https://file.aiquickdraw.com/mathbot/file/1722658561787g0p07p9l.jpg

Let's analyze the latest image and solve the problem step-by-step.

From the new image, we have:

Ownership percentages:
- Fred's Graphite: 9.61%
- Jerry's: 4.49%
- Textron: 7.38%
- The Gompers Group: 14.72%

The question asks for the weighted average, given specific values.

1. **Determine the values associated with each company:**
   - Fred's Graphite: \(X_1 = 9.61\%\)
   - Jerry's: \(X_2 = 4.49\%\)
   - Textron: \(X_3 = 7.38\%\)
   - The Gompers Group: \(X_4 = 14.72\%\)

2. **Calculate the weighted average:**

\[
\text{Weighted Average} = \frac{(w_1 \times X_1) + (w_2 \times X_2) + (w_3 \times X_3) + (w_4 \times X_4)}{w_1 + w_2 + w_3 + w_4}
\]

Substituting the given values:

\[
\text{Weighted Average} = \frac{(9.61 \times 9.61) + (4.49 \times 4.49) + (7.38 \times 7.38) + (14.72 \times 14.72)}{9.61 + 4.49 + 7.38 + 14.72}
\]

3. **Perform the calculations:**

\[
\text{Numerator} = (9.61 \times 9.61) + (4.49 \times 4.49) + (7.38 \times 7.38) + (14.72 \times 14.72)
\]

Calculating each term separately:
\[
9.61 \times 9.61 = 92.3521
\]
\[
4.49 \times 4.49 = 20.1601
\]
\[
7.38 \times 7.38 = 54.4644
\]
\[
14.72 \times 14.72 = 216.6784
\]

Adding them together:
\[
\text{Numerator} = 92.3521 + 20.1601 + 54.4644 + 216.6784 = 383.655
\]

4. **Calculate the sum of the weights:**

\[
\text{Denominator} = 9.61 + 4.49 + 7.38 + 14.72 = 36.20
\]

5. **Calculate the weighted average:**

\[
\text{Weighted Average} = \frac{383.655}{36.20} \approx 10.59
\]

Thus, the weighted average based on the given percentages and values is approximately \(10.59\).

### Related Questions
1. What is a weighted average, and how does it differ from a simple average?
2. How can weighted averages be applied in real-life scenarios?
3. Why are weights important in calculations involving averages?
4. Can you provide another example of calculating a weighted average?
5. How would the weighted average change if the weights were different?
6. How do you interpret the result of a weighted average?
7. What are the common mistakes to avoid when calculating weighted averages?
8. How can software tools be used to calculate weighted averages efficiently?

**Tip**: Always ensure to double-check your calculations and the weights used to avoid errors in computing the weighted average.

Learn how to calculate the weighted average from ownership percentages using a detailed step-by-step solution. This problem involves calculating the weighted average based on specific ownership percentages of different companies. Suitable for advanced high school students and those interested in financial mathematics.

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