Abag contains three red marbles, six blue marbles, and three yellow marbles. what is the probability of selecting one red marble, replacing it, and then selecting one blue marble?

A bag contains three red marbles, six blue marbles, and three yellow marbles.

therefore total no. of marbles = 3 + 6 + 3 = 12

total no. of red marble = 3

therefore probablity of selecting one red marble is 3/12 = 1/4

again total no. of blue marbles is 6

therefore probability of selecting one blue marble is 6/12 = 1/2

now total probability of selecting one red ball replacing it then selecting one blue marble is. 1/4 * 1/2 = 1/8

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y

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.