Adolphin show is scheduled to start at 9: 00 a. m., 9: 30 a. m., and 10: 00 a. m. once the show starts, the gate will be closed. a visitor will arrive at the gate at a time uniformly distributed between 8: 30 a. m. and 10: 00 a. m. determine a) the cumulative distribution function of the time (in minutes) between 8: 30 a. m. and arrival.

The cumulative distribution function of the time (in minutes) between 8:30 A.M. and arrival is such that 0 < x < 90.

Step-by-step explanation:

Consider the provided information.

A dolphin show is scheduled to start at 9:00 AM, 9:30 A.M and 10:00 A.M.

Once the show starts, the gate will be closed. The arrival time of the visitor at the gate is uniformly distributed between 8:30 A.M and 10:00 A.M.

The time in minutes is between arrival and 8:30A.M.

Uniform distribution is defined as, where a<x<b

Here a=0 and b=90

Thus, the probability density function is:

The cumulative distribution function of the time between arrival and 8.30 A.M is,

Hence, the cumulative distribution function of the time (in minutes) between 8:30 A.M. and arrival is such that 0 < x < 90.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

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