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For which of these sets of data would all the points be displayed on a scatterplot if the window size on a regression calculator were set to 5 less-than-or-equal-to x less-than-or-equal-to 15; 25 less-than-or-equal-to y less-than-or-equal-to 75?

A 2-column table with 6 rows. Column 1 is labeled x with entries 6, 7, 9, 11, 13, 14. Column 2 is labeled y with entries 27, 33, 39, 49, 58, 71.
A 2-column table with 6 rows. Column 1 is labeled x with entries 6, 7, 9, 11, 13, 16. Column 2 is labeled y with entries 27, 33, 39, 49, 58, 71.
A 2-column table with 6 rows. Column 1 is labeled x with entries 27, 33, 39, 49, 58, 71. Column 2 is labeled y with entries 6, 7, 9, 11, 13, 14.
A 2-column table with 6 rows. Column 1 is labeled x with entries 27, 33, 39, 49, 58, 71. Column 2 is labeled y with entries 6, 7, 9, 11, 13, 16.

1 answer

To determine which set of data would have all points displayed on a scatterplot with the specified window size of \(5 \leq x \leq 15\) and \(25 \leq y \leq 75\), we will analyze each option given.

Option A:

  • Column 1 (x values): 6, 7, 9, 11, 13, 14
    • All these values are within the range \(5 \leq x \leq 15\).
  • Column 2 (y values): 27, 33, 39, 49, 58, 71
    • All these values are within the range \(25 \leq y \leq 75\).

Conclusion for Option A:

All points will be displayed on the scatterplot.

Option B:

  • Column 1 (x values): 6, 7, 9, 11, 13, 16
    • The value 16 is outside the \(5 \leq x \leq 15\) range.
  • Column 2 (y values): 27, 33, 39, 49, 58, 71
    • All these values are within the range \(25 \leq y \leq 75\).

Conclusion for Option B:

Not all points will be displayed (16 is out of range).

Option C:

  • Column 1 (x values): 27, 33, 39, 49, 58, 71
    • All these values are outside the \(5 \leq x \leq 15\) range.
  • Column 2 (y values): 6, 7, 9, 11, 13, 14
    • All these values are within the range \(25 \leq y \leq 75\), but since x values fail, it doesn’t matter.

Conclusion for Option C:

Not all points will be displayed (x values are out of range).

Option D:

  • Column 1 (x values): 27, 33, 39, 49, 58, 71
    • All these values are outside the \(5 \leq x \leq 15\) range.
  • Column 2 (y values): 6, 7, 9, 11, 13, 16
    • All these values are also outside the \(25 \leq y \leq 75\) range.

Conclusion for Option D:

Not all points will be displayed (both x and y values are out of range).

Final Answer:

Only Option A will have all points displayed on the scatterplot.