During an eight-hour shift, the proportion of time y that a sheetmetal stamping machine is down for maintenance or repairs has a beta distribution with α = 1 and β = 2. that is f(y) =    2(1 − y), 0 ≤ y ≤ 1, 0, elsewhere. the cost (in hundreds of dollars) of this downtime, due to lost production and cost of maintenance and repair, is given by c = 10 + 20y + 4y 2 . find the mean and variance of c.

chemists are often responsible for designing a chemical reaction and analyzing the products obtained from it. one significant part of designing a chemical reaction is determining the amount of each reactant that is needed and the amount of each product that will be produced. in order to do so, chemists use stoichiometry, the quantitative relationships between reactants and products.

isn't it a pentagon? sense [3 (triangle) + 4 (rectangle)] - 2 (triangle and rectangle connected) = 5 (pentagon)