The owner of a 4000-gal oil truck loads the truck with gasoline and keroseno. the profit on each gallon of gasoline is 16e and on each gallon of kerosene it is 12¢. how many gallons of each fuel did the owner load it
the profit was $620?
there
gallons of gasoline and
of kerosene.

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You have 17 cats that live in houses on your street, 24 dogs, 3 fish, and 4 hamsters. what percent of animals on your block are dogs?

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.