Shaun recycles bottles and cans. He earns 10 cents for each bottle he recycles
and 5 cents for each can he recycles. After recycling a bag of bottles and cans, he
gets a receipt that states he earned $12.75 and recycled a total of 210 bottles
and cans. To determine the number of bottles and the number of cans he recycled,
Shaun writes the system of equations below.
x + y = 210
10x + 5y = 1275
Part A: Explain how you know that x represents the number of bottles Shaun
recycled. Write your answer on the lines provided.
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Asquare parking lot has 6,400 square meters what is the length in meters

Aclassroom is made up of 11 boys and 14 girls. the teacher has four main classroom responsibilities that she wants to hand out to four different students (one for each of the four students). if the teacher chooses 4 of the students at random, then what is the probability that the four students chosen to complete the responsibilities will be all boys?

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.