MIT

🔍

question:f Jerry needs 500 cherries per quart of syrup and it takes him 2 hours to pick 300 cherries and 3 hours to make the syrup, how much time will he require to make 9 quarts of syrup?

answer:Jerry needs 500 cherries per quart of syrup, so for 9 quarts of syrup, he will need a total of 500 cherries/quart * 9 quarts = 4500 cherries. Jerry can pick 300 cherries in 2 hours, so to pick 4500 cherries, he will need 2 hours/300 cherries * 4500 cherries = 30 hours. Jerry also needs 3 hours to make the syrup, so in total, he will require 30 hours + 3 hours = 33 hours. 33 The answer is: 33

question:Compute 2 times 2^5 - 8^{58} div 8^{56}

answer:Using the laws of exponents, we can simplify the expression as follows: 2 times 2^5 - 8^{58} div 8^{56} = 2 times 2^5 - 8^{58-56} = 2 times 2^5 - 8^2 = 2 times 32 - 64 = 64 - 64 = boxed{0}. The answer is: 0

question:Cortney is downloading some files to her computer. Her internet speed is 2 megabits per minute. If she can download the files one at a time and the files she is downloading have the size of 80 megabits, 90 megabits, and x megabits. It will take her 2 hours to download all of it. What is the value of unknown variable x?

answer:To solve this problem, we need to determine the value of x, which represents the size of the third file in megabits. Let's break down the information given: Internet speed: 2 megabits per minute Size of the first file: 80 megabits Size of the second file: 90 megabits Size of the third file: x megabits Total time to download all files: 2 hours We can set up the equation as follows: (Size of the first file / Internet speed) + (Size of the second file / Internet speed) + (Size of the third file / Internet speed) = Total time to download all files (80 / 2) + (90 / 2) + (x / 2) = 2 * 60 Let's simplify and solve for x: 40 + 45 + (x / 2) = 120 (x / 2) + 85 = 120 To isolate x, we subtract 85 from both sides of the equation: (x / 2) + 85 - 85 = 120 - 85 (x / 2) = 35 To solve for x, we multiply both sides of the equation by 2: 2 * (x / 2) = 35 * 2 x = 70 The value of x is 70. 70 The answer is: 70

question:Greta worked 40 hours and was paid 12 per hour. Her friend Lisa earned x per hour at her job. Lisa would have to work 32 hours to equal Greta's earnings for 40 hours. What is the value of unknown variable x? What is the value of unknown variable x?

answer:To solve this problem, we need to determine the value of x, which represents Lisa's hourly wage. Let's break down the information given: Greta's hours worked: 40 hours Greta's hourly wage: 12 per hour Lisa's hours worked: 32 hours Lisa's earnings for 32 hours: Greta's earnings for 40 hours We can set up the equation as follows: Greta's hours worked * Greta's hourly wage = Lisa's hours worked * Lisa's hourly wage 40 * 12 = 32 * x Let's simplify and solve for x: 480 = 32x To isolate x, we divide both sides of the equation by 32: 480 / 32 = 32x / 32 15 = x The value of x is 15. Lisa earns 15 per hour. 15 The answer is: 15