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Solution Manual for A Pathway to Introductory Statistics, 2nd Edition

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    ’ S S OLUTIONS M ANUAL J AMES L APP A P ATHWAY TO I NTRODUCTORY S TATISTICS S ECOND E DITION Jay Lehmann College of San Mateo

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    Table of Contents Chapter 1: Performing Operations and Evaluating Expressions 1.1 Variables, Constants, Plotting Points, and Inequalities ................................................................ 1 1.2 Expressions................................................................................................................................... 4 1.3 Operations with Fractions and Proportions; Converting Units ..................................................... 7 1.4 Absolute Value and Adding Real Numbers................................................................................ 11 1.5 Change in a Quantity and Subtracting Real Numbers ................................................................ 14 1.6 Ratios, Percents, and Multiplying and Dividing Real Numbers ................................................. 16 1.7 Exponents, Square Roots, Order of Operations, and Scientific Notation ................................... 20 Review Exercises ....................................................................................................................... 24 Chapter Test ............................................................................................................................... 27 Chapter 2: Designing Observational Studies and Experiments 2.1 Simple Random Sampling .......................................................................................................... 31 2.2 Systematic, Stratified, and Cluster Sampling ............................................................................. 34 2.3 Observational Studies and Experiments ..................................................................................... 36 Review Exercises ....................................................................................................................... 40 Chapter Test ............................................................................................................................... 43 Chapter 3: Graphical and Tabular Displays of Data 3.1 Frequency Tables, Relative Frequency Tables, and Bar Graphs ................................................ 45 3.2 Pie Charts and Two-Way Tables ................................................................................................ 49 3.3 Dotplots, Stemplots, and Time-Series Plots ............................................................................... 52 3.4 Histograms.................................................................................................................................. 58 3.5 Misleading Graphical Displays of Data...................................................................................... 64 Review Exercises ....................................................................................................................... 66 Chapter Test ............................................................................................................................... 71 Chapter 4: Summarizing Data Numerically 4.1 Measures of Center ..................................................................................................................... 75 4.2 Measures of Spread .................................................................................................................... 80 4.3 Boxplots ..................................................................................................................................... 85 Review Exercises ....................................................................................................................... 90 Chapter Test ............................................................................................................................... 92 Chapter 5: Computing Probabilities 5.1 Meaning of Probability ............................................................................................................... 95 5.2 Complement and Addition Rules ............................................................................................... 97 5.3 Conditional Probability and the Multiplication Rule for Independent Events .......................... 100 5.4 Discrete Random Variables ...................................................................................................... 103 5.5 Finding Probabilities for a Normal Distribution ....................................................................... 106 5.6 Finding Values of Variables for Normal Distributions ............................................................ 110 Review Exercises ..................................................................................................................... 112 Chapter Test ............................................................................................................................. 114 Chapter 6: Describing Associations of Two Variables Graphically 6.1 Scatterplots ............................................................................................................................... 117 6.2 Determining the Four Characteristics of an Association .......................................................... 121 6.3 Modeling Linear Associations .................................................................................................. 125 Review Exercises ..................................................................................................................... 130 Chapter Test ............................................................................................................................. 133

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    Chapter 7: Graphing Equations of Lines and Linear Models; Rate of Change 7.1 Graphing Equations of Lines and Linear Models ..................................................................... 135 7.2 Rate of Change and Slope of a Line ......................................................................................... 138 7.3 Using Slope to Graph Equations of Lines and Linear Models ................................................. 142 7.4 Functions .................................................................................................................................. 148 Review Exercises ..................................................................................................................... 152 Chapter Test ............................................................................................................................. 156 Chapter 8: Solving Linear Equations and Inequalities to Make Prediction 8.1 Simplifying Expressions ........................................................................................................... 159 8.2 Solving Linear Equations in One Variable ............................................................................... 161 8.3 Solving Linear Equations to Make Predictions ........................................................................ 163 8.4 Solving Formulas ..................................................................................................................... 170 8.5 Solving Linear Inequalities to Make Predictions...................................................................... 175 Review Exercises ..................................................................................................................... 181 Chapter Test ............................................................................................................................. 186 Chapter 9: Finding Equations of Linear Models 9.1 Using Two Points to Find an Equation of a Line ..................................................................... 191 9.2 Using Two Points to Find an Equation of a Linear Model ....................................................... 193 9.3 Linear Regression Model ......................................................................................................... 198 Review Exercises ..................................................................................................................... 204 Chapter Test ............................................................................................................................. 207 Chapter 10: Using Exponential Models to Make Predictions 10.1 Integer Exponents ..................................................................................................................... 209 10.2 Rational Exponents................................................................................................................... 211 10.3 Graphing Exponential Models .................................................................................................. 213 10.4 Using Two Points to Find an Equation of an Exponential Model ............................................ 216 10.5 Exponential Regression Model ................................................................................................. 221 Review Exercises ..................................................................................................................... 226 Chapter Test ............................................................................................................................. 230

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    Chapter 1: Performing Operations and Evaluating Expressions 1 Chapter 1: Performing Operations and Evaluating Expressions Homework 1.1 2. A constant is a symbol that represents a specific number. 4. Data are quantities or categories that describe people, animals, or things. 6. In 2017, about 37% of children aged 6–12 participated in a team sport (organized or unorganized) on a regular basis. 8. The temperature is 10 F   . That is, the temperature is 10 degrees below 0 (in Fahrenheit). 10. The statement 3 t   represents the year 2012 (3 years before 2015). 12. Answers may vary. Example: Let s be the annual salary (in thousands of dollars) of a person. Then s can represent the numbers 25 and 32, but s cannot represent the numbers 15  and 9  . 14. Answers may vary. Example: Let n be the number of students enrolled in a prestatistics class. Then n can represent the numbers 15 and 28, but n cannot represent the numbers 20  or 0.5. 16. Answers may vary. Example: Let T be the temperature (in degrees Fahrenheit) in an oven. Then T can represent the numbers 300 and 450, but T cannot represent the numbers 300  or 450  . 18. a. Answers may vary. Some possible answers are shown below. b. In the described situation, the symbols W and L are variables. Their values can change. c. In the described situation, the symbol A is a constant. Its value is fixed at 36 square feet. 20. a. Answers may vary. Some possible answers are shown below. b. In the described situation, the symbols W , L , and A are all variables. All their values can change. c. In the described situation, none of the symbols are constants. All their values can change. 22. 24. 26. 28. The counting numbers between 1 and 5 are 2, 3, and 4. 30. The integers between 6  and 3, inclusive, are 6, 5, 4, 3, 2, 1,       0, 1, 2, and 3. 32. 34. The positive integers between 4  and 4 are 1, 2, and 3. 36. Answers may vary. Example: 2, 5   and 40  . 38. Answers may vary. Example: 2.1, 2.3,   and 2.8  . 40. The temperature at the top of a skyscraper can be positive or negative, depending on the location of the skyscraper and the time of year. Temperature is not usually reported using fractions. So, among the choices, the integers are the smallest group of number that contains possible data.

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    2 ISM: A Pathway to Introductory Statistics 42. The commute time of an employee cannot be negative, but it can be measured in fractions. So, among the choices, the nonnegative real numbers are the smallest group of numbers that contains possible data. 44. McDonald’s sells hamburgers every day of every year and there is never just a portion of a hamburger sold. So, among the choices, the counting numbers is the smallest group of numbers that contains possible data. 46. 48. 50. 52. a. b. The number of hours of video uploaded to YouTube per minute increased between 2009 and 2014. The number of hours of video uploaded to YouTube per minute went up each year. c. The annual increases in the number of hours of video uploaded to YouTube per minute increased between 2009 and 2014. The annual increases are shown below. Years Increase 2009 to 2010 25 14 11 2010 to 2011 48 25 23 2011 to 2012 73 48 25 2012 to 2013 100 73 27 2013 to 2014 300 100 200           54. a. b. The number of microbreweries increased from 2013 to 2017. c. The increases in the number of microbreweries stayed approximately constant from 2013 to 2017. The annual increases are shown below. Years Increase 2013 to 2014 2.1 1.5 0.6 2014 to 2015 2.6 2.1 0.5 2015 to 2016 3.2 2.6 0.6 2016 to 2017 3.8 3.2 0.6         56. – 68. 70. The y -coordinate is 4  .

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    Chapter 1: Performing Operations and Evaluating Expressions 3 72. Point A is 2 units to the left of the origin and 4 units down. Thus, its coordinates are ( 2, 4)   . Point B is 3 units to the left of the origin on the x -axis. Thus, its coordinates are ( 3, 0)  . Point C is 5 units to the left of the origin and 4 units up. Thus, its coordinates are ( 5, 4)  . Point D is 4 units to the right of the origin and 2 units up. Thus, its coordinates are (4, 2) . Point E is 3 units below the origin on the y -axis. Thus, its coordinates are (0, 3)  . Point F is 3 units to the right of the origin and 2 units down. Thus, its coordinates are (3, 2)  . 74. True. The number 2  lies to the right of 6  on a number line. 76. False. 5 5    , thus 5  is not strictly greater than 5  . 78. 80. 82. 84. 86. Inequality: 5 x   Interval notation:   5,   Graph: 88. Inequality: 3 x  Interval notation:   ,3  Graph: 90. Inequality: 1 x   Interval notation:   1,   Graph: 92. In Words Inequality Graph Interval Notation numbers less than or equal to 6  6 x     , 6   numbers greater than 1 1 x    1,  numbers greater than or equal to 4  4 x     4,   numbers less than 5 5 x  ( ,5)  94. 96. 98. 100. In Words Inequality Graph Interval Notation numbers between –3 and 0 3 0 x    ( 3, 0)  numbers between 1 and 4, as well as 1 1 4 x   [1, 4) numbers between –3 and 1, as well as 1 3 1 x    ( 3,1]  numbers between –4 and –1, inclusive 4 1 x     [ 4, 1]  

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    4 ISM: A Pathway to Introductory Statistics 102. The student completes the homework assignment in 30 or more minutes. 104. Inequality: 44 h  Interval notation:   44,  Graph: 106. Inequality: 2 T  Interval notation:   , 2  Graph: 108. Inequality: 4.2 V  Interval notation:   4.2,  Graph: 110. The average gas mileage of a car on highways is between 35 and 40 miles per gallon. 112. Inequality: 41 56 T   Interval notation:   41,56 Graph: 114. Inequality: 140 145 w   Interval notation: (140,145) Graph: 116. No. Answers may vary. Example: The numbers 2 and 5 are not “between 2 and 5.” The integers between 2 and 5 are simply 3 and 4. 118. The ordered pairs selected and plotted points may vary. The points will lie on the same horizontal line. Answers may vary. 120. Answers may vary. The inequality represents “4 is less than or equal to 4,” and 4 is equal to 4. 122. The types of numbers discussed in this section are real numbers, rational number, irrational numbers, integers, and counting numbers (or natural numbers). Answers may vary. Homework 1.2 2. We evaluate an expression by substituting a number for each variable in the expression and then calculating the result. 4. The quotient of a and b is a / b , where b is not zero. 6. Substitute 6 for x in 5 x  :   5 6 11   8. Substitute 6 for x in 4 x  :   6 4 2   10. Substitute 6 for x in (9) x :     6 9 54  12. Substitute 6 for x in 30 x  : 30 (6) 5   14. Substitute 6 for x in x x  :     6 6 0   16. Substitute 6 for x in x x  :     6 6 1   18. Substitute 47 for r in 29 r  : 47 29 76   . So, if 47% of Republicans favor gays to marry legally in 2017, then in that same year, about 76% of Democrats favor gays to marry legally. 20. Substitute 13.5 for U in 6 U  : 13.5 6 7.5   . So, in 2016 if the average daily shipping volume for UPS was 13.5 million packages, in that same year, the average daily shipping volume for FedEx was about 7.5 million packages. 22. Substitute 17 for n in 599.99 n : 599.99 17 10,199.83   . So, if 17 thousand Fender Standard Jazz Electric Bass Guitars with maple fingerboards are sold, the total revenue is about $10,200,000. 24. Substitute 328 for T in 4 T  : 328 4 82   . So, if a student earns a total of 328 points on four tests, the student’s average test score is 82 points.

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    Chapter 1: Performing Operations and Evaluating Expressions 5 26. a. Speed Limit Driving Speed (miles per hour) (miles per hour) 35 35 5 40 40 5 45 45 5 50 50 5 5 s s      The expression 5 s  represents the driving speed if the speed limit is s miles per hour. b. Substitute 65 for s in 5 s  : 65 5 70   . So, if the speed limit is 65 miles per hour, the person will be driving 70 miles per hour. 28. a. Number of Shares Total Value (dollars) 1 74.74 1 2 74.74 2 3 74.74 3 4 74.74 4 74.74 n n     The expression 74.74 n represents the total value of the shares. b. Substitute 7 for n in 74.74 n :   74.74 7 523.18  . So, the total value of 7 shares is $523.18. 30. a. Number of Siblings Share of Cost (dollars) 2 3000 2 3 3000 3 4 3000 4 5 3000 5 3000 n n      The expression 3000 n  represents each sibling’s share of the cost in dollars. b. Substitute 6 for n in 3000 n  : 3000 6 500   . So, the share of each sibling’s cost is $500. 32. a. We can write an expression 10 v  to represent the total cost of parking and money spent on a vase. b. Substitute 25 for v in the expression 10 v  : 10 25 35   . So, if $10 is spent on parking then the total cost of parking and money spent on a vase is $35. 34. a. We can write an expression 2 r  to represent the net price of a shaver whose retail price is r dollars. b. Substitute 6 for r in the expression 2 r  : 6 2 4   . So, if the retail price of a shaver is $6, then the net price is $4. 36. a. We can write an expression 105 c to represent the total cost of tuition when enrolling in c credits of classes. b. Substitute 15 for c in the expression 105 c : 105 15 1575   . So, if a student enrolls in 15 credits of classes, then the total cost of tuition is $1575. 38. a. We can write an expression 420 n  to represent the equal share each of n siblings will receive of the inheritance. b. Substitute 3 for n in the expression 420 n  : 420 3 140   . So, each of 3 siblings will receive an equal share of $140,000 of a $420,000 inheritance.

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    6 ISM: A Pathway to Introductory Statistics 40. 8 x  ; substitute 8 for x in 8 x  :   8 8 0   . 42. 6 x  ; substitute 8 for x in 6 x  :   6 8 14.   44. 15; x  substitute 8 for x in 15: x  (8) 15 23.   46. 7 x  ; substitute 8 for x in 7 x  :   8 7 1   . 48. 5 x ; substitute 8 for x in 5 x :   5 8 40  . 50. The quotient of 6 and the number 52. Two less than the number 54. The sum of 4 and the number 56. The product of the number and 5 58. The sum of the number and 3 60. The quotient of the number and 5 62. Substitute 6 for x and 3 for y in the expression y x  :     3 6 9   64. Substitute 6 for x and 3 for y in the expression x y :     6 3 18.  66. Substitute 6 for x and 3 for y in the expression x y  : 6 3 2.   68. x y  ; substitute 9 for x and 3 for y in the expression x y  :     9 3 12.   70. x y  ; substitute 9 for x and 3 for y in the expression x y  :     9 3 3.   72. Substitute 90.0 for c and 104.8 for r in the expression c r  : 90.0 104.8 194.8.   So, in 2015 the average annual per-person consumption of chicken and red meat was 194.8 pounds. 74. Substitute 11.26 for w and 19.98 for a in the expression a w  : 19.98 11.26 8.72.   So, in 2015 the college enrollments of all students who were not women was 8.72 million. 76. Substitute 2.5 for N and 1.8 for A in the expression NA : 2.5 1.8 4.5.   So, in 2016 the average number of AP exams taken was 4.5 million. 78. Substitute 205,200 for s and 3.6 for n in the expression s n  : 205, 200 3.6 57, 000.   So, in 2014 the average money earned by a teacher was about $57,000. 80. a. Substitute 4 for x in the expression 2 x  :   4 2 6.   Substitute 5 for x in the expression 2 x  :   5 2 7   . Substitute 6 for x in the expression 2 x  :   6 2 8   . b. Substitute 4 for x in the expression 2 : x   2 4 8  . Substitute 5 for x in the expression 2 x :   2 5 10  . Substitute 6 for x in the expression 2 : x   2 6 12  . c. Observe the values after substitution are different for the two expressions. 2 2 4 4 2 6 2(4) 8 5 5 2 7 2(5) 10 6 6 2 8 2(6) 12 x x x           82. a. 3 1 3 1 3 2 3 2 6 3 3 3 9 4 3 4 12 n n         The price of bread is $3, $6, $9, and $12 for 1, 2, 3, and 4 loaves, respectively. b. The cost per loaf of bread is $3. The cost per loaf is a constant while the number of loaves is a variable. In the expression 3 , n the constant is 3 and the variable is n . c. Answers may vary. Example: For each additional loaf bought, the total price increases by $3.

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    Chapter 1: Performing Operations and Evaluating Expressions 7 84. a. 2 1 2 1 2 2 2 2 4 3 2 3 6 4 2 4 8 t t         The elevator rises are 2 yards, 4 yards, 6 yards, and 8 yards for every 1, 2, 3, and 4 seconds, respectively. b. The elevator is rising at a speed of 2 yards per second. The distance risen is a constant amount of 2 yards while the number of seconds is a variable. In the expression 2 , t the constant is 2 and the variable is t . c. Answers may vary. Example: For each second that passes, the distance the elevator rises is another 2 yards. 86. Answers may vary. 88. Answers may vary. Homework 1.3 2. The reciprocal of a b is . b a 4. If an object is made up of two or more parts, then the sum of their proportions equals 1. 6. The numerator of 2 5 is 2. 8.   18 2 9 2 3 3 2 3 3         10.     24 4 6 2 2 2 3 2 2 2 3           12.   27 3 9 3 3 3 3 3 3         14.   105 5 21 5 3 7 3 5 7         16. 10 2 5 2 5 5 14 2 7 2 7 7       18. 27 3 3 3 3 3 3 1 1 54 3 3 3 2 3 3 3 2 2              20. 9 3 3 3 3 1 1 1 81 3 3 3 3 3 3 3 3 3 3 9              22. 15 3 5 3 5 5 5 18 3 3 2 3 3 2 3 2 6           24. 5 4 5 4 5 2 2 20 7 9 7 9 7 3 3 63           26. 2 5 2 5 2 5 5 5 3 6 3 6 3 2 3 3 3 9            28. 5 5 2 5 2 5 5 2 12 12 1 2 2 3 2 3 6           30. 7 2 7 3 7 3 12 3 12 2 12 2 7 3 7 7 2 2 3 2 2 2 2 8                32. 4 8 4 3 4 3 2 2 3 3 3 7 3 7 8 7 8 7 2 2 2 7 2 14                34. 4 4 1 4 1 2 2 2 2 2 9 9 2 9 2 3 3 2 3 3 9              36. 2 8 2 8 10 2 5 2 15 15 15 15 3 5 3         38. 13 9 13 9 4 2 2 2 2 18 18 18 18 2 3 3 3 3 9            40. The LCD is 9: 1 5 1 3 5 3 5 8 3 9 3 3 9 9 9 9        42. The LCD is 24: 3 1 3 3 1 4 9 4 8 6 8 3 6 4 24 24 13 24         44. The LCD is 7: 3 2 7 3 14 3 17 2 7 1 7 7 7 7 7        46. The LCD is 4: 3 1 3 1 2 3 2 1 4 2 4 2 2 4 4 4        48. The LCD is 42: 5 4 5 7 4 6 35 24 6 7 6 7 7 6 42 42 11 42         50. The LCD is 7: 9 1 7 9 7 9 2 1 7 1 7 7 7 7 7 2 7          

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    8 ISM: A Pathway to Introductory Statistics 52. 3 3 7 3 5 15 4 7 4 5 4 7 28 5      54. 5 5 20 5 21 5 3 7 7 3 20 3 21 3 20 3 2 2 5 4 21            56. 25 25 15 25 3 5 5 3 5 9 15 9 3 9 15 3 3 3 5 9 3            58. Substitute 3 for x and 12 for z in the expression z x : 12 3 2 2 2 2 4 4 3 3 1 1 1         60. Substitute 4 for w , 3 for x , 5 for y , and 12 for z in the expression y w z x  : 5 4 5 2 2 5 5 12 3 2 2 3 3 3 3 9           62. Substitute 3 for x , 5 for y , and 12 for z in the expression y y x z  : 5 5 3 12  The LCD is 12: 5 5 5 4 5 20 5 25 3 12 3 4 12 12 12 12        64. 67 381 0.90 71 399   66. 149 31 1.16 215 52   68. 614 391 1.85 701 400   70. Answers may vary. Example: 72. In 2018, since 10 of the top 40 songs sold on iTunes were pop songs, we can write a proportion of the songs that were pop songs as 10 1 40 4  . 74. The whole survey group consists of the proportions of the three political parties, so the sum of the proportions equals 1.

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    Chapter 1: Performing Operations and Evaluating Expressions 9 76. The category of American adults who picked football as their favorite sport to watch OR who picked basketball as their favorite sport to watch is the category of adult Americans who picked football together with the adults who picked basketball. So, we add the fractions 4 1 11 9  . 4 1 4 9 1 11 11 9 11 9 9 11 36 11 99 99 47 99         78. Proportion of employees who spend at least $101 on commuting to work: 1 1 7 5 12 5 7 35 35 35     80. Proportion of the disk that is orange: 2 7 2 5 1 7 7 7 7     82. Proportion of Hispanic adults that do not use at least one social media site: 8 11 8 3 1 11 11 11 11     . 84. Proportion of the disc that is red and blue: 1 1 3 2 5 2 3 6 6 6     Proportion of the disc that is yellow: 5 6 5 1 1 6 6 6 6     86. Proportion of Hispanic and Caucasian undergraduates: 2 1 4 7 11 7 2 14 14 14     . Proportion of undergraduates of ethnicities other than Hispanic and Caucasian: 11 14 11 3 1 14 14 14 14     . 88. Let m be the proportion of income for mortgage and f be the proportion of income for food. The proportion remaining is given by the expression 1 m f   . Substitute 1 3 for m and 1 6 for f in the expression. 1 1 1 1 3 6 1 6 1 2 1 1 6 3 2 6 6 2 1 6 6 6 6 2 1 6 3 6 1 2 m f                   So, 1 2 of the income remains.

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    10 ISM: A Pathway to Introductory Statistics 90. a. i. 2370 out of 3180 degrees were bachelor’s degrees. Proportion of bachelor’s degrees: 2370 0.745 3180  . ii. 2370 3180 2370 810 1 0.255 3180 3180 3180 3180      iii. 496 + 84 = 580 degrees were master’s and doctoral degrees. Proportion of master’s and doctoral degrees: 580 0.182 3180  . b. The six exact proportions consist of all the degrees the university awards, so the sum of the exact proportions equals 1. This may not be the case for the sum of the approximations. Rounding may cause the sum to differ slightly from 1. 92. 23 centimeters 1 inch 9.06 inches 1 2.54 centimeters   94. 113 kilometers 1 mile 70.19 miles per hour 1 hour 1.61 kilometers   96. 42.5 milligrams 1 gram 16 ounces 0.68 grams = 0.68 grams per pound 1 ounce 1000 milligrams 1 pound 1 pound    98. 25 meters 3600 seconds 1 kilometer 1 mile 55.90 miles per hour 1 second 1 hour 1000 meters 1.61 kilometers     100. 2250 milligrams 1 gram 16 ounces = 3.6 grams per pound 10 ounces 1000 milligrams 1 pound   102. 1 26, 000 cup milligrams 26 grams 1000 milligrams 8 8 3250 milligrams per ounce 1 cup 1 gram 1 ounce 1 ounce     104. Answers may vary. Example: In this case, Student 2 actually did better. When you compare the proportion of question right for Student 1, 82 41 100 50  with the proportion of question right for Student 2, 43 50 , we see that Student 2 did better since 43 41 50 50  . 106. a. i. 2 3 2 3 6 1 3 2 3 2 6       ii. 4 7 4 7 28 1 7 4 7 4 28       iii. 1 6 1 6 6 1 6 1 6 1 6       b. Answers may vary. Example: The product of a fraction and its reciprocal equals 1. 108. Answers may vary. Example: The student should have only multiplied the numerator by 2. Rewrite 2 as 2 1 and then multiply across. 3 2 3 2 3 6 2 5 1 5 1 5 5        110. Answers may vary. Example: The denominator of a fraction is the name of the things it represents. The numerator of a fraction is the number of those things it represents. When we add two fractions with the same denominator, we keep the same denominator, or name, and add the two numerators, or number of things.

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    Chapter 1: Performing Operations and Evaluating Expressions 11 Homework 1.4 2. The absolute value of a number is the distance the number is from 0 on the number line. 4. False. The sum of –4 and 2 is negative: 4 2 2     . The sum of 5 and –1 is positive: 5 ( 1) 4    . 6.   9 9    8.       2 2 2        10. 6 6  because 6 is a distance of 6 units from 0 on a number line. 12. 1 1   because 1  is a distance of 1 unit from 0 on a number line. 14.   5 5 5      16.   9 9 9       18. The numbers have different signs, so subtract the smaller absolute value from the larger. 5 3 5 3 2      Since 5 is greater than 3  , the sum is positive.   5 3 2    20. The numbers have the same sign, so add the absolute values. 3 2 3 2 5       The numbers are negative, so the sum is negative.   3 2 5      22. The numbers have different signs, so subtract the smaller absolute value from the larger. 9 6 9 6 3      Since 9  is greater than 6 , the sum is negative.   6 9 3     24. The numbers have different signs, so subtract the smaller absolute value from the larger. 4 3 4 3 1      Since 4 is greater than 3  , the sum is positive. 3 4 1    26. The numbers have the same sign, so add the absolute values. 9 5 9 5 14       The numbers are negative, so the sum is negative.   9 5 14      28. The numbers have different signs, so subtract the smaller absolute value from the larger. 8 2 8 2 6      Since 8 is greater than 2  , the sum is positive.   8 2 6    30.   8 8 0    because the numbers are opposites and the sum of opposites is 0. 32. 7 7 0    because the numbers are opposites and the sum of opposites is 0. 34. The numbers have different signs, so subtract the smaller absolute value from the larger. 17 14 17 14 3      Since 17 is greater than 14  , the sum is positive.   17 14 3   

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    12 ISM: A Pathway to Introductory Statistics 36. The numbers have different signs, so subtract the smaller absolute value from the larger. 89 57 89 57 32      Since 89  is greater than 57 , the sum is negative. 89 57 32     38. The numbers have the same sign, so add the absolute values. 347 594 347 594 941       The numbers are negative, so the sum is negative.   347 594 941      40.   127,512 127,512 0    because the numbers are opposites and the sum of opposites is 0. 42. The numbers have the same sign, so add the absolute values. 3.7 9.9 3.7 9.9 13.6       The numbers are negative, so the sum is negative.   3.7 9.9 13.6      44. The numbers have different signs, so subtract the smaller absolute value from the larger. 7 0.3 7 0.3 6.7      Since 7 is greater than 0.3  , the sum is positive. 0.3 7 6.7    46. The numbers have different signs, so subtract the smaller absolute value from the larger. 37.05 19.26 37.05 19.26 17.79      Since 37.05 is greater than 19.26  , the sum is positive.   37.05 19.26 17.79    48. The numbers have different signs, so subtract the smaller absolute value from the larger. 2 1 2 1 1 5 5 5 5 5      Since 2 5 is greater than 1 5  , the sum is positive. 2 1 1 5 5 5          50. The numbers have different signs, so subtract the smaller absolute value from the larger. 5 1 5 1 4 2 6 6 6 6 6 3       Since 5 6  is greater than 1 6 , the sum is negative. 5 1 2 6 6 3     52. The numbers have the same sign, so add the absolute values. 2 5 2 5 2 2 5 4 5 9 3 3 6 3 6 3 2 6 6 6 6 2             The numbers are negative, so the sum is negative. 2 5 3 3 6 2           

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