Isaac wants to join a gym. he checked out the membership fees at two gyms.
gym a charges a new member fee of $65 and $20 per month.
gym b charges a new member fee of $25 and $35 per month, but isaac will get a discount of 20% on the monthly fee

What is an alternate exterior angle

Asquare and an equilateral triangle have the same perimeter. each side the triangle is 4 inches longer than each side of the square. what is the perimeter of the square

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.