Question

7 some of the items that sara sells are necklaces. can 60% of the items that sara sells be necklaces? explain. 8 sara surveys her friends and asks them to name their favorite item of jewelry. the circle graph shows the results. which type of jewelry do \\( \frac { 1 } { 2 } \\) of her friends like best? complete the equation: \\( \frac { 1 } { 2 } = \frac { } { 100 } \\) 9 about what percent of the friends sara surveyed choose each of the following as their favorite item of jewelry?

Explanation:

Step1: Analyze the circle - graph for question 7

A circle - graph represents \(100\%\) of the data. If necklaces were \(60\%\), then bracelets and rings together would be \(100 - 60=40\%\). But from the circle - graph (visually, if we assume it's divided into three parts, and if one part is \(60\%\), it doesn't match the typical division of a circle - graph for three items. Also, if we consider the proportion of a circle (a full circle is \(360^{\circ}\)), \(60\%\) of \(360^{\circ}=0.6\times360 = 216^{\circ}\), and the remaining \(40\%\) (\(0.4\times360 = 144^{\circ}\)) for two items. But usually, if there are three items (necklace, bracelet, ring) in a non - trivial way (not just two items), the division is more even - like each part is less than \(50\%\) (if we assume a more balanced survey result for three types of jewelry).

Step2: Solve for question 8

For the fraction \(\frac{1}{2}\), we use the formula \(\frac{a}{b}=\frac{x}{100}\), where \(a = 1\), \(b = 2\). Cross - multiply: \(2x=1\times100\), so \(x = 50\). A circle - graph: half of a circle (\(180^{\circ}\)) is not represented by necklace (which is less than half, if we assume a non - skewed graph for three items). But if we just consider the fraction \(\frac{1}{2}=\frac{50}{100}\)

Answer:

1. No. A circle - graph represents \(100\%\) of the data. If necklaces were \(60\%\), the sum of the percentages of the other two items (bracelets and rings) would be \(40\%\), which does not match the visual and logical division of a circle - graph for three non - trivial items (usually each part for three items is less than \(50\%\) in a more balanced survey).
2. \(\frac{1}{2}=\frac{50}{100}\)