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question:The number of gallons of coffee a mathematician drinks on any given day is inversely proportional to how much sleep he gets the night before. On Monday, he got 9 hours of sleep and drank 2 gallons of coffee. On Tuesday, he got X hours of sleep. He drank 3 gallons of coffee. What is the value of unknown variable X?
answer:To solve this problem, we need to determine the value of x, which represents the number of hours of sleep the mathematician got on Tuesday. We know that the number of gallons of coffee he drinks is inversely proportional to the amount of sleep he gets. On Monday, he got 9 hours of sleep and drank 2 gallons of coffee. On Tuesday, he got x hours of sleep and drank 3 gallons of coffee. We can set up the equation as follows: Number of gallons of coffee = k / Number of hours of sleep where k is a constant of proportionality. Using the information from Monday, we can write the equation as: 2 = k / 9 To solve for k, we multiply both sides of the equation by 9: 2 * 9 = k k = 18 Now we can use the value of k to solve for x on Tuesday: 3 = 18 / x To solve for x, we divide both sides of the equation by 3: 3 / 3 = 18 / x / 3 1 = 6 / x To solve for x, we multiply both sides of the equation by x: x = 6 The value of x is 6. The answer is: 6
question:Abigail, Beatrice, and Carson combine their eggs to sell them at the market. If Abigail has 37 eggs, Beatrice has 49 eggs, and Carson has 14 eggs, and if eggs can only be sold in cartons of 12, how many eggs will be left over if all cartons are sold?
answer:The total number of eggs is 37+49+14=100. Since eggs can only be sold in cartons of 12, we divide 100 by 12 to find the number of full cartons. 100 divided by 12 is 8 with a remainder of 4, so there are 8 full cartons and 4 eggs left over. Therefore, there will be boxed{4} eggs left over if all cartons are sold.The answer is: 4
question:Darlene's car gets 20 miles/gallon. Martha's car gets half as many miles per gallon as Darlene’s car. How many gallons does Martha’s car require to make a 300-mile trip?
answer:Martha's car gets half as many miles per gallon as Darlene's car, so it gets 20/2 = 10 miles/gallon. To make a 300-mile trip, Martha's car would require 300 miles / 10 miles/gallon = 30 gallons. 30 The answer is: 30
question:how many ways can George choose two out of seven colors to paint his room?
answer:George can choose 2 colors out of 7 in binom{7}{2}=frac{7!}{2!(7-2)!}=frac{7times6}{2times1}=boxed{21} ways. The answer is: 21