1. **Problem 1: Calculate the mean height of all 50 members of the basketball club.** 2. We have two groups: - Juniors: 30 members, mean height 1.6 m - Seniors: 20 members, mean height 2.05 m 3. The formula for the combined mean height is: $$\text{Mean height} = \frac{(\text{number}_1 \times \text{mean}_1) + (\text{number}_2 \times \text{mean}_2)}{\text{total number}}$$ 4. Substitute the values: $$\text{Mean height} = \frac{(30 \times 1.6) + (20 \times 2.05)}{30 + 20}$$ 5. Calculate the numerator: $$30 \times 1.6 = 48$$ $$20 \times 2.05 = 41$$ So, $$\text{Mean height} = \frac{48 + 41}{50} = \frac{89}{50}$$ 6. Simplify the fraction: $$\frac{89}{50} = 1.78$$ 7. **Answer:** The mean height of all 50 members is **1.78 m**. --- 1. **Problem 2: Calculate the cost of a phone screen given the tablet screen area and cost per square metre.** 2. Given: - Tablet screen area = 420 cm² - Tablet height = 15 cm - Phone height = 6 cm - Cost per square metre = 7000 3. First, find the scale factor for the areas based on heights, assuming similar rectangles: $$\text{Scale factor for height} = \frac{6}{15} = \frac{2}{5}$$ 4. Area scales with the square of the scale factor: $$\text{Scale factor for area} = \left(\frac{2}{5}\right)^2 = \frac{4}{25}$$ 5. Calculate the phone screen area: $$\text{Phone area} = 420 \times \frac{4}{25} = \frac{1680}{25} = 67.2 \text{ cm}^2$$ 6. Convert phone area from cm² to m²: $$67.2 \text{ cm}^2 = 67.2 \times 10^{-4} = 0.00672 \text{ m}^2$$ 7. Calculate the cost: $$\text{Cost} = 0.00672 \times 7000 = 47.04$$ 8. **Answer:** The cost of the phone screen is **47.04** (currency units).