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Question- Find X

You are making a battery for a science project. you have copper wire for your first electrode. you need to choose a conductor, a second electrode, and a device to plug into your battery. you have already chosen a lemon conductor. complete each statement below about the options that include a lemon conductor.

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.

Point b lies between points a and c on . let x represent the length of segment ab in inches. use the segment to complete the statements. the value of x is . the length of in inches is . the length of in inches is .