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The following table shows some of the data gathered by a company on average water usage in homes - Leaving Cert Mathematics - Question 8 - 2016

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The following table shows some of the data gathered by a company on average water usage in homes. | Activity | Percentage used | Angle (Degre... show full transcript

Worked Solution & Example Answer:The following table shows some of the data gathered by a company on average water usage in homes - Leaving Cert Mathematics - Question 8 - 2016

Step 1

Find the percentage used for the ‘Other’ activity.

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Answer

To find the percentage used for the 'Other' category, we first need to ensure that the total percentages add up to 100%.

The added percentages are:

  • WC flushing: 30%
  • Personal Washing – Baths and Taps: 21%
  • Personal Washing – Showers: 12%
  • Clothes Washing: 13%

Calculating the sum:

30+21+12+13=7630 + 21 + 12 + 13 = 76

Thus, the percentage for 'Other' can be calculated as:

10076=24100 - 76 = 24

Therefore, fill in the table: Other activity uses 24%.

Step 2

Complete the table above to show the remaining angles in the pie chart.

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Answer

To find the angles corresponding to each percentage in the pie chart, we use the formula:

Angle=(Percentage100)×360\text{Angle} = \left( \frac{\text{Percentage}}{100} \right) \times 360

  • For WC flushing: (30100)×360=108°\left( \frac{30}{100} \right) \times 360 = 108°

  • For Personal Washing – Baths and Taps: (21100)×360=75.6°\left( \frac{21}{100} \right) \times 360 = 75.6°

  • For Personal Washing – Showers: (12100)×360=43.2°\left( \frac{12}{100} \right) \times 360 = 43.2°

  • For Clothes Washing: The angle is already provided: 46°-8°

  • For Other: (24100)×360=86.4°\left( \frac{24}{100} \right) \times 360 = 86.4°

The completed table of angles is:

ActivityPercentage usedAngle (Degrees)
WC flushing30%108°
Personal Washing – Baths and Taps21%75.6°
Personal Washing – Showers12%43.2°
Clothes Washing13%46°-8°
Other24%86.4°

Step 3

Draw a pie chart to represent the data.

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Answer

To construct the pie chart:

  1. Draw a circle with an appropriate radius.
  2. Create sectors corresponding to the angles calculated:
    • 108° for WC flushing
    • 75.6° for Personal Washing – Baths and Taps
    • 43.2° for Personal Washing – Showers
    • 46°-8° for Clothes Washing
    • 86.4° for Other
  3. Label each sector with the corresponding activity name and angle.

Ensure:

  • All angles are drawn correctly.
  • Each section is appropriately labeled with the name of the activity and the size of the angle.

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