Dave fails quizzes with probability 1/4, independent of other quizzes. (a) what is the probability that dave fails exactly two of the next six quizzes? (b) what is the expected number of quizzes that dave will pass before he has failed three times? (c) what is the probability that the second and third time dave fails a quiz will occur when he takes his eighth and ninth quizzes, respectively? (d) what is the probability that dave fails two quizzes in a row before he passes two quizzes in a row?

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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.

no

explanation:

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