In the diagram shown, cd = bc and bc = ab. choose the reasons that best support the following reasoning used to show that x = 11. 1. cd = bc and bc = ab; therefore, cd = ab 2. cd = ab, ab = x, and cd = 11; therefore, 11 = x 3. 11 = x; therefore, x = 11 a. 1. substitution property 2. transitive property 3. symmetric property b. 1. transitive property 2. substitution property 3. symmetric property c. 1. symmetric property 2. substitution property 3. transitive property d. 1. transitive property 2. symmetric property 3. substitution property

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."

Four individuals pool money together to start a new business and agree to split the profits equally. n invests $6,000, x invests $2,000, y invests $8,000 and z invests $4,000. if the profits for the first month were $100,000, y receives than if the profits were divided in proportion to how much they invested.

Simplify. 3(4+4x) (type your answer in with no spaces)