(Addition and Multiplication Rules for Probability LC)P(A) = 0.61, P(B) = 0.15, and P(A ∪ B) = 0.76. Are events A and B mutually exclusive? Justify mathematically.

(Set Operations and Relations MC)Given U = {g, h, i, j, k, l, m, n, o, p}, A = {g, h, m, o, p}, and B = {h, j, k, m, n, p}. If A′ ∩ B′ = {i, l}, determine (A ∪ B)′.

  (Logic Operations and Equivalence MC)Use the statements and truth table to determine which statements are equivalent. p: It is a university. q: It offers a degree in aviation management. p q ∼p ∼q p → q ∼p → ∼q q → p ∼q → ∼p T T F F T T T T T F F T F T T F F T T F T F F T F F T T T T T T

Hematopoiesis occurs in the _______ bone marrow.

(Exponential Models MC)The level of fame of an artist is assigned from 1 to 10, with 10 signifying the most famous artist. Data are collected about selling prices for painting and the level of fame of the artists. The model ŷ = 948.25(2.998)x is calculated, where x represents the artist’s fame score and ŷ represents the predicted selling price of the painting. Use the model to predict the selling price of a painting whose artist’s fame is a level 4.

(Linear Models MC)Data collected from real estate agents were used to calculate the model ŷ = 86x + 102,540, where x represents the size of a house in square feet and ŷ represents the predicted selling price of the house in dollars. Using the model, predict the size of a house that sells for $325,000.

(Logic and Truth Tables MC)Complete the truth table for the logical statement ~q ∧ p.

(If…Then Statements MC)Given the statement, rewrite it as the biconditional statement p ↔ q.Statement: The cookie jar is filled with oatmeal raisin cookies.

(Laws of Logic and Valid Arguments MC)Given the premises and conclusion:Premise 1: All cups have handles.Premise 2: The object is not a cup.Conclusion: The object does not have a handle.Disprove the argument by giving a counterexample.

(Laws of Logic and Valid Arguments MC)Given the statements, use the Law of Syllogism to create a valid argument.p: I plan to go to a vocational school.q: I take carpentry classes.r: I will be a ship carpenter.