Suppose a jar contains 7 green marbles, 3 blue marbles. If one marble is drawn at random, then replaced and then another marble is drawn at random, what is the probability of drawing one green marble then one blue marble?

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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.

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.