Let x denote the amount of gravel sold (in tons) during a randomly selected week at a particular sales facility. Suppose that the density curve has height f(x) above the value x where f(x) =    2(1 − x)     0 ≤ x ≤ 1 0     otherwise. The density curve (the graph of f(x)) is shown in the following figure. A line segment is graphed on the coordinate plane. The horizontal x axis is labeled "Gravel (tons)" and has tick marks at 0 and 1. The vertical axis is labeled "Density" and has a single tick mark at 2. The solid line segment begins at the coordinate (0, 2), goes down and right, and ends at the coordinate (1, 0). Use the fact that the area of a triangle =  1 2(base)(height) to calculate each of the probabilities. (Hint: Drawing a picture and shading the appropriate area will help.) (a) P   x <  1 4   = (b) P   x ≤  1 4   = (c) P   x <  1 8   = (d) P    1 8 < x <  1 4

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