To determine which scatterplot shows a linear association among the provided datasets, we can analyze the relationship between the given \( x \) and \( y \) values.
A linear association typically displays a straight-line pattern as the values increase or decrease. Here’s an analysis of each dataset:
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First Dataset:
- \( x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7 \)
- \( y: 800, 700, 350, 450, 500, 1000, 900, 250, 400, 750 \)
The scatter plot would likely show a mixed pattern without a definitive linear trend.
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Second Dataset:
- \( x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7 \)
- \( y: 550, 800, 250, 300, 700, 1000, 650, 300, 100, 700 \)
Here too, the scatterplot might reveal variability and would not represent a clear linear trend.
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Third Dataset:
- \( x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7 \)
- \( y: 550, 800, 350, 450, 700, 1000, 900, 250, 400, 750 \)
Similar to the previous ones, this dataset would likely show some scatter but still not a clear linear trend.
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Fourth Dataset:
- \( x: 5, 8, 2, 4, 6, 12, 10, 1, 3, 7 \)
- \( y: 550, 800, 250, 500, 500, 400, 650, 150, 400, 750 \)
This dataset also exhibits variability but does not present a consistent linear trend.
Upon reviewing the datasets, None seem to represent a clear linear association based on how \( y \) varies with \( x \). Typically, one might expect to see a trend where as \( x \) increases, \( y \) either consistently increases or decreases, but none of these datasets illustrates that.
To visualize this more closely, plotting each of those values on a scatter plot (if done) would help to confirm the linearity. However, based purely on analyzing the numbers, we can conclude that none of these scatterplots seem to show a discernible linear association.
If you were given specific scatterplots to visually assess and select the one with a linear association, please provide those visuals or more information.