Question

Which table does not show a proportional relationship between xx and yy?
A
xx yy
33 88
99 2424
2121 5656
2424 6464
B
xx yy
1010 6161
1414 8585
2323 139139
2828 169169
C
xx yy
22 11
44 22
1010 55
1616 88
D
xx yy
77 1414
1010 2020
1717 3434
3030 6060

Answer 1

To determine which table does not show a proportional relationship between \( xx \) and \( yy \), we need to check if the ratios \( \frac{yy}{xx} \) are constant for each table.

### Table A
| xx | yy | Ratio \( \frac{yy}{xx} \) |
|-----|------|-----------------------------|
| 33 | 88 | \( \frac{88}{33} \approx 2.67 \) |
| 99 | 2424 | \( \frac{2424}{99} \approx 24.49 \) |
| 2121| 5656 | \( \frac{5656}{2121} \approx 2.67 \) |
| 2424| 6464 | \( \frac{6464}{2424} \approx 2.67 \) |

### Table B
| xx | yy | Ratio \( \frac{yy}{xx} \) |
|-----|---------|-----------------------------|
| 1010| 6161 | \( \frac{6161}{1010} \approx 6.11 \) |
| 1414| 8585 | \( \frac{8585}{1414} \approx 6.07 \) |
| 2323| 139139 | \( \frac{139139}{2323} \approx 59.97 \) |
| 2828| 169169 | \( \frac{169169}{2828} \approx 59.85 \) |

### Table C
| xx | yy | Ratio \( \frac{yy}{xx} \) |
|-----|-----|-----------------------------|
| 22 | 11 | \( \frac{11}{22} = 0.5 \) |
| 44 | 22 | \( \frac{22}{44} = 0.5 \) |
| 1010| 55 | \( \frac{55}{1010} \approx 0.0545 \) |
| 1616| 88 | \( \frac{88}{1616} \approx 0.0543 \) |

### Table D
| xx | yy | Ratio \( \frac{yy}{xx} \) |
|-----|------|-----------------------------|
| 77 | 1414 | \( \frac{1414}{77} \approx 18.38 \) |
| 1010| 2020 | \( \frac{2020}{1010} = 2 \) |
| 1717| 3434 | \( \frac{3434}{1717} = 2 \) |
| 3030| 6060 | \( \frac{6060}{3030} = 2 \) |

### Conclusion:
- **Table A** has differing ratios.
- **Table B** has differing ratios.
- **Table C** has differing ratios as well.
- **Table D** has a constant ratio of 2 for the last three rows, but the first row has a different ratio.

The table that does not show a proportional relationship at all is most clearly **Table B**, due to its extremely varied ratios. In summary:

**Table B** does not show a proportional relationship between \( xx \) and \( yy \).