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question:Daniel has exactly 20 pieces of candy. He has to divide them equally among his 3 sisters. What is the least number of pieces he should take away so that he could distribute the candy equally?
answer:To divide the candy equally among his 3 sisters, Daniel needs to have a number of candy that is divisible by 3. Since 20 is not divisible by 3, Daniel needs to take away some pieces of candy. The remainder when 20 is divided by 3 is 2, so Daniel needs to take away boxed{2} pieces of candy in order to distribute the candy equally. The answer is: 2
question:James paves a new parking lot. It is 400 feet by 500 feet. Only 80% of that is useable for parking. It takes x square feet to park a car. 16000 cars can be parked. 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 square feet it takes to park a car. Let's break down the information given: Size of the parking lot: 400 feet by 500 feet Usable area for parking: 80% of the total area Number of cars that can be parked: 16000 We can set up the equation as follows: Usable area for parking / Number of square feet to park a car = Number of cars that can be parked (400 feet * 500 feet * 0.8) / x = 16000 Let's simplify and solve for x: (400 * 500 * 0.8) / x = 16000 (200000 * 0.8) / x = 16000 160000 / x = 16000 To isolate x, we divide both sides of the equation by 16000: 160000 / 16000 = x 10 = x The value of x is 10. 10 The answer is: 10
question:What is the expected value of the roll of a fair octahedral die? (An octahedral die has X faces, numbered from 1 to 8.) Express your answer as a decimal. The answer is 4.5. What is the value of unknown variable X?
answer:ariable x is 8. The answer is: 8
question:What is the sum of all potential values of the greatest common divisor of 3n + 4 and n as n varies over the positive integers?
answer:By the Euclidean algorithm, we have [ text{gcd}(3n + 4, n) = text{gcd}(n, 3n + 4 - 3n) = text{gcd}(n, 4). ] Therefore, the greatest common divisor can be any divisor of 4. The positive divisors of 4 are 1, 2, and 4, so the sum of all potential values is 1 + 2 + 4 = boxed{7}. The answer is: 7