An English teacher needs to pick 12 books to put on his reading list for the next school year, and he needs to plan the order in which they should be read. He has narrowed down his choices to 6 novels, 8 plays, and 8 nonfiction books. If he wants to include an equal number of novels, plays, and nonfiction books, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

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.

step-by-step explanation:

the answer is 40.

proof: