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

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

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]

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

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

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

A gasoline tank is leaking at a rate of n gallons in t hours. If the gasoline cost $2 per gallon, what is the value of the gasoline that will be lost in m minutes? n gallons / t hours = n/t gallons per hour are leaking The value of the gas that leaks each hour is $2, so we have: 2n/t dollar per hour is leaking Value per minute means we divide by 60: 2n/60t Dividing top and bottom by 2 to simplify, we have: n/30t Given m minutes, we multiply to get: [B]nm/30t[/B]

A 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 rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find its length and width. The area of a rectangle (A) is: A = lw --> where l is the length and w is the width We're given l = 2w, so we substitute this into the Area equation: A = (2w)w A = 2w^2 We're given the area of the pitch is 360, so we set: 2w^2 = 360 We [URL='https://www.mathcelebrity.com/1unk.php?num=2w%5E2%3D360&pl=Solve']type this equation into our search engine[/URL], follow the links, and get: w = [B]6*sqrt(5) [/B] Now we take this, and substitute it into this equation: 6*sqrt(5)l = 360 Dividing each side by 6*sqrt(5), we get: l = [B]60/sqrt(5)[/B]

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel? [LIST] [*]Each ride will cost 1.50 + 0.8x where x is the number of miles per trip. [*]This expression must be less than 12. [/LIST] [U]Setup the inequality:[/U] 1.5 + 0.8x < 12 [U]Subtracting 1.5 from each side of the inequality[/U] 0.8x < 10.5 [U]Simplifying even more by dividing each side of the inequality by 0.8, we have:[/U] [B]x < 13.125[/B]

An analysis of the final test scores for Managerial Decision Making Tools reveals the scores follow the normal probability distribution. The mean of the distribution is 75 and the standard deviation is 8. The instructor wants to award an "A" to students whose score is in the highest 10 percent. What is the dividing point for those students who earn an "A"? Top 10% is equivalent to the 90th percentile. Using our [URL='http://www.mathcelebrity.com/percentile_normal.php?mean=+75&stdev=8&p=+90&pl=Calculate+Percentile']percentile calculator[/URL], the 90th percentile cutoff point is [B]85.256[/B]

Ande has 8 pints of milk. If he drinks 1/4 of a pint of milk each day, how long will the 8 pints of milk last him? Milk Days = Total Pints of Milk / pints drank per day Milk Days = 8 / 1/4 Dividing by a fraction is the same as multiplying by it's reciprocal. The [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=3%2F8&pl=Reciprocal']reciprocal of[/URL] 1/4 is 4/1, so we have: 8 * 4/1 = [B]32 days[/B]

April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that June has. April has two-thirds of the number of sweets that May has. How many sweets does June have? Let the April sweets be a. Let the May sweets be m. Let the June sweets be j. We're given the following equations: [LIST=1] [*]m = 3j/4 [*]a = 2m/3 [*]a + j + m = 90 [/LIST] Cross multiply #2; 3a = 2m Dividing each side by 2, we get; m = 3a/2 Since m = 3j/4 from equation #1, we have: 3j/4 = 3a/2 Cross multiply: 6j = 12a Divide each side by 12: a = j/2 So we have: [LIST=1] [*]m = 3j/4 [*]a = j/2 [*]a + j + m = 90 [/LIST] Now substitute equation 1 and 2 into equation 3: j/2 + j + 3j/4 = 90 Multiply each side by 4 to eliminate fractions: 2j + 4j + 3j = 360 To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%2B4j%2B3j%3D360&pl=Solve']type it in our search engine[/URL] and we get: j = [B]40[/B]

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Connor runs 2 mi more each day than David. The sum of the distances they run each week is 56 mi. How far does David run each day? Let Connor's distance be c Let David's distance be d We're given two equations: [LIST=1] [*]c = d + 2 [*]7(c + d) = 56 [/LIST] Simplifying equation 2 by dividing each side by 7, we get: [LIST=1] [*]c = d + 2 [*]c + d = 8 [/LIST] Substitute equation (1) into equation (2) for c d + 2 + d = 8 To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=d%2B2%2Bd%3D8&pl=Solve']type this equation into our calculation engine[/URL] and we get: d = [B]3[/B]

Dan has a favorite fast food restaurant where he always orders French fries and a milk shake. If the fries contain 15 grams of fat and the shake contains 9 grams of fat, how many burgers, at 17 grams of fat each, can Dan add to his fries and milkshake if he wants to keep the total fat content of his meal no greater than 69 grams? His original meal is 1 fry and 1 shake. This contains 15 + 9 = 24 grams of fat. To limit his meal to 69 grams of fat, he has 69 - 24 = 45 grams of fat left over. Therefore, he can consume: 17b <= 45 where b is the number of burgers Dividing by 17, we get b = 2.65. Since he does not want to go over 45, he can eat 2 burgers.

David obtained 5 out of 20 votes in the election. What percentage of the votes did david receive? 5/20 is the fraction. You can simplify by dividing top and bottom by 5 to get 1/4 As a decimal, this is 0.25 To get a percentage, multiply the decimal by 100 100 * 0.25 = 25% You can also use our [URL='http://www.mathcelebrity.com/perc.php?num=+5&den=+20&pcheck=1&num1=6500&pct1=70&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pof1=40&pof2=20&pl=Calculate']decimal-percentage-fraction converter[/URL]

Find two consecutive positive integers such that the sum of their squares is 25. Let the first integer be x. The next consecutive positive integer is x + 1. The sum of their squares equals 25. We write this as:: x^2 + (x + 1)^2 Expanding, we get: x^2 + x^2 + 2x + 1 = 25 Group like terms: 2x^2 + 2x + 1 = 25 Subtract 25 from each side: 2x^2 + 2x - 24 = 0 Simplify by dividing each side by 2: x^2 + x - 12 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-12%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get x = 3 or x = -4. The problem asks for positive integers, so we discard -4, and use 3. This means, our next positive integer is 3 + 1 = 4. So we have [B](3, 4) [/B]as our answers. Let's check our work: 3^2 + 4^2 = 9 + 16 = 25

Fiona thinks of a number. fiona halves the number and gets an answer of 72.8. Form an equation with x from the information Halving means dividing by 2, so our equation is: [B]x/2 = 72.8[/B]

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How many one-fifths are there in 200? Using the rule of dividing by a fraction is the same as multiplying by the reciprocal, we have: 200 / 1/5 = 200 * 5 = [B]1000[/B]

I have 8 cookies. My friend at 7/10 of the 8 cookies. How many cookies did he have? 8 * (7/10) 56/10 Simplify by dividing the top and bottom by 2: [B]28/5 = 5.6 cookies[/B]

If x is divided by 9, the remainder is 5. What is the remainder if 3x is divided by 9? pick an integer x where when dividing by 9, we get a remainder of 5. 14/9 gives us a remainder of 5. Now multiply 14 by 3: 14 * 3 = 42 [URL='https://www.mathcelebrity.com/modulus.php?num=42mod9&pl=Calculate+Modulus']42/9 gives a remainder of[/URL] [B]6[/B]

In 2000 a company increased its workforce by 50%. In 2001 it decreased its workforce by 50%. How does the size of its workforce at the end of 2001 compare with the size of the workforce at the beginning of 2000? Let w be the size of the workforce before any changes. We have: [LIST] [*]w(2000) = w(1999) * 1.5 [I](50% increase is the same as multiplying by 1.5)[/I] [*]w(2001) = w(2000)/1.5 [I](50% decrease is the same as dividing by 1.5)[/I] [/LIST] Substitute the first equation back into the second equation w(2001) = w(1999) * 1.5/1.5 Cancel the 1.5 on top and bottom w(2001) = w(1999) This means the workforce had [B]zero net change[/B] from the beginning of 2000 to the end of 2001.

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]

Layla buys 2 1/2pounds of chocolate for 3.50 how much is she paying for a pound of chocolate? [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%261%2F2&frac2=3%2F8&pl=Simplify']Using our mixed fraction converter[/URL], 2&1/2 = 5/2 Cost per pound = 3.50 / 5/2 pounds Dividing by 5/2 is the same as multiplying by the reciprocal 2/5: 3.50 * 2/5 7/5 [B]$1.40 per pound[/B]

Of the 800 students of a school, 600 have traveled. What percentage of the students went on a trip? Our percentage is found as 600/800. Simplifying by dividing top and bottom by 100, we have: 6/8 Divide top and bottom by 2, we get: 3/4 or [B]75% [/B] You can also type in the [URL='http://www.mathcelebrity.com/perc.php?num=600&den=800&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']search engine[/URL]: 600/800 as percent.

Sum of 8 equal to 5/36 shown [URL='http://www.mathcelebrity.com/2dice.php?gl=1&pl=8&opdice=1&rolist=+2%2C3%2C9%2C10&dby=2%2C3%2C5&ndby=4%2C5&montect=+100']here[/URL]. At least one 4 means one of three scenarios: [LIST=1] [*](4, not 4) = 1/6 * 5/6 = 5/36 [*](not 4, 4) = 5/6 * 1/6 = 5/36 [*](4, 4) = 1/6 * 1/6 = 1/36 [/LIST] The phrase "or", means we add both probabilities (sum of 8) and (at least one 4): 5/36 + (5/36 + 5/36 + 1/36) 16/36 Simplify by dividing each part of the fraction by 4 [B]4/9[/B]

Raise f to the 8th power, divide the result by 5, then multiply 10 f to the 8th power means we raise f to the power of 8 using an exponent: f^8 Divide f^8 by 5 (f^8)/5 Now multiply this by 10: 10(f^8)/5 We can simplify this algebraic expression by dividing 10/5 to get 2 on top: 2[B](f^8)[/B]

Solve 100 / 1/2 Dividing by a fraction is the same as multiplying by the reciprocal of the fraction: [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F2&pl=Reciprocal']Reciprocal of 1/2[/URL] = 2 100 * 2 = [B]200[/B]

Start with t , add 6, divide by 2, then subtract 5. Start with t: t Add 6: t + 6 Divide by 2: (t + 6)/2 [I]Add parentheses because we're dividing the [U]quantity[/U] by 2 [/I] Then subtract 5: [B](t + 6)/2 - 5[/B]

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The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. What is the value of N ? Average of the first number set is [URL='https://www.mathcelebrity.com/statbasic.php?num1=17%2C26%2C42%2C59&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']using our average calculator[/URL] is: 36 Now, the mean (average) or 19 and N is found by adding them together an dividing by 2: (19 + N)/2 Since both number sets have equal means, we set (19 + N)/2 equal to 36: (19 + N)/2 = 36 Cross multiply: 19 + N = 36 * 2 19 + n = 72 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=19%2Bn%3D72&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]53[/B]

The average of 20 numbers is 18 while the average of 18 numbers is 20. What is the average of the 38 numbers? The average of averages is found by getting the sum of both groups of numbers and dividing by the count of numbers. Calculate the sum of the first group of numbers S1: Average = S1 / n1 18 = S1 / 20 S1 = 20 * 18 S1 =360 Calculate the sum of the second group of numbers S2: Average = S2 / n2 20 = S2 / 18 S2 = 18 * 20 S2 =360 Our average of averages is found by the following: A = (S1 + S2)/(n1 + n2) A = (360 + 360)/(20 + 18) A = 720/38 [B]A = 18.947[/B]

The difference of 2 positive numbers is 54. The quotient obtained on dividing the 1 by the other is 4. Find the numbers. Let the numbers be x and y. We have: [LIST] [*]x - y = 54 [*]x/y = 4 [*]Cross multiply x/y = 4 to get x = 4y [*]Now substitute x = 4y into the first equation [*](4y) - y = 54 [*]3y = 54 [*]Divide each side by 3 [*][B]y = 18[/B] [*]If x = 4y, then x = 4(18) [*][B]x = 72[/B] [/LIST]

[I]Is at least [/I]means greater than or equal to: 5x + 2x >= 70 If we combine like terms, we have: 7x >=70 We can further simplify by dividing each side of the inequality by 7 x >=10 If you want the interval notation for that, use the [URL='http://www.mathcelebrity.com/interval-notation-calculator.php?num=x%3E%3D10&pl=Show+Interval+Notation']interval notation calculator[/URL].

the sum of x and its reciprocal The reciprocal of x is found by dividing 1 by x: 1/x the sum of x and its reciprocal means we add 1/x to x: [B]x + 1/x[/B]

What fraction lies exactly halfway between 2/3 and 3/4? A) 3/5 B) 5/6 C) 7/12 D) 9/16 E) 17/24 Halfway means taking the average, which is dividing the sum of the fractions by 2 for 2 fractions: 1/2(2/3 + 3/4) 1/2(2/3) + 1/2(3/4) 1/3 + 3/8 We need common denominators, so [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F3&frac2=3%2F8&pl=Add']we type this fraction sum into our search engine[/URL] and get: [B]17/24 - Answer E[/B]

What is the inverse of dividing by 3 [B]Multiplying by 3[/B] Suppose we have 2 divided by 3: 2/3 To undo this operation to get to 2 again, we'd multiply by 3: 2/3 * 3 = 2