(Logic and Truth Tables HC)Two propositional statements are given.p: Some koalas sleep during the day.q: All koalas stay up late.Part A: Write a logical function to represent If some koalas sleep during the day, then some koalas do not stay up late. (5 points)Part B: Determine the truth table values for the column ~p → q. (5 points) p q ~p ~q ~p → q T T F F   T F F T   F T T F   F F T T  

(Combinations and Permutations MC)A pet store has 14 types of dog treats. A customer purchases 3 different types of dog treats. Determine how many different 3-treat orders a customer can purchase.

(Addition and Multiplication Rules for Probability MC)A cafe offers 9 types of coffee, 3 types of tea, and 4 types of soft drinks. Determine the total number of beverages from which a customer can choose.

(Interpreting Data Distributions MC)The display shows data collected from a group of volunteers who attended a community service meeting.What percentage of the volunteers were aged 11 to 24?

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

(Linear Models MC)Data collected from real estate agents were used to calculate the model ŷ = 89x + 102,790, 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 $350,000.

(Logic Operations and Equivalence MC)Use the statements and truth table to determine which statements are equivalent.p: It is a burger.q: It has ketchup on it. p q ~p ~q p → q ~q → ~p q → p T T F F T T T T F F T F F T F T T F T T F F F T T T T T

(Exponential Models MC)A music streaming platform used data to calculate the model ŷ = 803.3(1.138)x, where x represents the number of days since a song was released and ŷ represents the predicted number of downloads. Interpret the percent rate of change of the model in the context of the problem.

Identify the “cup.”

(Combinations and Permutations LC)Calculate the number of combinations, given n = 17 and r = 3.