A local pizza store knows the mean amount of time it takes them to deliver an order is 454545 minutes after the order is placed. The manager has a new system for processing delivery orders, and they want to test if it changes the mean delivery time. They take a sample of delivery orders and find their mean delivery time is 484848 minutes.

H0 :μ=45 minutes

Ha:μ  doesnt not equal45 minutes

Step-by-step explanation:

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.