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Let R be the region bounded by the curves f(x) = ln(x+3) +2 and g(x) = x^2 - 8x + 18.
a) Using the washer method, find the volume of the shape which is formed if R is rotated around the x- axis.
b) Using the cylindrical shells method, find the volume of the shape which is formed is R is rotated around the line x = -2.
Show all work including the integrals used and the limits of integrations.
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Suppose you randomly draw two marbles, without replacement from a bag, containing six green, four red and three black marbles. a) Determine the probability that both marbles are red.
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