Pls 20pts a rental car company offers two rental plans, plan a and plan b, for the same economy size car. for both plans, the total rental cost, ƒ(m ) is a function of the number of miles, m, that the car is driven. plan a: ƒ(m ) = 0.12m + 75 plan b: ƒ(m ) = 0.35m part a: in complete sentences, translate each function into a verbal model describing the total cost of the rental in terms of the number of miles that the car is driven. part b: for each function, determine how the rate of change will affect the total cost of a car rental. part c: for a car rental that will include a maximum of 250 miles for the duration of the rental, which plan is the most cost-effective.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.