Kognity Airlines is known for its punctuality across the world. The probability, P(D), that one of its flights departs on time is 0.91, the probability, P(A), that it arrives on time is 0.94, and the probability that it both departs and arrives on time is 0.87. Find the probability that:
(i) the flight departed on time given that it arrives on time.

(ii) the flight arrived on time given that it did not depart on time.

F(x)=x/2-2 and g(x)=2x^2+x-3 find (f+g)(x)

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.

What is a correct first step in solving the inequality-4(3-5x)> -6x+9