Math 103x Exam 1 Review Sp23

3 Answer: ____________lb ___________oz ii. (3 points) Alejandro wants to bring 11 lb of chocolate on a trip. Including the two bars he already has, how much more does he need? Specify your answer in lb and oz. Answer: ____________lb ___________oz 2) Alejandro has chocolate bars weighing 3 lb 11 oz, and 2 lb 14 oz. There are 16 oz in 1 lb. i. (3 points) How much in total do these bars weigh? Write your answer in lb and oz. Answer: ____________lb ___________oz ii. (3 points) Alejandro wants to bring 8 lb of chocolate on a trip. Including the two bars he already has, how much more does he need? Specify your answer in lb and oz. Answer: ____________lb ___________oz 2) Alejandro has chocolate bars weighing 1 lb 10 oz, and 2 lb 11 oz. There are 16 oz in 1 lb. i. (3 points) How much in total do these bars weigh? Write your answer in lb and oz. Answer: ____________lb ___________oz ii. (3 points) Alejandro wants to bring 9 lb of chocolate on a trip. Including the two bars he already has, how much more does he need? Specify your answer in lb and oz.

6 trig Answer: _________________meters 4) (6 points) Carla is standing at the edge of a canyon. She yells loudly and hears an echo 3.5 seconds later. How far away is the other side of the canyon in meters? You may assume the speed of sound is 340 meters per second. Round to the nearest tenth, as necessary. Answer: _________________meters 4) (6 points) Carla is standing at the edge of a canyon. She yells loudly and hears an echo 4.3 seconds later. How far away is the other side of the canyon in meters? You may assume the speed of sound is 340 meters per second. Round to the nearest tenth, as necessary. Answer: _________________meters 4) (6 points) Carla is standing at the edge of a canyon. She yells loudly and hears an echo 3.1 seconds later. How far away is the other side of the canyon in meters? You may assume the speed of sound is 340 meters per second. Round to the nearest tenth, as necessary. Answer: _________________meters

9 6) In 1993, the US minimum wage was $4.25. In 2009, the US minimum wage was $7.25. i. (3 points) Find the Absolute Change of the minimum wage between 1993 and 2009. Absolute Change ___________________ ii. (3 points) Find the Relative Change of the minimum wage between 1993 and 2009. Round to the nearest 10 th of a percent. Relative Change ___________________ 6) In 1993, the US minimum wage was $4.25. In 2004, the US minimum wage was $5.15. i. (3 points) Find the Absolute Change of the minimum wage between 1993 and 2004. Absolute Change ___________________ ii. (3 points) Find the Relative Change of the minimum wage between 1993 and 2004. Round to the nearest 10 th of a percent. Relative Change ___________________ 6) In 1988, the US minimum wage was $3.35. In 2004, the US minimum wage was $5.15. i. (3 points) Find the Absolute Change of the minimum wage between 1988 and 2004. Absolute Change ___________________

12 Answer: _________________minutes 8) (6 points) It takes a hose 6 minutes to fill a rectangular aquarium 6 inches long, 9 inches wide, and 12 inches tall. How long will it take the same hose to fill an aquarium measuring 20 inches by 24 inches by 28 inches? Round to the nearest tenth of a minute. Answer: _________________minutes 8) (6 points) It takes a hose 3 minutes to fill a rectangular aquarium 6 inches long, 8 inches wide, and 10 inches tall. How long will it take the same hose to fill an aquarium measuring 15 inches by 20 inches by 25 inches? Round to the nearest tenth of a minute. Answer: _________________minutes 9 Circle and R ecta ngl e Area 9) (6 points) A local pizza parlor is selling two different shapes of cheese pizza for the same price. You can get two small square pizzas that have sides of 8 inches or a large round pizza with a diameter of 12 inches. How much more pizza do you get with the larger choice? Round to the nearest tenth of a square inch. (Hint: Recall the area of a circle is given by ? = 𝜋 𝑟 2 )

15 Answer: $ _________________ 10) (6 points) You want to carpet your 15 ft by 19 ft room. If the carpet you have chosen costs $9.75 per square foot, who much will it cost to carpet your room? Answer: $ _________________ II Trigon omet ry 11 Pythagorean Money Savi ngs 11) (6 points) A phone line runs east along a field for 2 miles and then north along the edge of the same field for 2.5 miles. If the phone line cost $2500 per mile to install, how much could have been saved if the phone line had been installed diagonally across the field? Round to the nearest dollar. Answer: $_________________ 11) (6 points) A phone line runs east along a field for 3 miles and then north along the edge of the same field for 2.5 miles. If the phone line cost $2100 per mile to install, how much could have been saved if the phone line had been installed diagonally across the field? Round to the nearest dollar. Answer: $_________________

18 13 Find hei ght from angle 13) A tree is growing 43-ft feet from a home. The homeowner is worried the tree could fall onto the house during a storm and is considering having a tree service come out and cut the tree down. To determine if the tree needs to be cut down the homeowner stands eighteen feet (18’) from the tree and measures the angle of elevation from the ground to the top of the tree to be 67 𝑜 . a. (4 points) What is the height of the tree? (Round to 2 decimal places) Answer:_________________feet b. (2 points) Should the homeowner have the tree cut down? Why?

21 13) A tree is growing 26-ft feet from a home. The homeowner is worried the tree could fall onto the house during a storm and is considering having a tree service come out and cut the tree down. To determine if the tree needs to be cut down the homeowner stands fifteen feet (15’) from the tree and measures the angle of elevation from the ground to the top of the tree to be 61 𝑜 . a. (4 points) What is the height of the tree? (Round to 2 decimal places) Answer:_________________feet 13) b. (2 points) Should the homeowner have the tree cut down? Why? 14 Find angle from si des 14) (6 points) A playground slide is 14.5 feet long with an 8.5-foot-tall ladder. What is the measure of the angle that the slide makes with the ground, to the nearest degree? Answer:_______________degrees

22 16.5 ft 12.5 ft 18.5 ft 14) (6 points) A playground slide is 16.5 feet long with a 9.5-foot-tall ladder. What is the measure of the angle that the slide makes with the ground, to the nearest degree? Answer:_______________degrees 14) (6 points) A playground slide is 12.5 feet long with a 6.5-foot-tall ladder. What is the measure of the angle that the slide makes with the ground, to the nearest degree? Answer:_______________degrees 14) (6 points) A playground slide is 18.5 feet long with an 8.5-foot-tall ladder. What is the measure of the angle that the slide makes with the ground, to the nearest degree? Answer:_______________degrees 9.5 ft 6.5 ft 8.5 ft

23 15 Angle of De pression 15) (6 points) From the top of a 226-ft lighthouse, the angle of depression to a ship on the ocean is 9 ∘ . How far is the ship from the base of the lighthouse? Give your answer to the nearest foot. Answer:_______________feet 15) (6 points) From the top of a 179-ft lighthouse, the angle of depression to a ship on the ocean is 13 ∘ . How far is the ship from the base of the lighthouse? Give your answer to the nearest foot. Answer:_______________feet 15) (6 points) From the top of a 152-ft lighthouse, the angle of depression to a ship on the ocean is 10 ∘ . How far is the ship from the base of the lighthouse? Give your answer to the nearest foot.

24 Answer:_______________feet 15) (6 points) From the top of a 200-ft lighthouse, the angle of depression to a ship on the ocean is 7 ∘ . How far is the ship from the base of the lighthouse? Give your answer to the nearest foot. Answer:_______________feet 16 Angle of Elev ation 16) (6 points) The angle of elevation a to the top of a building in New York is found to be 10 degrees from the ground, at a distance of D=5000 feet from the base of the building. Using this information, find the height of the building. Round to the nearest foot. Height is _____________________ft 16) (6 points) The angle of elevation a to the top of a building in New York is found to be 12 degrees from the ground, at a distance of D=4000 feet from the base of the building. Using this information, find the height of the building. Round to the nearest foot.

25 Height is _____________________ft 16) (6 points) The angle of elevation a to the top of a building in New York is found to be 9 degrees from the ground, at a distance of D=3500 feet from the base of the building. Using this information, find the height of the building. Round to the nearest foot. Height is _____________________ft 16) (6 points) The angle of elevation a to the top of a building in New York is found to be 15 degrees from the ground, at a distance of D=2500 feet from the base of the building. Using this information, find the height of the building. Round to the nearest foot. Height is _____________________ft

26 III Set Theo ry and Logic 17 Set: Basic symbol s and ques tions 17) Let 𝑈 be the universal set, where 𝑈 = {1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,11 ,12 } . Let sets ? , ? , and ? be subsets of 𝑈 , where: ? = {2 ,3 ,5 ,8 ,9 ,10 ,11 ,12 } , ? = {1 ,2 ,5 ,9 ,10 ,11 } , ? = {1 ,6 ,7 ,9 ,12 } . Find the following: i. (2 points) ? ′ = ii. (2 points) ? ∩ ? = iii. (2 points) ? ′ ∪ ( ? ∩ ?) = 17) Let 𝑈 be the universal set, where 𝑈 = {1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,11 ,12 } . Let sets ? , ? , and ? be subsets of 𝑈 , where: ? = {1 ,3 ,5 ,6 ,9 ,10 ,11 ,12 } , ? = {1 ,2 ,5 ,9 ,10 ,11 } , ? = {2 ,6 ,7 ,8 ,11 } . Find the following: i. (2 points) ? ′ = ii. (2 points) ? ∩ ? = iii. (2 points) ? ′ ∪ ( ? ∩ ?) = 17) Let 𝑈 be the universal set, where 𝑈 = {1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,11 ,12 } . Let sets ? , ? , and ? be subsets of 𝑈 , where: ? = {2 ,3 ,4 ,5 ,6 ,8 ,9 ,12 } , ? = {1 ,2 ,5 ,6 ,10 ,12 } , ? = {1 ,4 ,7 ,9 ,12 } . Find the following: i. (2 points) ? ′ = ii. (2 points) ? ∩ ? = iii. (2 points) ? ′ ∪ ( ? ∩ ?) = 17) Let 𝑈 be the universal set, where 𝑈 = {1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,11 ,12 } . Let sets ? , ? , and ? be subsets of 𝑈 , where: ? = {1 ,2 ,3 ,5 ,7 ,8 ,9 ,10 } , ? = {1 ,2 ,4 ,9 ,10 ,11 } , ? = {3 ,4 ,7 ,10 ,12 } . Find the following:

27 i. (2 points) ? ′ = ii. (2 points) ? ∩ ? = iii. (2 points) ? ′ ∪ ( ? ∩ ?) = 18 Set: Create Ve nn 18) A survey of 95 people was conducted at TCC, and it was found that 49 people carried a cell phone, 38 people carried a tablet computer, and 25 carried both a cell phone and a tablet. (Hint: Fill out the provided Venn Diagram) i. (2 points) How many people carried a cell phone or a tablet? ii. (2 points) How many people carried neither a cell phone nor a tablet? iii. (2 points) How many people carried only a tablet? 18) A survey of 70 people was conducted at TCC, and it was found that 13 people carried a cell phone, 22 people carried a tablet computer, and 5 carried both a cell phone and a tablet. (Hint: Fill out the provided Venn Diagram) i. (2 points) How many people carried a cell phone or a tablet?

28 ii. (2 points) How many people carried neither a cell phone nor a tablet? iii. (2 points) How many people carried only a tablet? 18) A survey of 55 people was conducted at TCC, and it was found that 15 people carried a cell phone, 25 people carried a tablet computer, and 7 carried both a cell phone and a tablet. (Hint: Fill out the provided Venn Diagram) i. (2 points) How many people carried a cell phone or a tablet? ii. (2 points) How many people carried neither a cell phone nor a tablet? iii. (2 points) How many people carried only a tablet? 18) A survey of 101 people was conducted at TCC, and it was found that 58 people carried a cell phone, 27 people carried a tablet computer, and 4 carried both a cell phone and a tablet. (Hint: Fill out the provided Venn Diagram) i. (2 points) How many people carried a cell phone or a tablet? ii. (2 points) How many people carried neither a cell phone nor a tablet?

29 iii. (2 points) How many people carried only a tablet? 19 Logi c: Truth Ta ble Basi cs 19) (2 points per column) Complete the columns in the following truth table. A B A ∧ B A ∨ B A → B T T T F F T F F 19) (2 points per column) Complete the columns in the following truth table. A B A ∨ B A ∧ B A → B T T T F F T F F 19) (2 points per column) Complete the columns in the following truth table. A B A → B A ∨ B A ∧ B T T T F F T F F 19) (2 points per column) Complete the columns in the following truth table. A B A ∧ B A → B A ∨ B T T T F F T

30 F F 20 Logi c: Truth Ta ble 20) (6 points) Complete the truth table for the statement ~? ∧ ( ? ∨ ?) ? ? ? ~? ? ∨ ? ~? ∧ (? ∨ ?) T T T T T F T F T T F F F T T F T F F F T F F F 20) (6 points) Complete the truth table for the statement ~ (? ∧ ? ) ∨ ? ? ? ? ? ∧ ? ~(? ∧ ?) ~(? ∧ ?) ∨ ? T T T T T F T F T T F F F T T F T F F F T F F F 20) (6 points) Complete the truth table for the statement ? ∨ ~( ? ∧ ?) ? ? ? ? ∧ ? ~(? ∧ ?) ? ∨ ~(? ∧ ?) T T T T T F

31 T F T T F F F T T F T F F F T F F F 20) (6 points) Complete the truth table for the statement ( ? ∨ ?) ∧ ~? ? ? ? ? ∨ ? ~? (? ∨ ?) ∧ ~? T T T T T F T F T T F F F T T F T F F F T F F F 21 Logi c: De d vs I nd and Euler 1 21) Consider the following argument and answer the questions: Some people who live in Utah live in Provo. Terry does not live in Provo. Therefore, Terry does not live in Utah. i. (1 Point) Is this argument deductive or inductive? ii. (4 points) Draw the Venn/Euler diagram that correctly represents this argument.

32 iii. (1 point) Is the argument valid or invalid? 21) Consider the following argument and answer the questions: All people who live in St. George live in Utah. Yolanda lives in St. George. Therefore, Yolanda lives in Utah. i. (1 Point) Is this argument deductive or inductive? ii. (4 points) Draw the Venn/Euler diagram that correctly represents this argument. iii. (1 point) Is the argument valid or invalid? 21) Consider the following argument and answer the questions: All people who live in Cedar City live in Utah. Amahl lives in Utah. Therefore, Amahl lives in Cedar City. i. (1 Point) Is this argument deductive or inductive? ii. (4 points) Draw the Venn/Euler diagram that correctly represents this argument.

33 iii. (1 point) Is the argument valid or invalid? 21) Consider the following argument and answer the questions: Some people who live in Utah live in Salt Lake City. Terry does not live in Utah. Therefore, Terry does not live in Salt Lake City. i. (1 Point) Is this argument deductive or inductive? ii. (4 points) Draw the Venn/Euler diagram that correctly represents this argument. iii. (1 points) Is the argument valid or invalid? 22 Logi c: De d vs I nd and Euler 2 22) Consider the following argument and answer the questions: All cats eat meat. Max is a cat. Therefore, Max eats meat. i. (1 Point) Is this argument deductive or inductive? ii. (4 points) Draw the Venn/Euler diagram that correctly represents this argument.

34 iii. (1 points) Is the argument valid or invalid? 22) Consider the following argument and answer the questions: Some cats eat broccoli. Max is a cat. Therefore, Max eats broccoli. i. (1 Point) Is this argument deductive or inductive? ii. (4 points) Draw the Venn/Euler diagram that correctly represents this argument. iii. (1 points) Is the argument valid or invalid? 22) Consider the following argument and answer the questions: All cats are mammals. Max is a cat. Therefore, Max is a mammal. i. (1 Point) Is this argument deductive or inductive? ii. (4 points) Draw the Venn/Euler diagram that correctly represents this argument. iii. (1 points) Is the argument valid or invalid?

35 22) Consider the following argument and answer the questions: Some cats have long hair. Max is a cat. Therefore, Max has long hair. i. (1 Point) Is this argument deductive or inductive? ii. (4 points) Draw the Venn/Euler diagram that correctly represents this argument. iii. (1 points) Is the argument valid or invalid? IV Graph Theo ry 23 Basic Theory 23) Consider the following graph and use it to answer the questions that follow: i. What is the degree of vertex G? (2 points) Degree:________________ ii. Is there an Euler circuit? Explain why or why not. (2 points) iii. Is the following trip through the graph a Hamiltonian circuit? AFBECGA. Explain why or why not. (2 points)

36 23) Consider the following graph and use it to answer the questions that follow: i. What is the degree of vertex G? (2 points) Degree:________________ ii. Is there an Euler circuit? Explain why or why not. (2 points) iii. Is the following trip through the graph a Hamiltonian circuit? AGBEDHA. Explain why or why not. (2 points) 23) Consider the following graph and use it to answer the questions that follow: i. What is the degree of vertex G? (2 points) Degree:________________ ii. Is there an Euler circuit? Explain why or why not. (2 points) iii. Is the following trip through the graph a Hamiltonian circuit? AFDEBFCGA. Explain why or why not. (2 points)

37 23) Consider the following graph and use it to answer the questions that follow: i. What is the degree of vertex G? (2 points) Degree:________________ ii. Is there an Euler circuit? Explain why or why not. (2 points) iii. Is the following trip through the graph a Hamiltonian circuit? AFBEDHCFA. Explain why or why not. (2 points) 24 Sorted Edges Mi nimum Cost From Ta ble 24) (6 points) The weights of the edges in a graph are shown in the table. Find the minimum cost of the circuit found using the sorted edges algorithm. Minimum cost:_____________________ 24) (6 points) The weights of the edges in a graph are shown in the table. Find the minimum cost of the circuit found using the sorted edges algorithm.

38 Minimum cost:_____________________ 24) (6 points) The weights of the edges in a graph are shown in the table. Find the minimum cost of the circuit found using the sorted edges algorithm. Minimum cost:_____________________ 24) (6 points) The weights of the edges in a graph are shown in the table. Find the minimum cost of the circuit found using the sorted edges algorithm. Minimum cost:_____________________ 25 Sorted Edges Mi nimum Cost From Graph 25) (6 points) For the graph below find the minimum cost of the circuit found using the sorted edges algorithm.

39 Minimum cost:_____________________ 25) (6 points) For the graph below find the minimum cost of the circuit found using the sorted edges algorithm. Minimum cost:_____________________ 25) (6 points) For the graph below find the minimum cost of the circuit found using the sorted edges algorithm. Minimum cost:_____________________ 25) (6 points) For the graph below find the minimum cost of the circuit found using the sorted edges algorithm.

40 Minimum cost:_____________________ 26 Nearest Neighbor from Graph 26) (6 points) Apply the Nearest Neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Circuit:_________________________ 26) (6 points) Apply the Nearest Neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Circuit:_________________________ 26) (6 points) Apply the Nearest Neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A.

41 Circuit:_________________________ 26) (6 points) Apply the Nearest Neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Circuit:_________________________ 27 Nearest Neighbor from Ta ble 27) (6 points) The weights of the edges in a graph are shown in the table. Apply the Nearest Neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A.

42 Circuit:_________________________ 27) (6 points) The weights of the edges in a graph are shown in the table. Apply the Nearest Neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Circuit:_________________________ 27) (6 points) The weights of the edges in a graph are shown in the table. Apply the Nearest Neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A.

43 Circuit:_________________________ 27) (6 points) The weights of the edges in a graph are shown in the table. Apply the Nearest Neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Circuit:_________________________ 28 Minimum Cos t Spanning Tree From Graph 28) Find the minimum cost spanning tree on the graph below using Kruskal's algorithm. Draw the edges included in the minimum cost spanning tree. (4 points) What is the total weight of the minimum cost spanning tree? (2 points) Total weight:_________________

44 28) Find the minimum cost spanning tree on the graph below using Kruskal's algorithm. Draw the edges included in the minimum cost spanning tree. (4 points) What is the total weight of the minimum cost spanning tree? (2 points) Total weight:_________________ 28) Find the minimum cost spanning tree on the graph below using Kruskal's algorithm. Draw the edges included in the minimum cost spanning tree. (4 points) What is the total weight of the minimum cost spanning tree? (2 points) Total weight:_________________ 28) Find the minimum cost spanning tree on the graph below using Kruskal's algorithm. Draw the edges included in the minimum cost spanning tree. (4 points)

45 What is the total weight of the minimum cost spanning tree? (2 points) Total weight:_________________ 29 Minimum Cos t Spanning Tree From Ta ble 29) (6 points) The weights of edges in a graph are shown in the table below. Using Kruskal's algorithm, find the cost of the minimum cost spanning tree. Minimum Cost:_________________ 29) (6 points) The weights of edges in a graph are shown in the table below. Using Kruskal's algorithm, find the cost of the minimum cost spanning tree.

46 Minimum Cost:_________________ 29) (6 points) The weights of edges in a graph are shown in the table below. Using Kruskal's algorithm, find the cost of the minimum cost spanning tree. Minimum Cost:_________________ 29) (6 points) The weights of edges in a graph are shown in the table below. Using Kruskal's algorithm, find the cost of the minimum cost spanning tree. Minimum Cost:_________________ V Voting The ory 30 Plurality wit h Elimina tion 1 30) (6 points) Find the winner under the Plurality with Elimination method (Instant Runoff Voting). Include how many votes they received during the final round. 32 25 14 26 1 st choice A B B C 2 nd choice B C A A 3 rd choice C A C B

47 Winner:__________ Votes:___________ 30) (6 points) Find the winner under the Plurality with Elimination method (Instant Runoff Voting). Include how many votes they received during the final round. Winner:__________ Votes:___________ 30) (6 points) Find the winner under the Plurality with Elimination method (Instant Runoff Voting). Include how many votes they received during the final round. Winner:__________ Votes:___________ 37 22 12 29 1 st choice A B B C 2 nd choice B C A A 3 rd choice C A C B 27 21 16 28 1 st choice A B B C 2 nd choice B C A A 3 rd choice C A C B

48 30) (6 points) Find the winner under the Plurality with Elimination method (Instant Runoff Voting). Include how many votes they received during the final round. Winner:__________ Votes:___________ 31 Plurality wit h Elimina tion 2 31) Here is the preference schedule for a recent election among four candidates: Number of voters 14 4 16 3 11 9 1st choice C A A C B B 2nd choice B B C A C A 3rd choice A C B B A C i. (1 points) How many voters voted in this election? Voters:________________ ii. (1 points) How many first-place votes are needed for a majority? Votes:_________________ iii. (4 points) Find the winner under Plurality with Elimination (Instant Runoff Voting)? 36 21 10 39 1 st choice A B B C 2 nd choice B C A A 3 rd choice C A C B

49 Winner:__________ 31) Here is the preference schedule for a recent election among four candidates: Number of voters 15 5 17 4 10 8 1st choice C A A C B B 2nd choice B B C A C A 3rd choice A C B B A C i. (1 points) How many voters voted in this election? Voters:________________ ii. (1 points) How many first-place votes are needed for a majority? Votes:_________________ iii. (4 points) Find the winner under Plurality with Elimination (Instant Runoff Voting)? Winner:__________ 31) Here is the preference schedule for a recent election among four candidates: Number of voters 14 6 16 6 11 7 1st choice C A A C B B 2nd choice B B C A C A 3rd choice A C B B A C i. (1 points) How many voters voted in this election? Voters:________________ ii. (1 points) How many first-place votes are needed for a majority?

50 Votes:_________________ iii. (4 points) Find the winner under Plurality with Elimination (Instant Runoff Voting)? Winner:__________ 31) Here is the preference schedule for a recent election among four candidates: Number of voters 11 8 14 9 9 9 1st choice C A A C B B 2nd choice B B C A C A 3rd choice A C B B A C i. (1 points) How many voters voted in this election? Voters:________________ ii. (1 points) How many first-place votes are needed for a majority? Votes:_________________ iii. (4 points) Find the winner under Plurality with Elimination (Instant Runoff Voting)? Winner:__________

51 32 Pairwise Comparison 1 32) The table below summarizes the preference voting for four candidates A, B, C, and D. Use the table to answer the following questions. i. (4 points) Find the number of points Candidate A receives under Pairwise Comparison (Copeland’s Method) Points:_____________________ ii. (2 points) Is there a Condorcet Candidate? Explain. 32) The table below summarizes the preference voting for four candidates A, B, C, and D. Use the table to answer the following questions. i. (4 points) Find the number of points Candidate A receives under Pairwise Comparison (Copeland’s Method)

52 Points:_____________________ ii. (2 points) Is there a Condorcet Candidate? Explain. 32) The table below summarizes the preference voting for four candidates A, B, C, and D. Use the table to answer the following questions. i. (4 points) Find the number of points Candidate A receives under Pairwise Comparison (Copeland’s Method) Points:_____________________

53 ii. (2 points) Is there a Condorcet Candidate? Explain. 32) The table below summarizes the preference voting for four candidates A, B, C, and D. Use the table to answer the following questions. i. (4 points) Find the number of points Candidate A receives under Pairwise Comparison (Copeland’s Method) Points:_____________________ ii. (2 points) Is there a Condorcet Candidate? Explain.

54 33 Pairwise Comparison 2 33) Here is the preference schedule for a recent election among three candidates: i. (4 points) Find the winner of this election under the Pairwise Comparison method (Copeland's Method). List total points for each. A:________________ B:________________ C:________________ Winner:________________ ii. (2 points) Is there a Condorcet Candidate? Explain. 33) Here is the preference schedule for a recent election among three candidates: i. (4 points) Find the winner of this election under the Pairwise Comparison method (Copeland's Method). List total points for each. A:________________ B:________________ C:________________ Winner:________________ ii. (2 points) Is there a Condorcet Candidate? Explain. Number of voters 15 13 2 1st choice C B C 2nd choice A C B 3rd choice B A A Number of voters 4 10 6 1st choice A B C 2nd choice C A A 3rd choice B C B

55 33) Here is the preference schedule for a recent election among three candidates: i. (4 points) Find the winner of this election under the Pairwise Comparison method (Copeland's Method). List total points for each. A:________________ B:________________ C:________________ Winner:________________ ii. (2 points) Is there a Condorcet Candidate? Explain. 33) Here is the preference schedule for a recent election among three candidates: i. (4 points) Find the winner of this election under the Pairwise Comparison method (Copeland's Method). List total points for each. A:________________ B:________________ C:________________ Winner:________________ ii. (2 points) Is there a Condorcet Candidate? Explain. Number of voters 11 14 3 1st choice A B C 2nd choice C A B 3rd choice B C A Number of voters 16 4 12 1st choice A B C 2nd choice C C B 3rd choice B A A

56 34 Borda Count 1 34) (6 points) Using the following table, find the Borda Count for Candidate A. Use the count that assigns 1 point to last place. Count:_____________________ 34) (6 points) Using the following table, find the Borda Count for Candidate A. Use the count that assigns 1 point to last place. Count:_____________________ 34) (6 points) Using the following table, find the Borda Count for Candidate A. Use the count that assigns 1 point to last place.

57 Count:_____________________ 34) (6 points) Using the following table, find the Borda Count for Candidate A. Use the count that assigns 1 point to last place. Count:_____________________ 35 Borda Count 2 35) Below is the preference schedule for a recent election among candidates A, B and C. Using the Borda Count method, assigning 1 point to last place, answer the following questions. i. What candidate is the winning option? (2 points) Winner:________________ ii. What count did the winning candidate receive? (2 points) Number of voters 12 11 5 1st choice A B C 2nd choice C A B 3rd choice B C A

58 Count:_________________ iii. What count did the last place candidate receive? (2 points) Count:_________________ 35) Below is the preference schedule for a recent election among candidates A, B and C. Using the Borda Count method, assigning 1 point to last place, answer the following questions. i. What candidate is the winning option? (2 points) Winner:________________ ii. What count did the winning candidate receive? (2 points) Count:_________________ iii. What count did the last place candidate receive? (2 points) Count:_________________ 35) Below is the preference schedule for a recent election among candidates A, B and C. Using the Borda Count method, assigning 1 point to last place, answer the following questions. i. What candidate is the winning option? (2 points) Winner:________________ ii. What count did the winning candidate receive? (2 points) Count:_________________ Number of voters 15 9 12 1st choice A B C 2nd choice C C B 3rd choice B A A Number of voters 5 7 11 1st choice C B C 2nd choice A A B 3rd choice B C A

59 iii. What count did the last place candidate receive? (2 points) Count:_________________ 35) Below is the preference schedule for a recent election among candidates A, B and C. Using the Borda Count method, assigning 1 point to last place, answer the following questions. i. What candidate is the winning option? (2 points) Winner:________________ ii. What count did the winning candidate receive? (2 points) Count:_________________ iii. What count did the last place candidate receive? (2 points) Count:_________________ 36 Approval V oting 1 36) The table below summarizes the results of approval voting between the options A, B, C, and D. Each column shows the number of people with a certain approval vote. Approvals are marked with an X. Use the table to answer the following questions. iv. What is the winning option under approval voting? (2 points) Winner:________________ v. How many votes did the winning option receive? (2 points) Votes:_________________ vi. How many votes did the last place option receive? (2 points) Number of voters 7 3 9 1st choice B B C 2nd choice A C B 3rd choice C A A

60 Votes:_________________ 36) The table below summarizes the results of approval voting between the options A, B, C, and D. Each column shows the number of people with a certain approval vote. Approvals are marked with an X. Use the table to answer the following questions. i. What is the winning option under approval voting? (2 points) Winner:________________ ii. How many votes did the winning option receive? (2 points) Votes:_________________ iii. How many votes did the last place option receive? (2 points) Votes:_________________ 36) The table below summarizes the results of approval voting between the options A, B, C, and D. Each column shows the number of people with a certain approval vote. Approvals are marked with an X. Use the table to answer the following questions. i. What is the winning option under approval voting? (2 points) Winner:________________ ii. How many votes did the winning option receive? (2 points) Votes:_________________

61 iii. How many votes did the last place option receive? (2 points) Votes:_________________ 36) The table below summarizes the results of approval voting between the options A, B, C, and D. Each column shows the number of people with a certain approval vote. Approvals are marked with an X. Use the table to answer the following questions. i. What is the winning option under approval voting? (2 points) Winner:________________ ii. How many votes did the winning option receive? (2 points) Votes:_________________ iii. How many votes did the last place option receive? (2 points) Votes:_________________ 37 Approval V oting 2 37) The table below summarizes the results of approval voting between the options A, B, C, and D. Each column shows the number of people with a certain approval vote. Approvals are marked with an X. Use the table to answer the following questions. i. (1 point) How many total voters participated in this vote? Voters:________________ ii. (4 points) How many votes did each option receive? Proposal A:______________ # of Voters 8 7 6 3 Proposal A X X Proposal B X X X Proposal C X X X Proposal D X X X

62 Proposal B:______________ Proposal C:______________ Proposal D:______________ iii. (1 point) Which proposal will be the new marketing campaign? Winner:_________________ 37) The table below summarizes the results of approval voting between the options A, B, C, and D. Each column shows the number of people with a certain approval vote. Approvals are marked with an X. Use the table to answer the following questions. i. (1 point) How many total voters participated in this vote? Voters:________________ ii. (4 points) How many votes did each option receive? Proposal A:______________ Proposal B:______________ Proposal C:______________ Proposal D:______________ iii. (1 point) Which proposal will be the new marketing campaign? Winner:_________________ 37) The table below summarizes the results of approval voting between the options A, B, C, and D. Each column shows the number of people with a certain approval vote. Approvals are marked with an X. Use the table to answer the following questions. # of Voters 9 6 4 5 Proposal A X X Proposal B X X X Proposal C X X X Proposal D X X # of Voters 9 3 2 5 Proposal A X X X Proposal B X X X Proposal C X X X

63 i. (1 point) How many total voters participated in this vote? Voters:________________ ii. (4 points) How many votes did each option receive? Proposal A:______________ Proposal B:______________ Proposal C:______________ Proposal D:______________ iii. (1 point) Which proposal will be the new marketing campaign? Winner:_________________ 37) The table below summarizes the results of approval voting between the options A, B, C, and D. Each column shows the number of people with a certain approval vote. Approvals are marked with an X. Use the table to answer the following questions. i. (1 point) How many total voters participated in this vote? Voters:________________ ii. (4 points) How many votes did each option receive? Proposal A:______________ Proposal B:______________ Proposal C:______________ Proposal D:______________ Proposal D X X # of Voters 3 9 2 5 Proposal A X X X Proposal B X X X Proposal C X X X Proposal D X X

64 iii. (1 point) Which proposal will be the new marketing campaign? Winner:_________________