Mark starts a rock climb when he is 1 mile above sea level. he can climb at the rate of 1.5 miles per hour. which of the following functions would express mark's height above sea level over time? f(x) = 1.5x f(x) = 1 + 1.5x f(x) = 2.5x explain how you got your answer

What is the equation of the line that is parallel to the line with the equation y= -3/4x +1 and passes through the point (12,-12)

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.

The width of a rectangle is half as long as the length. the rectangle has an area of 18 square feet. what are the length and width of the rectangle?