1. Problem 5: Given that a sector measures 54° and 75 people chose tulips as their favorite flower, find the total number of people. 2. To solve this, we use the formula relating the sector angle to the total number of people: $$\frac{\text{sector angle}}{360^\circ} = \frac{\text{number of people for tulips}}{\text{total number of people}}$$ 3. Substitute the known values: $$\frac{54}{360} = \frac{75}{x}$$ 4. Cross-multiply to solve for $x$: $$54x = 360 \times 75$$ 5. Simplify the right side: $$54x = 27000$$ 6. Divide both sides by 54: $$x = \frac{27000}{54}$$ 7. Show cancellation: $$x = \frac{\cancel{27000}^{500} \times 54}{\cancel{54}} = 500$$ 8. So, the total number of people is $500$. 1. Problem 6: The sales in March were double the sales in May. The central angle for March is 47.5°. Find the percent of sales in May. 2. Let the sales in May be $M$, then sales in March are $2M$. 3. The total sales are $M + 2M = 3M$. 4. The central angle for March corresponds to $2M$ sales, so: $$\frac{47.5^\circ}{360^\circ} = \frac{2M}{3M} = \frac{2}{3}$$ 5. Check the ratio: $$\frac{47.5}{360} \approx 0.1319$$ but $$\frac{2}{3} \approx 0.6667$$, so the given angle does not match the ratio directly. 6. Instead, find the total central angle for all sales: Since March is double May, total angle is $\theta_{May} + \theta_{March} = 360^\circ$. 7. Let $\theta_{May} = x$, then $\theta_{March} = 2x$. 8. So: $$x + 2x = 360^\circ$$ $$3x = 360^\circ$$ $$x = 120^\circ$$ 9. But March angle is given as 47.5°, so this contradicts the assumption. 10. Instead, use the given March angle 47.5° to find May angle: $$\theta_{May} = \frac{1}{2} \times 47.5^\circ = 23.75^\circ$$ 11. Total angle: $$47.5^\circ + 23.75^\circ = 71.25^\circ$$ 12. This is less than 360°, so the rest of the circle represents other sales. 13. To find the percent of sales in May relative to total sales (March + May only), use: $$\text{Percent May} = \frac{23.75^\circ}{47.5^\circ + 23.75^\circ} \times 100 = \frac{23.75}{71.25} \times 100 \approx 33.33\%$$ 1. Problem 7: Is the statement "You can construct a circle graph without using percents" true or false? 2. Explanation: - Circle graphs represent parts of a whole, usually expressed as percents or fractions. - While percents are common, you can use fractions or degrees directly to construct a circle graph. - For example, if you know the fraction of each category, you can convert it to degrees by multiplying by 360. 3. Therefore, the statement is true because percents are not strictly necessary; fractions or degrees can be used instead. Final answers: Problem 5: Total number of people is $500$. Problem 6: Percent of sales in May is approximately $33.33\%$. Problem 7: The statement is true.