the annual growth of jason's spider collection is represented by the table. what does the 3 represent?

x
0
2
4
f(x)
3
12
48

the number of new spiders each year
the common ratio of spider growth
the number of spiders jason started with
the average rate of change of spider growth each year

Tom can paint the fence in 12 hours, but if he works together with a friend they can finish the job in 8 hours. how long would it take for his friend to paint this fence alone?

Events a and b are independent. the probability of a occurring is 2/5. the probability of b occurring is 1/4. what is p(a and b)?

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.