A bowling ball manufacturer ships 8 bowling balls in a cubic box with edge length 17 inches, as shown. The bowling balls that are packaged are all the same size and are tangent to each other and the side of the box. To ensure the bowling balls and prevent any damage during shipping, finely shredded paper is blown into all of the space that is not taken up by the bowling balls. Which of the following is closest to the total volume, in cubic inches, of finely shredded paper that will be needed to completely fill the box of bowling balls to prepare for shipping?

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."

The boiling point of water at an elevation of 0 feet is 212 degrees fahrenheit (°f). for every 1,000 feet of increase in elevation, the boiling point of water decreases by about 2°f. which of the following represents this relationship if b is the boiling point of water at an elevation of e thousand feet? a) e = 2b - 212 b) b = 2e - 212 c) e = -2b + 212 d) b = -2e + 212

If value of cos330° is √3/2 then find tan165°.