To determine which lake activity has a central angle of [tex]\( 39.6^\circ \)[/tex] when represented by a circle graph, we need to follow these steps:
1. Understand the Circle Graph Connection:
- In a circle graph or pie chart, each activity's proportional representation is determined by the number of campers picking that activity.
- Since a circle has a total of [tex]\( 360^\circ \)[/tex], we need to find which activity corresponds to a segment of [tex]\( 39.6^\circ \)[/tex].
2. Identify the Given Data:
- Total number of campers surveyed: [tex]\( 100 \)[/tex]
- Distribution of campers per activity:
- Kayaking: 15 campers
- Wakeboarding: 11 campers
- Windsurfing: 7 campers
- Waterskiing: 13 campers
- Paddleboarding: 54 campers
3. Calculate the Central Angle for Each Activity:
- The central angle for a specific activity can be calculated by the formula:
[tex]\[
\text{Central angle} = \left(\frac{\text{Number of campers for the activity}}{\text{Total number of campers}}\right) \times 360^\circ
\][/tex]
4. Calculate the Central Angles:
- Kayaking:
[tex]\[
\left(\frac{15}{100}\right) \times 360^\circ = 54^\circ
\][/tex]
- Wakeboarding:
[tex]\[
\left(\frac{11}{100}\right) \times 360^\circ = 39.6^\circ
\][/tex]
- Windsurfing:
[tex]\[
\left(\frac{7}{100}\right) \times 360^\circ = 25.2^\circ
\][/tex]
- Waterskiing:
[tex]\[
\left(\frac{13}{100}\right) \times 360^\circ = 46.8^\circ
\][/tex]
- Paddleboarding:
[tex]\[
\left(\frac{54}{100}\right) \times 360^\circ = 194.4^\circ
\][/tex]
5. Determine the Activity Matching [tex]\( 39.6^\circ \)[/tex]:
- From the calculations above, we can see that Wakeboarding is the activity whose central angle is [tex]\( 39.6^\circ \)[/tex].
Therefore, the lake activity that has a central angle of [tex]\( 39.6^\circ \)[/tex] in the circle graph is Wakeboarding.
