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The data in the table below represents the square footage and rents (dollars per month) for apartments in a section of a large city. Complete parts (a) through (c) below. 799 Square Footage, x 689 767 829 796 805 905 Rent per Month, R 1575 1625 1725 1660 1670 1775 1680 (a) Using a graphing utility, draw a scatter diagram of the data treating square footage as the independent variable. What type of relation appears to exist between square footage and rent? Which graph below is a scatter diagram of the data? O A. AR 1780- 1560- 680 920 Q OB. B. AR OA. R=0.976x²2 +0.166x+893 OC. R=0.166x² +0.000509x+1214 OE. R=0.000509x + 1214 OG. There is no relation. 1780- 1560-++ 680 920 Q Which sentence below best describes the relation between square footage and rent? OA. There appears to be a linear relation between square footage and rent. OB. There appears to be a quadratic relation between square footage and rent. OC. There does not appear to be any relation between square footage and rent. O C. Ax 920- 680- 1560 RG 1780 (b) Based on your response to part (a), find either a linear or quadratic model that describes the relation between square footage and rent. Which equation below best describes the relation between square footage and rent? OB. R 893x +0.976 OD. R=0.000509x² +0.166x+1214 OF. R=0.976x + 893 O D. 920 Ax 680++ 1560 1780

The data in the table below represents the square footage and rents (dollars per month) for apartments in a section of a large city. Complete parts (a) through (c) below. 799 Square Footage, x 689 767 829 796 805 905 Rent per Month, R 1575 1625 1725 1660 1670 1775 1680 (a) Using a graphing utility, draw a scatter diagram of the data treating square footage as the independent variable. What type of relation appears to exist between square footage and rent? Which graph below is a scatter diagram of the data? O A. AR 1780- 1560- 680 920 Q OB. B. AR OA. R=0.976x²2 +0.166x+893 OC. R=0.166x² +0.000509x+1214 OE. R=0.000509x + 1214 OG. There is no relation. 1780- 1560-++ 680 920 Q Which sentence below best describes the relation between square footage and rent? OA. There appears to be a linear relation between square footage and rent. OB. There appears to be a quadratic relation between square footage and rent. OC. There does not appear to be any relation between square footage and rent. O C. Ax 920- 680- 1560 RG 1780 (b) Based on your response to part (a), find either a linear or quadratic model that describes the relation between square footage and rent. Which equation below best describes the relation between square footage and rent? OB. R 893x +0.976 OD. R=0.000509x² +0.166x+1214 OF. R=0.976x + 893 O D. 920 Ax 680++ 1560 1780

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Understanding the Relationship between Square Footage and Rent The table below lists square footage and corresponding monthly rents (in dollars) for apartments in a section of a large city. | Square Footage (x) | Rent per Month (R) | |-------------------|-------------------| | 689 | 1575 | | 767 | 1625 | | 829 | 1725 | | 796 | 1660 | | 805 | 1670 | | 905 | 1775 | | 799 | 1680 | #### Graphical Analysis (a) Using a graphing tool, plot a scatter diagram with square footage as the independent variable. Determine the relationship type between square footage and rent. **Scatter Diagrams:** - **Option A:** Shows a positive correlation between square footage and rent, indicating a potential linear relationship. - **Option B:** Incorrectly plots axes; does not represent data properly. - **Option C and D:** Axes are swapped, and they don't represent the intended relationship. **Which sentence best describes the relationship?** - **Option A:** A linear relation seems to exist between square footage and rent. #### Mathematical Modeling (b) Based on the graph in part (a), identify a linear or quadratic model to describe the relationship. **Possible Equations:** - **Option A:** \( R = 0.976x^2 + 0.166x + 893 \) - **Option B:** \( R = 893x + 0.976 \) - **Option C:** \( R = 0.166x^2 + 0.000509x + 1214 \) - **Option D:** \( R = 0.000509x^2 + 0.166x + 1214 \) - **Option E:** \( R = 0.000509x + 1214 \) - **Option F:** \( R = 0.976x + 893 \) - **Option G:** No relation **Best Describing Equation:** - **Option D:** \( R = 0.000509x^2 + 0.166x + 1214 \) – offers a quadratic model for the relationship. The analysis indicates a quadratic correlation between square footage and rent, derived from plotting and mathematical modeling.
Transcribed Image Text:### Understanding the Relationship between Square Footage and Rent The table below lists square footage and corresponding monthly rents (in dollars) for apartments in a section of a large city. | Square Footage (x) | Rent per Month (R) | |-------------------|-------------------| | 689 | 1575 | | 767 | 1625 | | 829 | 1725 | | 796 | 1660 | | 805 | 1670 | | 905 | 1775 | | 799 | 1680 | #### Graphical Analysis (a) Using a graphing tool, plot a scatter diagram with square footage as the independent variable. Determine the relationship type between square footage and rent. **Scatter Diagrams:** - **Option A:** Shows a positive correlation between square footage and rent, indicating a potential linear relationship. - **Option B:** Incorrectly plots axes; does not represent data properly. - **Option C and D:** Axes are swapped, and they don't represent the intended relationship. **Which sentence best describes the relationship?** - **Option A:** A linear relation seems to exist between square footage and rent. #### Mathematical Modeling (b) Based on the graph in part (a), identify a linear or quadratic model to describe the relationship. **Possible Equations:** - **Option A:** \( R = 0.976x^2 + 0.166x + 893 \) - **Option B:** \( R = 893x + 0.976 \) - **Option C:** \( R = 0.166x^2 + 0.000509x + 1214 \) - **Option D:** \( R = 0.000509x^2 + 0.166x + 1214 \) - **Option E:** \( R = 0.000509x + 1214 \) - **Option F:** \( R = 0.976x + 893 \) - **Option G:** No relation **Best Describing Equation:** - **Option D:** \( R = 0.000509x^2 + 0.166x + 1214 \) – offers a quadratic model for the relationship. The analysis indicates a quadratic correlation between square footage and rent, derived from plotting and mathematical modeling.
**Educational Website Content: Analyzing Relations Between Square Footage and Rent** **Question:** Which sentence below best describes the relation between square footage and rent? - **A.** There appears to be a linear relation between square footage and rent. - **B.** There appears to be a quadratic relation between square footage and rent. - **C.** There does not appear to be any relation between square footage and rent. **Task:** Based on your response to part (a), find either a linear or quadratic model that describes the relation between square footage and rent. Which equation below best describes the relation between square footage and rent? - **A.** \( R = 0.976x^2 + 0.166x + 893 \) - **B.** \( R = 893x + 0.976 \) - **C.** \( R = 0.166x^2 + 0.000509x + 1214 \) - **D.** \( R = 0.000509x^2 + 0.166x + 1214 \) - **E.** \( R = 0.000509x + 1214 \) - **F.** \( R = 0.976x + 893 \) - **G.** There is no relation. **Predictive Task:** Use the model you selected in part (b) to predict the rent of an apartment in the section that is 850 square feet. **Outcome:** The predicted rent of an apartment with 850 square feet is about $____. *(Use the answer from part (b) to find this answer. Round to the nearest whole number as needed.)*
Transcribed Image Text:**Educational Website Content: Analyzing Relations Between Square Footage and Rent** **Question:** Which sentence below best describes the relation between square footage and rent? - **A.** There appears to be a linear relation between square footage and rent. - **B.** There appears to be a quadratic relation between square footage and rent. - **C.** There does not appear to be any relation between square footage and rent. **Task:** Based on your response to part (a), find either a linear or quadratic model that describes the relation between square footage and rent. Which equation below best describes the relation between square footage and rent? - **A.** \( R = 0.976x^2 + 0.166x + 893 \) - **B.** \( R = 893x + 0.976 \) - **C.** \( R = 0.166x^2 + 0.000509x + 1214 \) - **D.** \( R = 0.000509x^2 + 0.166x + 1214 \) - **E.** \( R = 0.000509x + 1214 \) - **F.** \( R = 0.976x + 893 \) - **G.** There is no relation. **Predictive Task:** Use the model you selected in part (b) to predict the rent of an apartment in the section that is 850 square feet. **Outcome:** The predicted rent of an apartment with 850 square feet is about $____. *(Use the answer from part (b) to find this answer. Round to the nearest whole number as needed.)*
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