To determine which lake activity corresponds to a central angle of [tex]\(54^{\circ}\)[/tex] in a circle graph (or pie chart), we need to follow these steps:
1. Understand the connection between degrees and the percentage of the total circle:
- A circle has a total of 360 degrees.
- Each degree represents [tex]\(\frac{1}{360}\)[/tex] of the total circle, or about [tex]\(0.278\%\)[/tex].
2. Determine what percentage [tex]\(54^{\circ}\)[/tex] represents of the entire circle:
- Since the entire circle is 360 degrees, we calculate the percentage of the circle represented by [tex]\(54^{\circ}\)[/tex] as follows:
[tex]\[
\text{Percentage} = \left(\frac{54}{360}\right) \times 100
\][/tex]
3. Calculate this percentage:
- [tex]\(\frac{54}{360} = 0.15\)[/tex]
- [tex]\(0.15 \times 100 = 15\%\)[/tex]
4. Calculate the number of campers represented by this percentage:
- The survey includes a total of 100 campers.
- Thus, [tex]\(15\%\)[/tex] of 100 campers is:
[tex]\[
0.15 \times 100 = 15 \text{ campers}
\][/tex]
5. Identify which lake activity corresponds to the number of campers (15 campers):
- According to the table, Kayaking has 15 campers.
So, the lake activity that corresponds to a central angle of [tex]\(54^{\circ}\)[/tex] on the circle graph is Kayaking.
