Attempt to draw a graph with an Euler circuit that has a bridge. What conclusion can you develop from this exercise?
> 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 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
> 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
> 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
> What percent of cars are traveling between 58 mph and 66 mph? 60. What percent of cars are traveling faster than 70 mph? 62. If 200 cars are selected at random, how many will be traveling faster than 70 mph?
> A roulette wheel typically contains slots with numbers 1–36 and slots marked 0 and 00. A ball is spun on the wheel and comes to rest in one of the 38 slots. Eighteen numbers are colored red, and 18 numbers are colored black. The 0 and 0
> Determine the odds against an even number or a number greater than 3 being rolled on a die.
> In a four-point grade system, an A corresponds to 4.0 points, a B corresponds to 3.0 points, a C corresponds to 2.0 points, and a D corresponds to 1.0 points. No points are awarded for an F. Last semester, Tanya received a B in a four-credit hour course,
> Is it possible to determine your expectation when you purchase a lottery ticket? Explain.
> Bookcase Assembly Suppose that the probability that all the parts needed to assemble a bookcase are included in the carton is 7/8 . Determine the odds in favor of the carton including all the needed parts.
> 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
> Dispense less than 7.0 oz. 56. Result in the cup overflowing (therefore dispense more than 8 oz).
> Assume that you are blind folded and throw a dart at the dart board shown below. Assume that your dart sticks in the dart board, and not on a line. (a) Determine the probabilities that the dart lands on $1, $10, $20, and $100, respectively. (b) If you wi
> The ratio of the probability that the event will occur to the probability that the event will fail to occur is called the odds ________ an event. (4). If the odds against winning at Monopoly are 5 : 1, then the odds in favor of winning at Monopoly are __
> Suppose that the probability that a mechanic fixes a car correctly is 0.9. Determine the odds against the mechanic fixing a car correctly.
> Consider the following five sets of values. (a) Compute the mean of each of the five sets of data. (b) Compute the mean of the five means in part (a). (c) Find the mean of the 27 pieces of data. (d) Compare your answer in part (b) to your answer in part
> The maps of states that are in other Navy regions (see Example 4 on page 815) are shown. Use these graphs to complete the exercises. Navy Region Southeast (a) Represent the map as a graph. Use the state abbreviations to label the vertices of the graph. (
> Write the statements in symbolic form. Let P: The temperature is 908. Q: The air conditioner is working. R: The apartment is hot. 50. The temperature is not 90° and the air conditioner is working, but the apartment is hot. 52. If the temperature is 90°,
> The expenses for Jorge, a real estate agent, to list, advertise, and attempt to sell a house are $1400. If Jorge succeeds in selling the house, he will receive a commission of 6% of the sales price. If an agent with a different company sells the house, J
> Jonathan took an admission test for the University of California and scored in the 85th percentile. The following year, Jonathan’s sister Kendra took a similar admission test for the University of California and scored in the 90th percentile. (a) Is it p
> CPI Use the following table. CPI represents consumer price index. (a) Calculate r. (b) If 2008 is subtracted from each year, the table obtained becomes: If r is calculated from these values, how will it compare with the r determined in part (a)? Explain.
> Don is considering bringing a lawsuit against the Dummote Company. His lawyer estimates that there is a 70% chance Don will make $60,000, a 10% chance Don will break even, and a 20% chance they will lose the case and Don will need to pay $30,000 in legal
> The prices of the 20 top-rated top-loading washing machines, as reported in the August, 2014, issue of Consumer Reports, are as follows: Determine (a) Q2 (b) Q1 (c) Q3
> What percent of students who took the test have a mathematics score above 680? 50. What percent of students who took the test have a mathematics score below 300? 52. What percent of students who took the test have a mathematics score above 480?
> A candidate who wins a first election, then gains additional support without losing any of the original support, should also win a second election. This criterion is called the _________ criterion. 4. If a candidate is the winner of an election and in a
> Attempt to draw a graph that has an odd number of odd vertices. What conclusion can you draw from this exercise?
> The tables on page 765 list the 10 highest-paid athletes in Major League Baseball and in the National Football League. (a) Without doing any calculations, which do you believe is greater, the mean salary of the 10 baseball players or the mean salary of
> The following circle graph shows the percent of Americans with the various types of blood. The probability that the person has B- blood. (48). The following circle graph shows the percent of Americans with the various types of blood. The odds in favor of
> The owner of an antique store estimates that there is a 40% chance she will make $2000 when she sells an antique china cabinet, a 50% chance she will make $750 when she sells the cabinet, and a 10% chance she will break even when she sells the cabinet. D
> A union leader is told that, when all workers’ salaries are considered, the first quartile is $27,750. Explain what that means.
> Consider the following graph, which shows the U.S. population in 2000 and the projected U.S. population in 2050. / (a) Compute the projected percent increase in population from 2000 to 2050 by using the formula given on page 565. (b) Measure the radius
> By studying the standard deviation formula, explain why the standard deviation of a set of data will always be greater than or equal to 0.
> A mechanical contractor is preparing for a construction project. He determines that if he completes the project on schedule, his net profit will be $450,000. If he completes the project between 0 and 3 months late, his net profit decreases to $120,000. I
> Josie scored in the 73rd percentile on the verbal part of her College Board test. What does that mean?
> Assume the hold time of callers to General Cable is normally distributed with a mean of 3.0 minutes and a standard deviation of 0.8 minute. 44. Determine the percent of callers who are on hold between 2.2 minutes and 4.6 minutes. 46. In a random sample o
> A table that summarizes the results of an election is called a (n) _________ table. 4. When using the pair wise comparison method, the number of comparisons, c, needed when there are n candidates is determined by the formula c =_________. 6. In the Borda
> In Exercises 42, assume that the heights of 7-year-old girls are normally distributed. The heights of 8 girls are given in z-scores below. (a) Which girl is the tallest? (b) Which girl is the shortest?
> Without actually doing the calculations, decide which, if either, of the following two sets of data will have the greater standard deviation. Explain why.
> According to Bristol Mutual Life Insurance’s mortality table, the probability that a 20-year-old woman will survive 1 year is 0.994 and the probability that she will die within 1 year is 0.006. If a 20-year-old woman buys a $10,000 1-year policy for $100
> The Taylors have recorded their weekly grocery expenses for the past 12 weeks and determined that the mean weekly expense was $85.20. Later Mrs. Taylor discovered that 1 week’s expense of $74 was incorrectly recorded as $47. What is the correct mean?
> Suppose that the people of Königsberg decide to add severa bridges to their city. Two such possibilities are shown. (a) Would the townspeople be able to walk across all the bridges without crossing the same bridge twice? (b) If so, where sho
> Consider the set of data 1, 1, 1, 2, 2, 2. If one 2 is changed to a 3, which of the following will change: mean, median, mode, midrange?
