In a bag there are two $20 bills, one $10 bill, four $5 bills, and three $1 bills.
if frank picks one bill from the bag, the expected value of the bill he chooses is $. if one more $20 bill and one more $10 bill are added to the bag, the expected value will change to $.

Apinhole camera is made out of a light-tight box with a piece of film attached to one side and pinhole on the opposite side. the optimum diameter d(in millimeters) of the pinhole can be modeled by d=1.9[ (5.5 x 10^-4) l) ] ^1/2, where l is the length of the camera box (in millimeters). what is the optimum diameter for a pinhole camera if the camera box has a length of 10 centimeters