T = 5000 + 150000 x [(0.002 x 196 x (260.4 - 215) / 215)]

To solve the given expression for \( T \), we will follow these steps:

1. Calculate the value inside the brackets.
2. Multiply this value by 150,000.
3. Add 5,000 to the result.

The given expression is:

\[ T = 5000 + 150000 \times \left[0.002 \times 196 \times \frac{260.4 - 215}{215}\right] \]

Let's break it down step by step.

1. Calculate \( 260.4 - 215 \):
\[ 260.4 - 215 = 45.4 \]

2. Calculate the fraction:
\[ \frac{45.4}{215} \approx 0.2112 \]

3. Multiply the fraction by 196:
\[ 196 \times 0.2112 \approx 41.3952 \]

4. Multiply by 0.002:
\[ 0.002 \times 41.3952 \approx 0.0827904 \]

5. Multiply by 150000:
\[ 150000 \times 0.0827904 \approx 12418.56 \]

6. Add 5000:
\[ 5000 + 12418.56 = 17418.56 \]

Therefore, the value of \( T \) is approximately:
\[ T \approx 17418.56 \]

Would you like more details or have any questions? Here are some related questions you might want to explore:

1. How do you solve for variables in more complex algebraic expressions?
2. What are some common mistakes to avoid when simplifying mathematical expressions?
3. How do you convert fractions to decimal form accurately?
4. Can you explain the order of operations in detail?
5. What are some useful tips for checking your work in math problems?

**Tip:** When solving mathematical expressions, always follow the order of operations (PEMDAS/BODMAS) to avoid mistakes.

Learn how to solve the expression T = 5000 + 150000 * [(0.002 * 196 * (260.4 - 215) / 215)]. This problem involves arithmetic operations, fractions, and algebraic simplification. Suitable for students in Grades 9-12.

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