Jamie needs to determine the distance across a river. She selects a rock, R, on the opposite river bank. She finds a tree, T, on her side of the river such that is perpendicular to the river. Next, Jamie walks 50 yards down the river from the tree, T, to a spot, C. Using a compass that she made from two sticks, she measures . She then walks from C in a direction that makes the same angle as with the river bank on her side of the river. She keeps walking in that direction until she sees the tree and the rock in a straight line from her position. She marks this point B and then paces from B to T to measure the distance from point B to the tree. If BT turns out to be 75 yards, what is RT, the distance across the river?

Formulate alisha has a number in mind. if she adds three to her number the result is less than five. use this information to write and solve an inequality about alisha's number. then graph the solution set.

Find the zeros of each function. f(x) = 6x^2 - 7x - 20

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.