Peter is saving for a down payment of $50,000 for a new home. yesterday, he created an equation that models his current savings plan to
determine how long it will take him reach his goal. in his model, y represents the total amount saved and x represents the number of
months since yesterday. which statement is true?
step 1:
y = 30,000 + 2,000x
y-30,000 = 30,000 + 2,000x
step 2:
- 30,000
step 3:
step 4:
step 5:
y- 30.000 = 2,000x
y - 30,000 2,0005
2,000 = 2,000
3 - 30,000
2,000
50,000 – 30,000
2,000 = x
10 = x
step 6:
step 7: 10=x

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.