You are trying to help Matt understand the concept of a 5% slack in the line. You explain that having a 5% slack means that the length is 5% longer than
it would be if it were completely straight. You compare AABC to Figure DEF,
where curve DE is 5% longer than line segment AB.
Right Triangle without Slack
Figure with Slack
B
E
3
3
A
с
D
F
4
4
Enter the length of curve DE given that the curve is 5% longer than line
segment AB.

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.