Appearance
question:What is the arithmetic mean of the integers from -4 through 5, inclusive? Express your answer as a decimal to the nearest tenth.
answer:The integers from -4 through 5, inclusive, are -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. To find the arithmetic mean, we add up all the numbers and divide by the total number of numbers (which is 10). Sum of the numbers: -4 + (-3) + (-2) + (-1) + 0 + 1 + 2 + 3 + 4 + 5 = 5 Mean = frac{5}{10} = 0.5. Rounded to the nearest tenth, the mean is boxed{0.5}. The answer is: frac{1}{2}
question:Jessica was half her mother's age when her mother died. If her mother were alive now, ten years later, she would have been 70. How old is Jessica currently?
answer:If Jessica's mother would have been 70 years old now, ten years later, then her mother's current age would be 70 - 10 = 60. Since Jessica was half her mother's age when her mother died, Jessica's age at that time would have been 60 / 2 = 30. Since ten years have passed since her mother died, Jessica's current age would be 30 + 10 = 40. Therefore, Jessica is currently 40 years old. 40 The answer is: 40
question:Jenny wants to know whether bone meal or cow manure makes better fertilizer. The control plant with no fertilizer grows 36 inches high, the plant with bone meal grows to 125% of the height of the control plant, and the cow manure plant grows to 200% of the height of the bone meal plant. How tall is the cow manure plant in inches?
answer:The control plant grows to 36 inches. The plant with bone meal grows to 125% of the height of the control plant, which is 36 * 1.25 = 45 inches. The cow manure plant grows to 200% of the height of the bone meal plant, which is 45 * 2 = 90 inches. Therefore, the cow manure plant is 90 inches tall. 90 The answer is: 90
question:The function f is defined on positive integers as follows: [f(n) = left{ begin{array}{cl} n + 10 & text{if n < 10}, f(n - 5) & text{if n ge 10}. end{array} right.]Find the maximum value of the function.
answer:If we start with a number less than 10, then we can add 10 to it to get a larger number. So, the maximum value of the function when n is less than 10 is n+10. If we start with a number greater than or equal to 10, then we can subtract 5 from it to get a smaller number. We can keep subtracting 5 until we reach a number less than 10, and then we can add 10 to it to get a larger number. So, the maximum value of the function when n is greater than or equal to 10 is f(n-5)+10. To find the maximum value of the function, we need to find the largest possible value of n. Since n is a positive integer, the largest possible value of n is 9. Therefore, the maximum value of the function is f(9)=9+10=boxed{19}. The answer is: 19