Jackie runs and dances for a total of 55 minutes every day. she dances for 25 minutes longer than she runs.
part a: write a pair of linear equations to show the relationship between the number of minutes jackie runs (x) and the number of minutes she dances (y) every day.
part b: how much time does jackie spend running every day? show your work.
part c: is it possible for jackie to have spent 45 minutes dancing if she runs and dances for a total of exactly 55 minutes and dances for 25 minutes longer than she
runs? explain your reasoning.
me

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.