Two-step equations. Solve 4x -7 =17

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.

Crickets can jump with a vertical velocity of up to 14 ft/s. which equation models the height of such a jump, in feet, after t seconds? h(t) = –16t2 + v0t + h0 h(t) = –16t2 + v0t + 14 h(t) = –16t2 + 14t h(t) = –16t2 + 14t + 14 what is the maximum height the cricket reaches? round to the nearest thousandth. h = feet

Barrett is comparing the membership fees for two museums.the art museum charges a one-time fee of $8.25 plus $2.25 per month. the science museum charges a one-time fee of $10.75 plus $3.50 per month. how much does barrett save by joining the art museum instead of the science museum?