A student recorded the favorite dipping sauces of the 70 people in his class. He wants to plot these data in a circle graph:

\begin{tabular}{|c|c|}
\hline Favorite dipping sauce & Number of students \\
\hline Ranch & 14 \\
Barbecue & 20 \\
Honey mustard & 10 \\
Sweet and sour & 18 \\
Ketchup & 8 \\
\hline
\end{tabular}

What angle should the wedge for Ranch have?

A. [tex]$20^{\circ}$[/tex]
B. [tex]$72^{\circ}$[/tex]
C. [tex]$60^{\circ}$[/tex]
D. [tex]$14^{\circ}$[/tex]



Answer :

To determine the angle for the wedge representing ranch sauce in a circle graph, we need to follow these steps:

1. Understand Total and Specific Data:
- Total students surveyed: 70
- Students who prefer ranch: 14

2. Determine Proportion for Ranch:
The proportion of students who prefer ranch out of the total students is calculated as:
[tex]\[ \text{Proportion for Ranch} = \frac{\text{Number of Ranch Votes}}{\text{Total Students}} = \frac{14}{70} \][/tex]

3. Convert Proportion to an Angle:
Since a circle has [tex]\(360^{\circ}\)[/tex], we need to multiply the proportion by [tex]\(360^{\circ}\)[/tex] to get the angle:
[tex]\[ \text{Angle for Ranch} = \left(\frac{14}{70}\right) \times 360^{\circ} \][/tex]

4. Result:
Based on our calculation, the angle for the ranch wedge in the circle graph would be:
[tex]\[ \text{Angle for Ranch} = 72^{\circ} \][/tex]

Thus, the answer is:

B. [tex]\(72^{\circ}\)[/tex]