I know how to solve but not getting correct answer based off answer key. Please help Directions: Solve for missing lengths and leave answer in rads simplest form

Rhombus adef is inscribed into a triangle abc so that they share angle a and the vertex e lies on the side bc . what is the length of the side of the rhombus if ab=c, and ac=b.

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.

Tim knows the volume and base area of a wooden chest that is in the shape of a rectangular prism. if the volume is 524 cubic unit and the base area is 15 square unit, what is the height of the chest? 124 unit 1124 units 112 unit 1112 units