The pitcher has thrown a fast ball, a curve ball, then two fast balls, and two curve balls, then three fast balls. a. Predict the next 5 pitches. b. Which type of reasoning, inductive or deductive, did you use? Explain. c. Write an if-then statement to describe your conjecture. d. Write the inverse of the statement. e. Write the converse, and contrapositive of the statement.

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?