CC A bag contains five batteries, all of which are the same size and are equally likely to be
selected. Each battery is a different brand. If you select three batteries at random, use the
counting principle to
determine how many points will be in the sample space if the
batteries are selected
a) with replacement?
b) without replacement?

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.

the answer to this would be 5x^3-6x^2-24 over 3x^2

hope this if needed hmu