The length of a rectangle is 5 meters less than twice its width. If the perimeter of the rectangle is 38 meters, then
what is the value of the length (in meters)?

Either enter an exact answer in terms of \piπ or use 3.143.14 for \piπ and enter your answer as a decimal.

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.

42. if 20 men can eat 200 kg of wheat in 40 days, then 10 men can eat 300 kg of wheat in how many days? a) 120 days b) 60 days c) 80 days d) none of these