You decide that you want new carpeting in your bedroom that measures 12 feet 6 inches wide by 15 feet 9 inches long. The price of the carpet and the underlying pad is $3.49 per square foot. You decide to upgrade to the deluxe underlying pad that costs an additional $0.62 per square foot. The fee for installation is a flat fee of $180. What is the total cost, including sales tax of 6.7%, of the carpet, pad, and installation? Round your answer to the nearest cent. Write the equation that represents the total cost.

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.