Han two points in common why 3.
You need a compass and straightedge.
Cedar City boasts two city parks and is in the process of designing a third. The planning committee would like all
three parks to be equidistant from one another to better serve the community. A sketch of the city appears below,
with the centers of the existing parks labeled as P, and P. Identify two possible locations for the third park, and
label them as Psa and Ps, on the map. Clearly and precisely list the mathematical
steps used to determine each of
the two potential locations.
Residential area
Elementary School
Р.
High School
Light commercial
(grocery, drugstore,
dry cleaners, etc.)
Library
P2

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.