12 taken 12 at a time is written as: [URL='https://www.mathcelebrity.com/permutation.php?num=12&den=12&pl=Permutations']12P12[/URL] = [B]479,001,600[/B]

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. Four times a number: 4x nine more than four times a numbrer 4x + 9 The phrase [I]is[/I] means equal to. We set 4x + 9 equal to 25 as our algebraic expression: [B]4x + 9 = 25 [/B] If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D25&pl=Solve']type it in our math solver[/URL] and get: x = [B]4[/B]

Twice a first number decreased by a second number is 16. The first number increased by 3 times the second number is 1. Find the numbers. Let the first number be x and the second number be y. We're given: [LIST=1] [*]2x - y = 16 [*]x + 3y = 1 [/LIST] Using our simultaneous equations calculator, you can solve this 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter what method we use, we get the same answers: [B]x = 7 y = -2 (x, y) = (7, -2) [/B] Let's check our work in equation 1: 2(7) - -2 ? 16 14 + 2 ? 16 16 = 16 <-- Check Let's check our work in equation 2: 7 + 3(-2) ? 1 7 - 6 ? 1 1 = 1 <-- Check

twice the difference between x and 28 is 3 times a number The difference between x and 28: x - 28 Twice the difference means we multiply x - 28 by 2: 2(x - 28) The phrase [I]a number[/I] means an arbitrary variable, let's call it x x 3 times a number: 3x The word [I]is[/I] means equal to, so we set 2(x - 28) equal to 3x: [B]2(x - 28) = 3x[/B]

twice the difference of a number and 3 is equal to 3 times the sum of a number and 2. We've got 2 algebraic expressions here. Let's take them in parts. Left side algebraic expression: twice the difference of a number and 3 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]The word [I]difference[/I] means we subtract 3 from the variable x [*]x - 3 [*]Twice this difference means we multiply (x - 3) by 2 [*]2(x - 3) [/LIST] Right side algebraic expression: 3 times the sum of a number and 2 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]The word [I]sum[/I] means we add 2 to the variable x [*]x + 2 [*]3 times the sum means we multiply (x + 2) by 3 [*]3(x + 2) [/LIST] Now, we have both algebraic expressions, the problem says [I]is equal to[/I] This means we have an equation, where we set the left side algebraic expression equal to the right side algebraic expression using the equal sign (=) to get our answer [B]2(x - 3) = 3(x + 2)[/B]

twice the difference of a number and 55 is equal to 3 times the sum of a number and 8 Take this algebraic expression in pieces. Left side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The difference of this number and 55 means we subtract 55 from x x - 55 Twice the difference means we multiply x - 55 by 2 2(x - 55) Right side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The sum of a number and 8 means we add 8 to x x + 8 3 times the sum means we multiply x + 8 by 3 3(x + 8) Now that we have the left and right side of the expressions, we see the phrase [I]is equal to[/I]. This means an equation, so we set the left side equal to the right side: [B]2(x - 55) = 3(x + 8)[/B]

[SIZE=6]Twice the sum of a number and 6 is equal to three times the difference of the number and 3. Find the number. The phrase [/SIZE][I][SIZE=7]a number[/SIZE][/I][SIZE=6] means an arbitrary variable, let's call it x. The sum of a number and 6 means we add 6 to x: x + 6 Twice the sum of a number and 6 means we multiply x + 6 by 2: 2(x + 6) the difference of the number and 3 means we subtract 3 from x x - 3 three times the difference of the number and 3 means we multiply x - 3 by 3: 3(x- 3) The word [I]is[/I] means we set 2(x + 6) equal to 3(x - 3) 2(x + 6) = 3(x - 3) Use the distributive property to multiply through: 2x + 12 = 3x - 9 Subtract 2x from each side: 2x - 2x + 12 = 3x - 2x - 9 x - 9 = 12 Add 9 to each side: x - 9 + 9 = 12 + 9 x = [B]21[/B] [B][/B] [B][MEDIA=youtube]CeZl_oZnSiw[/MEDIA][/B][/SIZE]

Two coins are flipped 2 times. Calculate the total outcomes of these coins. 2 coins * 2 outcomes per coin = 4 possible outcomes [LIST=1] [*][B]H,H[/B] [*][B]H,T[/B] [*][B]T,H[/B] [*][B]T,T[/B] [/LIST]

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Use number 7,6,5 and 3 only one time to get 75 We do it using this order of operations: [B](7 + 5) * 6 + 3[/B] Simplifying, we get: 12*6 + 3 72 + 3 75

The only way you can roll a 12 with two dice is 6 and 6. Since each die roll is independent, we have: [LIST] [*]P(12) = P(6) * P(6) [*]P(12) = 1/6 * 1/6 [*]P(12) = 1/36. [/LIST] Now, what is the probability we roll a 12 five times in a row? The same rules apply, each new roll is independent of the last, so we multiply: [LIST] [*]P(12, 12, 12, 12, 12) = 1/36 * 1/36 * 1/36 * 1/36 * /36 [*]P(12, 12, 12, 12, 12) = [B]1/60,466,176[/B] or [B]1.65381717e-8[/B] [/LIST]

What pair of consecutive integers gives the following: 7 times the smaller is less than 6 times the larger? Let x and y be consecutive integers, where y = x + 1 We have 7x < 6y as our inequality. Substituting x, y = x + 1, we have: 7x < 6(x + 1) 7x < 6x + 6 Subtracting x from each side, we have: x < 6, so y = 6 + 1 = 7 (x, y) = (6, 7)

A certain number means an arbitrary variable, let's call it x x 3 times x 3x 20 is subtracted from 3 time x 3x - 20 The result is means equal to, so we set 3x - 20 equal to 43 for our algebraic expression [B]3x - 20 = 43 [/B] If you need to solve this, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-20%3D43&pl=Solve']equation calculator[/URL]: [B]x = 21[/B]

When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negative solution. Let the number be n. Square of a number: n^2 28 is subtracted from the square of a number: n^2 - 28 3 times the number: 3n [I]The result is[/I] mean an equation, so we set n^2 - 28 = 3n n^2 - 28 = 3n Subtract 3n from each side: n^2 - 3n - 28 = 3n - 3n The right side cancels to 0, so we have: n^2 - 3n - 28 = 0 This is a quadratic equation in standard form, so we [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-3n-28%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']use our quadratic calculator[/URL] to solve: We get two solutions for n: n = (-4, 7) The question asks for the negative solution, so our answer is: [B]n = -4[/B]

When 3 consecutive positive integers are multiplied, the product is 16 times the sum of the 3 integers. What is the difference of the product minus the sum? Let the 3 consecutive positive integers be: [LIST=1] [*]x [*]x + 1 [*]x + 2 [/LIST] The product is: x(x + 1)(x + 2) The sum is: x + x + 1 + x + 2 = 3x + 3 We're told the product is equivalent to: x(x + 1)(x + 2) = 16(3x + 3) x(x + 1)(x + 2) = 16 * 3(x + 1) Divide each side by (x + 1) x(x + 2) = 48 x^2 + 2x = 48 x^2 + 2x - 48 = 0 Now subtract the sum from the product: x^2 + 2x - 48 - (3x + 3) [B]x^2 - x - 51[/B]

When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unknown number. Write the translated equation below. [LIST=1] [*]39 added to a number is written as n + 39 [*]40 times the number is written as 40n [*]The result is means we have an equation, so set (1) equal to (2) [/LIST] n+ 39 = 40n Running [URL='http://www.mathcelebrity.com/1unk.php?num=n%2B39%3D40n&pl=Solve']n + 39 = 40n through the search engine[/URL], we get[B] n = 1[/B].

When 4 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution. Let the number be n. We have: n^2 - 4 = 3n Subtract 3n from each side: n^2 - 3n - 4 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-3n-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Typing this quadratic equation into the search engine[/URL], we get: n = (-1, 4) The problem asks for the positive solution, so we get [B]n = 4[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. Find the number The phrase [I]a number, [/I]means an arbitrary variable, let's call it "x". 4 times a number, increased by 40, means we multiply 4 times x, and then add 40 4x + 40 100 decreased by the number means we subtract x from 100 100 - x The problem tells us both of these expressions are the same, so we set them equal to each other: 4x + 40 = 100 - x Add x to each side: 4x + x + 40 = 100 - x + x The x's cancel on the right side, so we have: 5x + 40 = 100 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B40%3D100&pl=Solve']Typing this equation into the search engine[/URL], we get [B]x = 12[/B].

When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 4 times a number means we multiply x by 4: 4x Increased by 40 means we add 40 to 4x: 4x + 40 100 decreased by the number means we subtract x from 100: 100 - x The phrase [I]is the same as[/I] means equal to, so we set 4x + 40 equal to 100 - x 4x + 40 = 100 - x Solve for [I]x[/I] in the equation 4x + 40 = 100 - x [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4x and -x. To do that, we add x to both sides 4x + 40 + x = -x + 100 + x [SIZE=5][B]Step 2: Cancel -x on the right side:[/B][/SIZE] 5x + 40 = 100 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 40 and 100. To do that, we subtract 40 from both sides 5x + 40 - 40 = 100 - 40 [SIZE=5][B]Step 4: Cancel 40 on the left side:[/B][/SIZE] 5x = 60 [SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE] 5x/5 = 60/5 x = [B]12[/B] Check our work for x = 12: 4(12) + 40 ? 100 - 12 48 + 40 ? 100 - 12 88 = 88

When 54 is subtracted from the square of a number, the result is 3 times the number. 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 Square the number, means raise it to the 2nd power: x^2 Subtract 54: x^2 - 54 The phrase [I]the result[/I] means an equation, so we set x^2 - 54 equal to 3 [B]x^2 - 54 = 3[/B]

When 9 is subtracted from 5 times a number ,the result is 31 A number means an arbitrary variable, let's call it x. 5 times this number is written as 5x. 9 subtracted from this is written as 5x - 9 [I]The result[/I] means we have an equation, so we set [B]5x - 9 = 31[/B]. This is our algebraic expression. Now if we want to solve for x, we [URL='http://www.mathcelebrity.com/1unk.php?num=5x-9%3D31&pl=Solve']plug this equation into the search engine [/URL]and get [B]x = 8[/B].

When a dog noticed a fox, they were 60 meters apart. The dog immediately started to chase the fox at a speed of 750 meters per minute. The fox started to run away at a speed of 720 meters per minute. How soon will the dog catch the fox? The dog sits a position p. Distance = Rate x Time The dogs distance in minutes is D = 720t The fox sits at position p + 60 Distance = Rate x Time The fox's distance in minutes is D = 750t - 60 <-- Subtract 60 since the fox is already ahead 60 meters. We want to know when their distance (location) is the same. So we set both distance equations equal to each other: 720t = 750t - 60 [URL='https://www.mathcelebrity.com/1unk.php?num=720t%3D750t-60&pl=Solve']Using our equation calculator[/URL], we get [B]t = 2[/B]. Let's check our work: Dog's distance is 720(2) = 1440 Fox's distance is 750(2) - 60 = 1,440

while scuba diving jerey rose directly toward the surface of the water at a constant velocity for 2.0 minutes. he rose 9.0 meters in that time. what was his velocity? 9 meters / 2 minutes = [B]4.5 meters / minute[/B]

Winnie earns an annual salary of $55,117. If she pays $3,715 a year in taxes and receives a paycheck every other week, how much does Winnie receive from each paycheck? Subtract the taxes to get Winnie's Total net pay: Total Net Pay = Annual Salary - Annual Taxes Total Net Pay =$55,117 - $3,715 Total Net Pay = $51,402 Now, if Winnie gets paid every other week, and there are 52 weeks in a year, then she gets paid 26 times. Calculate single paycheck amount Single Paycheck Amount = Total Net Pay / 26 payments Single Paycheck Amount = $51,402 / 26 Single Paycheck Amount = [B]$1,977[/B]

A man is three times as old as his son was at the time when the father was twice as old as his son will ne two years from now. Find the present ages of each person.

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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Hugo is going to send some flowers to his wife. Somerville Florist charges $2 per rose, plus $39 for the vase. Dwaynes Flowers, in contrast, charges $3 per rose and $10 for the vase. If Hugo orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be? How many roses would there be? Let r be the number of roses and C(r) be the cost function. The vase is a one-time cost. Somerville Florist: C(r) = 2r + 39 Dwaynes Flowers C(r) = 3r + 10 Set them equal to each other: 2r + 39 = 3r + 10 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2r%2B39%3D3r%2B10&pl=Solve']equation calculator[/URL], we get: [B]r = 29[/B]

write an algebraic expression for 197 times y [B]197y [/B] This can also be found by typing 197 times y into our search engine

Write p times p times p times p times p times p and n index form We have p times itself 6 times, so the index form is: [B]p^6[/B]

Write the verbal expression for: 9x Using our [URL='http://www.mathcelebrity.com/verbalphrase.php?num=9x&pl=Verbal+Phrase']verbal expression calculator[/URL], we get either of the following: [LIST] [*][B]9 times x[/B] [*][B]9 multiplied by x[/B] [/LIST]

Write these times as 24 hours times: 1:00 pm 8:10 am 4:45 pm 10:12 pm Write these times as 12 hours time: 15:45 7:12 20:38 12:01 Write these times as 24 hours times (any time on or after 1:00 pm, we add 1 to the 12 noon marker: 1:00 pm = 12 + 1 = 13:00 8:10 am = 8:10 <-- since not past 12 noon 4:45 pm = 4 hours and 45 minutes past 12 noon, so we have 16:45 10:12 pm = 10 hours and 12 minutes past 12 noon, so we have 22:12 Write these times as 12 hours time: 15:45 = 15:45 - 12 = 3:45 PM 7:12 = 7:12, not past noon, so 7;12 am 20:38 = 20:38 - 12 = 8:38 PM 12:01 = 12:01 pm

X plus 9 is equal to 3 times x minus 4 x plus 9: x + 9 3 times x minus 4: 3x - 4 The phrase [I]is equal to[/I] means an equation, so we set x + 9 equal to 3x - 4: [B]x + 9 = 3x - 4[/B]

x plus y times x minus y Plus means we add. Minus means we subtract. So we have: [B](x + y)(x - y)[/B]

x squared times the difference of x and y x squared means we raise x to the power of 2: x^2 The difference of x and y x - y x squared times the difference of x and y [B]x^2(x - y)[/B]

Yael worked out at a gym for 2 hours. Her workout consisted of stretching for 21 minutes,jogging for 45 minutes, and lifting weights for the remaining amount of time. What percentage of Yael’s workout was spent lifting weights? Each hour is 60 minutes, so we have 2 * 60 = 120 minutes of workout time for Yael. We subtract off the stretching and jogging time to get the time Yael lifted weights: 120 - 21 - 45 = 54 minutes

Yolanda is riding her bicycle. She rides for 5 hours at a speed of 12.5 kilometers per hours. For how many kilometers does she ride? This is a distance problem, where distance = rate * time. We are given time of 5 hours, at a rate of 12.5km/hour. Using our [URL='http://www.mathcelebrity.com/drt.php?d=+&r=12.5&t=5&pl=Calculate+the+missing+Item+from+D%3DRT']distance calculator[/URL], we get D = [B]62.5km[/B].

You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save 75 per week, and your friend saves 50 per week. When vacation time comes, you have 950, and your friend has 800. How much did you start with, and for how many weeks did you save? [U]Let w be the number of weeks. Set up two equations where s is the starting amount:[/U] (1) s + 75w =950 (2) s + 50w = 800 [U]Rearrange (1) into (3) to solve for s by subtracting 75w[/U] (3) s = 950 - 75w [U]Rearrange (2) into (4) to solve for s by subtracting 50w[/U] (4) s = 800 - 50w [U]Set (3) and (4) equal to each other so solve for w[/U] 950 - 75w = 800 - 50w [U]Add 75w to each side, and subtract 950 from each side:[/U] 25w = 150 [U]Divide each side by w[/U] [B]w = 6[/B] Now plug w = 6 into (3) s = 950 - 75(6) s = 950 - 450 [B]s = 500[/B]

You can get 2 different moving companies to help you move. The first one charges $150 up front then $38 an hour. The second one charges $230 then $30 an hour, at what exact time will Both companies cost the same [U]Company 1: We set up the cost equation C(h) where h is the number of hours[/U] C(h) = Hourly Rate * h + up front charge C(h) = 38h + 150 [U]Company 2: We set up the cost equation C(h) where h is the number of hours[/U] C(h) = Hourly Rate * h + up front charge C(h) = 30h + 230 The question asks for h when both cost equations C(h) are equal. So we set both C(h) equations equal to other: 38h + 150 = 30h + 230 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=38h%2B150%3D30h%2B230&pl=Solve']type this equation into our search engine [/URL]and we get: h = [B]10[/B]

You have $250,000 in an IRA (Individual Retirement Account) at the time you retire. You have the option of investing this money in two funds: Fund A pays 5.4% annually and Fund B pays 7.9% annually. How should you divide your money between fund Fund A and Fund B to produce an annual interest income of $14,750? You should invest $______in Fund A and $___________in Fund B. Equation is x(.079) + (250,000 - x).054 = 14,750 .025x + 13,500 = 14,750 .025x = 1,250 [B]x = 50,000 for Fund A[/B] So at 5.4%, we have 250,000 - 50,000 = [B]200,000[/B] for the other fund B.

You have saved $50 over the last two weeks and decide to treat yourself by buying some new clothes. You go to the store and find two shirts and three pairs of jeans you like. The two shirts are buy-one-get-one half off, at $22.35 each. The three pairs of jeans are buy-two-get-one-free, at $23.70. Tax Rate for Harmonized Sales Tax is 13% a. What would be the total for the two shirts (don’t forget to include taxes)? b. What would be the total for the three pairs of jeans (don’t forget to include taxes)? c. Which would you buy and why? a. Half of 22.35 is 11.18 So two shirts cost: 22.35 + 11.18 = 33.53 Cost with Tax of 13% is: 33.53 * 1.13 = [B]37.89 [/B] b. Three pairs of jeans are calculated by cost of 1 pair times 2 jeans and you get the third one free: 23.70 * 2 = 47.40 Cost with Tax of 13% is: 47.40 * 1.13 = [B]53.56 [/B] c. Calculate unit cost, which is cost per item Unit cost of Shirts = 37.89 / 2 = [B]18.95[/B] Unit cost of Jeans = 53.56 / 3 = [B]17.85 Buy the jeans since they have a lower unit cost[/B]

You need $480 for a camp in 3 months. How much money do you need to save each week? [URL='https://www.mathcelebrity.com/timecon.php?quant=3&pl=Calculate&type=month']3 months[/URL] = 12 weeks $480 / 12 weeks = [B]$40 per week[/B]

You practice the piano for 30 minutes each day. Write and solve an equation to find the total time t you spend practicing the piano in a week. Since there is 7 days in a week, we have: t = 30 * 7 [B]t = 210[/B]

You purchase a new car for $35,000. The value of the car depreciates at a rate of 8.5% per year. If the rate of decrease continues, what is the value of your car in 5 years? Set up the depreciation function D(t), where t is the time in years from purchase. We have: D(t) = 35,000(1 - 0.085)^t Simplified, a decrease of 8.5% means it retains 91.5% of it's value each year, so we have: D(t) = 35,000(0.915)^t The problem asks for D(5) D(5) = 35,000(0.915)^5 D(5) = 35,000(0.64136531607) D(5) = $[B]22,447.79[/B]

You put $5500 in a bond fund which has an annual yield of 4.8%. How much interest will be earned in 23 years? Build the accumulation of principal. We multiply 5,500 times 1.048 raised to the 23rd power. Future Value = 5,500 (1.048)^23 Future Value =5,500(2.93974392046) Future Value = 16,168.59 The question asks for interest earned, so we find this below: Interest Earned = Future Value - Principal Interest Earned = 16,168.59 - 5,500 Interest Earned = [B]10,668.59[/B]

Your job pays you $7 per hour. What is the algebraic expression if you worked h hours? If your pay is rate times hours, we have: [B]7h[/B]

z , subtract 5 then times by 3 Take this algebraic expression two parts: [LIST] [*]z subtract 5: z - 5 [*][I]Then times by 3[/I] means we multiply the expression z - 5 by 3 [/LIST] [B]3(z - 5)[/B]