Compare the two functions. f(x) = 4x x f(x) 0 1 1 4 2 16 3 64 4 256 5 1,024 g(x) = 5x + 6 x g(x) 0 6 1 11 2 16 3 21 4 26 5 31 which statement is true? a. on every interval of x, the rate of change of f(x) exceeds the rate of change of g(x). b. as x increases, the rate of change of g(x) exceeds the rate of change of f(x). c. at x = 2, the rate of change of g(x) is equal to the rate of change of f(x). d. as x increases, the rate of change of f(x) exceeds the rate of change of g(x).

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.

your mom

step-by-step explanation: