Chapter 1 Answers Practice 1-1 Practice 1-5 1. 7 + x 2. 3p 3. 10 - m 4. 7 - n 5. 2q 6. m + 3 7. 8 divided by a 8. 10 less than s 9. 13 more than x 10. 2 more than the product of a and b 11. 8 - n 12. 4 + n 13. 2n 14. 3 + n 15. 10 1 n 15 16. n - 12 17. c = 24.95s 18. g = 30t 19. m = 0.10d 20. n = 48 - g 21. c = 8p 22. c = 32.95p 23–28. Choice of variables may vary. 1. Practice 1-3 1. rational, real 2. rational, real 3. natural, whole, integers, rational, real 4. irrational, real 5. irrational, real 6. integers, rational, real 7. rational, real 8. natural, whole, integers, rational, real 9. true 10. false; -2 11. true 12. false; 7 3 2 = 14 13. . 14. , 15. , 16. = 17. . 18. , 19. 289 , 222 , 287 20. 23 12 , 23.45, 23 94 25 25 21. 2 1 , 2 1 , 2 1 22. 21 79 , 21 3 , 21.7 23. 2 7 , 2 3 , 2 2 3 4 5 4 8 4 3 24. 2 5 , 2.7, 2 3 25. whole 26. rational 27. whole 8 4 3 28. irrational 29. 10 30. 327 31. 3.46 32. 21 33. $154.23, 0.0375, 30 , $.48, 0.055, and 3 1 are rational 2 365 and real; $8000 and $1540 are whole, integers, rational, and real. Practice 1-4 1. p = 9t 2. c = 13n 3. m = 5n + 20 4. c = 2.50n + 7.50 5. number of hours; amount earned 6. number of people; cost 7. number of minutes; volume 8. price; number of people 9. 96; 120; b = 24c 10. $.90; $1.00; c = 0.10m + 0.50 32 Answers Hourly Pay (dollars) Speed of Winds in Some U.S. Cities 100 90 80 70 60 0 All rights reserved. 1. 52 2. 2 3. 38 4. 4 5. 18.9 6. 87 7. 25 8. 7 9. 2 10. 1 11. 9 12. 30.4 13. 19 14. 5 15. 2 16. 6 17. 26 18. 29 19. 31 20. 88 21. 14.18 22. 85 23. 28 24. 12 25. 26 26. 5 27. 55 28. 56 29. 72 30. 60 31. 40 32. 2 33. 11 34. 4 35. 131 36. 141 37. 33 38. 16 39. 22 40. 12 41. 2 42. 1 43. 56 44. $33.95 45. $63.34 46. 24 47. 2.25 48. 0 49. 99 50. 5 51. 6 2. 60 65 70 75 Height (in.) 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 Average Speed (mi/h) 3. positive correlation 4. negative correlation 5. no correlation 6. no correlation 7. positive correlation 8. no correlation; a person’s age is not related to the number of pets he/she may have. 9. negative correlation; the more times you brush, the fewer the cavities you are likely to have. 10. positive correlation; the more rainy days, the more umbrellas are likely to be sold. 11a. Each point represents one infant’s age and weight. 11b. There will be points with the same y-coordinate. 11c. The points will have the same x-coordinate. 11d. Yes, there is a positive correlation. Weight increases with age. Practice 1-6 1. 2.5; 2; 1; median 2. $120.50; $123; no mode; mean 3. $31.16; $31.25; no mode; median 4. 7.11; 8; 8 and 10; median 5. $2.81 6. 3 7. 4.8 1 1.6 41 5.2 1 x 5 3.7; 3.2 102 1 21 1 x 5 88; 173 8. 40 1 98 1 94 1 6 9. 100 1 172 1585 1 92 1 x 5 115; 126 10. 25.6 1 19.34 1 19 1 x 5 24; 32.1 11. yes; The range is 0.9 fl oz. 12. no; The mean was 6.7 ppm. 13. 98 Algebra 1 Chapter 1 © Pearson Education, Inc., publishing as Pearson Prentice Hall. Practice 1-2 8.50 8.00 7.50 7.00 6.50 6.00 5.50 5.00 0 Highest Speed (mi/h) t = number of tickets, c = total cost; h = number of hours, d = distance; h = number of hours, p = total pay; c = change, a = total cost; d = number of days, l = length; r = miles traveled, t = miles remaining 23. c = 3.50t 24. d = 55h 25. p = 5h 26. a = 10 - c 27. l = 0.45d 28. r = 500 - t Height and Hourly Pay of Ten People Loaves of Bread Sold All rights reserved. 1 2 3 4 5 6 7 7 189 34567789 00122345 014 1. 2 1 | 7 means 17 14b. mean: 39.5; median: 39.5; modes: 37, 40 and 42; range: 55 15. Dept. A: mean = 49.643, median = 50, mode = 58, range = 31; Dept. B: mean = 51.857, median = 52, mode = 52, range = 40 16. Locn. A: mean = 79.2, median = 81, modes: 83 and 90, range = 24; Locn. B: mean = 75.933, median = 75, mode = 66, range = 26 Reteaching 1-1 1. n + 5 2. n - 8 3. n 4. 5n - 3 5. 12n = 84 9 5 18 6. n - 7 = 22 7. 8x = 72 8. n 3 Reteaching 1-2 1. Check students’ work. 2. Check students’ work. 3. Check students’ work. 4. Check students’ work. 5. -3 6. -75 7. 2 8. 28 9. 3 10. -1 11. -20 12. -56 © Pearson Education, Inc., publishing as Pearson Prentice Hall. Reteaching 1-5 Reteaching 1-3 1. rational, real 2. rational, real 3. whole, integer, rational, real 4. rational, real 5. irrational, real 6. integers, rational, real 7. rational, real 8. natural, whole, integers, rational, real 9. natural, whole, integers, rational, real 10. integers, rational, real 11. rational, real 12. irrational, real 13.–18. Check students’ work. Reteaching 1-4 1. 60; 0; 60; s = 60b 2. 10; 5; 10; 5; c = 10h + 5 10 8 6 4 2 0 2. 2 6 8 4 U.S. Open Wins 10 2 6 8 4 Wimbledon Wins 10 10 Australian Open Wins 14a. (continued) French Open Wins Chapter 1 Answers 8 6 4 2 0 3. no correlation 4. positive correlation Reteaching 1-6 1. $915.60; $900; no mode 2. 5.375; 5; no mode 3. 12; 9; no mode 4. 73.5; 73; 72 5. 70; 70; 70 Enrichment 1-1 1. O = 2I + 1 2. O = 3I - 1 3. O 5 I 2 2 1 4. S = 16T2 5. R 5 43 T 1 7 6. P = 2E + 1 7. Check students’ work. Enrichment 1-2 Answers may vary. Samples include: 1. 3 3 2 3 2 2. "(8 1 8) 3. 23 4. (3 + 7) 3 4 5. (3 + 6) 3 6. 30 6 3 5 7. (3 3 9) - 2 8. 4 1 32 9. (10 2) + (3 3 3) 10. "25 3 3 2 2 2 1 11. (5 + 3 - 4) 3 3 12. 3 3 (8 - 2) 13. (4 3 4) + (2 3 4) - 6 Algebra 1 Chapter 1 Answers 33 (continued) Enrichment 1-3 Chapter Project Check students’ work. Activity 1: Researching Check students’ work. 1. The graph of the relation includes the line y = x. 2. It is the empty relation (no ordered pairs). 3. equivalence relation 4. reflexive, transitive 5. asymmetric, transitive 6. none 7. symmetric, transitive 8. transitive 9. symmetric 10. symmetric 11. reflexive 12. symmetric 13. symmetric, transitive 14. symmetric 15. asymmetric, transitive Enrichment 1-5 1. Answers may vary slightly. 800 cc: $8000, fairly confident 1100 cc: $12,000, somewhat confident; 1350 cc: $14,000, not very confident. 2. You could draw two trend lines, one running near the upper edge of the pattern and the other near the lower edge. This would mark off a range of likely prices for any given engine size. 3. Answers will vary. Possible answer: Gathering data on larger-engine motorcycles, for instance up to 1500 cc, would improve the basis for predictions in that range. The data might also be reviewed to see whether selected data points can be discarded to obtain a pattern with better correlation. For instance, one could discard data for a motorcycle brand known to be exceptionally expensive. 4. Answers may vary. Possible answer: The scatter plot might look like this: Activity 2: Modeling In Geraldo’s equation, x represents the amount of money he should save per week. The expression 40 + 16x represents the total savings over 4 months, or 16 weeks, given that he has already saved $40. Since Geraldo wants to determine how much to save each month so that his total savings over 16 weeks is $129, he should solve 40 + 16x = 129 for x ; check students’ work. Activity 3: Organizing Check students’ work. Activity 4: Graphing Check students’ work. ✔ Checkpoint Quiz 1 1. 14 + x; 18 2. 5z; 60 3. x + y; 7 4. 24 x ;6 5. 4z; 48 6. (y + z) + 10; 25 7. y + 2x; 11 8. xz; 48 9. false; Answers may vary. Sample: The opposite of -2 is -2, which is not a positive number. 10. false; Answers may vary. Sample: -5°F is a reasonable temperature but is not a whole number. ✔ Checkpoint Quiz 2 1. c = 5+ 0.5g 2. negative correlation 3. mean: 16; median: 16; mode: 17; mean and median 4. mean: 2; median: 2; mode: 1; mean and median 5. mean: 29; median: 27.5; mode: 25; median Chapter Test, Form A Weather tends to be more variable at high elevations than at low ones, and more variable weather would involve greater variations in temperature. 1. s = 150m 2. r = 100 - t 3. 20 4. 77 5. 5 6. 21 7. 29 8. 16 9. 20 10. 9.4 11. 4 12. 3 5 13. -5.1, 5.001, 5.01, 5.1 14. 21 , 23 , 1 , 2 2 Enrichment 1-6 1. mode; by the phrase “most frequent” 2. Check students’ work. 3. 34.25 mi/gal, 35 mi/gal, 41 mi/gal; The mean and median are close, but the mode is much higher. 4. Answers may vary. Sample: Not very reliable. Only 25% of the cars tested got 41 mi/gal or better. 5. Answers may vary. Sample: 75% of Worldwide Motors’ cars tested at less than 40 mi/gal. 8 5 3 15. false; " 2 is a real number that is not rational. 1 1 19. independent 16. true 17. 4 - (x + 6) 18. n 2 variable: number of teachers; dependent variable: number of students; s = 30t 20. independent variable: number of long distance minutes; dependent variable: cost; c = 0.10m + 15 21. time of day; air temperature 22. height; reach 23. memory; speed 24. mean: 6.2; median: 6.2; mode: 6.2; all 25. mean: 48.6; mode: 47; median: 47; mode and median 26. 13 27. 6.3 28. 29. positive 1 26 2 49 3 278 4 1 5 9 30. 65 in. 31. 0.23 is greater than 29 since 29 5 0.22 and 0.23 . 0.22 34 Answers All rights reserved. Enrichment 1-4 Algebra 1 Chapter 1 © Pearson Education, Inc., publishing as Pearson Prentice Hall. Chapter 1 Answers Chapter 1 Answers (continued) Chapter Test, Form B 1. c = 3n 2. r = 162 - p 3. 8 4. 1 5. 16 6. 36 7. 0 8. 49 9. 27 10. 51.4 11. true 12. false; Answers may vary. Sample: The opposite of ∆7« is -7, which is not positive. TASK 3 Scoring Guide: a. Check students’ work. b. A = 5h Domain: 0 to 6 hours Range: $0 to $30 13. 4m 14. x + 5x All rights reserved. 15. independent variable: number of hours; dependent variable: number of dollars earned; d = 8h 16. mean: 5; median: 5; mode 2; range: 9 17. mean: 31; median: 34; mode: 35; range: 26 18. negative correlation 19. one h 20. 22 23 is less than -2.6 since 22 2 5 22.6 3 and 22.6 , 22.6 . Alternative Assessment, Form C TASK 1 Scoring Guide: a. 8x 5 7 1 x 4 c. x2 + y = 42 3 Clear and coherent rules are given. Function rule is correct, and domain and range are clearly described. 2 Rules are basically correct but are unclear or incomplete. Domain and range are not specific. 1 Student makes some attempt to answer prompts. 0 No attempt is made, or no solution is presented. TASK 4 Scoring Guide: 3 The response is complete and demonstrates a clear understanding of mean, median, and mode. Data are correctly expressed as percents, with ten scores between 70% and 79%, ten scores in the combined ranges 80%–89% and 60%–69%, and five scores in the combined ranges 0%–59% and 90%–100%. The mean, median, and mode are correctly calculated on the basis of the student’s data. An appropriate graph is chosen to display the data. b. 5x - 8 = 32 d. 1 x 1 x 5 3(x 2 7) 3 3 Shows a clear understanding of the concepts of translating words to mathematical equations and can identify the key words or phrases. The sentences are all written correctly. 2 The answer is mostly correct. Data are correctly chosen, but there are slight errors in calculations. Explanations are clear. 2 Translations are given for each of the exercises with © Pearson Education, Inc., publishing as Pearson Prentice Hall. minor errors. 1 Student makes some attempt to write the translations. 1 Data do not fit the distribution correctly. There are serious errors in calculations, or explanations are unclear or incorrect. The equations are translated incorrectly. 0 No attempt is made, or no solution is presented. 0 Student makes no attempt, or no solution is presented. TASK 2 Scoring Guide: a. 26 Cumulative Review b. In either case, the same order of operations must 1. A 2. G 3. A 4. F 5. B 6. H 7. C 8. H 9. A 10. H 11. D 12. H 13. 9 14. 71 15. 31 16. c = 1.5n 17. r = 8 - w 18. mean: 2.1; median: 2; modes: 1 and 2; median 19. mean: 14; median: 13; mode: 13; median, mode 20. Answers may vary. Sample: 30, 17, 80, 15, 8; To find the be followed. c. Check students’ work. 3 Both expressions are correctly simplified. Each step is clearly identified and explained. The steps are compared, and explanations show a thorough understanding of grouping symbols, exponents, and order of operations. A new expression is presented and simplified correctly. 2 The answer is mostly correct, but some steps are omit- average of the five numbers, add them and divide by 5. 21. 5 6 7 8 9 26 01158 134 ted. A clear explanation is given, but it shows a lesser degree of insight. 1 The response is partially satisfactory, but major steps are omitted. Explanations are incomplete or unclear. 0 No attempt is made, or no solution is presented. Algebra 1 Chapter 1 Answers 35

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