https://file.aiquickdraw.com/mathbot/file/1726083073750gfyv6xey.jpg

The given summation problem is:

\[
7 \sum_{t=4}^{9} (t - 4)
\]

### Step-by-step solution:

1. **Identify the expression inside the summation:**  
   The expression being summed is \( (t - 4) \), where \( t \) runs from 4 to 9.

2. **Write out the values of \( t - 4 \) for each \( t \) from 4 to 9:**
   \[
   t = 4: \quad (4 - 4) = 0
   \]
   \[
   t = 5: \quad (5 - 4) = 1
   \]
   \[
   t = 6: \quad (6 - 4) = 2
   \]
   \[
   t = 7: \quad (7 - 4) = 3
   \]
   \[
   t = 8: \quad (8 - 4) = 4
   \]
   \[
   t = 9: \quad (9 - 4) = 5
   \]

3. **Sum these values:**
   \[
   0 + 1 + 2 + 3 + 4 + 5 = 15
   \]

4. **Multiply by 7 (the factor outside the summation):**
   \[
   7 \times 15 = 105
   \]

### Final Answer:
\[
\boxed{105}
\]

Would you like more details on any part of this solution, or do you have any questions?

### Related questions:
1. How do you evaluate more complex summations with variables?
2. How can summation notation be used in calculus?
3. What are some common mistakes to avoid in summation problems?
4. How do you simplify summations with products inside?
5. What are some examples of summation properties (e.g., distributive property)?

**Tip:** Always simplify the expression inside the summation before calculating individual terms!

Evaluate the summation below: 7 * Σ (t - 4) from t = 4 to 9

Learn how to evaluate the summation 7 * Σ (t - 4) from t = 4 to 9 with a detailed step-by-step solution. This problem covers key mathematical concepts including summation and arithmetic sequences, making it suitable for students in Grades 8-10.

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