An injection-molded part is likely to be obtained from any one of 8 cavities on a mold. round your answers to three decimal places (e. g. 98.765). (b) what is the probability that a part is from cavity 1, 2 or 3? (c) what is the probability that a part is neither from cavity 3 nor 4?

(b) The probability is 0.375

(c) The probability is 0.750

Step-by-step explanation:

The probability is calculated as a division between the number of options that satisfy a condition and the total number of options.

For part (b), we have 8 cavities or options for obtain the part but we want to obtain the part from cavity 1, 2 or 3, so we have 3 options. Therefore, the probability is:

For part (c), We have 8 cavities or options for obtain the part and we want to obtain the part from any cavity except cavity 3 or 4, so we have 6 options. These options are cavity 1, cavity 2, cavity 5, cavity 6, cavity 7 and cavity 8. Then, the probability is:

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.