A fly is trapped in a house with three rooms - room A, room B and room C. The fly moves between the rooms in the following manner: From room A, he will next move to B or C with probability 1/2 each; from B, it will next move to A with probability 3/4 and to C with probability 1/4; from C it always goes to room A. Since this fly is a continuous-time Markov fly, it stays for a random amount of time in each room that is exponentially distributed. In particular, it stays in each of the rooms A and B for an exponential amount of time with mean 5 minutes, and in room C for an exponential amount of time with mean 4 minutes. Required:
Construct the rate matrix Q

William invested $5000 in an account that earns 3.8% interest, compounded annually. the formula for compound interest is a(t) = p(1 + i)t. how much did william have in the account after 6 years? (apex)

Christine wong has asked dave and mike to her move into a new apartment on sunday morning. she has asked them both, in case one of them does not show up. from past experience, christine knows that there is a 40% chance that dave will not show up and a 30% chance that mik a. what is the probability that both dave and mike will show up? (round your answer to 2 decimal places.) b. what is the probability that at least one of them will show up? c. what is the probability that neither dave nor mike will show up? (round your answer to 2 decimal places.)e will not show up. dave and mike do not know each other and their decisions can be assumed to be independent.

The box plots show the average speeds, in miles per hour, for the race cars in two different races. which correctly describes the consistency of the speeds of the cars in the two races?