Cars5439561499TotalThe table shows the number of cars and trucks that used a certain toll road on a particular day. The number o
f cars and trucks that used, and did not use, an electronic toll pass on that same day was also recorded.Toll PassTrucks TotalUsed341Did not use61015669512450by one of these vehicles is selected at random, determine the probability that the vehicle did not use a toll pass given that the vehicle was a truck.one of these vehicles in selected at random, determine the probability that the vehicle did not use a toll pass.The probability that the randomly selected vehicle did not use a toll pass in(Round to four decimal places as needed.)The probability that the vehicle did not use a toll pass given that the vehicle is a truck, is(Round to four decimal places as needed.)
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First find the critical points of <em>f</em> :
so the point (1, 0) is the only critical point, at which we have
Next check for critical points along the boundary, which can be found by converting to polar coordinates:
Find the critical points of <em>g</em> :
where <em>n</em> is any integer. We get 4 critical points in the interval [0, 2π) at
So <em>f</em> has a minimum of -7 and a maximum of 299.