Mario was visiting the carnival when he noticed a few number relationships.
he made then into brainteasers for you.
a. if three-tenths of the visitors were adults and there were 100 visitors, how many visitors were adults?
b. five-eighths of the prizes at the giant spin were dolls. if there were 64 prizes, how many prizes were not dolls?

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.