A company has two types of machine that run 24 hours a day, 7 days a week. Type A machine breaks down on average 10 breakdowns per day. This is equivalent to saying the mean wait time per breakdown is days per breakdown. For type B machine, the mean wait time between breakdowns is 0.7 days per breakdown.

For each type of machine, assume breakdowns occur as a time homogeneous Poisson process, so that for each type of machine the waiting time for a breakdown has exponential distribution, but with differing parameters depending on whether the machine is type A or type B.

Suppose 25% of the machines at this company are type A.

You observe a machine but cannot tell what type it is. But you do observe that within the next 5 hours it does not break down. What is the posterior probability this is a type A machine? Answer as a decimal accurate to 4 decimal places.

The equation shown below represents function f. f(x)= -2x+5 the graph shown below represents function g. which of the following statements is true? a. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is less than the y-intercept of function g. b. over the interval [2, 4], the average rate of change of f is greater than the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. c. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. d. over the interval [2, 4], the average rate of change of f is less than the average rate of change of g. the y-intercept of function f is the same as the y-intercept of function g.

Apyramid fits exactly inside a cube. the cube and the pyramid share the same square base, and they are both exactly the same height. the volume of the cube is 66 cubic inches. what is the volume of the pyramid? explain your answer. answer asap

Use the balanced scale to find the number of grams in 17 kilograms.