The linear function graphed below represents tim’s age in the years since he was married. which of these statements is correct? a(the initial value is 22, and the rate of change is 1. b(the initial value is 22, and the rate of change is 15. c(the initial value is 32, and the rate of change is 1. d(the initial value is 32, and the rate of change is 15.

Sienna planned a trapezoid-shaped garden, as shown in the drawing below. she decides to change the length of the top of the trapezoid-shaped garden from 32 ft to 24 ft. which expression finds the change in the scale factor?

The length of a rectangle plus its width is 25 cm. the area is 156 square cm. what are the length and width of the rectangle? separate the answers with a comma.

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.