1. **State the problem:** We have a biased spinner with 5 colors: pink, green, red, yellow, and blue. 2. **Given probabilities:** - Pink: 0.14 - Green: 0.23 - Red: 2x - Yellow: 0.18 - Blue: 7x 3. **Total probability rule:** The sum of all probabilities must equal 1. $$0.14 + 0.23 + 2x + 0.18 + 7x = 1$$ 4. **Combine like terms:** $$0.14 + 0.23 + 0.18 + 2x + 7x = 1$$ $$0.55 + 9x = 1$$ 5. **Solve for $x$:** $$9x = 1 - 0.55$$ $$9x = 0.45$$ $$x = \frac{0.45}{9}$$ $$x = 0.05$$ 6. **Find the probability of blue:** $$P(blue) = 7x = 7 \times 0.05 = 0.35$$ 7. **Expected number of times blue lands in 500 spins:** $$\text{Expected} = 500 \times 0.35 = 175$$ **Final answer:** The spinner is expected to land on blue 175 times out of 500 spins.