MAT 1500 Week 5 Practice Test With Correct Answers

MAT 1500 Week 5 Practice Test With Correct Answers.This review covers the new Week 5 content. Reminder: The Week 5 quiz is a comprehensive assignment and is rather long! You will be asked questions on concepts from Week 1 through Week 5. Be sure to start this quiz well before the due date and allow enough time to complete it. Please use this to prepare for the Week 5 quiz. In this document, you will find: Practice problems Solutions Common errors Please don’t miss any of these sections. Taking the time now to prepare will help you do your very best on the quiz. Please be sure to show your work for every problem that requires it. Full credit cannot be awarded when work is missing. #1 In the figure below, ∠1 and ∠2 are supplementary. Find the measures of ∠1 and ∠2. #2 In the figure below, ∠1 and ∠2 are complementary. Find the measures of ∠1 and ∠2. #3 Determine the measures of side KM and ∠a for the congruent triangles. #4 A yard is being sodded using 2 foot squares. If the yard measures 100 feet by 120 feet and the sod costs $1.25 per square, what will be the cost to sod the yard? #5 Determine the volume and surface area of the 3-dimensional figure below. Use the π key on your calculator and round to the nearest hundredth. #6 Create a graph with 5 vertices and exactly 4 bridges. #7 The graph below has at least 1 Euler path. Determine a Euler path that begins with the letter A. #8 Use set builder notation with descriptions to rename the set below. S = {6, 13, 20, 27, …} #9 Consider the set below. P = {a, b, c, d} Determine the number of possible subsets of P and name the subsets. Which of these sets are not proper subsets of P?   #10 Consider the Venn diagram below. a. Determine the set M ∩ N’ and write it in roster form. b. Determine the set M U N’ and write it in roster form. #11 Consider the 3 set Venn diagram below: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} Let A = {1, 2, 3, 4, 8} Let B = {3, 4, 5, 6, 7} Let C = {1, 3, 7, 9, 10} Which elements should be contained in Regions I, II, III, IV, V, VI, VII, and VIII? #12 A survey of 350 customers was taken at Symphony Cinemas in Chattanooga, Tennessee, regarding the type of movies that customers liked. The following information was determined. 151 liked dramas. 194 liked comedies. 147 liked reality shows. 60 liked dramas and comedies. 45 liked dramas and reality shows. 74 liked comedies and reality shows. 33 liked all three types of movies. Of the customers surveyed, how many liked None of these types of movies? Only comedies? Only reality shows? #13 Given the statement No one lives on Mars. Write the negation of this statement. #14 Consider the following simple statements: p: I cook dinner. q: I make coffee. r: The family is happy. Consider the compound statement: I cook dinner and make coffee, or the family is not happy. Write the statement in symbolic form. Construct a truth table for this symbolic statement. #15 Consider the following compound statement: If 1^2 = 4, then 3^2 = 9 Consider the simple statements: p: 1^2 = 4 q: 3^2 = 9 Determine the truth value for the simple statements. Determine the truth value for the compound statement. #16 Consider the following statements: p → q and ~p → ~q Use truth tables to determine if the statements are equivalent. #17 Determine if the following argument is valid or invalid. If you go to the store, you buy bread. You do not go to the store. _  You do not buy bread. If the statement is valid, name the valid argument. If the statement is invalid, name the invalid argument, if it exists. Verify your results using a truth table.