Iam waiting for two friends to arrive at my house. the time until a arrives is exponentially distributed with rate lambda(a) and the time until b arrives is exponentially distributed with rate lambda(b). once they arrive, both will spend exponentially distributed times, with respective rates u(a) and u(b) at my home before departing. the four exponential random variables are independent.

a) what is the probability that a arrives before and departs after b?

b) what is the expected time of the last departure?

Aboat's value over time is given as the function f(x) and graphed below. use a(x) = 400(b)x + 0 as the parent function. which graph shows the boat's value increasing at a rate of 25% per year?

Data from 2005 for various age groups show that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $105. also, for workers of ages 25 to 54 the median weekly income for whites was $676 and for blacks was $527. (a) let w represent the median weekly income for whites and b the median weekly income for blacks, and write the equation of the line that gives b as a linear function of w. b = (b) when the median weekly income for whites is $760, what does the equation in (a) predict for the median weekly income for blacks?

In each diagram, line p is parallel to line f, and line t intersects lines p and f. based on the diagram, what is the value of x? ( provide explanation)