Shown here is the graph of a function f.

Suppose g(x) = −x2 + 10.

Select the function that has the smaller rate of change over the interval [1, 3].

A) f
B) g
C) They are the same.
D) Insufficient information.

C) They are the same.

Step-by-step explanation:

The function f(x) has points as per graph:

So the points are:

Rate of change for f(x):

The function g(x) has points:

So the points are:

Rate of change for f(x):

As we see both functions have same rate of change over the interval [1, 3]

The answer choice is: C) They are the same

step-by-step explanation:

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.