Amanager purchased a total of 21 coffee mugs and key chains. each coffee mug cost $8.50,and each key chain cost $2.75. if the manager spent a total of $132.50, how many mugs did the manager purchase

Multiplying an even number of negative numbers gives an answer that is choose from:

If mary had 320 toy cars and she gave her friend 50 cars and then she gave her brother 72 more cars how much toy cars would mary have left ● explain with proper details

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.