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Solution Manual for College Algebra and Trigonometry, 7th Edition

Solution Manual for College Algebra and Trigonometry, 7th Edition breaks down difficult textbook problems into simple solutions, making your study time more effective.

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    S OLUTIONS M ANUAL B EVERLY F USFIELD C OLLEGE A LGEBRA & T RIGONOMETRY S EVENTH E DITION and P RECALCULUS S EVENTH E DITION Margaret L. Lial American River College John Hornsby University of New Orleans David I. Schneider University of Maryland Callie J. Daniels St. Charles Community College

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    CONTENTS R Review of Basic Concepts R.1 Fractions, Decimals, and Percents.............................................................................. 1 R.2 Sets and Real Numbers ............................................................................................ 12 R.3 Real Number Operations and Properties .................................................................. 16 R.4 Integer and Rational Exponents ............................................................................... 23 R.5 Polynomials .............................................................................................................. 28 R.6 Factoring Polynomials.............................................................................................. 36 R.7 Rational Expressions ................................................................................................ 45 R.8 Radical Expressions ................................................................................................. 54 Chapter R Review Exercises ........................................................................................... 61 Chapter R Test ................................................................................................................ 67 1 Equations and Inequalities 1.1 Linear Equations ....................................................................................................... 69 1.2 Applications and Modeling with Linear Equations ..................................................73 1.3 Complex Numbers .................................................................................................... 79 1.4 Quadratic Equations .................................................................................................. 85 Chapter 1 Quiz (Sections 1.1 − 1.4).................................................................................. 96 1.5 Applications and Modeling with Quadratic Equations ............................................. 96 1.6 Other Types of Equations and Applications ........................................................... 106 Summary Exercises on Solving Equations ................................................................... 127 1.7 Inequalities ..............................................................................................................131 1.8 Absolute Value Equations and Inequalities ............................................................157 Chapter 1 Review Exercises ......................................................................................... 164 Chapter 1 Test ............................................................................................................... 182 2 Graphs and Functions 2.1 Rectangular Coordinates and Graphs...................................................................... 187 2.2 Circles ..................................................................................................................... 196 2.3 Functions ................................................................................................................. 205 2.4 Linear Functions ..................................................................................................... 212 Chapter 2 Quiz (Sections 2.1 − 2.4)................................................................................ 221 2.5 Equations of Lines and Linear Models ................................................................... 221 Summary Exercises on Graphs, Circles, Functions, and Equations ............................. 230 2.6 Graphs of Basic Functions ...................................................................................... 234 2.7 Graphing Techniques .............................................................................................. 241 Chapter 2 Quiz (Sections 2.5 − 2.7)................................................................................ 255 2.8 Function Operations and Composition ................................................................... 257 Chapter 2 Review Exercises ......................................................................................... 267 Chapter 2 Test ............................................................................................................... 278

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    3 Polynomial and Rational Functions 3.1 Quadratic Function and Models .............................................................................. 283 3.2 Synthetic Division................................................................................................... 305 3.3 Zeros of Polynomial Functions ............................................................................... 311 3.4 Polynomial Functions: Graphs, Applications, and Models .................................... 333 Summary Exercises on Polynomial Functions, Zeros, and Graphs .............................. 353 3.5 Rational Functions: Graphs, Applications, and Models ......................................... 367 Chapter 3 Quiz (Sections 3.1 − 3.5)................................................................................ 390 3.6 Polynomial and Rational Inequalities ..................................................................... 395 Summary Exercises on Solving Equations and Inequalities .........................................412 3.7 Variation .................................................................................................................420 Chapter 3 Review Exercises ......................................................................................... 426 Chapter 3 Test ............................................................................................................... 447 4 Inverse, Exponential, and Logarithmic Functions 4.1 Inverse Functions .................................................................................................... 454 4.2 Exponential Functions ............................................................................................ 470 4.3 Logarithmic Functions ............................................................................................ 487 Summary Exercises on Inverse, Exponential, and Logarithmic Functions .................. 499 4.4 Evaluating Logarithms and the Change-of-Base Theorem ..................................... 502 Chapter 4 Quiz (Sections 4.1 − 4.4)................................................................................ 508 4.5 Exponential and Logarithmic Equations ................................................................. 509 4.6 Applications and Models of Exponential Growth and Decay ................................ 523 Summary Exercises on Functions: Domains and Defining Equations ......................... 531 Chapter 4 Review Exercises ......................................................................................... 535 Chapter 4 Test ............................................................................................................... 542 5 Trigonometric Functions 5.1 Angles ..................................................................................................................... 546 5.2 Trigonometric Functions ......................................................................................... 553 5.3 Trigonometric Function Values and Angle Measures ............................................ 569 Chapter 5 Quiz (Sections 5.1–5.3) ................................................................................ 584 5.4 Solutions and Applications of Right Triangles .......................................................585 Chapter 5 Review Exercises ......................................................................................... 603 Chapter 5 Test ............................................................................................................... 611

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    6 The Circular Functions and Their Graphs 6.1 Radian Measure ...................................................................................................... 616 6.2 The Unit Circle and Circular Functions .................................................................. 626 6.3 Graphs of the Sine and Cosine Functions ............................................................... 637 6.4 Translations of the Graphs of the Sine and Cosine Functions ................................ 648 Chapter 6 Quiz (Sections 6.1 − 6.4)................................................................................ 662 6.5 Graphs of the Tangent and Cotangent Functions .................................................... 664 6.6: Graphs of the Secant and Cosecant Functions ....................................................... 676 Summary Exercises on Graphing Circular Functions ...................................................685 6.7 Harmonic Motion .................................................................................................... 688 Chapter 6 Review Exercises ......................................................................................... 694 Chapter 6 Test ............................................................................................................... 707 7 Trigonometric Identities and Equations 7.1 Fundamental Identities ............................................................................................ 713 7.2 Verifying Trigonometric Identities ......................................................................... 721 7.3 Sum and Difference Identities ............................................................................... 732 Chapter 7 Quiz (Sections 7.1 − 7.3)................................................................................ 746 7.4 Double-Angle and Half-Angle Identities ................................................................ 748 Summary Exercises on Verifying Trigonometric Identities ......................................... 760 7.5 Inverse Circular Functions ...................................................................................... 765 7.6 Trigonometric Equations ........................................................................................ 777 Chapter 7 Quiz (Sections 7.5–7.6) ................................................................................ 795 7.7 Equations Involving Inverse Trigonometric Functions .......................................... 797 Chapter 7 Review Exercises ......................................................................................... 806 Chapter 7 Test ............................................................................................................... 825 8 Applications of Trigonometry 8.1 The Law of Sines .................................................................................................... 830 8.2 The Law of Cosines ................................................................................................ 843 Chapter 8 Quiz (Sections 8.1 − 8.2)................................................................................ 856 8.3 Geometrically Defined Vectors and Applications .................................................. 857 8.4 Algebraically Defined Vectors and the Dot Product .............................................. 865 Summary Exercises on Applications of Trigonometry and Vectors ............................ 871 8.5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients.........873 8.6 DeMoivre’s Theorem; Powers and Roots of Complex Numbers ........................... 883 Chapter 8 Quiz (Sections 8.3 − 8.6)................................................................................ 896 8.7 Polar Equations and Graphs .................................................................................... 897 8.8 Parametric Equations, Graphs, and Applications ................................................... 912 Chapter 8 Review Exercises ......................................................................................... 923 Chapter 8 Test ............................................................................................................... 936

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    9 Systems and Matrices 9.1 Systems of Linear Equations .................................................................................. 942 9.2 Matrix Solution of Linear Systems ......................................................................... 970 9.3 Determinant Solution of Linear Systems ................................................................ 994 9.4 Partial Fractions .................................................................................................... 1018 Chapter 9 Quiz (Sections 9.1 − 9.4).............................................................................. 1033 9.5 Nonlinear Systems of Equations ........................................................................... 1037 Summary Exercises on Systems of Equations ............................................................ 1052 9.6 Systems of Inequalities and Linear Programming ................................................ 1061 9.7 Properties of Matrices ........................................................................................... 1079 9.8 Matrix Inverses ..................................................................................................... 1092 Chapter 9 Review Exercises ....................................................................................... 1113 Chapter 9 Test ............................................................................................................. 1134 10 Analytic Geometry 10.1 Parabolas ............................................................................................................. 1142 10.2 Ellipses ................................................................................................................1154 Chapter 10 Quiz (Sections 10.1 − 10.2)........................................................................ 1167 10.3 Hyperbolas .......................................................................................................... 1170 10.4 Summary of the Conic Sections .......................................................................... 1185 Chapter 10 Review Exercises ..................................................................................... 1193 Chapter 10 Test ........................................................................................................... 1203 11 Further Topics in Algebra 11.1 Sequences and Series .......................................................................................... 1207 11.2 Arithmetic Sequences and Series ........................................................................ 1221 11.3 Geometric Sequences and Series ........................................................................ 1230 Summary Exercises on Sequences and Series ............................................................ 1242 11.4 The Binomial Theorem ....................................................................................... 1244 11.5 Mathematical Induction ..................................................................................... 1251 Chapter 11 Quiz (Sections 11.1 − 11.5)........................................................................ 1265 11.6 Basics of Counting Theory ................................................................................. 1266 11.7 Basics of Probability ........................................................................................... 1274 Chapter 11 Review Exercises ..................................................................................... 1282 Chapter 11 Test ........................................................................................................... 1294 Appendices Appendix A Polar Form of Conic Sections ................................................................ 1298 Appendix B Rotation of Axes ..................................................................................... 1301

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    1 Chapter R REVIEW OF BASIC CONCEPTS Section R.1 Fractions, Decimals, and Percents 1. True 2. True 3. False. This is an improper fraction. Its value is 1. 4. False. The reciprocal of 6 2 is 2 6 or 1 3 . 5. C 6. C 7. 8 1 8 1 8 1 1 1 16 2 8 2 8 2 2 ⋅ = = ⋅ = ⋅ = ⋅ 8. 1 4 1 4 1 1 1 12 3 4 3 4 3 3 4 ⋅ = = ⋅ = ⋅ = ⋅ 9. 15 3 5 3 5 5 5 1 18 3 6 3 6 6 6 ⋅ = = ⋅ = ⋅ = ⋅ 10. 16 4 4 4 4 2 4 4 1 5 4 5 0 5 4 5 ⋅ = = ⋅ = ⋅ = ⋅ 11. 90 3 30 3 30 3 1 150 5 30 5 30 5 5 3 ⋅ = = ⋅ = ⋅ = ⋅ 12. 100 5 140 7 5 20 5 20 5 1 7 20 7 20 7 ⋅ = = ⋅ = ⋅ = ⋅ 13. 18 1 18 1 18 1 1 1 90 5 18 5 18 5 5 ⋅ = = ⋅ = ⋅ = ⋅ 14. 16 1 16 1 16 1 1 1 64 4 16 4 4 4 16 ⋅ = = ⋅ = ⋅ = ⋅ 15. 120 12 10 10 5 1 144 12 12 12 6       16. 77 7 11 7 7 1 132 12 11 12 12       17. 1 7 12 7 5 Therefore, 12 5 1 . 7 7 = 18. 1 9 16 9 7 Therefore, 16 7 1 . 9 9 = 19. 6 12 77 72 5 Therefore, 77 5 6 . 12 12 = 20. 5 13 67 65 2 Therefore, 67 2 5 . 13 13 = 21. Multiply the denominator of the fraction by the natural number and then add the numerator to obtain the numerator of the improper fraction. 5 2 10 ⋅ = and 10 3 13 + = The denominator of the improper fraction is the same as the denominator in the mixed number. Thus, 3 13 2 . 5 5 = 22. Multiply the denominator of the fraction by the natural number and then add the numerator to obtain the numerator of the improper fraction. 7 5 35 ⋅ = and 35 6 41 + = The denominator of the improper fraction is the same as the denominator in the mixed number. Thus, 6 41 5 . 7 7 = 23. Multiply the denominator of the fraction by the natural number and then add the numerator to obtain the numerator of the improper fraction. 3 12 36 ⋅ = and 36 2 38 + = The denominator of the improper fraction is the same as the denominator in the mixed number. Thus, 2 38 12 . 3 3 =

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    2 Chapter R Review of Basic Concepts 24. Multiply the denominator of the fraction by the natural number and then add the numerator to obtain the numerator of the improper fraction. 5 10 50 ⋅ = and 50 1 51 + = The denominator of the improper fraction is the same as the denominator in the mixed number. Thus, 1 51 10 . 5 5 = 25. 4 6 4 6 24 5 7 5 7 35 ⋅ ⋅ = = ⋅ 26. 2 5 2 10 7 9 7 5 9 63 ⋅ ⋅ = = ⋅ 27. 3 6 1 15 8 120 2 2 2 3 1 6 15 8 20 6 0 ⋅ ⋅ ⋅ = = = = ⋅ ⋅ 28. 3 5 15 1 20 21 42 3 5 1 15 20 21 28 0 8 15 2 ⋅ ⋅ ⋅ = = = = ⋅ ⋅ 29. 1 12 1 12 1 2 6 6 10 5 10 5 2 5 5 25 ⋅ ⋅ ⋅ ⋅ = = = ⋅ ⋅ ⋅ 30. 1 10 1 10 1 2 5 5 8 7 2 4 7 28 8 7 ⋅ ⋅ ⋅ ⋅ = = = ⋅ ⋅ ⋅ 31. 15 8 15 8 3 5 4 2 4 25 4 25 4 5 5 3 2 6 1 , or 1 5 5 5 ⋅ ⋅ ⋅ ⋅ ⋅ = = ⋅ ⋅ ⋅ ⋅ = = 32. 21 4 21 4 3 7 4 3 1 , or 1 7 8 7 4 2 7 2 8 2 ⋅ ⋅ ⋅ ⋅ = = = ⋅ ⋅ ⋅ 33. 3 21 3 21 3 3 7 3 3 3 21 9 7 1 7 1 7 1 7 1 ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ = = = = ⋅ ⋅ 34. 4 36 4 36 4 4 9 4 4 4 36 16 1 1 9 1 9 9 1 9 ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ = = = = ⋅ ⋅ 35. Change both mixed numbers to improper fractions. 1 2 13 5 13 5 65 5 3 1 , or 5 4 3 4 3 4 3 12 12 ⋅ ⋅ = ⋅ = = ⋅ 36. Change both mixed numbers to improper fractions. 2 3 3 3 3 8 8 8 8 64 4 2 1 , or 4 5 5 5 15 15 ⋅ ⋅ = ⋅ = = ⋅ 37. To divide fractions, multiply by the reciprocal of the divisor. 3 7 2 3 7 7 2 14 2 3 9 2 9 7 9 ⋅ ÷ = ⋅ = = ⋅ 38. To divide fractions, multiply by the reciprocal of the divisor. 6 5 6 4 24 1 6 4 11 5 1 4 11 5 55 ⋅ ÷ = ⋅ = = ⋅ 39. To divide fractions, multiply by the reciprocal of the divisor. 5 3 5 8 5 8 5 4 2 5 2 4 8 4 3 4 3 4 3 3 10 1 , or 3 3 3 ⋅ ⋅ ⋅ ⋅ ÷ = ⋅ = = = ⋅ ⋅ = 40. To divide fractions, multiply by the reciprocal of the divisor. 3 7 10 7 10 7 2 5 10 3 5 3 5 3 7 5 5 14 2 , or 4 3 3 ⋅ ⋅ ⋅ ÷ = ⋅ = = ⋅ ⋅ = 41. To divide fractions, multiply by the reciprocal of the divisor. 32 8 32 15 32 15 8 4 3 5 5 15 5 8 5 8 1 5 8 4 3 12 1 ⋅ ⋅ ⋅ ⋅ ÷ = ⋅ = = ⋅ ⋅ ⋅ ⋅ = = 42. To divide fractions, multiply by the reciprocal of the divisor. 24 24 21 24 21 4 6 3 7 7 6 6 7 21 7 1 7 6 4 3 12 6 1 ⋅ ⋅ ⋅ ⋅ ÷ = ⋅ = = ⋅ ⋅ ⋅ ⋅ = = 43. To divide fractions, multiply by the reciprocal of the divisor. 3 3 1 3 1 3 1 12 4 4 12 4 12 4 3 4 1 1 4 4 16 ⋅ ⋅ ÷ = ⋅ ⋅ ⋅ ⋅ = ⋅ = = = 44. To divide fractions, multiply by the reciprocal of the divisor. 2 2 1 2 1 2 1 1 1 30 30 5 30 5 2 15 5 15 5 5 75 = = ⋅ ⋅ ÷ = ⋅ = ⋅ ⋅ ⋅ ⋅ = 45. To divide fractions, multiply by the reciprocal of the divisor. 3 6 5 6 5 2 3 5 2 5 6 10 5 1 3 1 3 1 3 1 = = ⋅ ⋅ ⋅ ⋅ ⋅ = ÷ = ⋅ = ⋅ 46. To divide fractions, multiply by the reciprocal of the divisor. 4 8 9 8 9 2 4 9 2 9 8 18 1 1 4 4 9 1 4 1 = = ⋅ ⋅ ⋅ ⋅ ⋅ = ÷ = ⋅ = ⋅

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    Section R.1 Fractions, Decimals, and Percents 3 47. Change the first number to an improper fraction, and then multiply by the reciprocal of the divisor. 3 3 27 3 27 8 27 8 6 4 8 4 8 4 3 4 3 3 9 2 4 9 2 18 4 3 1 ⋅ = = = ÷ = ÷ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ⋅ 48. Change the first number to an improper fraction, and then multiply by the reciprocal of the divisor. 3 7 28 7 28 10 28 10 5 10 5 1 5 5 7 4 7 2 5 4 2 8 5 7 5 7 1 0 ⋅ ÷ = ÷ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = = = = 49. Change both mixed numbers to improper fractions, and then multiply by the reciprocal of the divisor. 1 5 5 12 5 7 5 7 2 1 2 7 2 7 2 12 2 12 35 11 , or 1 24 24 = ⋅ = ⋅ ÷ = ÷ ⋅ = 50. Change both mixed numbers to improper fractions, and then multiply by the reciprocal of the divisor. 20 9 5 9 5 9 7 2 2 20 7 5 20 5 2 1 9 7 100 37 , or 63 1 63          51. Change both mixed numbers to improper fractions, and then multiply by the reciprocal of the divisor. 5 15 21 47 21 32 21 32 2 1 8 47 21 8 4 21 4 84 37 , or 1 8 4 8 32 7 47 47 8 47 32 8 47                52. Change both mixed numbers to improper fractions, and then multiply by the reciprocal of the divisor. 3 4 23 9 23 5 23 5 2 1 10 9 2 5 9 23 5 , or 1 8 10 5 10 5 18           53. 7 4 7 4 11 15 15 15 15     54. 2 5 2 5 7 9 9 9 9     55. 7 1 7 1 8 2 4 2 12 12 12 12 3 4 3         56. 5 3 5 1 16 16 1 3 8 6 16 2      57. Because 9 3 3,   and 3 is prime, the LCD (least common denominator) is 3 3 9.   1 1 3 3 3 3 3 9    Now add the two fractions with the same denominator. 5 1 5 3 8 9 3 9 9 9     58. To add 4 15 and 1 , 5 first find the LCD. Since 15 3 5   and 5 is prime, the LCD is 15. 4 1 4 1 3 4 3 4 3 7 5 5 3 15 15 15 15 15 15          59. Because 8 2 2 2    and 6 2 3,   the LCD is 2 2 2 24. 3     3 3 3 9 8 8 3 24    and 5 5 4 20 6 6 4 24    Now add fractions with the same denominator. 3 5 9 20 29 8 6 24 24 4 , 2     or 5 1 24 60. Because 6 2 3   and 9 3 3,   the LCD is 2 3 3 18.    5 5 3 3 15 6 6 18    and 2 2 2 9 9 2 4 18    Now add fractions with the same denominator. 5 15 , 6 9 18 18 2 4 19 18     or 1 1 18 61. Because 9 3 3   and 16 4 4,   the LCD is 3 3 4 4 144.     16 80 9 9 1 5 5 6 144    and 3 3 9 27 16 16 9 144    Now add fractions with the same denominator. 5 3 80 27 9 16 144 144 107 144     62. Because 4 2 2   and 25 5 5,   the LCD is 2 2 5 5 100.     3 3 25 75 4 4 25 100    and 6 6 4 24 25 25 4 100    Now add fractions with the same denominator. 3 6 75 24 99 4 25 100 0 100 1 0    

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    4 Chapter R Review of Basic Concepts 63. 1 1 24 1 25 3 3 8 8 8 8 8 1 1 8 1 9 2 2 4 4 4 4 4 1 1 25 9 3 2 8 4 8 4              Because 8 2 2 2    and 4 2 2,   the LCD is 2 2 2   or 8. 1 1 25 9 2 3 2 8 4 8 4 2 25 18 8 8 43 3 , or 5 8 8        64. 2 12 2 14 4 4 1 1 12 1 13 2 2 2 3 3 3 3 3 6 6 6 6 6           Because 6 2 3,   the LCD is 6. 3 6 2 1 14 2 13 4 6 2 6 3 2 6 28 13 41 5 , 6 6 or 6        65. 7 2 7 2 5 9 9 9 9     66. 8 3 8 3 1 11 11 5 1 11     67. 13 3 13 3 10 2 5 2 15 15 15 15 3 5 3         68. 11 3 11 3 2 4 2 12 12 12 12 3 4 3 8 − ⋅ − = = = = ⋅ 69. Because 12 4 3 = ⋅ (12 is a multiple of 3), the LCD is 12. 1 4 4 3 4 12 ⋅ = Now subtract fractions with the same denominator. 7 1 7 4 3 1 3 1 12 3 12 12 12 4 3 4 ⋅ − = − = = = ⋅ 70. Because 6 3 2 = ⋅ (6 is a multiple of 2), the LCD is 6. 1 2 3 3 3 6 ⋅ = Now subtract fractions with the same denominator. 5 1 3 2 5 6 6 6 6 1 2 1 2 3 2 3 ⋅ − = − = = = ⋅ 71. Because 12 2 2 3 = ⋅ ⋅ and 9 3 3, = ⋅ the LCD is 2 2 3 36. 3 ⋅ ⋅ ⋅ = 7 7 3 21 12 12 3 36 = ⋅ = and 1 4 4 9 4 36 ⋅ = Now subtract fractions with the same denominator. 7 1 21 4 17 12 9 36 36 36 − = − = 72. The LCD of 12 11 1 11 3 1 4 and 16 is 48. 16 12 16 3 12 4 33 4 29 48 48 48 − = ⋅ − ⋅ = − = 73. 3 3 16 3 19 4 4 4 4 4 4 4 2 2 5 2 7 1 1 5 5 5 5 5 = + = + = = + = + = Because 4 2 2, = ⋅ and 5 is prime, the LCD is 2 2 5 20. ⋅ ⋅ = 3 2 19 5 7 4 4 1 4 5 4 5 5 4 95 28 67 7 , or 3 20 20 20 20 − = ⋅ − ⋅ = − = 74. Change both numbers to improper fractions then add, using 45 as the common denominator. 4 4 19 19 9 13 5 3 1 5 9 9 5 171 65 16 , or 2 4 13 5 9 5 9 106 45 45 45 5 − = − = ⋅ − ⋅ = − =

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    Section R.1 Fractions, Decimals, and Percents 5 75. 74 8 8 12 4 2 2 72 2 9 9 9 9 9 2 2 2 14 3 3 3 3 3 4 = + = + = = + = + = Because 9 3 3, = ⋅ and 3 is prime, the LCD is 3 3 9. ⋅ = 14 3 8 4 3 3 2 2 74 74 42 5 , or 3 9 9 3 9 9 9 32 9 − = − ⋅ = − = 76. 5 5 84 5 89 12 12 12 12 12 5 5 24 5 29 6 6 7 6 4 4 6 6 7 = + = + = = + = + = Since 12 2 2 3 = ⋅ ⋅ and 6 2 3, = ⋅ the LCD is 2 2 3 12. ⋅ ⋅ = 5 5 89 89 12 6 12 12 29 2 58 7 4 6 2 1 31 12 2 7 , or 2 12 − = − ⋅ = − = 77. Observe that there are 24 dots in the entire figure, 6 dots in the triangle, 12 dots in the rectangle, and 2 dots in the overlapping region. (a) 12 1 24 2 = of all the dots are in the rectangle. (b) 6 1 24 4 = of all the dots are in the triangle. (c) 2 1 6 3 = of the dots in the triangle are in the overlapping region. 2 1 12 6 = of the dots in the rectangle are in the overlapping region. 78. (a) 12 is 1 3 of 36, so Benita got a hit in exactly 1 3 of her at-bats. (b) 1 is a little less than 1 10 of 11, so Chase got a home run in just less than 1 10 of his at-bats. (c) 9 is a little less than 1 4 of 40, so Christine got a hit in just less than 1 4 of her at-bats. (d) 8 is 1 2 of 16, and 10 is 1 2 of 20, so Chin and Greg each got hits 1 2 of the time they were at bat. 79. 367.9412 (a) Tens: 6 (b) Tenths: 9 (c) Thousandths: 1 (d) Ones: 7 (e) Hundredths: 4 80. Answers will vary. One example is 5243.0164. 81. 46.249 (a) 46.25 (b) 46.2 (c) 46 (d) 50 82. (a) 0.889 (b) 0.444 (c) 0.976 (d) 0.865 83. 4 0.4 10  84. 6 0.6 10  85. 64 0.64 100  86. 82 0.82 100  87. 138 0.138 1000  88. 104 0.104 1000  89. 43 0.043 1000 

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    6 Chapter R Review of Basic Concepts 90. 87 0.087 1000  91. 805 3805 3.805 3 1000 1000   92. 166 5166 5.166 5 1000 1000   93. 25.320 109.200 8.574 143.094  94. 90.527 32.430 589.800 712.757  95. 28.73 3.12 25.61  96. 46.88 13.45 33.43  97. 43.50 28.17 15.33  98. 345.10 56.31 288.79  99. 3.87 15.00 2.90 21.77  100. 8.20 1.09 12.00 21.29  101. 32.560 47.356 1.800 81.716  102. 75.200 123.960 3.897 203.057  103. 18.000 2.789 15.211  104. 29.000 8.582 20.418  105. 12.8 1 decimal place 9.1 1 decimal place 128 1152 1 1 2 116.48 2 decimal places     106. 34.04 2 decimal places 0.56 2 decimal places 20424 17020 2 2 4 19.0624 4 decimal places     107. 22.41 2 decimal places 33 0 decimal places 6723 6723 2 0 2 739.53 2 decimal places     108. 55.76 2 decimal places 72 0 decimal places 11152 39032 2 0 2 4014.72 2 decimal places     109. 0.2 1 decimal place 0.03 2 decimal places 6 1 2 3 0.006 3 decimal places    110. 0.07 2 decimal places 0.004 3 decimal places 28 2 3 5 0.00028 5 decimal places   

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    Section R.1 Fractions, Decimals, and Percents 7 111. 7.15 11 78.65 77 16 11 55 55 0 112. 5.24 14 73.36 70 33 28 56 56 0 113. To change the divisor 11.6 into a whole number, move each decimal point one place to the right. Move the decimal point straight up and divide as with whole numbers. 2.8 116 324.8 232 92 0 0 000 8 928 0 Therefore, 32.48 11.6 2.8   . 114. To change the divisor 17.4 into a whole number, move each decimal point one place to the right. Move the decimal point straight up and divide as with whole numbers. 4.9 174 852.6 696 156 000 6 156 6 0 Therefore, 85.26 17.4 4.9   . 115. To change the divisor 9.74 into a whole number, move each decimal point two places to the right. Move the decimal point straight up and divide as with whole numbers. 2.05 974 1996.70 1948 4870 4870 0 Therefore, 19.967 9.74 2.05.   116. To change the divisor 5.27 into a whole number, move each decimal point two places to the right. Move the decimal point straight up and divide as with whole numbers. 8.44 527 4447.88 4216 2318 2108 2108 2108 0 Therefore, 44.4788 5.27 8.44.   117. Move the decimal point one place to the right. 123.26 10 1232.6   118. Move the decimal point one place to the right. 785.91 10 7859.1   119. Move the decimal point two places to the right. 57.116 100 5711.6   120. Move the decimal point two places to the right. 82.053 100 8205.3   121. Move the decimal point three places to the right. 0.094 1000 94   122. Move the decimal point three places to the right. 0.025 1000 25   123. Move the decimal point one place to the left. 1.62 10 0.162   124. Move the decimal point one place to the left. 8.04 10 0.804   125. Move the decimal point two places to the left. 124.03 100 1.2403   126. Move the decimal point two places to the left. 490.35 100 4.9035   127. Move the decimal point three places to the left. 23.29 1000 023.29 1000 0.02329     128. Move the decimal point three places to the left. 59.8 1000 059.8 1000 0.0598    

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    8 Chapter R Review of Basic Concepts 129. Convert from a decimal to a percent. 0.01 0.01 100% 1% = ⋅ = Fraction in Lowest Terms (or Whole Number) Decimal Percent 1 100 0.01 1% 130. Convert from a percent to a decimal. 2 2% 0.02 100 = = Fraction in Lowest Terms (or Whole Number) Decimal Percent 1 50 0.02 2% 131. Convert from a percent to a fraction. 5 5% 100 = In lowest terms, 5 1 5 1 100 20 5 20 ⋅ = = ⋅ Fraction in Lowest Terms (or Whole Number) Decimal Percent 1 20 0.05 5% 132. Convert to a decimal first. Divide 1 by 10. Move the decimal point one place to the left. 1 10 0.1 ÷ = Convert the decimal to a percent. 0.1 0.1 100% 10% = ⋅ = Fraction in Lowest Terms (or Whole Number) Decimal Percent 1 10 0.1 10% 133. Convert the decimal to a percent. 0.125 0.125 100% 12.5% = ⋅ = Fraction in Lowest Terms (or Whole Number) Decimal Percent 1 8 0.125 12.5% 134. Convert the percent to a decimal first. 20% 0.20, = or 0.2 Convert from a percent to a fraction. 20 20% 100 = In lowest terms, 20 1 20 1 100 5 20 5 ⋅ = = ⋅ Fraction in Lowest Terms (or Whole Number) Decimal Percent 1 5 0.2 20% 135. Convert to a decimal first. Divide 1 by 4. Add a decimal point and as many 0s as necessary. 0.25 4 1.00 8 20 20 0 Convert the decimal to a percent. 0.25 = 25% Fraction in Lowest Terms (or Whole Number) Decimal Percent 1 4 0.25 25% 136. Convert to a decimal first. Divide 1 by 3. Add a decimal point and as many 0s as necessary. 0.33... 3 1.00... 9 10 9 1 Note that the pattern repeats. Therefore, 1 0.3 3  Convert the decimal to a percent. 0.3 33.3%  or 1 0.3 33 % 3  Fraction in Lowest Terms (or Whole Number) Decimal Percent 1 3 0.3 33.3% or 1 33 % 3

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    Section R.1 Fractions, Decimals, and Percents 9 137. Convert the percent to a decimal first. 50% = 0.5 Convert from a percent to a fraction. 50 50% 100  In lowest terms, 50 1 50% 100 2   Fraction in Lowest Terms (or Whole Number) Decimal Percent 1 2 0.5 50% 138. Divide 2 by 3. Add a decimal point and as many 0s as necessary. 0.66... 3 2.00... 18 20 18 2 Note that the pattern repeats. Therefore, 2 0.6 3  Fraction in Lowest Terms (or Whole Number) Decimal Percent 2 3 0.6 2 66 % 3 or 66.6% 139. Convert the decimal to a percent first. 0.75 = 75% Convert from a percent to a fraction. 75 75% 100  In lowest terms, 75 3 75% 100 4   Fraction in Lowest Terms (or Whole Number) Decimal Percent 3 4 0.75 75% 140. Convert the decimal to a percent. 1.0 = 100% Fraction in Lowest Terms (or Whole Number) Decimal Percent 1 1.0 100% 141. Divide 21 by 5. Add a decimal point and as many 0s as necessary. 4.2 5 21.0 20 10 10 0 142. Divide 9 by 5. Add a decimal point and as many 0s as necessary. 1.8 5 9.0 5 40 40 0 143. Divide 9 by 4. Add a decimal point and as many 0s as necessary. 2.25 4 9.00 8 10 8 20 20 0 144. Divide 15 by 4. Add a decimal point and as many 0s as necessary. 3.75 4 15.00 12 30 28 20 20 0

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    10 Chapter R Review of Basic Concepts 145. Divide 3 by 8. Add a decimal point and as many 0s as necessary. 0.375 8 3.000 24 60 56 40 40 0 146. Divide 7 by 8. Add a decimal point and as many 0s as necessary. 0.875 8 7.000 64 60 56 40 40 0 147. Divide 5 by 9. Add a decimal point and as many 0s as necessary. 0.555... 9 5.000... 45 50 45 50 45 5 Note that the pattern repeats. Therefore, 5 0.5, 9 = or about 0.556. 148. Divide 8 by 9. Add a decimal point and as many 0s as necessary. 0.888... 9 8.000... 72 80 72 80 72 8 Note that the pattern repeats. Therefore, 8 0.8, 9 = or about 0.889. 149. Divide 1 by 6. Add a decimal point and as many 0s as necessary. 0.166... 6 1.000... 6 40 36 40 36 4 Note that the pattern repeats. Therefore, 1 0.16, 6 = or about 0.167. 150. Divide 5 by 6. Add a decimal point and as many 0s as necessary. 0.833... 6 5.000... 48 20 18 20 18 2 Note that the pattern repeats. Therefore, 5 0.83, 6 = or about 0.833. 151. 54% 0.54 = 152. 39% 0.39 = 153. 7% 07% 0.07 = = 154. 4% 04% 0.04 = = 155. 117% 1.17 = 156. 189% 1.89 = 157. 2.4% 02.4% 0.024 = = 158. 3.1% 03.1% 0.031 = = 159. 1 6 % 6.25% 06.25% 0.0625 4 = = = 160. 1 5 % 5.5% 05.5% 0.055 2 = = = 161. 0.79 79% = 162. 0.83 83% = 163. 0.02 2% = 164. 0.08 8% = 165. 0.004 0.4% =

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