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Probability; Eliminate the paramter to find a cartesian equation of the curve; Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases

1) The manager of a fast food restaurant determines that the average time that her customers wait for service is 2.5 minutes.
a) Find the probability that a customer has to wait for more than 4 mintues.
b) Find the probability that a customer is served within the first 2 minutes.

Now, this was all worked out, but some steps missing and need to know them.

a) Is the intergal from 4 to infinity and f(x) = 1/2.5 * e^(-t/2.5)

Whoever is helping me please solve for t. Show me step by step how to solve for t!
Then take the integral of "t" from 4 to infinity and show me and give the answer.

b) Take answer from a and intergrate it from 0 to 2. Answer b is 0.55. My calculator does not solve for infinity so need to see this.

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These problems have the heading of: 11, 13, 15, 17
a) Eliminate the paramter to find a cartesian equation of the curve.
b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

11) x = sin(theta), y = cos(theta) , 0 < or equal (theta) < or equal pi

13) x = sin^2(theta), y= cos^2(theta), (no limits are shown on problem so how get limits or do not care??)

15) x=e^t, y=e^-t, (no limits given in problem so do what for limits or do not care?)

17) x=coshT, y=sinht (again, no limits given.)

Solution Summary

Probability and parametric equations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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