second

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!

1000 bullets in 10 minutes. How many bullets per second 1000 bullets / 10 minutes * 1 minute / 60 seconds = 1000 bullets / 600 seconds = [B]1.6667 bullets per second[/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 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than twice a number of home runs the second player hit. how many home runs did each player hit? Declare variables: Let the first players home runs be a Let the second players home runs be b We're given two equations: [LIST=1] [*]a = 2b + 3 [*]a + b = 60 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for a: 2b + 3 + b = 60 Using our math engine, we [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B3%2Bb%3D60&pl=Solve']type this equation[/URL] in and get: b = [B]19 [/B] To solve for a, we substitute b = 19 into equation (1): a = 2(19) + 3 a = 38 + 3 a = [B]41[/B]

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

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

2 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 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 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]

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

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)

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

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

Set up a proportion, with meters to seconds: 50 meters/21.81 seconds = x meters / 1 second 50/21.81 = x/1 Using our proportion calculator, we have: [B]x = 2.293 meters per second[/B]

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

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

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]

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

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

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

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

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

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

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

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

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

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

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

A 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 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 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 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 can run 68 mph. How fast is a cheetah in feet per second (68 miles / hour) * (1 hour / 3600 seconds) * (5280 feet / 1 mile) = 68 * 5280 feet per 3600 seconds 395040 feet / 3600 seconds [B]99.73 feet per second[/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 copy machine makes 28 copies per minute. how many copies does it make in 3 minutes and 45 seconds? 45 seconds = 45/60 = 3/4 of a minute. 3/4 = 0.75 So we have 3.75 minutes. Set up a proportion of copies to minutes where c is the number of copies made in 3 minutes and 45 seconds: 28/1 = c/3.75 [URL='https://www.mathcelebrity.com/prop.php?num1=28&num2=c&den1=1&den2=3.75&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our calculator[/URL], we get: c = [B]105[/B]

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

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

A financial advisor has invested $7000 in two accounts. If one account contains x dollars, express the amount in the second account in terms of x The other account contains: [B]7000 - x[/B]

A first number plus twice a second number is 10. Twice the first number plus the second totals 29. Find the numbers. Let the first number be x. Let the second number be y. We are given the following two equations: [LIST=1] [*]x + 2y = 10 [*]2x + y = 29 [/LIST] We can solve this 3 ways using: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Substitution']Substitution[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Elimination']Elimination[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] Using any of the 3 methods, we get the same answers of [B](x, y) = (16, -3)[/B]

A first number plus twice a second number is 10. Twice the first number plus the second totals 35. Find the numbers. [U]The phrase [I]a number[/I] means an arbitrary variable[/U] A first number is written as x A second number is written as y [U]Twice a second number means we multiply y by 2:[/U] 2y [U]A first number plus twice a second number:[/U] x + 2y [U]A first number plus twice a second number is 10 means we set x + 2y equal to 10:[/U] x + 2y = 10 [U]Twice the first number means we multiply x by 2:[/U] 2x [U]Twice the first number plus the second:[/U] 2x + y [U]Twice the first number plus the second totals 35 means we set 2x + y equal to 35:[/U] 2x + y = 35 Therefore, we have a system of two equations: [LIST=1] [*]x + 2y = 10 [*]2x + y = 35 [/LIST] Since we have an easy multiple of 2 for the x variable, we can solve this by multiply the first equation by -2: [LIST=1] [*]-2x - 4y = -20 [*]2x + y = 35 [/LIST] Because the x variables are opposites, we can add both equations together: (-2 + 2)x + (-4 + 1)y = -20 + 35 The x terms cancel, so we have: -3y = 15 To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D15&pl=Solve']type it in our search engine[/URL] and we get: y = [B]-5 [/B] Now we substitute this y = -5 into equation 2: 2x - 5 = 35 To solve this equation for x, we[URL='https://www.mathcelebrity.com/1unk.php?num=2x-5%3D35&pl=Solve'] type it in our search engine[/URL] and we get: x = [B]20[/B]

A first number plus twice a second number is 11. Twice the first number plus the second totals 34. Find the numbers. Let the first number be x and the second number be y. We're given: [LIST=1] [*]x + 2y = 11 [*]2x + y = 34 [/LIST] Using our simultaneous equations calculator, we have 3 methods to solve this: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] All 3 methods give the same solution: [LIST] [*][B]x = 19[/B] [*][B]y = -4[/B] [/LIST]

A first number plus twice a second number is 14. Twice the first number plus the second totals 40. Find the numbers. [B][U]Givens and assumptions:[/U][/B] [LIST] [*]Let the first number be x. [*]Let the second number be y. [*]Twice means multiply by 2 [*]The phrases [I]is[/I] and [I]totals[/I] mean equal to [/LIST] We're given two equations: [LIST=1] [*]x + 2y = 14 [*]2x + y = 40 [/LIST] To solve this system, we can take a shortcut, and multiply the top equation by -2 to get our new system: [LIST=1] [*]-2x - 4y = -28 [*]2x + y = 40 [/LIST] Now add both equations together (-2 _ 2)x (-4 + 1)y = -28 + 40 -3y = 12 To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D12&pl=Solve']type it in our search engine[/URL] and we get: y = [B]-4 [/B] We substitute this back into equation 1 for y = -4: x + 2(-4) = 14 x - 8 = 14 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-8%3D14&pl=Solve']type it in our search engine[/URL] and we get: x = [B]22[/B]

A first number plus twice a second number is 22. Twice the first number plus the second totals 28. Find the numbers. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x + 2y = 22 <-- Since twice means multiply by 2 [*]2x + y = 28 <-- Since twice means multiply by 2 [/LIST] We have a set of simultaneous equations. We can solve this three ways [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28+&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter which method we use, we get the same answer: [LIST] [*][B]x = 11 & 1/3[/B] [*][B]y = 5 & 1/3[/B] [/LIST]

A first number plus twice a second number is 3. Twice the first number plus the second totals 24. Let the first number be x. Let the second number be y. We're given: [LIST=1] [*]x + 2y = 3 <-- Because [I]twice[/I] means multiply by 2 [*]2x + y = 24 <-- Because [I]twice[/I] means multiply by 2 [/LIST] We have a system of equations. We can solve it any one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which way we choose, we get: [LIST] [*]x = [B]15[/B] [*]y = [B]-6[/B] [/LIST]

A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Find the numbers. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x + 2y = 6 [*]2x + y = 15 [/LIST] Multiply the first equation by -2: [LIST=1] [*]-2x - 4y = -12 [*]2x + y = 15 [/LIST] Now add them -2x + 2x - 4y + y = -12 + 15 -3y = 3 Divide each side by -3: y = 3/-3 y =[B] -1[/B] Plug this back into equation 1: x + 2(-1) = 6 x - 2 = 6 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-2%3D6&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]8[/B]

A first number plus twice a second number is 7 Let the first number be x. Let the second number be y. We're given: [LIST] [*]A first number is x [*]A second number is y [*]Twice the second number means we multiply y by 2: 2y [*][I]Plus [/I]means we add x to 2y: x + 2y [*]The phrase [I]is[/I] means an equation, so we set x + 2y equal to 7 [/LIST] [B]x + 2y = 7[/B]

A first number plus twice a second number is 7. Twice the first number plus the second totals 23. Find the numbers Let the first number be a and the second number be b. We have: [LIST=1] [*]a + 2b = 7 [*]2a + b = 23 [/LIST] Rearrange (1) into (3) (3) a = 7 - 2b Substitute (3) into (2): 2(7 - 2b) + b = 23 Multiply through: 14 - 4b + b = 23 Combine like terms: 14 - 3b = 23 Subtract 14 from each side: -3b = 9 Divide each side by -3 [B]b = -3[/B] Substitute this into (3) a = 7 - 2b a = 7 - 2(-3) a = 7 + 6 [B]a = 13[/B] [B](a, b) = (13, -3)[/B]

A football team gained 8 yards on a first down, lost 12 yards on the second down, and gained 16 yards on the third down. How many yards did the team gain or lose? Assumptions: [LIST] [*]We reflect gains by adding [*]We reflect losses by subtracting [/LIST] Plays: [LIST] [*]Gain of 8 = +8 [*]Loss of 12 = -12 [*]Gain of 16 = +16 [/LIST] Net Gain/Loss +8 - 12 + 16 [B]+12 (gain)[/B]

A gardener plants flowers in the following order: carnations,daffodils, larkspurs, tiger lillies, and zinnias. if the gardener planted 47 plants, what kind of flower did he plant last? Let c be carnations, d be daffodils, l be larkspurs, t be tiger lillies, and z be zinnias. The order goes as follows: c, d, l, t, z. So each cycle of plants counts as 5 plants. We know that 9 * 5 = 45. So the gardener plants 9 full cycles. Which means they have 47 - 45 = 2 plans left over. In the order above, the second plant is the daffodil. So the gardener planted the [B]daffodil[/B] last. Now, can we shortcut this problem? Yes, using modulus. 47 plants, with 5 plants per cycle, we do [URL='https://www.mathcelebrity.com/modulus.php?num=47mod5&pl=Calculate+Modulus']47 mod 5 through our calculator[/URL], and get 2. So we have 2 plants left over, and the daffodil is the second plant.

A hummingbird moves its wings at a rate of 5400 wingbeats a minute. Write this rate in wingbeats per second. 5400 wingbeats per minute * 1 minute / 60 seconds = 5400/60 = [B]90 wingbeats per second[/B]

a jar contains a $5 note, two $10 notes, a $20 note and a $50 note. if 2 notes are taken out by random, find the probability that their sum is $15 To get a sum of $15, we'd need to pull the $5 and the $10. Since both events are indepdenent, we have: P($5 or 10) or P(whatever is not pulled in the first pull) First Pull: 2/4 (We can pull either a $10 or a $5, so 2 choices out of 4 bills) Second Pull: 1/3 <-- since there are only 3 bills and 1 bill to pull Each pull is independent, so we multiply: 2/4 * 1/3 = 2/12 We can simply this, so [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F12&frac2=3%2F8&pl=Simplify']we type this fraction in our search engine[/URL] and we get: [B]1/6[/B]

A 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 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 man walked at 2 metres / second? How many metres did he walk in an hour? 60 seconds in 1 minute and 60 minutes in 1 hour, so we have 3,600 seconds in an hour. 2 metres * 3,600 seconds = 7,200 m�tres in one hour.

A meter is defined as the distance light travels in 1/299,792,458 of a second. How many meters does light travel in 1/8 of a second? 1/8 second / 1/299,792,458 299,792,458/8 = [B]37,474,057.25 meters[/B]

a number of seconds in 50 minutes 60 seconds / minute * 50 minutes = 60 * 50 seconds = [B]3,000 seconds[/B]

A pair of standard dice is rolled, how many possible outcomes are there? We want the number of outcomes in the sample space. The first die has 6 possibilities 1-6. The second die has 6 possibilities 1-6. Our sample space count is 6 x 6 = [B]36 different outcomes [/B] [LIST=1] [*](1, 1) [*](1, 2) [*](1, 3) [*](1, 4) [*](1, 5) [*](1, 6) [*](2, 1) [*](2, 2) [*](2, 3) [*](2, 4) [*](2, 5) [*](2, 6) [*](3, 1) [*](3, 2) [*](3, 3) [*](3, 4) [*](3, 5) [*](3, 6) [*](4, 1) [*](4, 2) [*](4, 3) [*](4, 4) [*](4, 5) [*](4, 6) [*](5, 1) [*](5, 2) [*](5, 3) [*](5, 4) [*](5, 5) [*](5, 6) [*](6, 1) [*](6, 2) [*](6, 3) [*](6, 4) [*](6, 5) [*](6, 6) [/LIST]

A 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 robot runs 6 feet in a second. How many feet can it run in a minute? 6 feet / second * 60 seconds / minute =[B] 360 feet / minute[/B]

a rocket is propelled into the air. its path can be modeled by the relation h = -5t^2 + 50t + 55, where t is the time in seconds, and h is height in metres. when does the rocket hit the ground We set h = 0: -5t^2 + 50t + 55 = 0 Typing this quadratic equation into our search engine to solve for t, we get: t = {-1, 11} Time can't be negative, so we have: t = [B]11[/B]

A rocket travels at a rate of 160 meters in 3 seconds. What is the speed of the rocket in meters per second? 160 meters /3 seconds = [B]53.333333333 meters per second[/B]

A 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 skydiver falls 144 feet in three seconds. How far does the skydiver fall per second? 144 feet/3 seconds Divide top and bottom by 3 to get feet per second [B]48 feet per second[/B]

A spinner has 10 equally sized sections, 2 are gray 8 are blue. The spinner is spun twice. What is the probability that the first spin lands on blue and the second lands on gray? P(blue) = Blue sections / Total Sections P(blue) = 8/10 [URL='https://www.mathcelebrity.com/fraction.php?frac1=8%2F10&frac2=3%2F8&pl=Simplify']Reducing this using our simplified fraction calculator[/URL], we get: P(blue) = 4/5 P(gray) = Gray sections / Total Sections P(blue) = 2/10 [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F10&frac2=3%2F8&pl=Simplify']Reducing this using our simplified fraction calculator[/URL], we get: P(gray) = 1/5 We want the probability of blue,gray. Since each spin is independent, we multiply the two probabilities to get our answer: P(blue, gray) = P(blue) * P(gray) P(blue, gray) = 4/5 * 1/5 P(blue, gray) = [B]4/25[/B]

A sprinter runs 400 meters in 54 seconds. What is the runners average running rate in meters per second? 400 meters/54 seconds = [B]7.407 meters per second[/B].

a string measures 20 inches is cut into pieces. Let z represent the length of one of the resulting pieces. express length of the second piece in terms of the length z of the first pice Second piece length = [B]20 - z[/B]

A student and the marine biologist are together at t = 0. The student ascends more slowly than the marine biologist. Write an equation of a function that could represent the student's ascent. Please keep in mind the slope for the marine biologist is 12. Slope means rise over run. In this case, rise is the ascent distance and run is the time. 12 = 12/1, so for each second of time, the marine biologist ascends 12 units of distance If the student ascends slower, than the total distance gets reduced by an unknown factor, let's call it c. So we have the student's ascent function as: [B]y(t) = 12t - c[/B]

A student was trying to determine a formula for changing speeds that are written in feet per second into miles per hour. If a sprinter runs at a speed of n feet per second, what is her speed in miles per hour? 3600 seconds per hour = 3600n feet per hour 5280 feet per mile so we have: 3600n feet per hour / 5280 feet per mile = [B]0.6818n feet per second[/B]

A submarine is 75 feet below sea level. It descends another 25 feet every 10 seconds for 3 minutes. What integer represents the submarines current location? Assumptions and givens: [LIST] [*]Let m be the number of minutes [*]10 seconds is 1/6 of a minute, 6 (10) seconds blocks per minute * 3 minutes = 18 (10 second blocks) [*]Below sea level is a negative number [/LIST] [U]Current depth:[/U] -25(18) - 75 -450 - 75 [B]-525[/B]

A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take for the tank to be empty Assumptions and givens: [LIST] [*]Let the number of seconds be s. [*]An empty tank means 0 liters of water. [*]Leaks mean we subtract from the starting volume. [/LIST] We have the following relation: 800 - 12s = 0 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=800-12s%3D0&pl=Solve']type it in our search engine[/URL] and we get: s = 66.67 seconds

A three digit number, if the digits are unique [LIST=1] [*]For our first digit, we can start with anything but 0. So we have 9 options [*]For our second digit, we can use anything but 9 since we want to be unique. So we have 9 options [*]For our last digit, we can use anything but the first and second digit. So we have 10 - 2 = 8 options [/LIST] Our total 3 digit numbers with all digits unique is found by the fundamental rule of counting: 9 * 9 * 8 = [B]648 possible 3 digit numbers[/B]

A 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 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 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 water tank holds 236 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds 354 gallons but is leaking at a rate if 5 gallons per week. After how many weeks will the amount of water in the two tanks be the same Let w be the number of weeks of leaking. We're given two Leak equations L(w): [LIST=1] [*]L(w) = 236 - 3w [*]L(w) = 354 - 5w [/LIST] When the water in both tanks is the same, we can set both L(w) equations equal to each other: 236 - 3w = 354 - 5w To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=236-3w%3D354-5w&pl=Solve']type it in our search engine[/URL] and we get: w = [B]59[/B]

A wheel take 1/12 minutes to make a complete turn. How many turns does it make in a half a minute? 1 minute = 60 seconds 1/12 minutes = 60/12 = 5 seconds Half a minute = 60/2 = 30 seconds 1 turn/5 seconds * 6/6 = [B]6 turns[/B] per 30 seconds

A wide receiver sprints at a speed of 8.6 feet per second. How many feet would he expect the wide receiver to run in 25 seconds? 8.6 feet per second * 25 seconds = [B]212.5 feet[/B]

Aaron buys a bag of cookies that contains 8 chocolate chip cookies, 6 peanut butter cookies,7 sugar cookies and 6 oatmeal raisin cookies. What it�s the probability that Aaron randomly selects a peanut butter cookie from the bag, eats it,, then randomly selects another peanut butter cookie? First draw out of the bag is a peanut butter cookie: P(PB) = Total Peanut Butter Cookies / Total Cookies P(PB) = 6/27 Second draw out of the bag is a peanut butter cookie, but we have one less since Aaron ate one: P(PB) = Total Peanut Butter Cookies - 1 / Total Cookies - 1 P(PB) = (6 - 1)/(27 - 1) P(PB) = 5/26 Now, since each event is independent, we multiply them to see the probability of choosing a peanut butter cookie, eating it, then reaching in and choosing another peanut butter cookie: P(PB, PB) = 6/27 * 5/26 [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F27&frac2=5%2F26&pl=Multiply']P(PB, PB)[/URL] = [B]5/117[/B]

ADG,BEH,CFI,___,___,___ Looking at this pattern, we see: [LIST=1] [*]the first term starts with A and increments by 1 letter [*]the second term starts with D and increments by 1 letter [*]the third term starts with G and increments by 1 letter [/LIST] So terms 4, 5, and 6 are: [LIST] [*][B]DGJ[/B] [*][B]EHK[/B] [*][B]FIL[/B] [/LIST]

After a long journey, you finally arrive at the edge o a deep gorge where there are two identical bridges from which to choose your path to the other side. One bridge is safe, while the other is very dangerous and has caused the deaths of hundreds of travelers. The owner of the first bridge is a talking rat, while the owner of the second bridge is a talking frog. Friends told you before you left that one of the bridge owners always tells the truth, while the other always lies. You are allowed one question to ask of either the frog or the rat to find out which bridge is the safe bridge. What is the question that you would ask? [B]Ask the frog the following question: "If I were to ask the rat which bridge is the same bridge, which one would he point to?" [/B] If the frog is the truth teller, he would tell you that the rat would point to the dangerous bridge. If the frog is the liar, the truth telling rat would point out the safe bridge, but the lying frog would tell you he said the dangerous bridge. In both situations, the dangerous bridge would be pointed to. Take the other bridge.

Let the first number equal x. The second number is 3 more than twice the first number. Express the second number in terms of the first number x. [LIST] [*]Let the second number be y. [*]Twice means multiply by 2 [*]3 more than means we add 3 [/LIST] So we have the following algebraic expression: [B]y = 2x + 3[/B]

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 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 electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second? We want to convert revolutions per minute to revolutions per second: 3000 revolutions per minute / 60 seconds per minute = 50 revolutions per second Using our [URL='http://www.mathcelebrity.com/anglecon.php?quant=50&type=revolution&pl=Calculate']revolutions to degrees calculator[/URL], we get [B]18,000[/B]

An electrician starts off the day with 600 feet of copper wiring on his truck. During the course of the day he uses pieces 100, 82, 25, and 40 feet long. The next day, he purchases another 400 feet and puts it on his truck and later in the day uses pieces of 41, 39, and 44 feet long. How many feet of wiring are still on the truck at the end of the second day? If the electrician uses pieces, we subtract. If he purchases pieces, we add. So we have: 600 - 100 - 82 - 25 - 40 + 400 - 41 - 39 - 44 = [B]629 feet[/B]

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]

Annie got a new video game. She scored 152 points on the first level, 170 points on the second level, 188 points on the third level, and 206 points on the fourth level. What kind of sequence is this? This is an [URL='https://www.mathcelebrity.com/sequenceag.php?num=152%2C170%2C188%2C206&n=10&pl=Calculate+Series&a1=&d=']arithmetic series as seen on our calculator[/URL]:

Approximately 2,800 red blood cells are created in the bone marrow each second. How many red blood cells would be created in .03125 seconds? 2800 red blood cells / second * .01325 seconds = [B]87.5 red blood cells[/B]

Ava set her watch 2 seconds behind, every day it sets back 1 second. How many days has it been since she last set her watch if it is 41 seconds behind? Right now: Watch is 2 seconds behind [U]Let d be the day after right now[/U] (1)d + 2 = 41 d + 2 = 41 [U]Subtract 2 from each side[/U] [B]d = 39[/B]

Balls numbered 1 to 10 are placed in a bag. Two of the balls are drawn out at random. Find the probability that the numbers on the balls are consecutive. Build our sample set: [LIST] [*](1, 2) [*](2, 3) [*](3, 4) [*](4, 5) [*](5, 6) [*](6, 7) [*](7, 8) [*](8, 9) [*](9, 10) [/LIST] Each of these 9 possibilities has a probability of: 1/10 * 1/9 This is because we draw without replacement. To start, the bag has 10 balls. On the second draw, it only has 9. We multiply each event because each draw is independent. We have 9 possibilities, so we have: 9 * 1/10 * 1/9 Cancelling, the 9's, we have [B]1/10[/B]

Brandon can shovel his sidewalk in 8 minutes, while his brother can shovel the walk in 12 minutes. If they work together, how long will it take them to shovel the sidewalk? Set up unit rates: [LIST] [*]Brandon can shovel 1/8 of a sidewalk per minute [*]His brother can shovel 1/12 of a sidewalk per minute [/LIST] Together, they can shovel: [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F8&frac2=1%2F12&pl=Add']1/8 + 1/12[/URL] = 5/24 of a sidewalk per minute 1 minute = 60 seconds 5/24 / 60 seconds = 1/x seconds 5/24 * 60 = 1/x 5/1440 = 1/x Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5&num2=1&den1=1440&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get: x = 288 288/60 = [B]4 minutes and 48 seconds[/B]

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?

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]

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difference between 2 positive numbers is 3 and the sum of their squares is 117 Declare variables for each of the two numbers: [LIST] [*]Let the first variable be x [*]Let the second variable be y [/LIST] We're given 2 equations: [LIST=1] [*]x - y = 3 [*]x^2 + y^2 = 117 [/LIST] Rewrite equation (1) in terms of x by adding y to each side: [LIST=1] [*]x = y + 3 [*]x^2 + y^2 = 117 [/LIST] Substitute equation (1) into equation (2) for x: (y + 3)^2 + y^2 = 117 Evaluate and simplify: y^2 + 3y + 3y + 9 + y^2 = 117 Combine like terms: 2y^2 + 6y + 9 = 117 Subtract 117 from each side: 2y^2 + 6y + 9 - 117 = 117 - 117 2y^2 + 6y - 108 = 0 This is a quadratic equation: Solve the quadratic equation 2y2+6y-108 = 0 With the standard form of ax2 + bx + c, we have our a, b, and c values: a = 2, b = 6, c = -108 Solve the quadratic equation 2y^2 + 6y - 108 = 0 The quadratic formula is denoted below: y = -b � sqrt(b^2 - 4ac)/2a [U]Step 1 - calculate negative b:[/U] -b = -(6) -b = -6 [U]Step 2 - calculate the discriminant ?:[/U] ? = b2 - 4ac: ? = 62 - 4 x 2 x -108 ? = 36 - -864 ? = 900 <--- Discriminant Since ? is greater than zero, we can expect two real and unequal roots. [U]Step 3 - take the square root of the discriminant ?:[/U] ?? = ?(900) ?? = 30 [U]Step 4 - find numerator 1 which is -b + the square root of the Discriminant:[/U] Numerator 1 = -b + ?? Numerator 1 = -6 + 30 Numerator 1 = 24 [U]Step 5 - find numerator 2 which is -b - the square root of the Discriminant:[/U] Numerator 2 = -b - ?? Numerator 2 = -6 - 30 Numerator 2 = -36 [U]Step 6 - calculate your denominator which is 2a:[/U] Denominator = 2 * a Denominator = 2 * 2 Denominator = 4 [U]Step 7 - you have everything you need to solve. Find solutions:[/U] Solution 1 = Numerator 1/Denominator Solution 1 = 24/4 Solution 1 = 6 Solution 2 = Numerator 2/Denominator Solution 2 = -36/4 Solution 2 = -9 [U]As a solution set, our answers would be:[/U] (Solution 1, Solution 2) = (6, -9) Since one of the solutions is not positive and the problem asks for 2 positive number, this problem has no solution

Divide 73 into two parts whose product is 40 Our first part is x Our second part is 73 - x The product of the two parts is: x(73 - x) = 40 Multiplying through, we get: -x^2 + 73x = 402 Subtract 40 from each side, we get: -x^2 + 73x - 402 = 0 This is a quadratic equation. To solve this, we type it in our search engine, choose "solve Quadratic", and we get: [LIST=1] [*]x = [B]6[/B] [*]x = [B]67[/B] [/LIST]

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]

Erik is rolling two regular six-sided number cubes. What is the probability that he will roll an even number on one cube and a prime number on the other? P(Even on first cube) = (2,4,6) / 6 total choices P(Even on first cube) = 3/6 P(Even on first cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL] P(Prime on second cube) = (2,3,5) / 6 total choices P(Prime on second cube) = 3/6 P(Prime on second cube) = 1/2 <-- [URL='https://www.mathcelebrity.com/fraction.php?frac1=3%2F6&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL] Since each event is independent, we have: P(Even on the first cube, Prime on the second cube) = P(Even on the first cube) * P(Prime on the second cube) P(Even on the first cube, Prime on the second cube) = 1/2 * 1/2 P(Even on the first cube, Prime on the second cube) = [B]1/4[/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 velocity of a cheetah that runs 100m in 4 seconds 100m / 4 seconds Divide top and bottom by 4 [B]25m/second[/B]

Find two consecutive integers if the sum of their squares is 1513 Let the first integer be n. The next consecutive integer is (n + 1). The sum of their squares is: n^2 + (n + 1)^2 = 1513 n^2 + n^2 + 2n + 1 = 1513 2n^2 + 2n + 1 = 1513 Subtract 1513 from each side: 2n^2 + 2n - 1512 = 0 We have a quadratic equation. We [URL='https://www.mathcelebrity.com/quadratic.php?num=2n%5E2%2B2n-1512%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this into our search engine[/URL] and get: n = (-27, 28) Let's take the positive solution. The second integer is: n + 1 28 + 1 = 29

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]

Four children can eat a large pizza in 12 minutes. How long would it take 9 children to eat the same pizza? (Give your answer in minutes and seconds.) One child can eat the pizza in 4 * 12 minutes = 48 minutes 48 minutes per child / 9 children = 5.3333 minutes 1/3 of a minute = 20 seconds, so we have: [B]5 minutes and 20 seconds[/B]

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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]

Given that E[Y]=2 and Var [Y] =3, find E[(2Y + 1)^2] Multiply through E[(2Y + 1)^2] = E[4y^2 + 4y + 1] We can take the expected value of each term E[4y^2] + E[4y] + E[1] For the first term, we have: 4E[Y^2] We define the Var[Y] = E[Y^2] - (E[Y])^2 Rearrange this term, we have E[Y^2] = Var[Y] + (E[Y])^2 E[Y^2] = 3+ 2^2 E[Y^2] = 3+ 4 E[Y^2] = 7 So our first term is 4(7) = 28 For the second term using expected value rules of separating out a constant, we have 4E[Y] = 4(2) = 8 For the third term, we have: E[1] = 1 Adding up our three terms, we have: E[4y^2] + E[4y] + E[1] = 28 + 8 + 1 E[4y^2] + E[4y] + E[1] = [B]37[/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]

Gregg has 8 cards.Half red,half black. He picks 2 cards from the deck.What is the probability both of them are red? Half means 4 cards are red and 4 cards are black. The first draw probability of red is: 4 total red cards out of 8 total cards = 4/8. [URL='https://www.mathcelebrity.com/fraction.php?frac1=4%2F8&frac2=3%2F8&pl=Simplify']Simplified, this is[/URL] 1/2 The second draw is 3 total red cards out of 7 remaining cards. Since 1 red was drawn (4 - 1) = 3 reds left and 1 card was drawn (8 -1) = left 3/7 Since each draw is independent, we multiply the probabilities: 1/2 * 3/7 = [B]3/14[/B]

Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took four tests. She scored 10 points better on the second test than she did on the first, 20 points better on the third test than on the first, and 30 points better on the fourth test than on the first. If the mean of these four tests was 70, what was her score on the third test? Givens: [LIST] [*]Let the first test score be s: [*]The second test score is: s + 10 [*]The third test score is: s + 20 [*]The fourth test score is: s + 30 [/LIST] The mean of the four tests is 70, found below: Sum of test scores / Number of Tests = Mean Plugging in our number, we get: (s + s + 10 + s + 20 + s + 30) / 4 = 70 Cross multiply and simplify: 4s + 60 = 70 * 4 4s + 60 = 280 To [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B60%3D280&pl=Solve']solve this equation for s, we type it in our search engine[/URL] and we get: s = 55 So the third test score: s + 20 = 55 + 20 [B]75[/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 13,754 people voted for a politician in his first election, 15,420 voted for him in his second election, and 8,032 voted for him in the first and second elections, how many people voted for this politician in the first or second election? Let P(A) be the first election votes, P(B) be the second election votes, and P(A ? B) be votes for both the first AND the second elections. We want P(A U B). Use our [URL='http://www.mathcelebrity.com/probunion2.php?pa=+13754&pb=15420&paintb=8032&aub=+&pl=Calculate']two event calculator[/URL] P(A U B) = P(A) + P(B) - P(A ? B) P(A U B) = 13,754 + 15,420 - 8032 P(A U B) = 29,174 - 8,032 P(A U B) = [B]21,142[/B]

If 4 people have the same 7 shirts, what is the chance that they will wear the same shirt on one day? [LIST=1] [*]For each person, the probability they all wear the first shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the second shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the third shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the fourth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the fifth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the sixth shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [*]For each person, the probability they all wear the seventh shirt is 1/4 * 1/4 * 1/4 * 1/4 = 1/256 [/LIST] Now, we add up all those probabilities to get our answer, since any of the 7 scenarios above meets the criteria: (1 + 1 + 1 + 1 + 1 + 1 + 1)/256 [B]7/256[/B]

If Emma reads 1 page of a book in 44 seconds, how many pages will she read in 15 minutes Convert 15 minutes to seconds: 15 minutes = 60 * 15 = 900 seconds Set up a proportion of pages read to seconds where p is the number of pages read in 900 seconds (15 minutes): 1/44 = p/900 [URL='https://www.mathcelebrity.com/prop.php?num1=1&num2=p&den1=44&den2=900&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL], we get: p = [B]20.45[/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 sound travels 1/5 of a mile in one second, how many miles does it travel in 1/5 of a second? 1/5 mile / second * 1/5 second = [B]1/25 of a mile[/B]

If the slope is 6 what would the slope of a line parallel to it be? Our rule for the relation of second lines to first lines with regards to slope is this: [LIST] [*]Parallel lines have the [U]same[/U] slope [*]Perpendicular lines have the [U]negative reciprocal[/U] slope [/LIST] So the slope of the line parallel would also be [B]6[/B]

If the third of 6 consecutive numbers is 12, what is their sum? If 12 is the third of 6 consecutive numbers: First consecutive number is 12 - 2 = 10 Second consecutive number = 12 - 1 = 11 Third consecutive number = 12 Fourth consecutive number = 12 + 1 = 13 Fifth consecutive number = 13 + 1 = 14 Sixth consecutive number = 14 + 1 = 15 The sum of all consecutive numbers is: 10 + 11 + 12 + 13 + 14 + 15 =[B] 75[/B]

If there are 52 cards in a pack, what is the probability of picking 2 kings in a row when the first card picked is not put back? 4 kings in a deck, and 52 cards in a pack. First draw, the probability of drawing a king is 4/52. Second draw, we have 51 cards left since we do not put the first card back, and only 3 Kings left. So the second draw probability for a King is 3/51. Since each draw is independent, we multiply the first and second draws: 4/52 * 3/51 = [B]12/2652 = 0.0045[/B]

If there are 8 girls entered in a race, how many different ways can the runners place first, second, and third? We want 8 choose 3, or 8C3. [URL='https://www.mathcelebrity.com/permutation.php?num=8&den=3&pl=Combinations']Type 8C3 into the search engine[/URL], and we get [B]56[/B] different ways to place first, second, and third.

If there are 9000 seconds in 2.5 hours, how many hours are there in 13,500 seconds? Setup a proportion of hours to seconds where h is the number of hours in 13,500 seconds 2.5/9000 = h/13500 Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=2.5&num2=h&den1=9000&den2=13500&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL] we get: h = [B]3.75 hours[/B]

if two angles are supplementary and congruent then they are right angles Let the first angle be x. Let the second angle be y. Supplementary angles means their sum is 180: x + y = 180 We're given both angles are congruent, meaning equal. So we set x = y: y + y = 180 To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=y%2By%3D180&pl=Solve']type this equation into our search engine[/URL] and we get: y = [B]90. <-- 90 degrees is a right angle, so this is TRUE[/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]

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 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.

In the year 1999, Hicham El Guerrouj of Morocco set a new world record when he ran a mile in 3 minutes 43.13 seconds. What was his speed in miles per hour? (Round your answer to the nearest hundredth.) 3 minutes = 60 seconds per minute = 180 seconds 180 seconds + 43.13 seconds = 223.13 seconds 223.13 seconds/3600 seconds per hour = 1 mile/n miles Cross multiply: 223.13n = 3600 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=223.13n%3D3600&pl=Solve']equation solver[/URL], we get: n = [B]16.13 miles per hour[/B]

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.

Joe talked for n seconds. How many hours did Joe talk? 1 hour = 60 minutes * 6o seconds per minute = 3600 seconds So 1 second = 1/3600 hours Joe spoke [B]n/3600 hours[/B]

John took 20,000 out of his retirement and reinvested it. He earned 4% for one investment and 5% on the other. How much did he invest in each if the total amount earned was 880? The first principal portion is x. Which means the second principal portion is 20,000 - x. We have: 0.04x + 0.05(20,000 - x) = 880 0.04x + 1,000 - 0.05x = 880 Group like terms: -0.01x + 1000 = 880 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=-0.01x%2B1000%3D880&pl=Solve']equation solver[/URL], we get x = [B]12,000[/B]. Which means the other fund has 20,000 - 12,000 = [B]8,000[/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]

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]

Kendrick set his watch 9 seconds behind, and it falls behind another 1 second everyday.How far behind is Kendrick's watch if he last set it 23 days ago? Seconds Behind = 9 seconds behind + 1 second everyday * 23 days Seconds Behind = 9 + 23 Seconds Behind = 32

Kimberly wants to become a member of the desert squad at a big catering company very badly, but she must pass three difficult tests to do so. On the first Terrifying Tiramisu test she scored a 68. On the second the challenging Chocalate-Sprinkled Creme Brulee she scored a 72. If kimberly needs an average of 60 on all three tests to become a member on the squad what is the lowest score she can make on her third and final test This is a missing average problem. Given 2 scores of 68, 72, what should be score number 3 in order to attain an average score of 60? [SIZE=5][B]Setup Average Equation:[/B][/SIZE] Average = (Sum of our 2 numbers + unknown score of [I]x)/[/I]Total Numbers 60 = (68 + 72 + x)/3 [SIZE=5][B]Cross Multiply[/B][/SIZE] 68 + 72 + x = 60 x 3 x + 140 = 180 [SIZE=5][B]Subtract 140 from both sides of the equation to isolate x:[/B][/SIZE] x + 140 - 140 = 180 - 140 x = [B]40[/B]

Let n be the middle number of three consecutive integers This means: [LIST] [*]n is the second of three consecutive integers [*]The first consecutive integer is n - 1 [*]The third consecutive integer is n + 1 [/LIST] The sum is found by: n - 1 + n + n + 1 Simplifying, we get: (n + n + n) + 1 - 1 [B]3n[/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]

maggie has two job offers. The first job offers to pay her $50 per week and 10 1/2 cents per flier. The second job offer will pay only $30 per week but gives 20 cents per flier. Write and solve an equation to find how many fliers must she deliver so that the two offers pay the same per week? Let the number of fliers be f. First job: 0.105f + 50 Second job: 20f + 30 Set them equal to each other: 0.105f + 50 = 20f + 30 [URL='https://www.mathcelebrity.com/1unk.php?num=0.105f%2B50%3D20f%2B30&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]f = 1[/B]

Ms. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngest and the middle son gets $35 more than the youngest, how much does each boy get? Let 0 be the oldest son, m be the middle sun, and y be the youngest son. Set up our given equations [LIST] [*]o = 2y [*]m = y + 35 [*]o + m + y = 975 [/LIST] [U]Substitute the first and second equations into Equation 3[/U] 2y + y + 35 + y = 975 [U]Combine the y terms[/U] 4y + 35 = 975 Subtract 35 using our [URL='http://www.mathcelebrity.com/1unk.php?num=4y%2B35%3D975&pl=Solve']equation calculator[/URL] to solve and get [B]y = 235[/B] [U]Plug y = 235 into equation 2[/U] m = 235 + 35 [B]m = 270[/B] [U]Plug y = 235 into equation 2[/U] o = 2(235) [B]o = 470[/B]

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Oakdale School is sponsoring a canned food drive. In the first week of the drive, the students collected 638 cans. They collected 698 cans in the second week and 758 cans in the third week. If the students continue to collect cans at this rate, in which week will they collect more than 1,000 cans? We have an arithmetic sequence where each successive term increases by 50. [URL='https://www.mathcelebrity.com/sequenceag.php?num=638%2C698%2C758&n=10&pl=Calculate+Series&a1=5&d=3']Using our sequence calculator[/URL], we find that week #8 is when the students cross 1,000 cans.

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a total of $82. The school took in $67 on the second day by selling 8 senior citizen tickets And 5 child tickets. What is the price of each ticket? Let the number of child tickets be c Let the number of senior citizen tickets be s We're given two equations: [LIST=1] [*]10c + 3s = 82 [*]5c + 8s = 67 [/LIST] We have a system of simultaneous equations. We can solve it using any one of 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [LIST] [*][B]c = 7[/B] [*][B]s = 4[/B] [/LIST]

One number exceeds another by 15. The sum of the numbers is 51. What are these numbers? Let the first number be x, and the second number be y. We're given two equations: [LIST=1] [*]x = y + 15 [*]x + y = 51 [/LIST] Plug (1) into (2) (y + 15) + y = 51 Combine like terms: 2y + 15 = 51 [URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B15%3D51&pl=Solve']Plug this equation into the search engine[/URL] and we get: [B]y = 18[/B] Now plug this into (1) to get: x = 18 + 15 [B]x = 33[/B]

One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a comma to separate your answers. Let the first number be x and the second number be y. We're given: [LIST=1] [*]x = 1/4y [*]x + y = 25 [/LIST] Substitute (1) into (2) 1/4y + y = 25 Since 1/4 = 0.25, we have: 0.25y + y = 25 [URL='https://www.mathcelebrity.com/1unk.php?num=0.25y%2By%3D25&pl=Solve']Type this equation into the search engine[/URL] to get: [B]y = 20 [/B] Now, substitute this into (1) to solve for x: x = 1/4y x = 1/4(20) [B]x = 5 [/B] The problem asks us to separate the answers by a comma. So we write this as: [B](x, y) = (5, 20)[/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 number is equal to the square of another. Find the numbers if both are positive and their sum is 650 Let the number be n. Then the square is n^2. We're given: n^2 + n = 650 Subtract 650 from each side: n^2 + n - 650 = 0 We have a quadratic equation. [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-650%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']We type this into our search engine[/URL] and we get: n = 25 and n = -26 Since the equation asks for a positive solution, we use [B]n = 25[/B] as our first solution. the second solution is 25^2 = [B]625[/B]

one number is twice a second number. the sum of those numbers is 45. Let the first number be x and the second number be y. We're given: [LIST=1] [*]x = 2y [*]x + y = 45 [/LIST] Substitute Equation (1) into Equation (2): 2y + y = 45 [URL='https://www.mathcelebrity.com/1unk.php?num=2y%2By%3D45&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]y = 15[/B] Plug this into equation (1) to solve for x, and we get: x = 2(15) [B]x = 30[/B]

One positive number is one-fifth of another number. The difference between the two numbers is 192, find the numbers. Let the first number be x and the second number be y. We're given two equations: [LIST=1] [*]x = y/5 [*]x + y = 192 [/LIST] Substitute equation 1 into equation 2: y/5 + y = 192 Since 1 equals 5/5, we rewrite our equation like this: y/5 = 5y/5 = 192 We have fractions with like denominators, so we add the numerators: (1 + 5)y/5 = 192 6y/5 = 192 [URL='https://www.mathcelebrity.com/prop.php?num1=6y&num2=192&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Type this equation into our search engine[/URL], and we get: [B]y = 160[/B] Substitute this value into equation 1: x = 160/5 x = [B]32[/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]

I don't understand this word problem: If each of these shapes in Figure 1 were separated and filled with water, could the sphere that contains the cube hold all of the water? [I]Assume in the second image the corners of the cube touch the sphere so the diagonal from one corner of the cube to the opposite diagonal corner is the diameter of the sphere. [IMG]https://classroom.ucscout.org/courses/1170/files/191225/preview?verifier=mT7v59BhdVHalyprWq0KmBEItbf4CPWFqOgwoEa8[/IMG][IMG]https://classroom.ucscout.org/courses/1170/files/191494/preview?verifier=nsLscsxToebAVXTSYsoMr7rwIl536LrCJSDGPaHp[/IMG][/I] Could you guys help me please?

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?

Let x be the first number, y be the second number, and z be the number. We have the following equations: [LIST=1] [*]x + y + z = 305 [*]x = y - 5 [*]z = 3y [/LIST] Substitute (2) and (3) into (1) (y - 5) + y + (3y) = 305 Combine like terms: 5y - 5 = 305 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=5y-5%3D305&pl=Solve']equation solver[/URL] [B]y = 62 [/B] Substitute y = 62 into (3) z = 3(62) [B]z = 186 [/B] x = (62) - 5 [B]x = 57[/B]

Raise F to the second power then divide G by the result F to the second power: F^2 Divide G by the result: [B]G/F^2[/B]

Raise the sum of k and j to the second power The sum of k and j is written as: k + j Raise the sum to the second power: [B](k + j)^2[/B]

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Sam is eating a Big Hamburger. The first bite was 20% of the Hamburger, the second bite was 20% of what is left and so every next bite is 20% of what is left. b Is it possible for Sam to eat it all if he will bite 20% of what it is left? [B]No, this will go on for infinity. [/B] The number gets closer to 0 but never hits 0.

If a business sells for $1,000,000 (hypothetically)and the proceeds are paid out over 5 years, using the following breakdown: 10% in the first year 15% in the second year 25% in years 3 through 5 Calculate the payouts: [LIST] [*]Year 1: 10% * $1,000,000 = $100,000 [*]Year 2: 15% * $1,000,000 = $150,000 [*]Year 3: 25% * $1,000,000 = $250,000 [*]Year 4: 25% * $1,000,000 = $250,000 [*]Year 5: 25% * $1,000,000 = $250,000 [/LIST] To check our work, add up our proceed payouts: $100,000 + $150,000 + $250,000 + $250,000 + $250,000 = $1,000,000

Serial numbers for a product are to be using 3 letters followed by 4 digits. The letters are to be taken from the first 8 letters of the alphabet with no repeats. The digits are taken from numbers 0-9 with no repeats. How many serial numbers can be generated The serial number is organized with letters (L) and digits (D) like this: LLLDDDD Here's how we get the serial number: [LIST=1] [*]The first letter can be any of 8 letters A-H [*]The second letter can be any 7 of 8 letters A-H [*]The third letter can be any 6 of 8 letters A-H [*]The fourth digit can be any of 10 digits 0-9 [*]The fifth digit can be any 9 of 10 digits 0-9 [*]The sixth digit can be any 8 of 10 digits 0-9 [*]The seventh digit can be any 7 of 10 digits 0-9 [/LIST] We multiply all possibilities: 8 * 7 * 6 * 10 * 9 * 8 * 7 [B]1,693,440[/B]

Set of all consonants in the word,'SECONDARY' Our set has 6 elements below: [B]{C, D, N, R, S, Y}[/B]

Seth is constantly forgetting the combination to his lock. He has a lock with four dials. (Each has 10 numbers 0-9). If Seth can try one lock combination per second, how many seconds will it take him to try every possible lock combination? Start with 0001, 0002, all the way to 9999 [URL='https://www.mathcelebrity.com/inclusnumwp.php?num1=0&num2=9999&pl=Count']When you do this[/URL], you get 10,000 combinations. One per second = 10,000 seconds

Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is running at 5 feet per second and Claire is running at 3 feet per second. i. After how many seconds will Sophie catch Claire? ii. If the race is 500 feet, who wins? i. Sophie's distance formula is given as D = 5s Claire's distance formula is given as D = 3s + 100 Set them equal to each other 5s = 3s + 100 Subtract 3s from both sides: 2s = 100 Divide each side by 2 [B]s = 50[/B] ii. [B]Sophie since after 50 seconds, she takes the lead and never gives it back.[/B]

Sound takes 5 seconds to go one mile. Clark is standing near a rock wall and when he shouts, it takes 20 seconds for the echo to reach his ears. How far away is the rock wall? The sound makes a round trip from Clark to the wall back to Clark. 20 seconds / 5 seconds per mile = 4 miles 4 miles / 2 for round trip = [B]2 miles[/B]

Sound travels about 340 m/s. The function d(t) = 340t give the distance d(t),in meters., that sound travel in T seconds. How far goes sound traveling 59s? What we want is d(59) d(59) = 340m/s(59s) = [B]20,060m[/B]

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]

Suppose that previously collected traffic data indicate that, during the afternoon rush hour, an average of 4 cars arrive at a toll bridge each second. If it is assumed that cars arrive randomly, and can thus be modeled with Poisson distribution, what is the probability that in the next second, [U][B]NO[/B][/U] cars will arrive? Use the [I]Poisson Distribution[/I] with λ = 4 and x = 0 Using the [URL='http://www.mathcelebrity.com/poisson.php?n=+10&p=+0.4&k=+0&t=+3&pl=P%28X+=+k%29']Poisson Distribution calculator[/URL], we get P(0; 4) = [B]0.0183[/B]

Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6. When you divide x by 11 you get the same quotient but a remainder of 2. Find x. [U]Use the quotient remainder theorem[/U] A = B * Q + R where 0 ? R < B where R is the remainder when you divide A by B Plugging in our numbers for Equation 1 we have: [LIST] [*]A = x [*]B = 7 [*]Q = q [*]R = 6 [*]x = 7 * q + 6 [/LIST] Plugging in our numbers for Equation 2 we have: [LIST] [*]A = x [*]B = 11 [*]Q = q [*]R = 2 [*]x = 11 * q + 2 [/LIST] Set both x values equal to each other: 7q + 6 = 11q + 2 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=7q%2B6%3D11q%2B2&pl=Solve']equation calculator[/URL], we get: q = 1 Plug q = 1 into the first quotient remainder theorem equation, and we get: x = 7(1) + 6 x = 7 + 6 [B]x = 13[/B] Plug q = 1 into the second quotient remainder theorem equation, and we get: x = 11(1) + 2 x = 11 + 2 [B]x = 13[/B]

The ages of three siblings are all consecutive integers. The sum of of their ages is 39. Let the age of the youngest sibling be n. This means the second sibling is n + 1. This means the oldest/third sibling is n + 2. So what we want is the[URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof3consecutiveintegersequalto39&pl=Calculate'] sum of 3 consecutive integers equal to 39[/URL]. We type this command into our search engine. We get: n = 12. So the youngest sibling is [B]12[/B]. The next sibling is 12 + 1 = [B]13[/B] The oldest/third sibling is 12 + 2 = [B]14[/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 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 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 first group orders 3 pizzas and 4 drinks for $33.50. The second group orders 5 pizzas and 6 drinks for $54. Find the cost for each pizza and each drink Assumptions: [LIST] [*]Let the cost of each pizza be p [*]Let the cost of each drink be d [/LIST] Givens: [LIST=1] [*]4d + 3p = 33.50 [*]6d + 5p = 54 [/LIST] We have a simultaneous group of equations. To solve this, we can use 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we use, we get the same answer: [LIST] [*]d = [B]$2.75[/B] [*]p = [B]$7.5[/B] [/LIST]

The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The second plan had a $21 monthly fee and charges an additional $.10 for each minute of calls. For how many minutes of calls will the cost of the two plans be equal? Set up the cost equation C(m) for the first plan, where m is the amount of minutes you use C(m) = 0.14m + 14 Set up the cost equation C(m) for the second plan, where m is the amount of minutes you use C(m) = 0.10m + 21 Set them equal to each other: 0.14m + 14 = 0.10m + 21 [URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B14%3D0.10m%2B21&pl=Solve']Typing this equation into our search engine[/URL], we get: m = [B]175[/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 mean of two numbers is 49.1. The first number is 18.3. What is the second number We call the second number n. Since the mean is an average, in this case 2 numbers, we have: (18.3 + n)/2 = 49.1 Cross multiply: 18.3 + n = 98.2 [URL='https://www.mathcelebrity.com/1unk.php?num=18.3%2Bn%3D98.2&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]n = 79.9[/B]

The pieces of a 500 piece puzzle are stored in three containers. 220 pieces are in the first container and 180 pieces are in the second container. What percentage of the pieces is in the third container? [U]Calculate the number of pieces in the 3rd container:[/U] Pieces in container 3 = Total Puzzle Pieces - Pieces in container 2 - Pieces in container 1 Pieces in container 3 = 500 - 220 - 180 Pieces in container 3 = 100 Calculate the percentage of pieces in the 3rd container: Percentage of pieces in container 3 = 100% * Pieces in container 3 / Total puzzle pieces Percentage of pieces in container 3 = 100% * 100 / 500 Percentage of pieces in container 3 = 100% * 0.2 Percentage of pieces in container 3 = [B]20%[/B]

The Radio City Music Hall is selling tickets to Kayla�s premiere at the Rockettes. On the first day of ticket sales they sold 3 senior citizen tickets and 9 child tickets for a total of $75. It took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of each senior citizen ticket and each child ticket? Let the cost of child tickets be c Let the cost of senior tickets be s Since revenue = cost * quantity, we're given two equations: [LIST=1] [*]9c + 3s = 75 [*]5c + 8s = 67 [/LIST] To solve this simultaneous group of equations, we can use 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we use, we get the same answer: [LIST] [*][B]c = 7[/B] [*][B]s = 4[/B] [/LIST]

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 sound from a thunderstorm travels approximately 1/5 of a mile in one second. How far will the sound travel in 18.6 seconds? 1/5 mile per second * 18.6 seconds = [B]3.72 miles[/B]

The square of the sum of twice a number x and y Take this in algebraic expression in 3 parts: [LIST=1] [*]Twice a number x means we multiply x by 2: 2x [*]The sum of twice a number x and y means we add y to 2x above: 2x + y [*]The square of the sum means we raise the sum (2x + y) to the second power below: [/LIST] [B](2x + y)^2[/B]

the square of the sum of two numbers Let the first number be x. Let the second number be y. The sum is: x + y Now we square that sum by raising the sum to a power of 2: [B](x + y)^2[/B]

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 3 consecutive integers is greater than 30. Let the first consecutive integer be n The second consecutive integer is n + 1 The third consecutive integer is n + 2 The sum is written as: n + n + 1 + n + 2 Combine like terms: (n + n + n) + (1 + 2) 3n + 3 The phrase [I]greater than[/I] means an inequality, which we write as: [B]3n + 3 > 30[/B]

The sum of three numbers is 171. The second number is 1/2 of the first and the third is 3/4 of the first. Find the numbers. We have three numbers, x, y, and z. [LIST=1] [*]x + y + z = 171 [*]y = 1/2x [*]z = 3/4x [/LIST] Substitute (2) and (3) into (1) x + 1/2x + 3/4x = 171 Use a common denominator of 4 for each x term 4x/4 + 2x/4 + 3x/4 = 171 (4 + 2 + 3)x/4 = 171 9x/4 = 171 [URL='https://www.mathcelebrity.com/prop.php?num1=9x&num2=171&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Plug this equation into our search engine[/URL], and we get [B]x = 76[/B] So y = 1/2(76) --> [B]y = 38[/B] Then z = 3/4(76) --> [B]z = 57[/B]

The teacher is handing out note cards to her students. She gave 20 note cards to the first student, 30 note cards to the second student, 40 note cards to the third student, and 50 note cards to the fourth student. If this pattern continues, how many note cards will the teacher give to the fifth student? [LIST] [*]Student 1 has 20 [*]Student 2 has 30 [*]Student 3 has 40 [*]Student 4 has 50 [/LIST] The teacher adds 10 note cards to each student. Or, if we want to put in a sequence formula, we have: S(n) = 10 + 10n where n is the student number Simplified, we write this as: S(n) = 10(1 + n) The question asks for S(5) S(5) = 10(1 + 5) S(5) = 10(6) [B]S(5) = 60 [/B] If we wanted to simply add 10 and not use a sequence formula, we see that S(4) = 50. So S(5) = S(4) + 10 S(5) = 50 + 10 [B]S(5) = 60[/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 2 consecutive integers. Twice the first increased by the second yields 16. What are the numbers? Let x be the first integer. y = x + 1 is the next integer. We have the following givens: [LIST=1] [*]2x + y = 16 [*]y = x + 1 [/LIST] Substitute (2) into (1) 2x + (x + 1) = 16 Combine x terms 3x + 1 = 16 Subtract 1 from each side 3x = 15 Divide each side by 3 [B]x = 5[/B] So the other integer is 5 + 1 = [B]6[/B]

There are 24 competitors in a cycling race. How many different selections are possible for first and second place? We want unique combinations, so we have: [URL='https://www.mathcelebrity.com/permutation.php?num=24&den=2&pl=Combinations']24 C 2[/URL] = [B]276[/B]

There are 5 orange books, 12 black books, and 8 tan books on Mr. Johnsons bookshelf. Calculate the probability of randomly selecting a black book and then a tan book without replacement. Write your answer as a percent. P(black book first draw) P(black book first draw) = 12 black / (5 orange + 12 black + 8 tan) P(black book first draw) = 12 / 25 P(tan book second draw) P(tan book second draw) = 8 tan / (5 orange + 11 black + 8 tan) <-- 11 black because we already drew one black P(tan book second draw) = 8 / 24 Using our fraction reduction calculator, this simplifies to 1/3 Since each draw is independent, we multiply both probabilities: P(black book first draw, tan book second draw) = 12/25 * 1/3 P(black book first draw, tan book second draw) = 12/75 P(black book first draw, tan book second draw) = [B]16%[/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 3 blue, 4 red and 5 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting exactly 1 green? Calculate Total marbles Total marbles = Blue + Red + Green Total marbles = 3 + 4 + 5 Total marbles = 12 Probability of a green = 5/12 Probability of not green = 1 - 5/12 = 7/12 To get exactly one green in two draws, we either get a green, not green, or a not green, green [U]First Draw Green, Second Draw Not Green[/U] [LIST] [*]1st draw: Probability of a green = 5/12 [*]2nd draw: Probability of not green = 7/11 <-- 11 since we did not replace the first marble [*]To get the probability of the event, since each draw is independent, we multiply both probabilities [*]Probability of the event is (5/12) * (7/11) = 35/132 [/LIST] [U]First Draw Not Green, Second Draw Not Green[/U] [LIST] [*]1st draw: Probability of not a green = 7/12 [*]2nd draw: Probability of not green = 5/11 <-- 11 since we did not replace the first marble [*]To get the probability of the event, since each draw is independent, we multiply both probabilities [*]Probability of the event is (7/12) * (5/11) = 35/132 [/LIST] To get the probability of exactly one green, we add both of the events: First Draw Green, Second Draw Not Green + First Draw Not Green, Second Draw Not Green 35/132 + 35/132 = 70/132 [URL='https://www.mathcelebrity.com/fraction.php?frac1=70%2F132&frac2=3%2F8&pl=Simplify']Using our fraction simplify calculator[/URL], we get: [B]35/66[/B]

There is a sales tax of $15 on an item that costs $153 before tax. A second item costs $81.60 before tax. What is the sales tax on the second item? We assume the goods are bought in the same store, so tax rates are the same: Tax Rate = Tax Amount / Cost before tax Tax Rate = 15/153 Tax Rate = 0.098 or 9.8% Calculate sales tax on the second item Sales Tax = Cost before Tax * Tax Rate Sales Tax = 81.60 * 0.098 Sales Tax = 7.9968 We round to 2 decimals for dollars and cents and we get: Sales Tax = [B]$8.00[/B]

There is a sales tax of $4 on an item that cost $54 before tax. The sales tax on a second item is $14. How much does the second item cost before tax? Sales Tax on First Item = Tax Amount / Before Tax Sale Amount Sales Tax on First Item = 4/54 Sales Tax on First Item = 0.07407407407 For the second item, let the before tax sale amount be b. We have: 0.07407407407b = 14 To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.07407407407b%3D14&pl=Solve']type it in our search engine[/URL] and we get: b = [B]189[/B]

There is a sales tax of $5 on an item that costs $51 before tax. A second item costs $173.40 before tax. What is the sales tax on the second item? Calculate the sales tax percent using the first item: Sales Tax Decimal = 100% * Sales Tax / Pre-Tax Bill Sales Tax Decimal = 100% * 5/51 Sales Tax Decimal = 0.098 Calculate the sales tax on the second item: Sales Tax = Pre-Tax bill * (1 + Sales Tax) Sales Tax = $173.40 (1 + 0.098) Sales Taax = $173.40 * 1.098 Sales Tax = [B]$190.39[/B]

There is a stack of 10 cards, each given a different number from 1 to 10. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an odd number and the second card is greater than 7. First Event: P(1, 3, 5, 7, 9) = 5/10 = 1/2 or 0.5 Second Event: P(8, 9, 10) = 3/10 or 0.3 Probability of both events since each is independent is 1/2 * 3/10 = 3/20 = [B]0.15 or 15%[/B]

Free Time Conversions Calculator - Converts units of time between:
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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

two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of 1225. what was the rate charged per hour by each mechanic if the sum of the two rates was 170 per hour? Set up two equations: (1) 10x + 5y = 1225 (2) x + y = 170 Rearrange (2) x = 170 - y Substitute that into (1) 10(170 - y) + 5y = 1225 1700 - 10y + 5y = 1225 1700 - 5y = 1225 Move 5y to the other side 5y + 1225 = 1700 Subtract 1225 from each side 5y =475 Divide each side by 5 [B]y = 95[/B] Which means x = 170 - 95, [B]x = 75[/B]

Two mechanics worked on a car. the first mechanic worked for 5 hours snd the second mechanic worked for 15 hours. Together they charged a total of $2375. What was the rate charged per hour by each mechanic if the sum of the two rates was $235 per hour? Setup equations where x is the rate of the first mechanic and y is the rate of the second mechanic: [LIST] [*]5x + 15y = 2375 [*]x + y = 235 [/LIST] Using Cramers method with our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=5x+%2B+15y+%3D+2375&term2=x+%2B+y+%3D+235&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: [LIST] [*][B]x = 115[/B] [*][B]y = 120[/B] [/LIST]

two numbers have an average of 2100 and one number is $425 more than the other number. What are the numbers Let the first number be x and the second number be y. We're given two equations: [LIST=1] [*](x + y)/2 = 2100 (Average) [*]y = x + 425 [/LIST] Rearrange equation (1) by cross multiplying x + y = 2 * 2100 x + y = 4200 So we have our revised set of equations: [LIST=1] [*]x + y = 4200 [*]y = x + 425 [/LIST] Substituting equation (2) into equation (1) for y, we get: x + (x + 425) = 4200 Combining like terms, we get: 2x + 425 = 4200 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B425%3D4200&pl=Solve']equation solver[/URL], we get: x = [B]1887.5[/B] Which means using equation (2), we get y = 1887.5 + 425 y = [B]2312.5[/B]

Two numbers total 12, and their differences is 20. Find the two numbers. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x + y = 12 [*]x - y = 20 [/LIST] Since we have y coefficients of (-1 and 1) that cancel, we add the two equations together: (x + x) + (y - y) = 12 + 20 The y terms cancel, so we have: 2x = 32 [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D32&pl=Solve']Type this equation into our search engine[/URL] and we get: x = [B]16[/B] Substitute this value of x = 16 back into equation 1: 16 + y = 12 [URL='https://www.mathcelebrity.com/1unk.php?num=16%2By%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get: y = [B]-4 [/B] Now, let's check our work for both equations: [LIST=1] [*]16 - 4 = 12 [*]16 - -4 --> 16 + 4 = 20 [/LIST] So these both check out. (x, y) = ([B]16, -4)[/B]

two pages that face each other in a book have a sum of 569 Pages that face each other are consecutive. Let the first page be p. The second page is p + 1. Their sum is: p + p + 1 = 569 [URL='https://www.mathcelebrity.com/1unk.php?num=p%2Bp%2B1%3D569&pl=Solve']Type this equation into our search engine to solve for p[/URL], and we get: p = 284 This means p + 1 = 284 + 1 = 285 So the pages that face each other having a sum of 569 are: [B]284, 285[/B]

What is the average of 7 consecutive numbers if the smallest number is called n? [LIST] [*]First number = n [*]Second number = n + 1 [*]Third number = n + 2 [*]Fourth number = n + 3 [*]Fifth number = n + 4 [*]Sixth number = n + 5 [*]Seventh number = n + 6 [/LIST] Average = Sum of all numbers / Total numbers Average = (n + n + 1 + n + 2 + n + 3 + n + 4 + n + 5 + n + 6)/7 Average = 7n + 21/7 Factor out a 7 from the top: 7(n + 3)/7 Cancel the 7's: [B]n + 3[/B]

What is the sum of four consecutive multiples of 5? First number = n Second number = n + 5 Third number = n + 10 Fourth number = n + 15 Add them together: (n + n + n + n) + (5 + 10 + 15) [B]4n + 30[/B]

When ringing up a customer, a cashier needs 3 seconds to scan each item and 9 seconds to process the payment. Let m represent the number of items and s represent the number of seconds to ring up a customer. Build our equation R(m): [B]R(m) = ms + 9[/B]

You are offered two different sales jobs. The first company offers a straight commission of 6% of the sales. The second company offers a salary of $330 per week plus 2% of the sales. How much would you have to sell in a week in order for the straight commission offer to be at least as good? Let s be the sales and C be the weekly commission for each sales job. We have the following equations: [LIST=1] [*]C = 0.06s [*]C = 330 + 0.02s [/LIST] Set them equal to each other: 0.06s = 330 + 0.02s Subtract 0.02s from each side: 0.04s = 330 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.04s%3D330&pl=Solve']equation solver[/URL], we get [B]s = 8,250[/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 240 grams of a radioactive kind of tellurium. How much will be left after 210 minutes if its half-life is 70 minutes? if the half life is 70 minutes, then we have 210/70 = 3 half life cycles. So the first half-life is 240 * 1/2 = 120 The second half life is 120 * 1/2 = 60 The third half life is 60 * 1/2 = [B]30 grams[/B]

Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same as subtracting 5 from the number then multiplying by 4. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We're given two expressions in relation to this number (x): [U]She subtracts 6 then multiplies the result by 5[/U] [LIST] [*]Subtract 6: x - 6 [*]Multiply the result by 5: 5(x - 6) [/LIST] [U]She subtracts 5 from the number then multiplying by 4[/U] [LIST] [*]Subtract 6: x - 5 [*]Multiply the result by 5: 4(x - 5) [/LIST] Finally, the expression [I]is the same as[/I] means an equation, so we set the first expression equal to the second expression to make the following equation: 5(x - 6) = 4(x - 5) Now, let's solve the equation for x. To do this, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%28x-6%29%3D4%28x-5%29&pl=Solve']type this equation into our search engine [/URL]and we get: x = [B]10[/B]

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