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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 honey mustard have?

Sagot :

GinnyAnswer
To find the angle for the wedge representing honey mustard on a circle graph, we need to determine what fraction of the total number of students prefer honey mustard and then convert this fraction into an angle.

Here is a step-by-step solution:

1. Calculate the Total Number of Students:
The total number of students is given as 70.

2. Determine the Number of Students Who Prefer Honey Mustard:
The number of students who prefer honey mustard is given as 10.

3. Compute the Fraction of Students Who Prefer Honey Mustard:
The fraction is calculated by dividing the number of students who prefer honey mustard by the total number of students:
[tex]\[ \text{Fraction of honey mustard} = \frac{10}{70} \][/tex]

4. Convert the Fraction to a Proportion of the Circle:
A circle graph totals 360 degrees. To find the angle corresponding to the honey mustard wedge, we multiply the fraction by 360 degrees:
[tex]\[ \text{Angle for honey mustard} = \left(\frac{10}{70}\right) \times 360^\circ \][/tex]

5. Simplify and Multiply:
Simplifying the fraction \(\left(\frac{10}{70}\right)\), we get:
[tex]\[ \frac{10}{70} = 0.14285714285714285 \][/tex]

Now, multiply this fraction by 360:
[tex]\[ 0.14285714285714285 \times 360^\circ = 51.42857142857142^\circ \][/tex]

So, the angle for the wedge representing students who prefer honey mustard should be \(51.43^\circ\) (rounded to two decimal places).

Thus, the wedge for honey mustard in the circle graph should have an angle of approximately [tex]\(51.43^\circ\)[/tex].
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