Jamie has a deck of 60 sports cards, of which some are baseball cards and some are football cards. jamie pulls out a card randomly from the deck, records its type, and replaces it in the deck. jamie has already recorded six baseball cards and nine football cards. based on these data, what is, most likely, the number of baseball cards in the deck?

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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.