If Jim paints 12 feet of fence in 8 minutes, how much does he paint in 2 minutes.

3 ft. in 2 minutes.

Step-by-step explanation:

This is because to get from 8 min. to 2 min. divide 8/4 to get 2 minutes. You have to divide 12 ft. by the same number so divide 12/4 which gives you your answer of 3 ft.

$15 each

step-by-step explanation:

$45/3 children= $15 each

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.