Lara has four packages of baseball cards. the first package has seventeen cards. the second package has twenty-one cards. the third package has twenty-two cards, and the fourth package has sixteen cards. using front end estimation what is the best estimate for the total number of baseball cards she has?

a.

90

b.

80

c.

70

d.

60

Orly uses 2 cups of raisins for every 12 cups of trail mix she makes. how many cups of trail mix will she make if she uses 8 cups of raisins?

Is the power produced directly proportional to the wind speed, give reasons for your answer?

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.