Mrs. Roberts has one of her students do a probability demonstration. The student uses tape to mark a line on the floor and spins a top in the middle of the line. He then records whether the top stops to the left or to the right of the line.

This is repeated 40 times, with the results shown in the table.

What is the RELATIVE FREQUENCY that the top STOPS TO THE LEFT of the line?

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."

Agraph of a trapezoid can have diagonals with slopes that are negative reciprocals and two pairs of adjacent sides that are congruent, true or false, and why

If 2(a^2+b^2)=(a+b)^2 then, > a+b=0, > ab=0, > a=b, > 2a=b