Rewrite the product as a power: (pls show work)

Jessica and martha each have a bag of cookies with unequal quantities. they have 30 cookies total between the two of them. each of them ate 6 cookies from their bag. the product of the number of cookies left in each bag is not more than 80. how many more cookies will jessica have martha? if x represents the number of cookies jessica started with, complete the statements below.the inequality that describes the relationship between the number of cookies each one of them has is x^2 - x +224 > = 0.jessica has at least cookies more than martha.

In the equation sqrt(n+5)-sqrt(11-10)=1. what is the value of n

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.