We can use the right outside diagonal of the empty lacsap's triangle as the coefficients of a polynomial: $$t^3 + 6t^2 + 12t + 8.$$ if we replace every $t$ with $t-1,$ we get $$(t-1)^3 + 6(t-1)^2 + 12(t-1) + 8.$$expand and simplify this polynomial. enter the polynomial as your answer.

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."

Aswimming pool is a rectangle with semicircles on the end. the rectangle is 12 meters wide and 30 meters long. the diameter and width of the swimming pool are equal. sketch and label an overhead diagram of the swimming pool. find the area of the swimming pool floor.

Larry wants to buy some carpeting for his living room. the length of the room is 4 times the width and the total area of the room is 16 square meters. what is the length of the living room