Chapter 9. Chapter 9 Opener. Section 9.1. Big Ideas Math Blue Worked-Out Solutions. Try It Yourself (p. 371) m = = = = 9.1 Activity (pp.

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1 Chapter 9 Opener Tr It Yourself (p. 7).. To plot (, ), start at the origin and move unit right and units up. The point is in Quadrant I.. To plot (, ), start at the origin and move units left and units up. The point is in Quadrant II.. To plot (,.5 ), start at the origin and move unit right and.5 units down. The point is in Quadrant IV.. To plot,, start at the origin and move units left and units down. The point is in Quadrant III. (, ) O x (, ) 8 m = = = = x x ( x ) = m x x = = x + = x + 5 m = = = = x x = m x x = 8 + = x 8 = x 8 ( ) ( x ) (, ) (,.5) m = = = = x x 6 = m x x 7 8 = = x 7 = x 6 Section 9. ( x ) 9. Activit (pp. 7 7). a. Sample answer: Circumference (inches) C x b. (, ), ( 5, 9 ), (.6, 5. ), ( 6, 8 ), (, 8 ), (., 7 ), ( 5, 7 ), ( 7, ), (, 6 ) Circumference (inches) C Weight (ounces) x Weight (ounces) c. Sample answer: As weight increases, the circumference increases. Yes, there appears to be two clusters of data points. d. You can describe the relationship as positive because as x increases, C increases. You can describe the relationship as linear because the data points lie close to a line. e. The ordered pair that represents the bowling ball is ( 5, 7 ). This data point is far removed from the other points. It is an outlier. Copright Big Ideas Learning, LLC 8

2 . a. (, 95 ), (, 88 ), (, 9 ), ( 5, 8 ), ( 7, 79 ), ( 9, 7 ), (, 85 ), (, 9 ), (, 9 ), (, 65 ), ( 8, 75 ) Final grade x Absences b. Sample answer: As the number of absences increases, the final grade decreases. It is similar because these data points also lie close to a line. It is different because the data points are falling from left to right. c. Sample answer: The points ( 5, 8 ) and 7, 79 are on the graph. When x = 6, the -value should be between 79 and 8. So, an estimate for a student who has been absent 6 das is a final grade of 8.. a. ii; There is no relationship between month of birth and birth weights of infants. So, the points should show no pattern. b. i; Because students who did well on the quiz will most likel do well on the test, as the quiz scores increase, so will the test scores. c. iii; As the age of the laptop computer increases, the value will decrease.. Sample answer: A scatter plot is a graph that shows the relationship between two data sets. 5. To construct a scatter plot, use the horizontal axis of a coordinate plane to represent one of the data sets. Use the vertical axis to represent the other data set. Write the ordered pairs that represent the data. Then plot the ordered pairs on our coordinate plane. Once the ordered pairs are plotted, ou can determine whether the points show a positive or negative relationship, a linear or nonlinear relationship, and whether there are an clusters or gaps in the data. You can also use a scatter plot to identif an outliers, points that are far from the other data points. 9. On Your Own (pp. 7 75). Sample answer: Draw a vertical line from the point that has a -value just below 65. It crosses the x-axis at about. So, a sandwich with 65 calories might have about 5 grams of fat.. Test score x Stud time (minutes) As the stud time increases, the test score increases. So, the scatter plot shows a positive linear relationship. There is a gap in the data from x = 9 to x =. An outlier, 7. There are no obvious clusters. on the graph is 9. Exercises (pp ) Vocabular and Concept Check. The data must be ordered pairs so there are equal amounts of x- and -values.. An outlier is a data point that is far removed from the other points in a data set.. A student's shoe size is not related to their IQ. So, ou would expect no relationship between the data.. As time passes, the distance to the destination decreases. So, ou would expect a negative linear relationship between the data. 5. On each successive bounce, the ball rebounds to a height less than its previous bounce. So, ou would expect a nonlinear relationship between the data. 6. As the number of toppings increases, the price of the pizza will increase. So, ou would expect a positive linear relationship between the data. Practice and Problem Solving 7. a. (, 5 ), (, 9 ), ( 8, ), ( 5, ), ( 6, 8 ) Pairs of jeans sold x Average price b. As the average price of jeans increases, the number of pairs of jeans sold decreases. 8 Copright Big Ideas Learning, LLC

3 8. a. Draw a vertical line from the point that has a -value of. It crosses the x-axis at. So, SUVs were sold in. b. Draw a horizontal line from the point that has an x-value of. It crosses the -axis at about 875. So, in, about 875 SUVs were sold. c. As the ear increases, the number of SUVs sold decreases. So, the scatter plot shows a negative linear relationship. 9. a. The point at x = has a -value below 7 and the point at x = has a -value above 7, so a value between and will ield a -value of 7. You can estimate that the server should work about.5 hours to earn $7. b. Draw a horizontal line from the point that has an x-value of 5. It crosses the -axis at about 85. So, the server earned about $85 for 5 hours of work. c. As the hours worked increase, the earnings increase. So, the scatter plot shows a positive linear relationship.. As x increases, decreases. So, the scatter plot shows a negative linear relationship. There is an outlier at (5, ), and a gap between the x-values of 5 to 5 and -values of to. There are no clusters.. The points lie in a shape of a curve. So, the scatter plot shows a nonlinear relationship. There are no outliers, gaps, or clusters.. The points show no pattern. So, the scatter plot shows no relationship. There are no outliers, gaps, or clusters.. As the ear increases, the price per pound for hone increases. So, the data show a positive linear relationship.. a. As the stud times increase, the test scores increase. So, the scatter plot shows a positive linear relationship. b. The more time ou spend studing, the higher the test score ou will receive. 5. Sample answer: As the number of weeks a movie has been in theaters increases, the weekl movie ticket revenue decreases. 6. a. Price (dollars) The data show a weak positive linear relationship. b. Sample answer: The point (, 5 ) is an outlier because the store onl offers one GB 7-inch tablet and GB is significantl greater than the other options. There are gaps between x =, x = 8, and x = 6 because these are the onl available options for memor. There are clusters along x =, x = 8, and x = 6 because these are the onl available options for memor. 7. no; A relationship does not indicate a causation. There could be other factors such as sunn, warm weather. Fair Game Review 8. 5x = x + 6 = 5x = x x The graphs intersect at (, ). So, the solution is x =. 8 6 Check: x = 5x = x + 6? 5 = + 6? 8 6 (, ) = 5x = + 6 = x Memor (GB) = x + 6 Copright Big Ideas Learning, LLC 85

4 9. 7x + = 9x = 7x + = 9x O The graphs intersect at ( 8, 59 ). So, the solution is x = 8. = 7x + Check: x = 8 7x + = 9x? () () 78 + = 98? 56 + = 7 59 = 59. x = x = x = x The graphs intersect at,. So, the solution is x =. Check: x = (8, 59) = 9x x = x (, ) x = x? + = 8? = 8 8 = 5 = x 6 x. B; m m =? = mx m ( ) = The point Section Activit (pp ). a b., m is not on the graph of = mx. c. Sample answer: The line passes through (, ) and ( 5, 7.5 ) m = = = =. x x 5 5 Because the line crosses the -axis at about (, ), the -intercept is. So, the equation of the line is =.x +. d. Sample answer: To predict the length next September, substitute for x in the equation.. a b. Length (inches) x Month =.x + =. + =. + = 5. The length of the bab alligator next September will be about 5. inches. Bats (thousands) x Year 86 Copright Big Ideas Learning, LLC

5 c. Sample answer: The line passes through (, 7 ) and ( 6, 5 ). 5 7 m = = = 8.7 x x 6 6 Because the line crosses the -axis at (, 7 ), the -intercept is 7. So, the equation of the line is = 8.7x + 7 d. Sample answer: In ears, it will be ear. To predict the number of bats in ears, substitute for x in the equation. = 8.7x + 7 = 8.7x + 7 = = The number of bats in the mine in ears will be about,.. You can plot data ou know and then draw a line that best approximates the points. Then, ou can write an equation and use it to predict an event.. Answer should include, but is not limited to: Make sure that the data can be described b a line. 9. On Your Own (pp. 8 8). a. Number of people x Year b. Sample answer: The line passes through (, ) and ( 5, 5 ). 5 5 m = = = = 7 x x 5 5 Because the line crosses the -axis at (, ), the -intercept is. So, the equation of the line of fit is = 7 x. c. The slope of the line of fit is 7. This means that the attendance is increasing b about 7 people each ear. The -intercept shows that the attendance in the ear prior to this 8-ear period was. d. Sample answer: = 7x = 7 = 7 The number of people who will attend the festival in ear should be about 7.. Using the linear regression feature of a graphing calculator, the equation of the line of best fit is =.9x +. The correlation coefficient is about.988. This means that the relationship between months and depths is a strong negative correlation and that the equation closel models the data. 9. Exercises (pp. 8 8) Vocabular and Concept Check. Because a line of fit is drawn close to most of the data points, the equation of the line can be used to estimate and predict values.. Sample answer: This line is not a good representation of the data because too man points lie below the line.. A correlation coefficient of.98 indicates a stronger relationship because it is closer to than.9 is to. Practice and Problem Solving. a b. 5. a. Weight (pounds) x Pints c. Sample answer: The line passes through (, ) and (,.).. m = = = =.75 x x Because the line crosses the -axis at (, ), the -intercept is. So, the equation of the line is =.75 x. =.75 =.75 = 7.5 d. Sample answer: x The weight of pints of blueberries should be about 7.5 pounds. e. Sample answer: Because pints of blueberries weigh 7.5 pounds, the cost of pints of blueberries is $ $6.88. Hot chocolates x Temperature ( F) Copright Big Ideas Learning, LLC 87

6 6. a. b. Sample answer: The line passes through (, 5) and (6, ). 5 5 m = = = =.5 x x 6 ( x ) = m x x =.5 6 =.5x + =.5x + 6 So, the equation of the line of fit is =.5x + 6. c. Sample answer: The slope is.5 and the -intercept is 6. So, ou could predict that 6 hot chocolates are sold when the temperature is F, and the sales decrease b about hot chocolate for ever F increase in temperature. d. Sample answer: =.5x + 6 = = + 6 = 5 About 5 hot chocolates will be sold when the high temperature is F. Distance (miles) x Hours b. Sample answer: The line passes through (, ) and ( 6, ). m = = = 55 x x 6 Because the line crosses the -axis at about (, 5 ), the -intercept is 5. So, the equation of the line of fit is = 55x + 5. c. The slope of the line of fit is 55. So, ou travel at a speed of 55 miles each hour. d. To find out how man miles ou were from home, let x =. = 55x + 5 = = 5 So, ou were 5 miles from home. e. Sample answer: = 55x + 5 = = = The distance traveled in 7 hours should be about miles. 7. Because there is no line that can be drawn close to most of the data points when the data set has no relationship, is not possible to find a line of fit for the data. 8. Using the linear regression feature of a graphing calculator, the equation of the line of best fit is = 9.6x The correlation coefficient is about.96. This means that the relationship between the ear and the attendance is a strong negative correlation and the equation closel models the data. 9. Using the linear regression feature of a graphing calculator, the equation of the line of best fit is =.9x +. The correlation coefficient is about.999. This means that the relationship between the number of hours and the snow depth is a strong positive correlation and the equation closel models the data. When x =, =.9 + =. So, there was about inches of snow before the snowstorm.. a. Using the linear regression feature of a graphing calculator, the equation of the line of best fit is = 5.8x 8. The correlation coefficient is about.98. This means that the relationship between the ear and the number of text messages is a strong positive correlation and the equation closel models the data. b. The slope of the line of best fit is 5.8. This means that the number of text messages sent increases b about 5.8 billion each ear. The -intercept is 8, which has no meaning in this context because there cannot be negative number of text messages sent. c. Sample answer: The ear 5 corresponds to x = 5. = 5.8x 8 = = 68 8 = About billion, or about trillion, text messages will be sent in 5.. a. Using the linear regression feature of a graphing calculator, the equation of the line of best fit is = 8x +. The correlation coefficient is about.98. This means that the relationship between the number of seconds and the height is a strong positive correlation and the equation closel models the data. 88 Copright Big Ideas Learning, LLC

7 b. Sample answer: = 8x + = = + = 5 The height of the ball is 5 feet after 5 seconds. c. The height of a hit baseball is not linear because the ball will descend at some point. The best fit line from part (a) onl models a small part of the data. Fair Game Review. Let x =.. x. x =. x =. ( x =.) 9x = x = = 9 So,. =. 9. Let x =.7. x =.7 x =.7 x = 7.7 ( x =.7) 9x = x = = So,.7 =. 9. Let x =.6. x =.6 x =.6 x =.6 ( x =.6) 9x =.. 7 x = = = = So,.6 = Let x =.8. x =.8 x =.8 x = 8.8 ( x =.8) 99x = x = = 99 9 So,.8 =. 6. D; V = πr Stud Help Available at BigIdeasMath.com. Quiz a. Draw a vertical line from the point that has a -value of 5. It crosses the x-axis at 7. So, the charit received $5, in 7. b. Draw a horizontal line from the point that has an x-value of. It crosses the -axis at. So, the charit received $, in. c. As the ear increases, the amount in donations decreases. So, the scatter plot shows a negative linear relationship.. As x increases, decreases. So, the scatter plot shows a negative linear relationship. There is an outlier at ( 6, ). There are no gaps or clusters.. The points show no pattern. So, the scatter plot shows no relationship. There are no outliers, gaps, or clusters.. As x increases, increases. So, the scatter plot shows a positive linear relationship. There is a cluster under = 6. There are no outliers or gaps. 5. a. Number of customers (millions) x Year As the ear increases, the number of customers increases. So, the scatter plot shows a positive linear relationship. There are no outliers, gaps, or clusters. Copright Big Ideas Learning, LLC 89

8 6. a. b. Using the linear regression feature of a graphing calculator, the equation of the line of best fit is = 5.x +. The correlation coefficient is about.998. This means that the relationship between the ear and the number of customers served is a strong positive correlation and that the equation closel models the data. b. Sample answer: The line passes through (, 6) and ( 8, 8 ). 8 6 m = = = = x x 8 6 Because the line crosses the -axis at (, ), the -intercept is. So, the equation of the line of fit is = x +. c. The slope of the line of fit is. This means that the number of cats adopted increases b each month. The -intercept is about, which means about cats were adopted in December. d. Sample answer: To predict the number of cats adopted in October, substitute for x in the equation. = x + = + = + = So, about cats will be adopted in October. Section Activit (pp ). a. Number of cats Color x Month T-Shirt Size S M L XL XXL Total Blue/White 5 Blue/Gold Red/White Black/White Black/Gold 5 Total b. no; The entr in the Black/Gold row and XL column is. This means that there are no black-andgold XL T-shirts left in stock. c.. a. Color d. Sample answer: For ever categor of shirt, order the number of shirts sold last ear minus the number remaining. If the result is a negative number, then do not order an shirts in that categor. Also, order a couple extra of the shirts that were all sold. For example, order 6 = 5 large blue-and-white shirts, order =, or small red-and-white shirts, and order extra of the extra-large black-andgold shirts. Hours T-Shirt Size S M L XL XXL Total Blue/White Blue/Gold Red/White Black/White Black/Gold Total Gender Bos Girls Total hours per week hours per week 7 8+ hours per week 9 Total 8 8 b. Sample answer: There are fewer bos working parttime jobs than girls. The number of students working hours per week is greater than the number of students working 7 hours per week, which is greater than the number of students working 8+ hours per week. c. The data do not support or oppose the claim because the data are not about students dropping out or working full-time jobs.. To read a two-wa table, note that each entr represents the number of data values that fit both the criteria for the row and column the entr is in. The entries in the Total row and column represent the number of data values that fit the one criterion in that column or row. To make a two-wa table for a data set, use one variable that describes the data for the rows for the table and another variable for the columns. Put the number of data points that fit both row and column criteria in each slot in the table. On the bottom and right edges of the table, sum up each column and row. 9 Copright Big Ideas Learning, LLC

9 . Answer should include, but is not limited to: The student will collect data from a real-world example and use the data to make a two-wa table. 9. On Your Own (pp ). a. The number in the Dance Attend row and Football Game Not Attend column is 5. b. So, 5 of the students in the surve will attend the dance but not the football game. Dance 5 students will attend the football game. 5 students will not attend the football game. students will attend the dance. 6 students will not attend the dance. 76 students were surveed. Football Game Attend Not Attend Total Attend 5 5 Not Attend 6 6 Total Exercises (pp. 9 9) Vocabular and Concept Check. The joint frequencies are the entries in the two-wa table that differentiate the two categories of data collected. The marginal frequencies are the sums of the rows and columns of the two-wa table.. A two-wa table displas two categories of data collected from the same source. Practice and Problem Solving.. Gender 7 females were surveed. 59 males were surveed. Fundraiser No Yes Total Female 5 7 Male 9 59 Fundraiser No Yes. a. Grade Total Gender Female 5 Male 9 b. Lunch Pack 6 5 Bu Total 5 Grade Total students surveed will not be participating in the fundraiser. 8 students surveed will be participating in the fundraiser. 5. The entr in the Female row and Yes column is 5. So, 5 females will be participating in the fundraiser. Lunch Sample answer: 9 of the students in 6th grade bu a school lunch. 9.5 = Pack 55% 6% 5% Bu 5% 5% 7% So, 5% of the 6th grade students in the surve bu a school lunch. c. The table does not show a relationship between grade level and lunch choice because about half of the students in each grade bu a school lunch. 6. The entr in the Male row and No column is. So, males will not be participating in the fundraiser. 7. Class 9 students surveed are attending the school pla. 5 students surveed are not attending the school pla. 7 students surveed are juniors. 75 students surveed are seniors. 6 students were surveed. School Pla Attend Not Attend Total Junior 7 Senior 5 75 Total Copright Big Ideas Learning, LLC 9

10 8. Text Plan 5 people surveed have limited cell phone minutes. 5 people surveed have unlimited cell phone minutes. 78 people surveed have limited text plans. 9 people surveed have unlimited text plans. 68 people were surveed. 9. a. The entr in the 7th row and Sports column is 9. So, 9 students in the 7th grade chose sports as being most important to them. b. The entr in the 8th row and Grades column is. So, students in the 8th grade chose grades as being most important to them. Grade students surveed chose grades as most important. students surveed chose popularit as most important. 59 students surveed chose sports as most important. 7 students in the 6th grade were surveed. 7 students in the 7th grade were surveed. 65 students in the 8th grade were surveed. students were surveed. c. 6th graders who chose popularit: 8 Total students surveed: 8.85 Cell Phone Minutes Limited Unlimited Total Limited Unlimited Total Goal Grades Popularit Sports Total 6th 8 7 7th th Total 59 So, about 8.5% of students in the surve are 6th graders who chose popularit.. a. b.. a. c. The table shows a relationship between age and whether people have at least $ in savings because as age increases, people are more likel to have at least $ in savings. b. 8 students surveed have green ees. c. Saved at Least $ Saved at Least $ Gender 5 students surveed have blue ees. 5 students surveed have brown ees. 8 males were surveed. females were surveed. 88 students were surveed. Gender Sample answer: of the 8 students with green ees are female..8 8 So, about 8% of the students with green ees in the surve are female. 7 of the 5 students with brown ees are male = Age Total Yes No Total Age Yes 8% 5% 6.5% No 7% 55% 7.5% Ee Color Green Blue Brown Total Male Female 9 8 Total Ee Color Green Blue Brown Male 6% 6% 6% Female 8% 5% % So, 6% of the students with brown ees in the surve are male. 9 Copright Big Ideas Learning, LLC

11 . Sample answer: 5 of the 8 male students have green ees So, about.% of the male students in the surve have green ees. 8 of the female students have brown ees. 8.5 = So, 5% of the female students in the surve have brown ees.. out of 88 students are females. 8 out of 88 students have green ees. out of 88 students are females and have green ees = So, about 5.% of the students in the surve are females or have green ees. 8 out of 88 students are males. 5 out of 88 students are males and have green ees. 8 5 = So, about 8.9% of the students in the surve are males that do not have green ees. 5.% + 8.9% = % This means that the sum of the percentage of students who are female or have green ees and the percentage of students who are male and do not have green ees accounts for everone who was surveed. Fair Game Review. Gender 5 6 m = = = = x x Ee Color Green Blue Brown Male.%.% 56.% Female 7.5% 7.5% 5% Using the point (, ), the -intercept is. So, the equation of the line is = x m = = = = 5 x x Using the point (, ), the -intercept is. So, the equation of the line is = 5x. m = = = = x x Using the point (, ), the -intercept is. So, the equation of the line is = x B; You cannot rewrite the equation x = 8 in slopeintercept form. So, it is a not a linear function. Section Activit (pp. 9 9). a. Sample answer: The data set represents parts of a whole, so a circle graph is an appropriate data displa. Birds 7 Roadkill b. Sample answer: The data values change over time, so a scatter plot is an appropriate data displa. Number of black bears 8 6 Mammals 76 Black Bear Roadkill Year Amphibians 5 Reptiles 75 Unknown 689 x Copright Big Ideas Learning, LLC 9

12 c. Sample answer: A stem-and-leaf plot shows how the raccoon weights are distributed. Raccoon Roadkill Weights Stem Leaf Ke: 9 = 9. pounds d. Sample answer: Reduce the speed limit on some roads.. Answer should include, but is not limited to: The student will write a report about an animal species that is (or has been) endangered. Make sure the students graphical displas are appropriate.. Sample answer: You can displa data using different plots and graphs so that it makes it eas for people to interpret and make conclusions from the data. Answer should include, but is not limited to: The student will find examples of each tpe of graph: bar graph, circle graph, scatter plot, stem-and-leaf plot, and box-and-whisker plot. 9. On Your Own (pp. 9 96). Sample answer: A histogram shows frequencies of data values in intervals of the same size. So, a histogram is an appropriate data displa.. Sample answer: You want to show the percent of students in specific categories. So, a bar graph is an appropriate displa.. A dot plot would show the number of times each number of hits occurred, not how the number of hits changed over time. So, it is not an appropriate displa.. A circle graph would show the number of hits for each month as a percent of the total hits for the 5-month period. So, it is an appropriate displa. 5. A stem-and-leaf plot would show how the number of hits for each month are distributed, not how the number of hits changed over time. So, it is not an appropriate displa. 6. The tickets var in width and the break in the vertical axis makes the difference in ticket prices appear to be greater. 7. The bars become wider as the ears progress, making the increase in profit appear greater. 9. Exercises (pp ) Vocabular and Concept Check. In man cases, more than one displa could be appropriate, depending on what aspect of the data needs to be emphasized. Pictographs, bar graphs, line graphs, scatter plots and circle graphs displa and compare data values. Histograms, stem-and-leaf plots, and dot plots show the distribution of data values.. Sample answer: Different sized intervals, a break in the vertical axis, an inappropriatel large or small scale on the vertical axis, or different bar widths can make a histogram misleading. Practice and Problem Solving. Sample answer: Because the data are grouped into specific categories, a bar graph is an appropriate displa for the data. Number of notebooks Notebooks Sold in One Week Red Pink Black Green Other White Orange Purple Yellow Blue Color. Sample answer: A stem-and-leaf plot shows the distribution of data. So, a stem-and-leaf plot is an appropriate displa. 5. Sample answer: A line graph shows changes over time. So, a line graph is an appropriate data displa. 6. Sample answer: A dot plot shows the number of times each outcome occurs. So, a dot plot is an appropriate data displa. 7. Sample answer: A line graph shows changes over time. So, a line graph is an appropriate data displa. 9 Copright Big Ideas Learning, LLC

13 8. a. The pictograph shows how the number of hours worked changed during the months. So, it is an appropriate displa. b. Each bar represents a month, so the bar graph shows how the number of hours worked changed during the months. So, it is an appropriate displa. 9. a. From the circle graph, ou can see that the portion of students who prefer math is %. So, it is an appropriate displa. b. The bar graph shows the number of students who prefer each school subject, but it does not show each number as a percent of the whole group of 8 students surveed. So, it is not an appropriate displa.. When the data are grouped into intervals of one categor, as opposed to multiple categories, a histogram would be used instead of a bar graph. Sample answer: A histogram is an appropriate displa for the test scores of the students in a class.. Each biccle represents the same distance. Because the icons for Monda are the largest and Wednesda are the smallest, it looks like the distance is the same each da, but the distance on Wednesda is four times the distance traveled on Monda.. The vertical axis has a break and begins at This makes it appear that the sales increased rapidl from April to Jul, but the difference is onl $ million $ million = $ million.. The intervals of the histogram are not the same size, making it difficult to compare the data.. The widths of the bars are unequal. This makes it appear that some months had more rainfall than the actuall did. 5. Sample answer: A bar graph would be an appropriate displa because each bar can represent a different vegetable. 6. The scatter plot is misleading because the vertical axis does not have a constant interval, which makes it look like the data decreased constantl over 9 hours, but the data decreased more rapidl during the first hour. 7. Sample answer: Because a dot plot shows the number of times each value occurs, the mode would be easil displaed. So, a dot plot is an appropriate displa. 8. a. Because the sum of the percentages is and not, a circle graph is misleading because the data are not parts of a whole. b. Sample answer: A bar graph shows data in specific categories. So, a bar graph would be more appropriate. 9. a. Frequenc,, b. Find the percent of each number :.%,,7 :.%, 998 : 9.9%,,5 :.%, 997 : 9.97%,,6 5:.%,,9 6:.%,,5 7:.%, : 9.98%, 99 9: 9.9%, First, Digits of π First, Digits of π Number c. Because the frequencies are all ver close, the circle graph does not compare the data as well. The bar graph is a more appropriate data displa because it shows that some digits occur slightl more than others. d. Each digit occurs about % of the time. Copright Big Ideas Learning, LLC 95

14 Fair Game Review. a. Make a table of numbers whose squares are close to. Number 5 6 Square of Number The table shows that is between the perfect squares 6 and 5. Because is closer to 6 than to 5, is closer to than to 5.. a. Make a table of numbers whose squares are close to. Number Square of Number 69 The table shows that is between the perfect squares and. Because is closer to than to, is closer to than to So,. b. Make a table of numbers between and 5 whose squares are close to. Number Square of Number Because is closer to.5 than to 9.6, closer to.5 than to So,.5.. a. Make a table of numbers whose squares are close to 7. Number Square of Number is The table shows that 7 is between the perfect squares 6 and 8. Because 7 is closer to 8 than to 6, 7 is closer to 9 than to 8. 9 So, b. Make a table of numbers between 8 and 9 whose squares are close to 7. Because 7 is closer to 7.96 than to 75.69, closer to 8.6 than to Number Square of Number is 77. So,. b. Make a table of numbers between and whose squares are close to. Because is closer to 9. than to.6, is closer to.8 than to.9. So,.8.. A; % of 5% of =.(.5 ) =.( ) = So, is % of 5% of. Quiz Gender Number Square of Number Reccle Yes No Total Female Male 8 Total of the people surveed reccle. of the people surveed do not reccle. 7 of the people surveed are female. 8 of the people surveed are male. 75 people were surveed So, Copright Big Ideas Learning, LLC

15 . Countr Jazz Likes Dislikes Total Likes 6 Dislikes Total 65 people surveed like countr music 5 people surveed dislike countr music. people surveed like jazz music. people surveed dislike jazz music. 65 people were surveed. 7. The graph is misleading because, the vertical axis has a break and begins at 5, which makes it look like the amount of mone raised increased more rapidl than it actuall did. Chapter 9 Review. a. Draw a vertical line from the point that has a -value of 7. It crosses the x-axis at. So, 7 geese migrated to the park in. b. Draw a horizontal line from the point that has an x-value of. It crosses the -axis at 5. So, in, 5 geese migrated to the park. c. As the ear increases, the number of geese increases. So, the scatter plot shows a positive linear relationship.. a. Voter s Age Total. As x increases, decreases. So, the scatter plot shows a negative linear relationship. There is an outlier at (, ). There are no gaps or clusters. Candidate Smith Jackson 68. The points show no pattern. So, the scatter plot shows no relationship. There is a cluster around (, 6 ). There are no outliers or gaps. Total voters surveed prefer Smith. 68 voters surveed prefer Jackson. 8 voters surveed are voters surveed are 5-6. voters surveed are voters were surveed. b. Voter s Age. As x increases, increases. So, the scatter plot shows a positive linear relationship. There is a gap between x = to x = 8. There are no outliers or clusters. 5. a. Number of students Year x Candidate Smith 75% % % Jackson 5% 56% 8% c. The table shows a relationship between age and candidate preference because as age increases, preference for Jackson increases.. Sample answer: A circle graph shows data as parts of a whole. Because percentages are parts of a whole, a circle graph is an appropriate data displa. 5. Sample answer: A line graph shows changes over time. So, a line graph is an appropriate data displa. 6. Sample answer: A box-and-whisker plot shows the spread of each data set. So, a box-and-whisker plot is an appropriate displa. b. Sample answer: The line passes through (, 9 ) and (, 5 ) m = = = = x x ( x ) = m x x 9 = 9 = x = x + 78 So, the equation of the line of fit is = x c. Sample answer: The slope is and the -intercept is 78. So, the number of students in the ear prior to the -ear period was about 78 and the number of students is increasing b about students per ear. Copright Big Ideas Learning, LLC 97

16 d. Sample answer: = x + 78 = + 78 = = 6 So, the number of students in ear will be about 6 students.. a. Weight (pounds) Using the linear regression feature of a graphing calculator, the equation of the line of best fit is =.x The correlation coefficient is about This means that the relationship between the ear and the number of students is a strong positive correlation and the equation closel models the data Age Group Age Group Food Court Likes Dislikes Total Teenagers 96 Adults 79 Senior Citizens 8 8 Total 5 65 Food Court Likes Dislikes Teenagers 96% % Adults % 79% Senior Citizens 8% 8%. 5 6 x Age (months) b. Sample answer: The line passes through (, ) and ( 5,.5 )..5.5 m = = = =.5 x x 5 ( x ) = m x x =.5 =.5x 6 =.5x + 7 So, the equation of the line of fit is =.5x + 7. c. Sample answer: The slope is.5 and the -intercept is 7. So, the bab is gaining.5 pounds per month and was born at a weight of 7 pounds. d. Sample answer: =.5x + 7 = = = 7.5 So, at 7 months the bab will weigh about 7.5 pounds. Nonfiction Likes Dislikes Total 9. The table shows a relationship because teenagers tend to like the food court, but adults and senior citizens tend to dislike the food court. Friction Likes 6 6 Dislikes. Sample answer: A line graph shows how data values change over time. So, a line graph is an appropriate data displa.. Sample answer: A scatter plot compares two different data sets. So, a scatter plot is an appropriate displa. Chapter 9 Test. a. Draw a vertical line from the point that has a -value of 8. It crosses the x-axis at 96. So, the population was about 8 million people in 96. b. Draw a horizontal line from the point that has an x-value of 99. It crosses the -axis at about 5. So, in 99, the population was about 5 million people. c. As the ear increases, the population increases. So, the scatter plot shows a positive linear relationship. Total students surveed like fiction books. students surveed dislike fiction books. 8 students surveed like nonfiction books. students surveed dislike nonfiction books. 7 students were surveed.. Sample answer: A histogram shows frequencies of data values in intervals of the same size. So, a histogram is an appropriate data displa. 5. Sample answer: A line graph shows how data change over time. So, a line graph is an appropriate data displa. 98 Copright Big Ideas Learning, LLC

17 6. Using the linear regression feature of a graphing calculator, the equation of the line of best fit is = 9.9x + 5. The correlation coefficient is about.986. This means that the relationship between the ear and the number of students taking the SAT is a strong positive correlation and the equation closel models the data. 7. Gender Chapter 9 Standards Assessment. B; Volume of clinder: V r h Volume of semi-circle: V = πr = π( 6) = π So, the volume of the trash can is π + π = 576 π cubic inches. = π = π 6 = π. F; Because and 6 are congruent angles formed b two parallel lines and a transversal, and 6 are corresponding angles.. ; The entr in the Male row and No column is. So, male students do not have a job.. D; Graph D shows a negative relationship because as x increases, decreases. 5. 7; Use the Pthagorean Theorem. a + b = c () 8 ( 5) + = c = c 89 = c ± 7 = c Use reusable bags? Yes No Total Male Female 6 5 Total Because distance is alwas positive, the length of the hpotenuse is 7 centimeters. 7. C; Use the Pthagorean Theorem. a + b = c? ( ) + ( 6) = ( 9) = 8? 785 = 8 So, triangle C is not a right triangle. 8. G; A line graph shows how data change over time. So, a line graph would best show how sales have increased over the past three ears. 9. A; So, the coordinates of point M are (, ).. Part A: 6 N Part B: There is a negative correlation between the number of hours of television watched and a student's test score. Part C: To justif our answer, find the correlation coefficient. When the correlation coefficient is close to, then there is a strong negative correlation between the data. K Test score N M L 6 K L x M x Hours of television 6. H; ( x ). + 6 =.x +.8.x +. =.x +.8.x +. =.8.x =.8 x = So, the solution of the equation is x =. Copright Big Ideas Learning, LLC 99

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