To determine which laboratory shows a proportional relationship between the number of leaf samples tested and the time spent testing, we need to check if the ratio of the number of leaf samples tested to the time spent is constant for each scientist in both laboratories.
Laboratory A:
-
Steve:
- Number of Leaf Samples: 90
- Time Spent: 30
- Ratio: \( \frac{90}{30} = 3 \)
-
Jesmy:
- Number of Leaf Samples: 180
- Time Spent: 45
- Ratio: \( \frac{180}{45} = 4 \)
-
Buck:
- Number of Leaf Samples: 210
- Time Spent: 60
- Ratio: \( \frac{210}{60} = 3.5 \)
Laboratory A Ratios:
- Steve's ratio: 3
- Jesmy's ratio: 4
- Buck's ratio: 3.5
Laboratory A does not have a constant ratio, indicating it does not show a proportional relationship.
Laboratory B:
-
Mary:
- Number of Leaf Samples: 140
- Time Spent: 35
- Ratio: \( \frac{140}{35} = 4 \)
-
Brian:
- Number of Leaf Samples: 160
- Time Spent: 40
- Ratio: \( \frac{160}{40} = 4 \)
-
Kate:
- Number of Leaf Samples: 220
- Time Spent: 55
- Ratio: \( \frac{220}{55} = 4 \)
Laboratory B Ratios:
- Mary's ratio: 4
- Brian's ratio: 4
- Kate's ratio: 4
All scientists in Laboratory B have the same ratio, which is 4.
Conclusion: Laboratory B shows a proportional relationship between the number of leaf samples tested and the time spent testing, while Laboratory A does not.
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