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The image appears to show a problem involving the calculation of a proportional relationship based on data from a table.

### Problem Breakdown:
- **Table Information:**
  - **Games Played (x):** 10, 15, 20, 25, 30
  - **Games Won (y):** 4, 10, 12, 15, 25

- **Question:**
  - You're asked to fill in the blank regarding the expected number of games won if a player participates in a certain number of games.

### Approach:
1. **Find the Ratio:** The problem may require calculating the ratio of games won to games played.
   - The ratio \( r = \frac{y}{x} \).
   - Calculate this ratio for each pair (x, y) in the table.

2. **Determine the Proportionality:** 
   - Check if the ratio remains consistent across the different data points.
   - If consistent, this indicates a direct proportional relationship between the number of games played and won.

3. **Linear Prediction:** 
   - If proportional, the number of games won can be predicted using the linear equation \( y = r \times x \).

Would you like to go ahead with this method to calculate the expected number of games won or provide further details on how to approach similar problems?

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**Relative Questions:**
1. How do you find if two variables have a proportional relationship?
2. What is the significance of finding a ratio in problems like this?
3. How can you predict outcomes using a linear relationship?
4. Why is it important to check the consistency of the ratio in the table?
5. What would be the next step if the ratio is not consistent?

**Tip:** When analyzing proportional relationships, ensure the ratio between corresponding quantities remains constant across all data points.

Select the correct answer from each drop-down menu. The table shows the number of games played by a player and the corresponding number of games won based on the number of games played.

Learn how to calculate the proportional relationship between the number of games played and the number of games won using a linear relationship. This problem covers key mathematical concepts such as proportionality, ratios, and the use of linear equations to predict outcomes.

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