Charlie is watching hot air balloons. Balloon A has risen at a 60° angle. Balloon B has risen at an 82° angle. If the distance from balloon A to the ground is 1,400 feet, how far is balloon B from balloon A? Round your answer to the nearest whole number.

Two points labeled Balloon A and Balloon B are connected to a point labeled Charlie, which is on a straight line labeled Ground. A dashed line connects point Balloon A to line Ground; another dashed line connects point Balloon B to line Ground; both dashed lines form a right angle with line Ground; the angle formed from point Balloon A, point Charlie, and line Ground measures x degrees; and the angle formed by point Balloon B, point Charlie, and line Ground measures y degrees.

999 feet
1,005 feet
1,052 feet
1,102 feet

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.