Given the values:
- \( f = 0.042404 \)
- \( m = 1.45 \)
- \( g = 4409.35 \)

We can use the formula derived earlier to calculate \( z \):
\[
z = \frac{g \times 100}{f \times (100 - m)}
\]

Substitute the given values into the formula:
\[
z = \frac{4409.35 \times 100}{0.042404 \times (100 - 1.45)}
\]

First, calculate the denominator:
\[
100 - 1.45 = 98.55
\]
\[
0.042404 \times 98.55 = 4.1792262
\]

Now, calculate the numerator:
\[
4409.35 \times 100 = 440935
\]

Finally, divide the numerator by the denominator:
\[
z = \frac{440935}{4.1792262} \approx 105472.4
\]

So, the value of \( z \) is approximately \( 105472.4 \).

Would you like further details or have any questions?

Here are some related questions that might interest you:

1. How does the value of \( z \) change if \( f \) is slightly increased or decreased?
2. What is the significance of the value \( z \) in a practical context?
3. Can you derive a similar formula if \( m \) is a function of \( z \) instead?
4. What steps can you take to ensure the accuracy of these calculations in a different scenario?
5. How would rounding off the values of \( f \), \( m \), and \( g \) affect the result?
6. Can you use logarithms to simplify any part of this equation?
7. What mathematical principles underlie the steps taken to isolate \( z \)?
8. How can you verify the calculated value of \( z \) through a different method?

**Tip:** When working with decimals in calculations, maintain precision by using as many significant digits as possible until the final result.

Learn how to calculate the value of z using mathematical modeling principles with a detailed step-by-step solution. This problem involves linear equations and is suitable for graduate-level study.

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