There are five balls in a bag. numbered 1,2,3,4 and 5. Kathleen pulls some number balls from the bag and does not put them back. How many ways can she do this such that th sum of the numbers on the balls she pulls out is odd?

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."

Aball is dropped from a height of 10m above the ground. it bounce to 90% of its previous height on each bounce. what is the approximate height that the ball bounce to the fourth bounce?

What is the value of the discriminant of the quadratic equation -2x = -8x + 8 and what does its value mean about thenumber of real number solutions the equation has?