1. **State the problem:** We have a spinner spun 100 times. The frequency of red is 35, and the ratio of black to red frequencies is 2:7. We need to find the estimated probability of landing on yellow as a decimal. 2. **Identify known values:** - Total spins: $100$ - Red frequency: $35$ - Ratio black:red = $2:7$ 3. **Find black frequency:** Since red frequency corresponds to 7 parts, black corresponds to 2 parts. Let the common factor be $x$. $$\text{Black frequency} = 2x, \quad \text{Red frequency} = 7x$$ Given red frequency is 35, so: $$7x = 35 \implies x = \frac{35}{7} = 5$$ Therefore, $$\text{Black frequency} = 2 \times 5 = 10$$ 4. **Find yellow frequency:** Total spins = black + red + yellow $$100 = 10 + 35 + \text{yellow}$$ $$\text{yellow} = 100 - 45 = 55$$ 5. **Calculate estimated probability of yellow:** $$P(\text{yellow}) = \frac{\text{yellow frequency}}{\text{total spins}} = \frac{55}{100} = 0.55$$ **Final answer:** The estimated probability of landing on yellow is **0.55**.