Mathematics, 29.01.2021 17:20 jennyhoang4330
Suiting at 6 a. m., cars, buses, and motorcycles arrive at a highway loll booth according to independent Poisson processes. Cars arrive about once every 5 minutes. Buses arrive about once every 10 minutes. Motorcycles arrive about once every 30 minutes.
(a) Find the probability that in the first 20 minutes, exactly three vehicles-two cars and one motorcycle-arrive at the booth.
(b) At the toll booth, the chance that a driver has exact change is 1/4. independent of vehicle. Find the probability that no vehicle has exact change in the first 10 minutes.
(c) Find the probability that the .seventh motorcycle arrives within 45 minutes of the third motorcycle.
(d) Find the probability that at least one other vehicle arrives at the toll booth between the third and fourth car arrival.
Answers: 3
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The first few steps in solving the quadratic equation 9x2 + 49x = 22 ? 5x by completing the square are shown. 9x2 + 49x = 22 ? 5x 9x2 + 54x = 22 9(x2 + 6x) = 22 which is the best step to do next to solve the equation by completing the square? 9(x2 + 6x + 3) = 25 9(x2 + 6x + 3) = 49 9(x2 + 6x + 9) = 31 9(x2 + 6x + 9) = 103
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