A triangle has a perimeter of 112 cm. Each of the two longer sides of the triangle is three times as long as the shortest side. Find the length of each side of the triangle.

The graph of y x3 is translated so that the point (1. 1) is moved to (1, 4). what is the equation of the new graph?

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.

In the next 10 month,colin wants to save $900 for his vacation.he plans to save $75 each of the first 8 months. how much must he save each of the last 2 months in order to meet his goal if he saves the same amount each month ?