Ajar contains only black and white marbles. when one marble is drawn at random, the probability that it is white is 1/3. after 20 black marbles were added to the jar, the probability of drawing a white was 1/5. how many marbles were in the jar originally?

there are 30 marbles in the jar originally

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.