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].
