Find the interval(s) over which the function is decreasing

Answer : (0,3) U  (3, ∞)

We need to find  the interval(s) over which the function is decreasing

We look at the intervals of x  where the graph is decreasing

Decreasing interval of the graph is the part where the graph goes down

We look at the part where the graph changes direction

In the middle  inverted U shaped graph , the graph changes direction and start decreasing at x=0

the graph is decreasing till x=3

so first decreasing interval is x=0  to 3. we write it as (0,3)

After x=3 the graph starts decreasing and it goes to infinity

So the second decreasing interval is 3  to infinity . We write it as (3, ∞)

Now combine both intervals by a 'U' union

(0,3) U  (3, ∞)

8/k

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.