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A student is constructing a circle graph for the set of data and rounding to the nearest degree as necessary. Find the number of degrees of the central angle for Potato.




Preferred Vegetable


Vegetable



Number of


Students






Beans
36


Carrots
24


Peas
18


Potato
22




degrees

A student is constructing a circle graph for the set of data and rounding to the nearest degree as necessary. Find the number of degrees of the central angle for Potato.\newline\begin{tabular}{|l|c|}\newline\hline \multicolumn{22}{|c|}{ Preferred Vegetable } \\\newline\hline \multicolumn{11}{|c|}{ Vegetable } & \begin{tabular}{c} \newlineNumber of \\\newlineStudents\newline\end{tabular} \\\newline\hline Beans & 3636 \\\newline\hline Carrots & 2424 \\\newline\hline Peas & 1818 \\\newline\hline Potato & 2222 \\\newline\hline\newline\end{tabular}\newlinedegrees

Full solution

Q. A student is constructing a circle graph for the set of data and rounding to the nearest degree as necessary. Find the number of degrees of the central angle for Potato.\newline\begin{tabular}{|l|c|}\newline\hline \multicolumn{22}{|c|}{ Preferred Vegetable } \\\newline\hline \multicolumn{11}{|c|}{ Vegetable } & \begin{tabular}{c} \newlineNumber of \\\newlineStudents\newline\end{tabular} \\\newline\hline Beans & 3636 \\\newline\hline Carrots & 2424 \\\newline\hline Peas & 1818 \\\newline\hline Potato & 2222 \\\newline\hline\newline\end{tabular}\newlinedegrees
  1. Calculate Total Students: Calculate the total number of students. Add the number of students who prefer each vegetable to find the total. Total number of students = Beans + Carrots + Peas + Potato Total number of students = 36+24+18+2236 + 24 + 18 + 22 Total number of students = 100100
  2. Determine Potato Proportion: Determine the proportion of students who prefer Potato.\newlineSince the total number of students is 100100, the proportion for Potato is the same as its percentage.\newlineProportion of Potato = Number of students who prefer PotatoTotal number of students\frac{\text{Number of students who prefer Potato}}{\text{Total number of students}}\newlineProportion of Potato = 22100\frac{22}{100}\newlineProportion of Potato = 0.220.22
  3. Calculate Central Angle: Calculate the number of degrees of the central angle for Potato.\newlineSince a circle has 360360 degrees, the central angle for Potato can be found by multiplying the proportion by 360360.\newlineDegrees for Potato =Proportion of Potato×Total degrees in a circle= \text{Proportion of Potato} \times \text{Total degrees in a circle}\newlineDegrees for Potato =0.22×360= 0.22 \times 360\newlineDegrees for Potato =79.2= 79.2 degrees
  4. Round Degrees: Round the number of degrees to the nearest degree as necessary.\newlineThe number 79.279.2 is closest to 7979 when rounded to the nearest whole number.\newlineDegrees for Potato (rounded) = 7979 degrees

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