The next one, I hope this is loading on your screens, cause for some reason its not loading the image on for me lol

For the inequality |c| < |d| to be true, which of the following must be true?

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 path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y=-0.4+3x, where t is the height above water and x is the horizontal distance in feet. if a beam of light is shone upward at an angle modeled by the equation x+y=10, at what height from the waters surface will the beam of light hit the dolphin