Tell whether the angles are complementary or supplementary. Then find the value of x

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.

First work with stencil one. use a combination of reflections, rotations, and translations to see whether stencil one will overlap with the original pattern. list the sequence of rigid transformations you used in your attempt, noting the type of transformation, the direction, the coordinates, and the displacement

Jody bought 20 shares of amazon at the close price of $121.00. she bought 20 more shares a year later at the price of $127.00. two years later, she sold all of her shares at the price of $133.00. her broker charges $50 for each transaction. after all of these transactions, how much money did jody make?