{"id":487,"date":"2016-04-21T22:43:37","date_gmt":"2016-04-21T22:43:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstats1xmaster\/?post_type=chapter&p=487"},"modified":"2016-04-21T22:43:37","modified_gmt":"2016-04-21T22:43:37","slug":"section-exercises-3","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-fmcc-introstats1\/chapter\/section-exercises-3\/","title":{"raw":"Section Exercises","rendered":"Section Exercises"},"content":{"raw":"

Linear Equations<\/h2>\n

Use the following information to answer the next three exercises<\/em>. A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of $25 and another fee of $12.50 an hour.<\/p>\n\n

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1. What are the dependent and independent variables?<\/p>\n\n<\/div>\n<\/section><\/div>\n

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2. Find the equation that expresses the total fee in terms of the number of hours the equipment is rented.<\/p>\n\n<\/div>\n<\/section><\/div>\n

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3. Graph the equation from 2.<\/p>\n\n<\/div>\n

\u00a0Use the following information to answer the next two exercises<\/em>. A credit card company charges $10 when a payment is late, and $5 a day each day the payment remains unpaid.<\/div>\n<\/section><\/div>\n
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4. Find the equation that expresses the total fee in terms of the number of days the payment is late.<\/p>\n\n<\/div>\n<\/section><\/div>\n

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5. Graph the equation from 4.<\/p>\n6. Is the equation y<\/em> = 10 + 5x<\/em> \u2013 3x<\/em>2<\/sup> linear? Why or why not?\n\n<\/div>\n<\/section><\/div>\n

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7. Which of the following equations are linear?<\/p>\n

a. y<\/em> = 6x<\/em> + 8<\/p>\n

b. y<\/em> + 7 = 3x<\/em><\/p>\n

c. y<\/em> \u2013 x<\/em> = 8x<\/em>2<\/sup><\/p>\n

d. 4y<\/em> = 8<\/p>\n\n<\/div>\n

\n<\/section><\/div>\n
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8. Does the graph show a linear equation? Why or why not?<\/p>\n\n

\"This<\/span><\/figure><\/div>\n<\/section><\/div>\n

The table below contains real data for the first two decades of AIDS reporting.<\/p>\n\n
Adults and Adolescents only, United States<\/span><\/caption>\n
Year<\/strong><\/td>\n# AIDS cases diagnosed<\/strong><\/td>\n# AIDS deaths<\/strong><\/td>\n<\/tr>
Pre-1981<\/td>\n91<\/td>\n29<\/td>\n<\/tr>
1981<\/td>\n319<\/td>\n121<\/td>\n<\/tr>
1982<\/td>\n1,170<\/td>\n453<\/td>\n<\/tr>
1983<\/td>\n3,076<\/td>\n1,482<\/td>\n<\/tr>
1984<\/td>\n6,240<\/td>\n3,466<\/td>\n<\/tr>
1985<\/td>\n11,776<\/td>\n6,878<\/td>\n<\/tr>
1986<\/td>\n19,032<\/td>\n11,987<\/td>\n<\/tr>
1987<\/td>\n28,564<\/td>\n16,162<\/td>\n<\/tr>
1988<\/td>\n35,447<\/td>\n20,868<\/td>\n<\/tr>
1989<\/td>\n42,674<\/td>\n27,591<\/td>\n<\/tr>
1990<\/td>\n48,634<\/td>\n31,335<\/td>\n<\/tr>
1991<\/td>\n59,660<\/td>\n36,560<\/td>\n<\/tr>
1992<\/td>\n78,530<\/td>\n41,055<\/td>\n<\/tr>
1993<\/td>\n78,834<\/td>\n44,730<\/td>\n<\/tr>
1994<\/td>\n71,874<\/td>\n49,095<\/td>\n<\/tr>
1995<\/td>\n68,505<\/td>\n49,456<\/td>\n<\/tr>
1996<\/td>\n59,347<\/td>\n38,510<\/td>\n<\/tr>
1997<\/td>\n47,149<\/td>\n20,736<\/td>\n<\/tr>
1998<\/td>\n38,393<\/td>\n19,005<\/td>\n<\/tr>
1999<\/td>\n25,174<\/td>\n18,454<\/td>\n<\/tr>
2000<\/td>\n25,522<\/td>\n17,347<\/td>\n<\/tr>
2001<\/td>\n25,643<\/td>\n17,402<\/td>\n<\/tr>
2002<\/td>\n26,464<\/td>\n16,371<\/td>\n<\/tr>
Total<\/strong><\/td>\n802,118<\/strong><\/td>\n489,093<\/strong><\/td>\n<\/tr><\/tbody><\/table>
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9. Use the columns \"year\" and \"# AIDS cases diagnosed. Why is \u201cyear\u201d the independent variable and \u201c# AIDS cases diagnosed.\u201d the dependent variable (instead of the reverse)?<\/p>\n\n<\/div>\n

\n<\/section><\/div>\nUse the following information to answer the next two exercises<\/em>. A specialty cleaning company charges an equipment fee and an hourly labor fee. A linear equation that expresses the total amount of the fee the company charges for each session is y<\/em> = 50 + 100x<\/em>.\n
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10. What are the independent and dependent variables?<\/p>\n\n<\/div>\n<\/section><\/div>\n

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11. What is the y<\/em>-intercept and what is the slope? Interpret them using complete sentences.<\/p>\n\n<\/div>\n

\n<\/section><\/div>\nUse the following information to answer the next three questions<\/em>. Due to erosion, a river shoreline is losing several thousand pounds of soil each year. A linear equation that expresses the total amount of soil lost per year is y<\/em> = 12,000x<\/em>.\n
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12. What are the independent and dependent variables?<\/p>\n\n<\/div>\n<\/section><\/div>\n

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13. How many pounds of soil does the shoreline lose in a year?<\/p>\n\n<\/div>\n

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14. What is the y<\/em>-intercept? Interpret its meaning.<\/p>\n\n<\/div>\n<\/section><\/div>\n

\nUse the following information to answer the next two exercises<\/em>. The price of a single issue of stock can fluctuate throughout the day. A linear equation that represents the price of stock for Shipment Express is y<\/em> = 15 \u2013 1.5x<\/em> where x<\/em> is the number of hours passed in an eight-hour day of trading.\n
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15. What are the slope and y<\/em>-intercept? Interpret their meaning.<\/p>\n\n<\/div>\n

16. If you owned this stock, would you want a positive or negative slope? Why?<\/div>\n<\/section><\/div>\n<\/section>
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17. For each of the following situations, state the independent variable and the dependent variable.<\/p>\n\n