Chipwich summer camp surveyed 100 campers to determine which lake activity is their favorite. The results are given in the table. 15 11 7 13 54. If a circle graph was constructed from the results. Which lake activity has a central angle of 46.8 degrees
To determine which lake activity has a central angle of 46.8 degrees, we need to find the corresponding percentage of that activity.
First, we need to calculate the total number of respondents:
15 + 11 + 7 + 13 + 54 = 100.
Next, we can calculate the percentage of each activity by dividing the number of respondents by the total number of respondents, then multiplying by 100:
15/100 * 100% = 15%
11/100 * 100% = 11%
7/100 * 100% = 7%
13/100 * 100% = 13%
54/100 * 100% = 54%
To find which activity has a central angle of 46.8 degrees, we need to find the activity that corresponds to 46.8% of the total circle.
Let's calculate the size of 46.8% of the circle:
46.8/100 * 360 = 169.92 degrees.
From the given percentages, we can see that 54% corresponds to the lake activity that has the greatest percentage. However, this is more than 46.8%.
Therefore, the lake activity with a central angle of 46.8 degrees is not represented in the given data.
To determine which lake activity has a central angle of 46.8 degrees, we need to calculate the central angle for each activity based on the given data.
First, let's add up the total number of campers surveyed:
15 + 11 + 7 + 13 + 54 = 100
Next, we need to find the central angle for each activity. We can calculate this by finding the percentage of campers choosing each activity and then converting it to degrees.
For the first activity:
Percentage = (Number of campers for the activity / Total number of campers) * 100
Percentage = (15 / 100) * 100 = 15%
The central angle can be calculated as:
Central Angle = Percentage * 360 degrees
Central Angle = 15% * 360 degrees = 54 degrees
For the second activity:
Percentage = (11 / 100) * 100 = 11%
Central Angle = 11% * 360 degrees = 39.6 degrees
For the third activity:
Percentage = (7 / 100) * 100 = 7%
Central Angle = 7% * 360 degrees = 25.2 degrees
For the fourth activity:
Percentage = (13 / 100) * 100 = 13%
Central Angle = 13% * 360 degrees = 46.8 degrees
For the fifth activity:
Percentage = (54 / 100) * 100 = 54%
Central Angle = 54% * 360 degrees = 194.4 degrees
From the calculations, we can see that the lake activity with a central angle of 46.8 degrees is the fourth activity.