An archery target is made of 3 concentric circles of radii 1/ √ 3, 1 and √ 3 feet. Arrows striking within the inner circle are awarded 4 points, arrows within the middle ring are awarded 3 points, and arrows within the outer ring are awarded 2 points. Shots outside the target are awarded 0 points. Consider a random variable X, the distance of the strike from the center (in feet), and let the probability density function of X be f(x) =    2 π(1+x 2 ) x > 0 0 otherwise What is the expected value of the score of a single strike?

Efficient homemakers ltd. makes canvas wallets and leather wallets as part of a money-making project. for the canvas wallets, they need two yards of canvas and two yards of leather. for the leather wallets, they need four yards of leather and three yards of canvas. their production unit has purchased 44 yards of leather and 40 yards of canvas. let x be the number of leather wallets and y be the number of canvas wallets. draw the graph showing the feasible region to represent the number of the leather and canvas wallets that can be produced.