An ecologist wishes to mark off a circular sampling region having radius 5 m . However, the radius of the resulting region is actually a random variable R with the following pat. f(r)={((3)/(4)[1-(5-r)^(2)],4

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An ecologist wishes to mark off a circular sampling region having radius 5 m . However, the radius of the resulting region is actually a random variable

R

with the following pat.

f(r)={((3)/(4)[1-(5-r)^(2)],4<=r<=6),(0 otherwise ):}

What is the expected area (in

m^(2)

) of the resulting circular region? (Round your answer to two decimal places.)

?

m^(2)

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