A visitor is staying in a cabin that is 3 miles west of the closest point on a shoreline to a coral reef. The coral reef is 2 miles due south of the shoreline. The visitor plans to travel from the cabin to the coral reef by running and swimming. If the visitor runs at a rate of 7 mph and swims at a rate of 2 mph, how far should the visitor run to minimize the time it takes to reach the coral reef

3.6miles

Step-by-step explanation:

Given:

distance of tent from the closest point on shore-line, d=3miles.

distance between shoreline point and coral reef, x=2miles

The shortest distance (say l) that the visitor runs towards the reef in order to swim a minimum distance which takes least time.

Now on reaching at the shore at this point the visitor will have to swim the least distance due east to reach coral reef.

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0

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