Sylvia is going to pick out a souvenir hat while she is on vacation. she knows the price of the hat will increase by 5% when she pays sales tax. she writes the expression h + 0.05h to find the total amount she will pay for the hat if it costs h dollars. jin correctly writes another expression, 1.05h, that will also find the the total amount sylvia will pay for the hat if it costs h dollars. use the drop-down menus to explain what each part of sylvia's and jin's expressions mean.

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 is 11.2 (i know i’m late)