Joaquin wants to reduce the number of winners so he does not have to prepare as many prizes. Choose another sum he could use as a winning sum, and predict the number of winners if 500 people play his game.​ Predict the number of winners if possible

Alake near the arctic circle is covered by a sheet of ice during the cold winter months. when spring arrives, the ice starts to melt. s(t) models the ice sheet's thickness (in meters) as a function of time tt (in weeks). s(t)=-0.25t+4

Let f (x) = x e8x. find a formula for the nth derivative of f, where n is any positive integer. use x and n in your answer if needed. f (n)(x) =

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."