1. Problem 9: Calculate the percentage of votes and pie chart angles for each sport. Total students = 120 Formula for percentage: $$\text{Percentage} = \frac{\text{Number of students for sport}}{\text{Total students}} \times 100$$ Formula for pie chart angle: $$\text{Angle} = \frac{\text{Number of students for sport}}{\text{Total students}} \times 360^\circ$$ Calculations: - Football: $$\frac{60}{120} \times 100 = 50\%$$ and $$\frac{60}{120} \times 360^\circ = 180^\circ$$ - Basketball: $$\frac{30}{120} \times 100 = 25\%$$ and $$\frac{30}{120} \times 360^\circ = 90^\circ$$ - Volleyball: $$\frac{20}{120} \times 100 = 16.67\%$$ and $$\frac{20}{120} \times 360^\circ = 60^\circ$$ - Tennis: $$\frac{10}{120} \times 100 = 8.33\%$$ and $$\frac{10}{120} \times 360^\circ = 30^\circ$$ 2. Problem 10: Find the month when gym membership reaches 110. Given: - Initial members $$M_0 = 30$$ - Monthly increase $$r = 8$$ - Members at month $$n$$: $$M_n = M_0 + r(n-1)$$ Set $$M_n = 110$$: $$110 = 30 + 8(n-1)$$ $$110 - 30 = 8(n-1)$$ $$80 = 8(n-1)$$ $$\cancel{8} \times 10 = \cancel{8}(n-1)$$ $$10 = n - 1$$ $$n = 11$$ So, the gym reaches 110 members in the 11th month. 3. Problem 11: Find the monthly growth rate of enrolments. Given: - Enrolments at month 1: $$E_1 = 150$$ - Enrolments at month 5: $$E_5 = 2430$$ Assuming constant monthly increase $$r$$: $$E_n = E_1 + r(n-1)$$ Set $$n=5$$: $$2430 = 150 + r(5-1)$$ $$2430 - 150 = 4r$$ $$2280 = 4r$$ $$\cancel{4} \times 570 = \cancel{4} r$$ $$r = 570$$ The growth rate is 570 enrolments per month.