Mike plans to sell apples at the local farmers' market. He makes a net profit of $40 for every apple he sells but incurs a net loss of $10 dollars for every apple he doesn't sell. The random demanded quantity X for the apples is uniform on [0,5]. Let a be the amount of apples that he brings to sell. (If the demand meets or exceeds however many apples he has, he sells all of them. If the demand is fewer than the number of apples he has, he incurs a loss.) How many apples should Mike bring to maximize his expected earnings from the farmers' market?

Bag has 5 blue and 20 green beads. You select 6 beads at random, without replacement. For each blue bead selected, you get $5. For each green bead you are charged $1. Let G be your net gain. Compute the following: (i) P(G=12) (ii) E(G) (iii) V(G)

Which test should I use for this problem: A fisheries biologist stocks three different species of sunfish into a pond at an equal rate (500 individuals of each species). She is interested in determining whether catch rates of those fish by anglers differ between the three species. Any person who fishes the pond during the month of June keeps a record of how many fish they caught by each species. Each fish caught is removed from the population (i.e., harvested). Across the entire month, 100 bluegill, 75 green sunfish, and 75 redear sunfish were caught.

Consider the following model of a market for hats in which Qs is quantity of hats produced, Qd is quantity of hats purchased and P is the price of a hat.  Qs=5+12P Qd=50-3P if production conditions change so that Qs=-10+12P, what will be the change in Q*? compared to the value 41, such that Q*=Qs=Qd remains true? a. 4 b. -3 c. -4 d. 3