An automobile manufacturer is preparing a shipment of cars and trucks on a cargo ship that can carry 21,600 tons. The cars weigh 3.6 tons each and the trucks weigh 7.5 tons each.

For one shipment, trucks are loaded first and cars are loaded afterwards. (Even though trucks are bulkier than cars, a shipment can consist of all trucks as long as it is within the weight limit.)

Find the number of cars that can be shipped if the cargo already has $$x trucks (answer should be an expression)

On a string instrument, the length of a string varies inversely as the frequency of its vibrations. an 11-inch string has a frequency of 400 cylces per second. find the frequency of a 10-icnch string.

Can someone me out here number 4 plz

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.