What is the probability that three number cubes rolled will each show an even number?

Demonstrate the proof of your new polynomial identity through an algebraic proof and a numerical proof in an engaging way! make it so the whole world wants to purchase your polynomial identity and can't imagine living without it! you must: label and display your new polynomial identity prove that it is true through an algebraic proof, identifying each step demonstrate that your polynomial identity works on numerical relationships create your own using the columns below. see what happens when different binomials or trinomials are combined. square one factor from column a and add it to one factor from column b to develop your own identity. column a column b (x − y) (x2 + 2xy + y2) (x + y) (x2 − 2xy + y2) (y + x) (ax + b) (y − x) (cy + d)

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."

Mary beth used the mapping rule to find the coordinates of a point that had been rotated 90° counterclockwise around the origin. examine the steps to determine whether she made an error. m (3, –6) is rotated 90° counterclockwise. (x, y) → (–y, x) 1. switch the x- and y-coordinates: (6, –3) 2. multiply the new x-coordinate by –1: (6(–1), –3) 3. simplify: (–6, –3) .