The volume of a cube is 36 cubic feet. what is the volume of a pyramid that fits exactly inside the cube? provide an explanation and proof for your answer to receive full credit.

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."

Sam is a waiter at a local restaurant where he earns wages of $5 per hour sam figures that he also eams about $3 in tips for each person he serves sam works 6 hours on a particular day. if n represents the number of people sam serves that day, which of the following functions could sam use to figure ehis total earings for the do o a. en) = 30 o b. en) = 5n+ 18

Tom can paint the fence in 12 hours, but if he works together with a friend they can finish the job in 8 hours. how long would it take for his friend to paint this fence alone?