An airplane travels 1800 miles in 3 hours flying with the wind. On the return trip, flying against the wind, it takes 4 hours to travel 20000 miles. Find the rate of the wind and the rate of the plane in still air.

Andrew and Michael are 15 miles apart. If they walk towards each other, they meet in 3
hours. If they both walk in the same direction, Michael overtakes, Andrew in 8 hours.
How fast does each boy walk?

Adj has a total of 1075 dance and rock songs on her system. the dance selection is 4 times the size of the rock selection. write a system of equations to represent the situation.

Identify the type of observational study described. a statistical analyst obtains data about ankle injuries by examining a hospital's records from the past 3 years. cross-sectional retrospective prospective

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.