THÔNG TIN TÀI LIỆU
© 2015 Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher except as may be permitted by the license terms below For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com ISBN-13: 978-130510553-9 ISBN-10: 1-30510553-2 Cengage Learning 200 First Stamford Place, 4th Floor Stamford, CT 06902 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan Locate your local office at: www.cengage.com/global Cengage Learning products are represented in Canada by Nelson Education, Ltd To learn more about Cengage Learning Solutions, visit www.cengage.com Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com NOTE: UNDER NO CIRCUMSTANCES MAY THIS MATERIAL OR ANY PORTION THEREOF BE SOLD, LICENSED, AUCTIONED, OR OTHERWISE REDISTRIBUTED EXCEPT AS MAY BE PERMITTED BY THE LICENSE TERMS HEREIN READ IMPORTANT LICENSE INFORMATION Dear Professor or Other Supplement Recipient: Cengage Learning has provided you with this product (the “Supplement”) for your review and, to the extent that you adopt the associated textbook for use in connection with your course (the “Course”), you and your students 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to the laws of the State of New York, without regard to such State’s conflict of law rules Thank you for your assistance in helping to safeguard the integrity of the content contained in this Supplement We trust you find the Supplement a useful teaching tool Table of Contents Chapter 1: Basic Concepts 1.1: Review of Basic Operations 1.2: Order of Operations 1.3: Area and Volume 1.4: Formulas 1.5: Prime Factorization Unit 1A Review 1.6: Introduction to Fractions 1.7: Addition and Subtraction of Fractions 1.8: Multiplication and Division of Fractions 1.9: The U.S System of Weights and Measures Unit 1B Review 1.10: Addition and Subtraction of Decimal Fractions 1.11: Rounding Numbers 1.12: Multiplication and Division of Decimal Fractions 1.13: Percent 1.14: Rate, Base, and Part 1.15: Powers and Roots 1.16: Applications Involving Percent: Business and Personal Finance Unit 1C Review Chapter Review Chapter Test 10 12 14 14 16 24 34 36 38 40 41 43 45 51 52 57 57 61 Chapter 2: Signed Numbers and Powers of 10 2.1: Addition of Signed Numbers 2.2: Subtraction of Signed Numbers 2.3: Multiplication and Division of Signed Numbers 2.4: Signed Fractions 2.5: Powers of 10 2.6: Scientific Notation 2.7: Engineering Notation Chapter Review Chapter Test Cumulative Review Chapters 1-2 64 64 65 65 70 72 76 77 79 80 Chapter 3: The Metric System 3.1: Introduction to the Metric System 3.2: Length 3.3: Mass and Weight 3.4: Volume and Area 3.5: Time, Current, and Other Units 3.6: Temperature 3.7: Metric and U.S Conversion Chapter Review Chapter Test 82 82 83 84 85 86 87 89 91 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 4: Measurement 4.1: Approximate Numbers and Accuracy 4.2: Precision and Greatest Possible Error 4.3A: The Vernier Caliper 4.3B: The Vernier Caliper 4.4A: The Micrometer Caliper 4.4B: The Micrometer Caliper 4.5: Addition and Subtraction of Measurements 4.6: Multiplication and Division of Measurements 4.7: Relative Error and Percent of Error 4.8: Color Code of Electrical Resistors 4.9: Reading Scales Chapter Review Chapter Test Cumulative Review Chapter 1-4 93 93 94 94 95 95 95 96 98 100 101 101 102 103 Chapter 5: Polynomials: An Introduction to Algebra 5.1: Fundamental Operations 5.2: Simplifying Algebraic Expressions 5.3: Addition and Subtraction of Polynomials 5.4: Multiplication of Monomials 5.5: Multiplication of Polynomials 5.6: Division by a Monomial 5.7: Division by a Polynomial Chapter Review Chapter Test 105 109 112 114 118 124 127 132 134 Chapter 6: Equations and Formulas 6.1: Equations 6.2: Equations with Variables in Both Members 6.3: Equations with Parentheses 6.4: Equations with Fractions 6.5: Translating Words into Algebraic Symbols 6.6: Applications Involving Equations 6.7: Formulas 6.8: Substituting Data into Formulas 6.9: Reciprocal Formulas Using a Calculator Chapter Review Chapter Test Cumulative Review: Chapters 1-6 136 141 144 152 160 161 166 171 177 180 184 187 Chapter 7: Ratio and Proportion 7.1: Ratio 7.2: Proportion 7.3: Direct Variation 7.4: Inverse Variation Chapter Review Chapter Test 190 192 201 205 209 211 Chapter 8: Graphing Linear Equations 8.1: Linear Equations with Two Variables 8.2: Graphing Linear Equations 8.3: The Slope of a Line 8.4: The Equation of a Line Chapter Review Chapter Test Cumulative Review Chapters 1-8 213 217 221 223 231 235 236 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 9: Systems of Linear Equations 9.1: Solving Pairs of Linear Equations by Graphing 9.2: Solving Pairs of Linear Equations by Addition 9.3: Solving Pairs of Linear Equations by Substitution 9.4: Applications Involving Pairs of Linear Equations Chapter Review Chapter Test 239 242 252 259 272 276 Chapter 10: Factoring Algebraic Expressions 10.1: Finding Monomial Factors 10.2: Finding the Product of Two Binomials Mentally 10.3: Finding Binomial Factors 10.4: Special Products 10.5: Finding Factors of Special Products 10.6: Factoring General Trinomials Chapter 10 Group Activities Chapter 10 Review Chapter 10 Test Cumulative Review Chapters 1-10 279 279 282 284 285 286 287 287 288 289 Chapter 11: Quadratic Equations 11.1: Solving Quadratic Equations by Factoring 11.2: The Quadratic Formula 11.3: Applications Involving Quadratic Equations 11.4: Graphs of Quadratic Equations 11.5: Imaginary Numbers Chapter 11 Group Activities Chapter 11 Review Chapter 11 Test 292 295 300 305 307 311 312 316 Chapter 12: Geometry 12.1: Angles and Polygons 12.2: Quadrilaterals 12.3: Triangles 12.4: Similar Polygons 12.5: Circles 12.6: Radian Measure 12.7: Prisms 12.8: Cylinders 12.9: Pyramids and Cones 12.10: Spheres Chapter 12 Group Activities Chapter 12 Review Chapter 12 Test Cumulative Review Chapters 1-12 318 319 324 329 332 338 341 344 349 355 358 358 361 363 Chapter 13: Right Triangle Trigonometry 13.1: Trigonometric Ratios 13.2: Using Trigonometric Ratios to Find Angles 13.3: Using Trigonometric Ratios to Find Sides 13.4: Solving Right Triangles 13.5: Applications Involving Trigonometric Ratios Chapter 13 Review Chapter 13 Test 367 368 370 375 379 383 385 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 14: Trigonometry with Any Angle 14.1: Sine and Cosine Graphs 14.2: Period and Phase Shift 14.3: Solving Oblique Triangles: Law of Sines 14.4: Law of Sines: The Ambiguous Case 14.5: Solving Oblique Triangles: Law of Cosines Chapter 14 Group Activities Chapter 14 Review Chapter 14 Test Cumulative Review Chapters 1-14 386 388 392 397 405 413 415 419 421 Chapter 15: Basic Statistics 15.1: Bar Graphs 15.2: Circle Graphs 15.3: Line Graphs 15.4: Other Graphs 15.5: Mean Measurement 15.6: Other Average Measurements and Percentiles 15.7: Range and Standard Deviation 15.8: Grouped Data 15.9: Standard Deviation for Grouped Data 15.10: Statistical Process Control 15.11: Other Graphs for Statistical Data 15.12: Normal Distribution 15.13: Probability 15.14: Independent Events Chapter 15 Review Chapter 15 Test 424 424 426 427 427 427 428 428 429 430 430 432 434 434 435 436 Chapter 16: Binary and Hexadecimal Numbers 16.1: Introduction to Binary Numbers 16.2: Addition of Binary Numbers 16.3: Subtraction of Binary Numbers 16.4: Multiplication of Binary Numbers 16.5: Conversion from Decimal to Binary System 16.6: Conversion from Binary to Decimal System 16.7: Hexadecimal System 16.8: Addition and Subtraction of Hexadecimal Numbers 16.9: Binary to Hexadecimal Conversion Chapter 16 Group Activities Chapter 16 Review Chapter 16 Test Cumulative Review Chapters 1-16 437 437 437 437 438 438 438 438 439 440 440 440 441 Appendices Appendix B: Exponential Equations Appendix C: Simple Inequalities 443 446 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 1: Basic Concepts Chapter 1: Basic Concepts Section 1.1: Review of Basic Operations 3255 21 27, 216 10, 793 22 1, 699,922 1454 23 18,172, 065 579 24 486, 400 795, 776 25 35,360, 000 4,845,000 26 122, 440,800 5164 27 1809 3298 28 61, 747 r 26, 008 29 389 10 130,130 30 434 r 24 11 2820 31 844 r 40 12 50,124 32 1566 r 80 13 4195Ω 33 31 mi/gal × 16 gal = 496 mi 14 8615Ω 34 65 L × 12 km/L = 780 km 15 The sum of the lengths is 224 feet, so 224 studs are required 35 1300 cm3 ÷ = 325 cm3 16 24 ft − ft − ft − ft = ft 17 39 ft 18 125 ft − 78 ft = 47 ft 19 Input: 1925 cm3 Output: 1425 cm3 1925 cm3 − 1425 cm = 500 cm3 20 Yes; 31 hr + hr + hr + hr + hr = 41 hr 43 36 1274 mi ÷ 49 gal = 26 mi/gal 37 2340 km ÷ 180 L = 13 km/L 38 $13/4 ft × 20 ft = $65 39 $516 ÷ h = $86/h 40 $508 ÷ = $127 41 125 mi/h × h = 500 mi 42 500 ft/min × 15 = 7500 ft 45 × 18 ft = 90 ft First draftperson: × 30 × 80 = 19, 200 drawings 42 × 15 ft = 630 ft 158 × 12 ft = 1896 ft Second draftperson: × 30 × 120 = 28,800 drawings Difference: 28,800 − 19, 200 = 9600 drawings 105 × 10 ft = 1050 ft 79 × ft = 632 ft 87 × ft = 522 ft Total = 4820 ft 44 There are 112 boards in the order 36 × 12 ft = 432 ft 28 × 10 ft = 280 ft 36 × ft = 288 ft 12 × 16 ft = 192 ft Total = 1192 ft 46 5232 ft ÷ 12 ft = 436 47 17 ft in = 17 ft × 12 in./ft + in = 209 in 209 in − 75 in = 134 in 134 in ÷ = 67 in from either corner 48 260 acres × 165 bu/acre = 42,900 bu © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Elementary Technical Mathematics, 11th 6864 bu 12, 000, 000 bu 50 = 44 bu/acre = 5897 cars 156 acre 2035 bu/car 51 a 856 lb + 754 lb + 1044 lb + 928 lb + 888 lb + 734 lb + 953 lb + 891 lb 7048 lb = = 881 lb/day 8 days 49 b 4320 lb 120 lb/day = 120 lb/day ; = 15 lb/day/steer 36 days steers 52 56 Number of bales = × 110 × 15 = 9900 Weight of bales = 9900 × 80 lb = 396 tons 2000 lb/ton 53 57 92, 480 lb = 2890 bu 32 lb/bu 2890 bu = 85 lb/acre 34 acre 54 15 tons × 2000 lb/ton = 30, 000 lb 30, 000 lb = 60 bales 500 lb $175, 000 − $300 = $172, 000 $172, 000 = $17, 200 10 60 I = E 48 = =2A R 24 61 E = IR = ( 2)(12) = 24 V 62 E = IR = ( 2)( 24) = 48 V 63 220 × oz = 880 oz × 60 mg = 180 g 180 g ÷ 30 g = tablets 65 800 mg ÷ 800 mg = tablets 66 × g = 10 g 67 30 ft × 12 in./ft = 360 in 360 in − × in = 350 in 350 in ÷ 10 in = 35 One additional daylily is required at the end of the planting so 35 + = 36 daylilies are needed in total 58 × 75 × = 1575 lb 59 I = 55 64 400 gal = 40 10 gal 40 × lb = 80 lb 14 ft in − × (2 ft in.) − × (1 ft ) = 14 ft in − 10 ft − ft = ft in (1 ft in.) ÷ = 18 in ÷ = in E 220 = =5A 44 R 68 The outer dimension of the back wall is 12 in 17 ft × + in = 208 in long and ft 12 in ft × = 96 in high so there would be ft 96 in 208 in = 12 rows of = 13 blocks, in 16 in for a total of × 12 × 13 = 312 blocks for both walls The outer dimensions of the side walls must fit inside the bricks of the back and front walls, so the side wall is 12 in 12 ft × + in − × in = 144 in ft 12 in long and ft × = 96 in high so there ft 96 in 144 in would be = 12 rows of =9 in 16 in blocks, for a total of × × 12 = 216 blocks for both walls A total of 312 + 216 = 528 blocks are needed © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 1: Basic Concepts 69 ft − × (10 in.) − × (1 ft in.) = 96 in − × 10 in − × 14 in = 96 in − 30 in − 28 in = 38 in 38 in ÷ = 19 in 70 × 30 gal = 60 gal 73 50 + 125 + 110 + 35 = 320 seats 74 a 125 ÷ 11 = 11 r so 12 beef loins are required b Each beef loin has two end cuts, so × 12 = 24 end cuts are available 75 × 90 + × + × = 180 + 12 + = 200 items 76 Number of tables = 10 + 12 = 22 Tables per server = 22 ÷ =3r4 Servers needed = 60 gal ÷ gal/drum = 12 drums Order size = 12 drums − drums = drums 71 2500 ÷ 1000 = 2.5 77 a $131 + $152 + $128 = $411 b $411 ữ = $137 2.5 ì 8540 bd ft = 213,500 bd ft 72 lb × $520 = $0.52/lb 2000 lb Section 1.2: Order of Operations − ( − 2) = − ( 2) = (14) − × 15 ÷ = 8−6 = 28 − 90 ÷ = 28 − 10 = 18 =2 (8 + 6) + = (14) + = (72) + 20 ÷ = 64 = 360 + (8 + 6) − (7 − 3) = 14 − = 10 × ( ì ) + (6 + 2) ữ = ì 12 + ữ = 48 + = 50 (8 × 9) + (13 + ) ÷ = (72) + 20 ÷ = 56 + (9 + 5) ì (13 + 2) ữ = 365 27 + 13 × (7 − 3)(12 + 6) ữ = 27 + 13 ì (4)(18) ÷ = 27 + 52 (18) ÷ = 27 + 936 ÷ = 27 + 104 = 131 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Elementary Technical Mathematics, 11th 123 − (8 + 9) + 17 16 = 123 − (17 ) + 17 = (20) + 24 ÷ = 123 − 51 + 17 = 120 + = 89 = 124 16 + (7 + 8) − 17 = 16 + (15) − = 42 + 72 (25) ÷ 30 = 73 (18 + 17 )(12 + 9) − (7 × 16)(4 + 2) = (35)( 21) − (112)(6) = 42 + 1800 ÷ 30 = 42 + 60 = 102 18 = 735 − 672 = 228 − 52 − 32 − (17 − 15) + 18 = − ( 2) + 18 = 144 19 = − + 18 (9 + 7) + 13 = (16) + 13 = 38 + 108 − = 137 20 = 80 + 13 = 93 13 = 21 − 14 21 (3 × ) + (8 + 4) ÷ = 27 − 18 − + 224 = 105 + 15 (8 + 6) − (13 + 3) ÷ 14 = (14) − (16) ÷ 14 = 42 − 112 ÷ 14 = 42 − = 34 27 − × (18 − 9) − + ( 43 − 15) = 27 − × − + (28) = (21) + 12 ÷ = 109 (19 + 8)(4 + 3) ữ 21 + (8 ì 15) ữ (4 ì 3) = (27 )(7 ) ÷ 21 + 120 ÷ 12 = 189 ÷ 21 + 10 = + 10 = 19 (39 − 18) − (23 − 18) = 16 38 + × (8 + 4) − (5 − 2) = 38 + × 12 − (3) = 23 12 228 − × (7 + 6) − (6 − 2) = 228 − × 13 − (4) = 63 11 42 + 12 (9 − 3)(12 + 13) ÷ 30 = 42 + 12 (6)(25) ÷ 30 = 16 + 60 − 10 ( × 5) + (15 + 9) ữ = 230 22 ì ữ ì ữ 12 + = 48 ữ ì ữ 12 + = 24 ì ữ 12 + = 192 ữ 12 + = 16 + = 24 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 1: Basic Concepts 23 12 ì ữ 18 ì 64 ữ + 30 = 108 ữ 18 ì 64 ữ + 24 25 18 ữ ì 24 ÷ ÷ = × 24 ÷ ÷ = 72 ÷ ÷ = 18 ÷ =3 = + 30 − − 30 =0 26 = + 60 + − 20 − = 50 31 32 33 34 = + 17 ( 4) − 67 28 = − 21 ÷ 21 − = −1− =0 29 35 10 + 42 = 10 + 16 = 26 − (9 − 2) ÷ 21 − = − (7) ÷ 21 − 28 − (2 × 3) + − (16 ì 8) ữ (4 ì 4) 28 / × − (6 + 10) / (6 − 2) = 14 × − 16 / = 98 − = 94 + 17 (2 × 2) − 67 = + 68 − 67 =4 × 15 ÷ + (13 − 5) / × − = 45 ÷ + / × − = 5+4×4−2 = + 16 − 19 = + (49) − − (11) 27 (36 − 6) / (5 + 10) + (16 − 1) / = 30 /15 + 15 / = 2+5 =7 + (7 × ) − − ( + ) = + 147 − − 22 = 124 24 / (6 − 2) + × − 15 / = 24 / + 12 − = + 12 − = 13 + (3 + ) − − ( + ) = + (5) − − (6) + (9 + 6) + − (7 + 3) (3 ì 12) ữ = + (15) + − (10) − 36 ữ = ì 64 ữ + = 384 ÷ + = 48 + = 55 36 + ⋅ 32 = + 2⋅9 = + 18 = 22 = 28 − (6) + − 128 ÷ 16 = 28 − 24 + − =0 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 1: Basic Concepts 53 (continued) b P = BR ( P = 35 deer/mi 56 P = BR P = (70 lb )(0.17 ) ) (0.40) = 11.9 lb Remaining = 70 lb − 11.9 lb = 58.1 lb = 14 deer/mi Population = 35 deer/mi + 14 deer/mi 57 = 45 deer/mi 54 a P = BR P = ( 4.6 lb )(0.25) = 1.15 lb Average per day = 4.6 lb − 1.15 lb = 3.45 lb b 3.45 lb × 75, 000 × 365 × ton 2000 lb = 47, 200 tons c 100% − 30% = 70% P R 73,500 tons B= 0.70 = 105, 000 tons B= 49 Total Less 5% Cash Discount Net 30 Days Net Total Total Cost 22 × $1.33 = $29.26 14 × $3.89 = $54.46 12 × $6.49 = $77.88 × $7.43 = $44.58 × $8.76 = $52.56 × $5.54 = $33.24 × $6.45 = $32.25 × $2.09 = $8.36 120 × $1.69 = $202.80 32 × $48.00 = $1536 $2, 071.39 $103.57 $1,967.82 55 Total cost = $5.66 P R $5.66 B= 0.34 = $16.65 B= © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part 50 Elementary Technical Mathematics, 11th 58 Net Weight Pound 12400 26720 − 9240 = 17480 20240 − 7480 = 12760 28340 − 9200 = 19140 26760 − 9160 = 17600 17880 − 7485 = 10395 25620 − 9080 = 16540 21560 − 7640 = 13920 26510 − 9060 = 17450 22630 − 7635 = 14995 22920 − 9220 = 13700 20200 − 7660 = 12540 25880 − 9160 = 16720 21300 − 7675 = 13625 18200 − 7665 = 10535 26200 − 9150 = 17050 22600 − 7650 = 14950 27100 − 9080 = 18020 22550 − 7635 = 14915 23600 − 7680 = 15920 26780 − 9160 = 17620 28310 − 9200 = 19110 21560 − 7665 = 13895 25750 − 9160 = 16590 No of Bushels 207 17480 / 60 = 291 12760 / 60 = 213 19140 / 60 = 319 17600 / 60 = 293 10395 / 60 = 173 16540 / 60 = 276 13920 / 60 = 232 17450 / 60 = 291 14995 / 60 = 250 13700 / 60 = 228 12540 / 60 = 209 16720 / 60 = 279 13625 / 60 = 227 10535 / 60 = 176 17050 / 56 = 304 14950 / 56 = 267 18020 / 56 = 322 14915 / 56 = 266 15920 / 56 = 284 17620 / 56 = 315 19110 / 56 = 341 13895 / 56 = 248 16590 / 56 = 296 Total Amount $1,173.69 291 × $5.71 = $1661.61 213 × $5.74 = $1222.62 319 × $5.81 = $1853.39 293 × $5.76 = $1687.68 173 × $5.76 = $996.48 276 × $11.72 = $3234.72 232 × $11.69 = $2712.08 291 × $11.68 = $3398.88 250 × $11.65 = $2912.5 228 × $11.72 = $2672.16 209 × $11.81 = $2468.29 279 × $11.9 = $3320.1 227 × $11.84 = $2687.68 176 × $11.79 = $2075.04 304 × $4.68 = $1422.72 267 × $4.65 = $1241.55 322 × $4.66 = $1500.52 266 × $4.61 = $1226.26 284 × $4.59 = $1303.56 315 × $4.63 = $1458.45 341 × $4.69 = $1599.29 248 × $4.67 = $1158.16 296 ì $4.65 = $1376.4 45190.14 â 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 1: Basic Concepts 59 60 66 × $7.97 = $526.02 30 × $3.95 = $118.50 14 × $3.39 = $47.46 17 × $6.59 = $112.03 × $12.10 = $48.40 × $5.39 = $48.51 × $4.97 = $34.79 10 × $11.97 = $119.70 × $16.89 = $101.34 11 × $18.55 = $204.05 15 × $24.25 = $363.75 27 × $16.95 = $457.65 × $14.39 = $100.73 × $24.96 = $24.96 10 × $10.37 = $103.7 27 × $19.85 = $535.95 × $12.25 = $85.75 × $17.85 = $17.85 × $12.19 = $85.33 × $3.49 = $27.92 × $17.65 = $52.95 80 × $17.29 = $1383.2 × $20.65 = $144.55 $5428.59 − $108.57 Net Price 3($18.58 − 0.40 × $18.58) = $33.44 5($65.10 − 0.25 × $65.10) = $244.13 5($73.95 − 0.25 × $73.95) = $277.31 8($43.90 − 0.25 × $43.90) = $263.40 2($124.60 − 0.20 × $124.60) = $199.36 5($18.80 − 0.15 × $18.80) = $79.90 Subtotal Less 5% if paid in 30 days Total $1097.54 $1097.54 × 0.05 = $54.877 $1042.66 × $33.59 = $33.59 × $34.97 = $104.91 250 × $2.18 = $545 $5428.59 $5428.59 × 0.02 Subtotal Less 2% Discount = $108.57 $5428.59 − $108.57 Subtotal ¾% Sales Tax NET TOTAL 51 = $5320.02 $5320.02 × 0.0575 = $305.90 $5320.02 + $305.90 = $5625.92 Section 1.15: Powers and Roots 225 2,940, 000,000 625 729 222 0.000778 2740 0.00000661 562 10 0.0000114 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part 52 Elementary Technical Mathematics, 11th 11 0.00483 17 68.9 12 15,300 18 0.0806 13 157 19 42.4 14 276, 000 20 2.12 15 2.96 21 0.198 16 112 22 8.78 Section 1.16: Applications Involving Percent: Business and Personal Finance a i = prt ⎛ r⎞ A = P ⎜1 + ⎟ ⎝ n⎠ i = ($2000 )(0.05)(3) = $300 ⎛ 0.055 ⎞ A = $15, 000 ⎜1 + ⎟ ⎝ ⎠ b principle + interest loan period $2000 + $300 payment = 36 = $63.89 16 = $23,152.64 ⎛ r⎞ A = P ⎜1 + ⎟ ⎝ n⎠ i = prt = $225 = $6000 (1.01875) (4)(5) 20 = $8699.69 nt ⎛ 0.065 ⎞ A = $7500 ⎜1 + ⎟ ⎝ ⎠ (4)(4) = $7500 (1.01625) 16 P = $150, 000 i = 0.065 /12 n = 30 × 12 = 360 ⎛ i (1 + i )n ⎞ A= P⎜ ⎟ ⎜⎝ (1 + i )n − ⎟⎠ = $9706.67 ⎛ r⎞ A = P ⎜1 + ⎟ ⎝ n⎠ nt ⎛ 0.075 ⎞ A = $6000 ⎜1 + ⎟ ⎝ ⎠ i = ($2500)(0.045)( 2) ⎛ r⎞ A = P ⎜1 + ⎟ ⎝ n⎠ ( 2)(8) = $15, 000 (1.0275) payment = nt nt ⎛ 0.0575 ⎞ A = $10,500 ⎜1 + ⎟ ⎝ ⎠ = $10,500 (1.02875) 12 ( 2)(6) ⎛ ⎛ 0.065 ⎞ ⎛ 0.065 ⎞ 360 ⎞ ⎜ ⎜⎝ ⎟ ⎜1 + ⎟ ⎟ 12 ⎠ ⎝ 12 ⎠ ⎟ A = $150, 000 ⎜ ⎜ ⎛ 0.065 ⎞ 360 ⎟ −1 ⎟ ⎜ ⎜1 + ⎟ 12 ⎠ ⎝ ⎝ ⎠ = $948.10 = $14, 753.92 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 1: Basic Concepts P = $75, 000 i = 0.0625 /12 n = 15 × 12 = 180 10 P = ([$45, 500 − $4500]) × 0.80 = $32,800 i = 0.0725 /12 n = × 12 = 60 ⎛ i (1 + i )n ⎞ A= P⎜ ⎟ ⎜⎝ (1 + i )n − ⎟⎠ ⎛ i (1 + i )n ⎞ A= P⎜ ⎟ ⎜⎝ (1 + i )n − ⎟⎠ ⎛ ⎛ 0.0625 ⎞ ⎛ 0.0625 ⎞180 ⎞ ⎜ ⎜⎝ ⎟ ⎜1 + ⎟ ⎟ 12 ⎠ ⎝ 12 ⎠ ⎟ A = $75, 000 ⎜ 180 ⎜ ⎟ ⎛ 0.0625 ⎞ + ⎜ ⎟ ⎜⎝ ⎟⎠ − 12 ⎝ ⎠ ⎛ ⎛ 0.0725 ⎞ ⎛ 0.0725 ⎞ 60 ⎞ ⎜ ⎜⎝ ⎟ ⎜1 + ⎟ ⎟ 12 ⎠ ⎝ 12 ⎠ ⎟ ⎜ A = $32,800 60 ⎜ ⎟ ⎛ 0.0725 ⎞ + ⎜ ⎜⎝ ⎟⎠ − ⎟ 12 ⎝ ⎠ = $643.07 53 = $653.36 Price = 275 acres × $4100/acre = $1,127,500 P = $1,127,500 × 0.75 = $845, 625 i = 0.0675 n = 20 ⎛ i (1 + i )n ⎞ A= P⎜ ⎟ ⎜⎝ (1 + i )n − ⎟⎠ ⎛ 0.0675 (1 + 0.0675)20 ⎞ A = $845, 625 ⎜ ⎟ ⎜⎝ (1 + 0.0675)20 − ⎟⎠ = $78, 276.71 The annual payment is $6429.83 × 12 = $77,157.96 11 a P = $24, 000 i = 0.0075 /12 n = × 12 = 36 ⎛ i (1 + i )n ⎞ A= P⎜ ⎟ ⎜⎝ (1 + i )n − ⎟⎠ ⎛ ⎛ 0.0075 ⎞ ⎛ 0.0075 ⎞ 36 ⎞ ⎜ ⎜⎝ ⎟ ⎜1 + ⎟ ⎟ 12 ⎠ ⎝ 12 ⎠ ⎟ A = $24, 000 ⎜ 36 ⎜ ⎟ ⎛ 0.0075 ⎞ + ⎜ ⎜⎝ ⎟⎠ − ⎟ 12 ⎝ ⎠ = $674.40 Total payment = $674.40 × 36 = $24, 278.40 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part 54 Elementary Technical Mathematics, 11th 11 (continued) b P = $24, 000 − $1500 = $22, 500 i = 0.085 /12 n = × 12 = 36 ⎛ i (1 + i )n ⎞ A= P⎜ ⎟ ⎜⎝ (1 + i )n − ⎟⎠ ⎛ ⎛ 0.0.085 ⎞ ⎛ 0.0.085 ⎞ 36 ⎞ ⎜ ⎜⎝ ⎟ ⎜1 + ⎟ ⎟ 12 ⎠ ⎝ 12 ⎠ ⎟ ⎜ A = $22, 500 36 ⎜ ⎟ ⎛ 0.0.085 ⎞ ⎜ ⎟ ⎜⎝1 + ⎟⎠ − 12 ⎝ ⎠ = $710.27 Total payment = $710.27 × 36 = $25, 569.71 Choice a costs $25, 569.71 − $24, 278.51 = $1291.20 less 12 a P = $19, 500 i = 0.0175 /12 n = × 12 = 36 ⎛ i (1 + i )n ⎞ A= P⎜ ⎟ ⎜⎝ (1 + i )n − ⎟⎠ ⎛ ⎛ 0.0175 ⎞ ⎛ 0.0175 ⎞ 36 ⎞ ⎜ ⎜⎝ ⎟ ⎜1 + ⎟ ⎟ 12 ⎠ ⎝ 12 ⎠ ⎟ A = $19, 500 ⎜ 36 ⎜ ⎟ ⎛ 0.0175 ⎞ + ⎜ ⎜⎝ ⎟⎠ − ⎟ 12 ⎝ ⎠ = $556.40 Total payment = $556.40 × 36 = $20, 030.40 b P = $19, 500 − $2500 = $17, 000 i = 0.065 /12 n = × 12 = 36 ⎛ i (1 + i )n ⎞ A= P⎜ ⎟ ⎜⎝ (1 + i )n − ⎟⎠ ⎛ ⎛ 0.065 ⎞ ⎛ 0.065 ⎞ 36 ⎞ ⎜ ⎜⎝ ⎟ ⎜1 + ⎟ ⎟ 12 ⎠ ⎝ 12 ⎠ ⎟ A = $17, 000 ⎜ ⎜ ⎛ 0.065 ⎞ 36 ⎟ −1 ⎟ ⎜ ⎜1 + ⎟ 12 ⎠ ⎝ ⎝ ⎠ = $521.03 Total payment = $521.03 × 36 = $18, 757.08 Choice b costs $20,030.57 − $18, 757.19 = $1273.38 less © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 1: Basic Concepts 55 13 P = $220,500 − $4500 − $9500 − $8000 = $198,500 i = 0.08 n=4 ⎛ i (1 + i )n ⎞ A= P⎜ ⎟ ⎜⎝ (1 + i )n − ⎟⎠ ⎛ (0.08)(1 + 0.08)4 ⎞ A = $198,500 ⎜ ⎟ ⎜⎝ (1 + 0.08)4 − ⎟⎠ = $59,931.28 14 Dealer price = $150,500 × (1 + 0.035 + 0.0095) = $157,197.25 P = $157,197.25 − $7500 − $10, 000 = $139, 697.25 i = 0.0725 n=5 ⎛ i (1 + i )n ⎞ A= P⎜ ⎟ ⎜⎝ (1 + i )n − ⎟⎠ ⎛ (0.0725)(1 + 0.0725)5 ⎞ A = $139, 697.25 ⎜ ⎟ ⎝⎜ (1 + 0.0725) − ⎟⎠ = $34, 299.23 15 18 ⎛ r⎞ A = P ⎜1 + ⎟ ⎝ n⎠ nt ⎛ r⎞ A = P ⎜1 + ⎟ ⎝ n⎠ ⎛ 0.05 ⎞ A = $30, 000 ⎜1 + ⎟ ⎝ ⎠ (1)(3) ⎛ 0.05 ⎞ A = $30, 000 ⎜1 + ⎟ ⎝ 52 ⎠ 19 = $34, 728.75 ⎛ r⎞ A = P ⎜1 + ⎟ ⎝ n⎠ 16 nt ⎛ 0.05 ⎞ A = $30, 000 ⎜1 + ⎟ ⎝ 12 ⎠ (12)(5) = $10, 003.92 20 ⎛ r⎞ A = P ⎜1 + ⎟ ⎝ n⎠ 17 nt ⎛ 0.05 ⎞ A = $30, 000 ⎜1 + ⎟ ⎝ 365 ⎠ nt ⎛ 0.035 ⎞ A = $8400 ⎜1 + ⎟ ⎝ 12 ⎠ (12)(3) = $34,844.17 ⎛ r⎞ A = P ⎜1 + ⎟ ⎝ n⎠ (52)(3) = $34,852.52 = $30, 000 (1.05) ⎛ r⎞ A = P ⎜1 + ⎟ ⎝ n⎠ nt (365)(3) nt ⎛ 0.055 ⎞ A = $4000 ⎜1 + ⎟ ⎝ 52 ⎠ (52)(4) = $4983.73 = $34,854.67 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part 56 Elementary Technical Mathematics, 11th 21 P = $37,500 − $37,500 × 0.10 + $37,500 × 0.06 = $36, 000 i = 0.042 /12 = 0.0035 n = × 12 = 36 ⎛ i (1 + i )n ⎞ A= P⎜ ⎟ ⎜⎝ (1 + i )n − ⎟⎠ ⎛ 0.0035 (1 + 0.0035)36 ⎞ A = $36, 000 ⎜ ⎟ ⎜⎝ (1 + 0.0035)36 − ⎟⎠ = $1066.07 22 Discount amount = (0.02)($12, 000 ) = $240 Discount amount Number of days per year × Invoice amount − Discount amount Number of days paid early $240 365 × = 37.2% Interest = $12, 000 − $240 20 Interest = 23 Discount amount = (0.03)($15,870) = $476.10 Discount amount Number of days per year × Invoice amount − Discount amount Number of days paid early $476.10 365 × = 56.4% Interest = $15,870 − $476.10 20 Interest = 24 Discount amount = (0.02)($3000) = $60 Discount amount Number of days per year × Invoice amount − Discount amount Number of days paid early $60 365 × = 41.4% Interest = $3000 − $60 18 Interest = 25 Discount amount = (0.025)($129,115.23) = $3227.88 Discount amount Number of days per year × Invoice amount − Discount amount Number of days paid early $3227.88 365 × = 46.8% Interest = $129,115.23 − $3227.88 20 Interest = 26 Discount amount = (0.02)($22, 000 ) = $440 Discount amount Number of days per year × Invoice amount − Discount amount Number of days paid early $440 365 × = 24.8% Interest = $22, 000 − $440 30 Interest = © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 1: Basic Concepts 27 57 Discount amount = (0.01)($21,500) = $215 Discount amount Number of days per year × Invoice amount − Discount amount Number of days paid early $215 365 × = 36.9% Interest = $21,500 − $215 10 Interest = 28 Discount amount = (0.015)($16, 000) = $240 Discount amount Number of days per year × Invoice amount − Discount amount Number of days paid early $240 365 × = 27.8% Interest = $16, 000 − $240 20 Interest = Unit 1C Review 1.625 13 0.25 45 = 100 20 10.129 14 72.4 15 P = ( 420)(0.165) 116.935 = 69.3 5.854 55.6 ft − 15.0 ft − 15.0 ft = 25.6 ft 16 P R 240 B= 0.12 = 2000 B= 55.6 ft 15.0 ft 15.0 ft 9.5 ft 25.6 ft 17 P B 96 yd R= 240 yd = 40.0% R= 9.5 ft 15.0 ft 15.0 ft 160.2 ft a 45.1 b 45.06 a 45.1 b 45.06 10 0.11515 11 18.85 12 18.5 in ÷ 2.75 in = r Six cables could be cut and there would be in remaining P = BR 18 P = BR P = ($16.50)(0.06) = $0.99 Her new salary is $16.50 + $0.99 = $17.49/h 19 2110 20 9.40 Chapter Review 8243 55,197 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part 58 Elementary Technical Mathematics, 11th 9,178, 000 226 r 240 = 45 ÷ − + 28 12 − (5 − 2) = 15 − + 28 = 12 − (3) = 37 = 12 − =3 18 ÷ × ÷ − + × = × ÷ − + 28 18 / (5 − 3) + (6 − 2) × − 10 = 18 / + × − 10 (6 + ) ÷ + = (10) ÷ + = + 32 − 10 = 31 = 80 ÷ + = 40 + = 43 Area of upper rectangle: 12 cm × cm = 60 cm Area of lower rectangle: 10 cm × 28 cm = 280 cm Total area: = 340 cm 10 Volume of left box: 10 cm × cm × cm = 10 cm3 Volume of middle box: 10 cm × cm × cm = 10 cm Volume of right box: Total Volume: 10 cm × cm × cm = 10 cm = 30 cm 11 12 C = ( F − 32) C = (50 − 32) = (18) = 10 P= P= Fs t (600)(50) 10 30, 000 = 10 = 3000 13 + + = 10 is not divisible by 3, so 28 is not divisible by 14 54 = ⋅ ⋅ ⋅ 19 18 18 3 = 3+ = 3+3 = 5 5 15 330 = ⋅ ⋅ ⋅11 20 16 36 ⋅ = = 56 14 ⋅ 14 ( × 8) + 21 = = 8 21 17 180 ⋅ 36 = = 216 ⋅ 36 (3 × 16) + 55 = = 16 16 16 22 18 16 =2 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 1: Basic Concepts 23 5 + + 12 10 = + + 12 12 12 18 = = =1 12 2 29 ×4 27 14 = × = 18 31 ÷6 = × = 16 25 +9 16 12 20 = +9 48 48 29 = 14 48 32 ÷1 16 = ÷ 9 = × 16 = 26 −4 12 14 = −4 24 24 33 14 =5 −4 24 24 19 =1 24 27 18 − 5 = 17 − 5 = 11 30 24 29 − 36 30 145 42 = − 180 180 103 = 180 59 33 ữ ì 11 16 25 35 = ữ ì 16 16 35 = × × 25 144 35 = × 125 336 11 = = 13 25 25 28 11 + − 12 12 11 = 16 + − 12 12 12 12 11 11 = 17 − 12 12 12 =5 16 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part 60 Elementary Technical Mathematics, 11th 51 a 200 34 in − in − in A = 12 16 16 in − in − in = 12 16 16 16 15 in − in = 12 16 16 21 15 in − in = 11 16 16 in = in =3 16 in − in + in B=9 32 32 16 in + in − in =9 32 32 32 19 in − in = 11 32 32 14 in = in =5 32 16 b 248.2 c 250 52 a 5.6 b 5.65 c 5.6491 53 15% = 54 % = 8.25% = 0.0825 55 6.5% 56 120% 57 37 72 ft × = $1050 58 Fraction 8 2 2000 12 in = 2016 in ft yd = 24 yd ft 38 36 mi × 1760 yd = 63, 360 yd mi 39 0.5625 40 0.416 45 41 = 100 20 625 = 19 1000 43 168.278 49 3.18 50 20.6 0.375 8.75 37 % 83 % 875% 2.4 240% 0.0015 0.15% 0.83 P B $32, 000 R= $84, 000 = 38.1% 45 68.665 48 1.9133 Percent 25% R= 44 17.25 47 3206.5 Decimal 0.25 59 42 19 46 33.72 P = BR P = ($12, 000)(0.0875) 16 oz ⎞ ⎛ 35 lb oz = ⎜ lb × ⎟ + oz = 105 oz ⎝ lb ⎠ 36 168 ft × 15 = 0.15 100 60 P B 11 11 32 R = 64 = × 13 64 13 32 = 42.3% R= © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 1: Basic Concepts 61 60 tons × 0.80 = 48 tons 63 62 ⎛ ⎞ ⎛1 ⎞ ⎛ ⎞ × ⎜3 in.⎟ + × ⎜ in.⎟ + × ⎜1 in.⎟ ⎝ 16 ⎠ ⎝4 ⎠ ⎝ ⎠ 64 61 14 in − in = in − in = in 16 16 16 16 Height = 20 in + × in = 30 in Length = × 10 in + in = 41 in ⎛ 49 ⎞ ⎛1 ⎞ ⎛9 ⎞ = 6× ⎜ in.⎟ + × ⎜ in.⎟ + × ⎜ in.⎟ ⎝ 16 ⎠ ⎝4 ⎠ ⎝8 ⎠ The sheet of cardboard would have to be 30 in × 41 in 147 in + in + in 4 147 10 18 = in + in + in 8 = 21 in = 65 4020 66 139 Chapter Test 5729 2,584.450 3516 1600 + (5 × + ) 15 − ữ + ì = 15 + 12 = 24 = + (30 + 8) = + (38) = + 76 = 84 Area of upper rectangle: 10 m × 40 m = 400 m Area of middle rectangle: 10 m × 15 m = 150 m Area of lower rectangle: 10 m × 20 m = 200 m Total area: = 750 m Volume of outer box: 10 in × 12 in × 20 in = 2400 in Volume of missing corner: in × in × 20 in = 240 in Total Volume: 10 120 V =3A 40 Ω = 2160 in 11 d r 1050 t= 21 = 50 t= P = 2l + w P = (20) + (15) = 40 + 30 = 70 12 P = 2a + b P = (36) + 15 = 72 + 15 = 87 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part 62 Elementary Technical Mathematics, 11th 13 90 = ⋅ ⋅ ⋅ 25 14 220 = ⋅ ⋅ ⋅11 15 30 15 ⋅ 15 = = 64 32 ⋅ 32 16 28 ⋅14 = = 42 ⋅14 17 23 =3r5=3 6 18 3 × + 13 = = 4 19 3 + = + = 8 8 20 5 10 5 − = − = 16 32 32 32 32 53 ÷3 = ÷ 16 16 16 = × 53 = 53 26 27 29 31 + × +1 × = 8 29 217 = + 20 145 434 = + 40 40 579 19 = = 14 40 40 21 1 =3 8 =2 =4 11 = 10 8 28 ⎛ 19 ⎞ ⎛5⎞ = 2⎜ ⎟ +2⎜ ⎟ ⎝4⎠ ⎝2⎠ 19 10 + 2 29 = = 14 2 = 29 5 A+2 A+4 A 16 10 12 =3 A+2 A+4 A 16 16 16 27 11 =9 A = 10 A 16 16 23 3 + −1 16 10 = + −1 16 16 16 13 = −1 16 16 =4 16 24 16 ⋅ 2 × = × = 27 ⋅ P = 2l + 2w ⎛ 3⎞ ⎛ 1⎞ P = ⎜4 ⎟ + ⎜2 ⎟ ⎝ 4⎠ ⎝ 2⎠ 22 10 − 16 = 10 − 16 16 18 = −3 16 16 13 =6 16 40 30 120 ft × yd = 40 yd ft 16 oz ⎞ ⎛ 31 lb oz = ⎜ lb × ⎟ + oz = 53 oz ⎝ lb ⎠ 32 = 0.625 33 2.12 = 12 =2 100 25 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Chapter 1: Basic Concepts 34 65.024 40 P B 88 R= 284 = 31.0% 35 397.19 R= 36 a 27.3 b 27.28 37 8.0784 38 0.05 39 P B= R 59.45 B= 0.41 = 145 63 41 P = BR P = ($612)(0.067 ) = $41 Her new salary is $612 + $41 = $653 42 0.0552 43 6.73 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part ... Chapter Review Chapter Test 10 12 14 14 16 24 34 36 38 40 41 43 45 51 52 57 57 61 Chapter 2: Signed Numbers and Powers of 10 2.1: Addition of Signed Numbers 2.2: Subtraction of Signed Numbers... Mentally 10. 3: Finding Binomial Factors 10. 4: Special Products 10. 5: Finding Factors of Special Products 10. 6: Factoring General Trinomials Chapter 10 Group Activities Chapter 10 Review Chapter 10. .. 32 10 15 16 + = + = = 18 18 18 18 11 11 + = + = 28 28 28 28 12 + = + = 45 45 45 45 1 15 14 35 + + = + + 14 15 210 210 210 64 = 210 32 = 105 23 63 15 56 + + = + + 10 14 15 210 210 210 134 = 210
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