Solution Manual for A Survey of Mathematics with Applications, 11th Edition

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SOLUTIONSMANUALJAMESLAPPASURVEY OFMATHEMATICSWITHAPPLICATIONSELEVENTHEDITIONAllen R. AngelMonroe Community CollegeChristine D. AbbottMonroe Community CollegeDennis C. RundeState College of Florida

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Table of ContentsChapter 1: Critical Thinking Skills1.1:Inductive and Deductive Reasoning ..................................................................................................11.2:Estimation Techniques ......................................................................................................................31.3:Problem-Solving Procedures.............................................................................................................5Review Exercises ............................................................................................................................11Chapter Test ....................................................................................................................................14Chapter 2: Sets2.1:Set Concepts....................................................................................................................................172.2:Subsets.............................................................................................................................................192.3:Venn Diagrams and Set Operations ................................................................................................212.4:Venn Diagrams with Three Sets and Verification of Equality of Sets ............................................262.5:Applications of Sets ........................................................................................................................322.6:Infinite Sets .....................................................................................................................................35Review Exercises ............................................................................................................................37Chapter Test ....................................................................................................................................40Chapter 3: Logic3.1:Statements and Logical Connectives...............................................................................................433.2:Truth Tables for Negation, Conjunction, and Disjunction ..............................................................453.3:Truth Tables for the Conditional and Biconditional........................................................................543.4:Equivalent Statements .....................................................................................................................653.5:Symbolic Arguments.......................................................................................................................733.6:Euler Diagrams and Syllogistic Arguments ....................................................................................803.7:Switching Circuits ...........................................................................................................................83Review Exercises ............................................................................................................................87Chapter Test ....................................................................................................................................93Chapter 4: Systems of Numeration4.1:Additive, Multiplicative, and Ciphered Systems of Numeration.....................................................974.2:Place-Value or Positional-Value Numeration Systems ...................................................................994.3:Other Bases ...................................................................................................................................1014.4:Perform Computations in Other Bases ..........................................................................................1064.5:Early Computational Methods.......................................................................................................111Review Exercises ..........................................................................................................................115Chapter Test ..................................................................................................................................119Chapter 5: Number Theory and the Real Number System5.1:Number Theory .............................................................................................................................1215.2:The Integers...................................................................................................................................1255.3:The Rational Numbers...................................................................................................................1285.4:The Irrational Numbers .................................................................................................................1335.5:Real Numbers and Their Properties ..............................................................................................1365.6:Rules of Exponents and Scientific Notation..................................................................................1385.7:Arithmetic and Geometric Sequences ...........................................................................................1415.8:Fibonacci Sequence.......................................................................................................................146Review Exercises ..........................................................................................................................148Chapter Test ..................................................................................................................................152

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Chapter 6: Algebra, Graphs, and Functions6.1:Order of Operations and Solving Equations..................................................................................1536.2:Formulas........................................................................................................................................1576.3:Applications of Algebra ................................................................................................................1626.4:Variation........................................................................................................................................1676.5:Solving Linear Inequalities ...........................................................................................................1716.6:Graphing Linear Equations ...........................................................................................................1766.7:Solving Systems of Linear Equations............................................................................................1846.8:Linear Inequalities in Two Variables and Systems of Linear Inequalities ....................................1956.9:Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula ..............2046.10: Functions and Their Graphs ..........................................................................................................210Review Exercises ..........................................................................................................................217Chapter Test ..................................................................................................................................227Chapter 7: The Metric System7.1:Basic Terms and Conversions Within the Metric System .............................................................2317.2:Length, Area, and Volume ............................................................................................................2327.3:Mass and Temperature ..................................................................................................................2357.4:Dimensional Analysis and Conversions to and from the Metric System ......................................237Review Exercises ..........................................................................................................................241Chapter Test ..................................................................................................................................243Chapter 8: Geometry8.1:Points, Lines, Planes, and Angles..................................................................................................2458.2:Polygons........................................................................................................................................2488.3:Perimeter and Area........................................................................................................................2528.4:Volume and Surface Area .............................................................................................................2568.5:Transformational Geometry, Symmetry, and Tessellations ..........................................................2608.6:Topology .......................................................................................................................................2658.7:Non-Euclidean Geometry and Fractal Geometry ..........................................................................266Review Exercises ..........................................................................................................................267Chapter Test ..................................................................................................................................270Chapter 9: Mathematical Systems9.1:Groups ...........................................................................................................................................2739.2:Finite Mathematical Systems ........................................................................................................2749.3:Modular Arithmetic.......................................................................................................................2779.4:Matrices.........................................................................................................................................282Review Exercises ..........................................................................................................................288Chapter Test ..................................................................................................................................290Chapter 10: Consumer Mathematics10.1:Percent...........................................................................................................................................29310.2:Personal Loans and Simple Interest ..............................................................................................29510.3:Compound Interest ........................................................................................................................30010.4:Installment Buying ........................................................................................................................30410.5:Buying a House with a Mortgage..................................................................................................31010.6:Ordinary Annuities, Sinking Funds, and Retirement Investments ................................................317Review Exercises ..........................................................................................................................318Chapter Test ..................................................................................................................................322

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Chapter 11: Probability11.1:Empirical and Theoretical Probabilities ........................................................................................32511.2:Odds ..............................................................................................................................................32811.3:Expected Value (Expectation).......................................................................................................33211.4:Tree Diagrams ...............................................................................................................................33611.5:ORandANDProblems..................................................................................................................34011.6:Conditional Probability .................................................................................................................34411.7:The Fundamental Counting Principle and Permutations ...............................................................34711.8:Combinations ................................................................................................................................34911.9:Solving Probability Problems by Using Combinations .................................................................35111.10: Binomial Probability Formula.......................................................................................................353Review Exercises ..........................................................................................................................355Chapter Test ..................................................................................................................................359Chapter 12: Statistics12.1:Sampling Techniques and Misuses of Statistics............................................................................36112.2:Frequency Distributions and Statistical Graphs ............................................................................36312.3:Measures of Central Tendency and Position .................................................................................36812.4:Measures of Dispersion .................................................................................................................37412.5:The Normal Curve.........................................................................................................................37912.6:Linear Correlation and Regression................................................................................................385Review Exercises ..........................................................................................................................395Chapter Test ..................................................................................................................................400Chapter 13: Graph Theory13.1:Graphs, Paths, and Circuits ...........................................................................................................40313.2:Euler Paths and Euler Circuits.......................................................................................................40413.3:Hamilton Paths and Hamilton Circuits..........................................................................................40813.4:Trees..............................................................................................................................................411Review Exercises ..........................................................................................................................415Chapter Test ..................................................................................................................................417Chapter 14: Voting and Apportionment14.1:Voting Methods.............................................................................................................................41914.2:Flaws of the Voting Methods ........................................................................................................42314.3:Apportionment Methods................................................................................................................42814.4:Flaws of the Apportionment Methods...........................................................................................433Review Exercises ..........................................................................................................................438Chapter Test ..................................................................................................................................445

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Section 1.1: Inductive and Deductive Reasoning1Chapter One: Critical Thinking SkillsSection 1.1: Inductive and Deductive Reasoning1. Natural2. Divisible3. Counterexample4. Hypothesis5. Inductive6. Deductive7. Deductive8. Inductive9.531510.191019011.(1 4)(46)(46)(1 4)1151010512.5100, 0001013.14.15.16.17. 9, 11, 13 (Add 2 to previous number.)18. 16, 19, 22 (Add 3 to the previous number.)19. 5, –5, 5 (Alternate 5 and –5.)20. 16, –32, 64 (Multiply previous number by –2.)21.111,,567(Increase denominator value by 1.)22.111,,911 13(Increase denominator value by 2.)23. 21, 28, 36(15621, 21728, 28836)24. 16, 22, 29 (Add 1, then 2, then 3, ….)25. 34, 55, 89 (Each number in the sequence is the sum of the previous two numbers.)26. 76, 123, 199 (Each number in the sequence is the sum of the previous two numbers.)27. There are three letters in the pattern.393117,so, the 117th entry is the second R in the pattern. Therefore,the 118th entry is Y.28.a)Answers will vary.b)The sum of the digits is 9.c)The sum of the digits in the product when a one- or two-digit number is multiplied by 9 is divisible by 9.29.a)36, 49, 64b)Square the numbers 6, 7, 8, 9 and 10.c)8864, 9981;72 is not a square number since it falls between the two square numbers 64 and 81.30.a)28 and 36b)To find the 7th triangular number, add 7 to the 6th triangular number.To find the 8th triangular number, add 8 to the 7th triangular number.To find the 9th triangular number, add 9 to the 8th triangular number.To find the 10th triangular number, add 10 to the 9th triangular number.To find the 11th triangular number, add 11 to the 10th triangular number.c)36945,451055,551166;661278;72 is not a triangular number since it falls betweenthe consecutive triangular numbers 66 and 78.31. Blue: 1, 5, 7, 10, 12; Purple: 2, 4, 6, 9, 11; Yellow: 3, 832.a)19 (Each new row has two additional triangles.)b)13579111315171910033.a)$3700b)We are using observation of specific cases to make a prediction.

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2Chapter 1: Critical Thinking Skills34.a)$410b)We are using observation of specific cases to make a prediction.35.36.37.a)You should obtain the original number.b)You should obtain the original number.c)Conjecture: The result is always the original number.d)3636336222333nnnnnnnn++=+=++-=38.a)You should obtain twice the original number.b)You should obtain twice the original number.c)Conjecture: The result is always twice the original number.d)4646446232332222nnnnnnnn39.a)You should obtain the number 5.b)You should obtain the number 5.c)Conjecture: The result is always the number 5.d)2102101(1)21219210555222nnnnnnnnnnnn40.a)You should obtain the number 0.b)You should obtain the number 0.c)Conjecture: The result is always the number 0.d)1010105101010055nnnnnnnnn41.3515 is one counterexample.42.101112 = 33, which is not a three digit number.43. Two is a counting number. The sum of 2 and 3 is 5. Five divided by two is5 2,which is not an even number.44. 900 is a three-digit number. The product of 900 and 900 is 810,000, which is not a five-digit number.45. One and two are counting numbers. The difference of 1 and 2 is121 , which is not a counting number.46. The sum of the odd numbers 1 and 5 is 6, which is not divisible by 4.47.a)The sum of the measures of the interior angles should be180 .b)Yes, the sum of the measures of the interior angles should be180 .c)Conjecture: The sum of the measures of the interior angles of a triangle is180 .48.a)The sum of the measures of the interior angles should be360 .b)Yes, the sum of the measures of the interior angles should be360 .c)Conjecture: The sum of the measures of the interior angles of a quadrilateral is360 .49. Inductive reasoning: a general conclusion is obtained from observation of specific cases.

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Section 1.2: Estimation Techniques350. Inductive reasoning: a general conclusion is obtained from observation of specific cases.51. 129; The numbers in the positions of each inner44square are determined as follows.abcabc52. 1881, 8008, 8118 (They look the same when looked at in a mirror.)53. cSection 1.2: Estimation TechniquesAnswers in this section will vary depending on how you round your numbers. The answers may differ from theanswers in the back of the textbook. However, your answers should be something near the answers given. Allanswers are approximate.)1. Estimation2. Equal3.26.967.3219143.330672201434604.8647.2289.8532.412.89050290530109705.197,5004.063200, 0004.00050, 0006.40540080000.0490.057.17760.009818000.01188.0.6315230.615009009.23.977.052471710.400.15297.8740030010011.22%911620%90000.209000180012.11% of 822110% of 80000.10800080013.$91.35$90$303314.$210$200$258815.12 months$4712$50$60016.19 gallons$3.1120$3$6017.$7.99$4.23$16.82$3.51$20.12$8$4$17$4$20$5318.$1.29$6.86$12.43$25.62$8.99$1$7$12$26$9$5519.95lb127 lb210 lb100100200400 lb20. 16.1 lb7.9 lb21.4 lb11.6 lb3.7 lb1682112461 lb21.15% of $26.3215% of $260.15$26$3.9022.$400$40016$23$2523.$595$289$120$110230$600$300$100$100$200$130024. Team A:189172191190170190550Team B:18322916718023017058058055030 lb25.118$1.50108$1.5010$12$12026.9 min, 55 sec/mi26.2 mi10 min26 mi260 min/mi;260 min14hours60 min327.599 Mexican pesos600$3020.14 Mexican pesos / U.S. dollars20

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4Chapter 1: Critical Thinking Skills28.$9736 $616 $976 $200$9706 $606 $1006 $200$970$360$600$1200$313029. 90 miles30. 75 miles31.a)23% of 70025% of 7000.25700175b)12% of 70010% of 7000.1070070c)21% of 70020% of 7000.2070014032.a)18% of 298718% of 30000.183000540b)42% of 298742% of 30000.4230001260c)7% of 29877% of 30000.07300021033.a)5 millionb)98 millionc)98 million33 million65 milliond)19 million79 million84 million65 million33 million280 million34.a)19%b)25%c)20% of 179 lb20% of 1800.218036 lb35.a)85%b)68%53%15%c)85% of 70 million acres = 59,500,000 acresd)No, since we are not given the area of each state.36.a)2 4104 5452 4004 50080020002800 caloriesb)Running:4 9204 9003600 caloriesWalking:4 3304 3001200 caloriesDifference:360012002400 caloriesc)3 5453 5453 5503 550165016503300 calories per week3300 calories per week 52 weeks300050150, 000 calories37. 2038. 2539. 120 bananas40. 100 grapes41.15042.31543. 10%44. 25%45. 9 square units46. 12 square units47. 160 feet48.2404(60)240 in. or20 ft1249. – 57. Answers will vary.

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Section 1.3: Problem-Solving Procedures558. Cost of one vitamin C tablet:$24.99$25$0.05500500Cost of one fish oil tablet:$47.99$48$0.40120120Cost of one vitamin D tablet:$17.99$18$0.10180180Cost of one multivitamin tablet:$19.99$20$0.258080Roberto’s daily cost:5$0.054$0.401$0.101$0.25$1.4059. There are 118 ridges around the edge.60.a)Answers will vary.b)11.6 days. There are 24 60 6086, 400seconds in a day, and1, 000, 000 / 86, 40011.5740.62. Answers will vary.63. Answers will vary.Section 1.3: Problem-Solving Procedures1.1 in.4.25 in.12 mimi12 4.2551 mixxx2.1 in.22.4 in.2.5 ydyd12.5 22.456 ydxxx3.3 ftft1.2 ft15.36 ft3 15.361.246.031.21.21.246.0338.4 ft1.2xxxx4.221 bagbags4000 ft35, 000 ft40001 35, 000400035, 0004000400035, 0008.75 bags4000xxxx5.4$113$4529.25% of $4520.0925$452$41.81$452$41.81$493.816.2$187$3749.5% of $3740.095$374$35.53$374$35.53$409.537.a)Entertainment/Miscellaneous:19.1% of $19500.191$1950$372.45Food:12.7% of $19500.127$1950$247.65$372.45$247.65$124.80b)Housing:34.4% of $19500.344$1950$670.80Transportation:16% of $19500.16$1750$312.00$670.80$312.00$358.808.a)Business:19% of 2,895, 0000.192,895, 000550, 050Engineering:5% of 2,895, 0000.052,895, 000144, 750550, 050144, 750405,300 degrees

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6Chapter 1: Critical Thinking Skills8. (continued)b)Health Professions:11% of 2,895, 0000.112,895, 000318, 450Psychology:6% of 2,895, 0000.062,895, 000173, 700318, 450173, 700144, 750 degrees9.43 rides$2.00 per ride$86.00;In order for the cost of rides with the $84.50 MetroCard to be less than thecost of the rides without the CharlieCard, Marcelo would have to take 43 bus rides per month.Note that$84.50$1.97 per ride.43rides10.45 rides$2.75 per ride$123.75;In order for the cost of rides with the $121.50 MetroCard to be less thanthe cost of the rides without the MetroCard, Karissa would have to take 45 subway rides per month.Note that$121.50$2.70 per ride45 rides11.$250$130 18$250$2340$2590Savings: $2590$2500$9012.$349.72$32.39(4)$349.72129.56$220.1613. 15-year mortgage:$887.63(12)(15)$159, 773.4030-year mortgage:$572.90(12)(30)$206, 244.00Savings:$206, 244.00$159, 773.40$46, 470.6014. Points needed for 80 average:80(5)400 pointsWallace’s points so far:79939168331 pointsGrade needed on fifth exam:4003316915.a)1010101010, 000b)1 in 10,00016.a)46018.4 min25b)155031 min50c)140040 min35d)15502200375047 min80808017.38, 687.0 mi38, 451.4 mi235.6 mi;235.6 mi18.7 mpg12.6 gal18.a)40$8.5052$17, 680b)Each week he makes 40$8.50$340,it will take him $12753.75 weeks.$34019. By mail:$52.80$5.60$8.564$66.964$267.84Tire store: $3240.08$324$324$25.92$349.92Savings:$349.92$267.84$82.0820.$1750$50 15$1750$750$1000and$100025 hours$40

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Section 1.3: Problem-Solving Procedures721. 15,000 ft3000 ft = 12,000 ft decrease in elevation. Temperature increases2.4 Ffor every 1000 ft decreasein elevation.6 F28.8 F22.8 F and6 F28.8 F22.8 F; The precipitation at the airport will be snow.22.a)$620 0.12$74.40b)$1200 0.22$264c)The store lost $1200$1000$200on the purchase, so the store’s profit is $264$200$64.23.a)Since $876 is less than10%$9525$952.50,Shenile’s tax was 10% of her taxable income. Her taxableincome was$876$8760.0.10b)Since $2017.50 is greater than $952.50 and less than $4453.50, Logan’s taxable income was in the 12%bracket. Since$2017.50$962.50$1065was 12% of his taxable income above $9525, he made anadditional$1065$8875.0.12His taxable income was$9625$8875$18, 400.24.a)Since $4541.50 is greater than $4453.50 and less than $14,089.50, Lewis’ taxable income was in the 22%bracket. Since $4541.50$4453.50$88was 22% of his taxable income above $38,700, he made anadditional$88$400.0.22His taxable income was$38, 700$400$39,100.b)Since $14,593.50.50 is greater than $14,089.50 and less than $32,089, Leticia’s taxable income was in the24% bracket. Since$14,593.50$14, 089.50$504was 24% of his taxable income above $82,500, shemade an additional$504$2100.0.24Her taxable income was$82,500$2100$84, 600.25.a)16024365525, 600 ozand525, 600 oz4106.25 gal128b)4106.25$11.204.10625$11.20$45.99100026.a)30.16060243653,153, 600 cmb)33Volume of basin(30 cm)(20 cm)(20 cm)12, 000 cm1.4;Daily water loss0.16060248640 cmIt would take about 1.4 days.27.a)20, 00020, 000961.538925.92635.61235.61 gal20.821.6b)35.61$3.00$106.83c)140, 000, 00035.614,985, 400, 000 gal28.a)Parking: $306$180Tax:9.5% of $1800.095$180$17.10Total:$180$17.10$197.10b)Parking: $17.956$107.70Tax:8.75% of $107.700.0875$107.70$9.42Total:$107.70$9.42$117.12c)She can save $197.10$117.12$79.98.

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8Chapter 1: Critical Thinking Skills29. Cost after 1 year:$9990.02($999)$999$19.98$1018.98Cost after second year:$1018.980.02($1018.98)$1018.98$20.38$1039.3630. Value after first year:$10000.10($1000)$1000$100$1100Value after second year:$11000.10 $1100$1100$110$990$990 is less than the initial investment of $1000.31. After paying the $100 deductible, Yungchen must pay 20% of the cost of x-rays.First x-ray:$1000.20 $620$100$124$224Second x-ray:0.20 $980$196Total:$224$196$42032. $3000 is the difference between one-fourth of the cost and one-fifth of the cost.1114520and20$3000$60, 00033.a)water/milk:3(1)3cupssalt:13388 tspCream of wheat:3 39tbsp916cup (because16tbsp =1cup)b)water/milk:32323237442cups2288salt:1133424tsp228cream of wheat:1355244cups =5 tbsp228c)water/milk:315411331244444cupssalt:1141328888tspcream of wheat:331239416161616cup =9tbspd)Differences exist in water/milk because the amount for 4 servings is not twice that for 2 servings.Differences also exist in Cream of Wheat because12cup is not twice 3 tbsp.

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Solution Manual for A Survey of Mathematics with Applications, 11th Edition - Page 15 preview image

Section 1.3: Problem-Solving Procedures934.a)rice: 1 422cupswater:  1416114453333cupssalt: 1 414tspbutter/margarine:1 44tspb)rice:1 22cupswater:  1918212224444442cupssalt: 1 212tspbutter/margarine:2 24tspc)rice:111341222222cupswater:11410142134333333cupssalt:1341444tspbutter/margarine:1 tsp1 tbsp1 tsp3 tsp4 tspd)rice:312 cups1249153water: 623cups4444411salt: 11 tsp22butter/margarine: 2 tbsp2 tsp2 3tsp2 tsp6 tsp2 tsp4 tspe)Differences exist in water because the amount for 4 servings is not twice that for 2 servings.35.a)20 DVDs12 DVDsTotal Number of DVDs1120123202121224b)$240$180$42036. Mark will win.37.21 ft12 in.12 in.144 square inches38.31 ft12 in.12 in.12 in.1728 cubic inches39. Area of original rectangle:lwArea of new rectangle:(2 )(2)4()lwlwThus, if the length and width of a rectangle are doubled, the area is 4 times as large.

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Solution Manual for A Survey of Mathematics with Applications, 11th Edition - Page 16 preview image

10Chapter 1: Critical Thinking Skills40.220 ft20 ft = 400 ft ;25ft5ft = 25 ft ;22400 ft16squares25ft41. Volume of original cube:lwhVolume of new cube:(2 )(2)(2 )8()lwhlwhThus, if the length, width, and height of a cube are doubled, the volume is 8 times as large.42. 11 ft is one-sixth of the pole, so the length is611 ft66 ft.43.10 pieces1000 pieces$10100010 10100010010001000100$0.1010¢1000xxxx44.Left sideRight side1( 6)61(2)22( 2)41(3)3(6)66( 4)1023611    Place it at –1, so the left side would total10( 1)1.  45. You have three ties, each a different color.46. There are 10 palindromes: 2002, 2112, 2222, 2332, 2442, 2552, 2662, 2772, 2882, 2992.47.a)refreshb)workout48. Answers will vary.49.50. Eight pieces51.52.53.862420; 375116; 101412844The sum of the four corner entries is 4 times the number in the center of the middle row.54. 15,12,33; Multiply the number in the center of the middle row by 3.55.45,36,99;Multiply the number in the center of the middle row by 9.56.351520 cubes57.3216 ways58. Each salesperson shakes hands with four people.

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