The width of a rectangle is the length minus 6 units. the area of the rectangle is 7 units. what is the, in units, of the rectangle?

Organisms that live in the alpine and taiga biomes have developed unique adaptations that aid in their survival. the douglas-fir is a conifer tree that grows in the taiga biome. it has an average height of about 70 feet, and its wood is an important source of lumber.

Of the 304 people who attended a school play, 5/8 were students. how many of the people who attended were students.

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.