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Vertical Axis Scale

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Vertical Axis Scale


1. **State the problem:** We need to find the best scale for the vertical axis for test scores data: Wilfred: 23 Hayley: 34 Patrick: 69 Kaylee: 51 The graph is 7 rows high, and the vertical axis currently has labels A, 10, 20, ..., 60. 2. **Understand the scale:** The vertical axis labels are separated by 10 units (e.g., 10, 20, 30, ...). 3. **Determine maximum data value:** The highest test score is 69 (Patrick). 4. **Current highest label:** 60 (as shown), which is not enough to cover 69. 5. **Need to find A such that vertical axis goes from A up to a number at least 69 in increments of 10 over 7 rows. Each row corresponds to a scale step. 6. Since there are 7 rows, and the increments between labels are 10, total vertical scale is $6 \times 10 = 60$ units starting from A (because if there are 7 rows, there are 6 intervals between labels). 7. We want $A + 60 \geq 69$, so $A \geq 9$. 8. Since A should be a number that matches the scale (multiples of 10), but 9 doesn't fit neatly, choose the nearest multiple of 10 less than or equal to 10. 9. If $A = 10$, the vertical axis labels will be 10, 20, ..., 70, covering the max data of 69. 10. If $A = 0$, the scale covers 0 to 60, which is not enough. **Conclusion:** $A = 10$ is the best number to replace A to cover the data well on the vertical axis. **Final answer:** $\boxed{10}$