Question: The City of Detroit is electing a
The City of Detroit is electing a communications director. The choices for the position are Allen (A), Brady (B), Conrad (C), Davis (D), and Evers (E). The election is conducted, and the preference table is shown below. 
Before calculating the results of this election, it is learned that Conrad has dropped out of the race for personal reasons. (a) Using the pairwise comparison method, which candidate is chosen if Conrad is included? (b) Using the pairwise comparison method, which candidate is chosen if Conrad is eliminated from the preference table? (c) Does this second result violate the irrelevant alternatives criterion?
> At a special clothing sale at the Crescent Oaks Country Club, after the cashier rings up your purchase, you select a slip of paper from a box. The slip of paper indicates the dollar amount, either $5 or $10, that is deducted from your purchase price. The
> Juan paid $7000 for a new central air-conditioning unit for his house. He paid 20% as a down payment and financed the balance with a 36-month fixed installment loan with an APR of 5%. (a) Determine Juan’s finance charge. (b) Determine Juan’s monthly paym
> Seattle Greenery In July in Seattle, the grass grows 1/2 in. a day on a sunny day and 1/4 in. a day on a cloudy day. If in Seattle in July, 75% of the days are sunny and 25% are cloudy (a) Determine the expected amount of grass growth on a typical day in
> In Exercises 11–20, identify the sampling technique used to obtain a sample. 12. Every 10th Samsung television coming off an assembly line is checked for defects. 14. A door prize is given away at a home improvement seminar. Tickets are
> Use the counting principle to determine the answer to part (a). Assume that each event is equally likely to occur. Boys and Girls A couple plans to have two children. (a) Determine the number of sample points in the sample space of the possible arrangeme
> Create a graph with the given properties. There are many possible answers for each problem. 10. Two even vertices 12. Four odd vertices 14. Eight vertices and one bridge
> (2) A loan on which you make variable payments each month is called a(n) _____installment loan. (4) The total amount of money the borrower must pay for borrowing the money is called the ____charge. (6) The period between when a purchase is made and whe
> Determine two different Hamilton paths in each of the following graphs. 10. 12. 14.
> In her wallet, Anne has 12 bills. Six are $1 bills, two are $5 bills, three are $10 bills, and one is a $20 bill. She passes volunteer seeking donations for the Salvation Army and decides to select one bill at random from her wallet and give it to the Sa
> In Exercises 8–10, determine the monthly payment for the installment loan. Unless told otherwise by your instructor, you may either use Table 10.2 or the installment payment formula (see Examples 1 and 2).
> Your television remote control has buttons for digits 0–9. If you press two buttons, how many numbers are possible if (a) The same button may be pressed twice. (b) The same button may not be pressed twice.
> Ergonomic Chairs A large company with offices in four cities must distribute 144 new ergonomic chairs to the four. Offices. The chairs will be apportioned based on the number of employees in each office as shown in the table below. (a) Apportion the chai
> Indicate whether the statement is a simple statement or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol (for
> In Exercises 1–10, fill in the blank with an appropriate word, phrase, or symbol(s). 2. Making generalizations or predictions from the data collected is called ____statistics. 4. All items or people of interest in an experiment are collectively called a
> Use the histogram below to answer the following questions. (a) How many students were surveyed? (b) What are the lower and upper class limits of the first and second classes? (c) How many students have an annual car insurance premium in the class with a
> In Exercises 28–30, part c), construct the frequency polygon on the same axes as the histogram. See Fig 12.9 on page 739. (28) Starting Salaries Starting salaries, in thousands of dollars, for social workers with a bachelor of science d
> Use these data to construct a frequency distribution with a first class of. (22) 80.0–89.9. (24) 88.7–101.6. (25)Jogging Distances Twenty members of a health club who jog were asked how many miles they jog per week. T
> In Exercises 18–20, the data represent the approximate 2013 population, in hundreds of thousands of people, of the 20 most populous cities in the United States. Use these data to construct a frequency distribution with a first class of
> In Exercises 14–16, use the data given in Table 12.1 on pages 736 and 737 to construct a frequency distribution with a first class (in thousands) of. (14) 100–399. (16) 138–417.
> A hot dog vendor is interested in the num be of hot dogs he sells each day at his hot dog cart. The number of hot dogs sold is indicated at the top of next column for 32 consecutive days. Construct a frequency distribution, letting each class have a widt
> In Exercises 10, use the frequency distribution to determine. (a) The total number of observations. (b) The width of each class. (c) The midpoint of the second class. (d) The modal class (or classes). (e) The class limits of the next class if an addition
> Determine the range and standard deviation of the set of data. When appropriate, round standard deviations to the nearest hundredth. 8. 10, 10, 14, 16, 8, 8 10. 5, 9, 10, 14, 2, 11, 13, 14, 8, 4 12. 9, 9, 9, 9, 9, 9, 9 14. 60, 58, 62, 67, 48, 51, 72, 70
> In Exercises 1– 8, fill in the blank with an appropriate word, phrase, or symbol(s). (2) In a frequency distribution, the class with the greatest frequency is called the ______class. (4) The class width of a frequency distribution with a first class of 1
> The following table gives the distribution of annual salaries for employees at Kulzer’s Home Improvement. Using the information provided in the table, determine the (a) mean annual salary. (b) median annual salary. (c) mode annual salar
> Suppose that turtles tan is a small country with a population of 8,000,000 that consists of four states, A, B, C, and D. There are 160 seats in the legislature that need to be apportioned among the four states. The population of each state is shown in th
> Determine each state’s apportionment using Hamilton’s method. Suppose that turtles tan is a small country with a population of 8,000,000 that consists of four states, A, B, C, and D. There are 160 seats in the legislat
> Suppose that a country with a population of 10,000,000 has 250 legislative seats to be apportioned among four states, where each state has a different population. Determine a population for each state in which Hamilton’s method, Jefferson’s method, Webst
> Determine each shift’s apportionment using Webster’s method.A hospital has 200 nurses to be apportioned among four shifts: shifts A, B, C, and D. the hospital decides to apportion the nurses based on the average number
> Determine each shift’s apportionment using Adams’ method. A hospital has 200 nurses to be apportioned among four shifts: shifts A, B, C, and D. the hospital decides to apportion the nurses based on the average number
> Determine each route’s apportionment using Webster’s method. The Transit Department in the city of Houston has 100 new buses to be apportioned among six routes. The department decides to apportion the buses based on th
> Determine each route’s apportionment using Jefferson’s method. The Transit Department in the city of Houston has 100 new buses to be apportioned among six routes. The department decides to apportion the buses based on
> Determine each dealership’s apportionment using Adams’ method. A boat manufacturer has 120 new boats of a new model to be apportioned to four dealerships. The manufacturer decides to apportion the boats based on the nu
> In Exercises 7–10, indicate if you believe that a correlation exists between the quantities on the horizontal and vertical axes. If so, indicate if you believe that the correlation is a strong positive correlation, a strong negative cor
> Determine each dealership’s apportionment using Jefferson’s method. A boat manufacturer has 120 new boats of a new model to be apportioned to four dealerships. The manufacturer decides to apportion the boats based on t
> A university is made up of five colleges: Liberal Arts, Sciences, Engineering, Business, and Humanities. There are 250 new computers to be apportioned among the five colleges based on their enrollment shown in the table below. The total enrollment is 13,
> Determine each college’s apportionment using Adams’ method. A university is made up of five colleges: Liberal Arts, Sciences, Engineering, Business, and Humanities. There are 250 new computers to be apportioned among t
> Sandy Shores Resorts operates four beach resorts in the Caribbean islands. Sandy Shores Resorts plans to apportion 50 new beach umbrellas among the four resorts based on the number of rooms in each resort as shown in the table below. Determine each resor
> Sandy Shores Resorts operates four beach resorts in the Caribbean islands. Sandy Shores Resorts plans to apportion 50 new beach umbrellas among the four resorts based on the number of rooms in each resort as shown in the table below. Determine each resor
> A large hotel chain needs to apportion 25 new staff members among three hotels based on the numbers of rooms in each hotel as shown in the table below. (a) Determine each hotel’s modified quota using the divisor 28.1. (b) Determine each
> Determine each hotel’s modified quota using the divisor 28. (b) Determine each hotel’s apportionment using Adams’ method. A large hotel chain needs to apportion 25 new staff members among three hotels
> Determine each hotel’s modified quota using the divisor 25.7. (b) Determine each hotel’s apportionment using Jefferson’s method. A large hotel chain needs to apportion 25 new staff members among three
> Determine each hotel’s apportionment using Hamilton’s method. A large hotel chain needs to apportion 25 new staff members among three hotels based on the numbers of rooms in each hotel as shown in the table below.
> Suppose that turtles tan is a small country with a population of 8,000,000 that consists of four states, A, B, C, and D. There are 160 seats in the legislature that need to be apportioned among the four states. The population of each state is shown in th
> Use the following graph. 8. Determine an Euler path that begins with vertex C. 10. Is it possible to determine an Euler circuit for this graph? Explain.
> Determine each state’s modified quota using the divisor 50,600. (b) Determine each state’s apportionment using Adams’ method. Suppose that turtles tan is a small country with a population of 8,000,000
> The planning committee of Tulsa Community College is considering three proposals, A, B, and C, for the design of a new technology building for the college. The nine members of the planning committee rank the proposals according to the preference table sh
> The children in Ms. Cohn’s seventh-grade class are voting on a theme for their class party. Their choices are beach (B), the world (W), superheroes (S), or rock and roll (R). The results are shown in the preference table below. (a) Whic
> Irvine Valley College is hiring a new director of counseling and advisement. The hiring committee ranks the four candidates, Alvarez (A), Brown (B), Singleton (S), and Yu (Y), according to the preference table below. Suppose that the Borda count method i
> Assume that a majority is needed to win the election. Since no candidate has a majority but C has the most firstplace votes, a runoff election is held between A and B. The winner of the runoff election will run against C. (a) Using the plurality method,
> The Motley Crew Investing Club wishes to purchase stock in a pharmaceutical company. The choices are American Pharmacy (A), BurrowsWelcome (B), Chicago Labs (C), Dow Chemical (D), and Emerging Medicines (E). The choice rankings are shown in the following
> Majority Criterion Suppose that the Borda count method is used on the following preference table. Is the majority criterion satisfied?
> Irrelevant Alternatives Criterion Suppose that the pairwise comparison method is used on the following preference table. If A, B, and E drop out, is the irrelevant alternatives criterion satisfied? Explain.
> Monotonicity Criterion Suppose that the Borda count method is used on the following preference table. If the five voters who voted D, A, C, B, in that order, change their votes to A, B, D, C and the three voters who voted C, A, D, B, in that order, chang
> For a small conference, organizers estimate that 195 people will attend if Dr. Tiebol is the guest speaker and 80 people will attend if she is not the guest speaker. There is a 40% chance that the organizers will be able to get Dr. Tiebol as the guest sp
> A distribution in which the frequency is either constantly increasing or constantly decreasing is called a(n) ______distribution. 4. A distribution in which two nonadjacent data values occur more frequently than any other values in a set of data is calle
> Monotonicity Criterion Suppose that the plurality with elimination method is used on the following preference table. If the three voters who voted C, B, A, in that order, change their vote to B, C, A, is the monotonicity criterion satisfied? Explain.
> Irrelevant Alternatives Criterion Suppose that the Borda count method is used on the following preference table. If B drops out, is the irrelevant alternatives criterion satisfied? Explain.
> Irrelevant Alternatives Criterion Suppose that the plurality method is used on the following preference table. If C drops out, is the irrelevant alternatives criterion satisfied? Explain.
> Twenty-five people are surveyed in the Mall of America and asked to taste and rank four different brands of coffee. The preference table below shows the rankings of the 25 voters. Suppose that the plurality with elimination method is used to determine th
> In many corporations and professional societies, the members of the board of directors are elected by a method called approval voting. With approval voting, a voter does not cast a ranked ballot. Instead, the voter votes for as many candidates as he or s
> Suppose that 20 voters rank three candidates. (a) What is the total number of points awarded to the candidates using the Borda count method? (b) Suppose that, using the Borda count method, candidate A receives 55 points and candidate C receives 25 points
> Friskies Cat Food is looking for a new cat for the cover of their 2016 calendar. Four cats are finalists: A, B, C, and D. They are ranked first, second, third, and fourth in each of the following four categories: looks, eye color, size, and attitude. The
> Determine a value of z such that z ≥ 0 and 97.5% of the standard normal curve lies to the left of the z-value.
> Describe one way other than flipping a coin to settle a tied election.
> How can you determine whether a distribution is approximately normal? A statistical theorem called Chebyshev’s theorem states that the minimum percent of data between plus and minus K standard deviations from the mean 1K 7 12 in any dis
> If two dates are selected at random from the 365 days of the year, use the counting principle to determine the number of possible outcomes if the dates are selected (a) With replacement. (b) Without replacement.
> The Wizards Computer Club is ordering five new computers. To obtain a discount price, the club has decided that all five should be the same brand. The choices they are considering are Mac (M), HewlettPackard (H), Dell (D), and Gateway (G). The 142 member
> Sudoku Refer to the Recreational Mathematics on page 94. Complete the following Sudoku puzzle.
> The programmers at the RetroVision cable television station are deciding which classic TV show should lead their prime-time programming. Their choices are Friends (F), Seinfeld (S), Mash (M), and Cheers (C). The 17 programmers rank their choices accordin
> In a distribution skewed to the left, which has the greatest value: the mean, median, or mode? Which has the smallest value? Explain.
> The state of Illinois is applying for a grant to connect several metropolitan areas of the state with a light-rail transport system. The cities involved are Urbana, Chicago, Peoria, Rockford, and Springfield. The distances in miles between these cities a
> Consider the following two normal curves. (a) Do these distributions have the same mean? If so, what is the mean? (b) One of these curves corresponds to a normal distribution with a standard deviation of 1. The other curve corresponds to a normal distrib
> The Ohio Recreation Council is interested in creating bicycle trails connecting the following cities: Akron, Cleveland, Dayton, Toledo, and Youngstown. The distances, in miles, between these cities are given in the table below (a) Use Kruskalâ
> Mr. Sanderson marks his class on a normal curve. Those with z-scores with z ≥1.80 will receive an A, those with 1.10 ≤ z 1.80 will receive a B, those with -1.20 ≤ z 6 < 1.10 will receive a C, those with -1.90 ≤ z < -1.20 will receive a D, those with z
> Five of the campuses in the University of Texas system would like to establish a high-speed telephone and data network between the campuses. The campuses are located in the following cities: Brownsville, Dallas, El Paso, San Antonio, and Tyler. The map b
> The warranty on a car battery is 36 months. If the breakdown times of this battery are normally distributed with a mean of 46 months and a standard deviation of 8 months, determine the percent of batteries that can be expected to require repair or replac
> Bobbi, an investment counselor, is advising her client on a particular investment. She estimates that if the tax law does not change, the client will make $15,000 but if the tax law changes, the client will lose $4000. Determine the client’s expected val
> Joe is creating a modern art sculpture that needs to have electricity available at five different sites. The figure below shows the items included in the sculpture. The distances shown are in inches. (a) Represent this sculpture with a weighted graph.
> (a) Select letters to represent the simple statements and write each statement symbolically by using parentheses if necessary and (b) indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. 72. If the meetin
> Number of Circuits The following tasks are intended to help you understand the formula for finding the number of unique Hamilton circuits in a complete graph. (a) Draw a complete graph with three vertices labeled A, B, and C. Assume that you are starting
> The State College of Florida Brain Bowl team is in Bradenton, Florida (B), and is planning a trip over spring break. The team plans to visit Washington, DC (W); Montgomery, AL (M); and Savannah, GA (S). The approximate distances among these cities are as
> Christina is searching for a new job. She lives in Shreveport, Louisiana, and has interviews in Barrow, Alaska; Tucson, Arizona; and Rochester, New York. The costs of the one-way flights between these four cities are as follows: Shreveport to Barrow cost
> Dale is a milk truck driver for Swiss Valley Farms Cooperative in eastern Iowa. Dale has to start at the processing plant and pick up milk on 10 different farms. In how many ways can Dale visit each farm and return to the processing plant?
> Use the following information to arrive at your answers. Many restaurant dinner menus include statements such as the following: All dinners are served with a choice of: soup or salad, and potatoes or pasta, and carrots or peas. Which of the following sel
> Craig, the president of Culver’s Restaurants, is at his home in Prairie du Sac, WI, and wishes to investigate locations for a new restaurant in the following cities: Robinson, IL; Erie, PA; Memphis, TN; Little Rock, AR; Tulsa, OK; Topeka, KS; and Dickins
> In Exercises 67–72, assume the annual day care cost per child is normally distributed with a mean of $8000 and a standard deviation of $1500. 68. What percent of day care costs are between $6500 and $8750 annually? 70. What percent of day care costs are
> Attempt to draw a graph with an Euler circuit that has a bridge. What conclusion can you develop from this exercise?
> Fill in the blank with an appropriate word, phrase, or symbol(s). 2. Averages are referred to as measures of central________ . 4. The value in the middle of a set of ranked data is called the_________. 6. The value halfway between the lowest and highest
> Imagine a very large connected graph that has 200 odd vertices and 200 even vertices. (a) Does an Euler path exist for this graph? Explain. (b) Does an Euler circuit exist for this graph? Explain.
> Imagine a very large connected graph that has two odd vertices and 398 even vertices. (a) Does an Euler path exist for this graph? Explain. (b) Does an Euler circuit exist for this graph? Explain.
> Determine an Euler circuit for the Country Oaks crime stopper group that begins with vertex J followed by vertex F.
> Determine the percent of watermelons that weigh more than 24.48 pounds. 66. If the farm produces 500 watermelons, how many will weigh more than 24.48 pounds? /
> Determine an Euler circuit for the Country Oaks crime stopper group (see Example 6 on page 817) that begin with vertex B followed by vertex E.
> Determine an Euler path for the Phenomenal Phitness Gym (see Example 5 on page 816) that begins in locker room (vertex) A.
> The Country Oaks crime stopper organization (see Example 6 on page 817) was so successful that the residents shared their strategies with friends living in the subdivisions of Crescent Lakes and Tree Tops. The respective maps of these communities are giv
> Recall Joe from Example 5 on page 816 who runs a gym-cleaning service. Joe is also responsible for locking the doors of four other gyms. The floor plans for these gyms are shown (a) Represent each floor plan as a graph. Use the letters shown to label the
> Locking Doors Recall Joe from Example 5 on page 816 who runs a gym-cleaning service. Joe is also responsible for locking the doors of four other gyms. The floor plans for these gyms are shown (a) Represent each floor plan as a graph. Use the letters show
> Write each symbolic statement in words. Let p: The water is 708. q: The sun is shining. r: We go swimming. 58. (p ( q) ( r 60. (q ( p) ( r 62. (q ( r) ( p 64. (p ( (q ( r) 66. q ( ( p ( r)
> 2. When each group’s population is divided by the standard divisor, a standard _________ is obtained. 4. A standard quota rounded down to the nearest integer is called a(n)________ quota. 6. Jefferson’s method, Webster’s method, and Adams’ method require
> Turn to the roulette wheel illustrated on page 661. If the wheel is spun, determine (a) The probability that the ball lands on red. (b) The odds against the ball landing on red. (c) The probability that the ball lands on 0 or 00. (d) The odds in favor
