Determining Angle Measures in Context A section of wall is being framed, A model of the framing
work is shown below.
Which best describes the relationship between the
125° angle and angle A?
They are same side interior angles. Angle A
measures 55°
They are alternate interior angles, Angle A
measures 125
They are vertical angles, Angle A measures 125,
They are corresponding angles, Angle A measures
55
1250
P
A
Done
) Intro

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.