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To help with the questions provided in the image, let's break them down one by one and work through them.

### Question 1: 
**Find the linear function \( y = f(x) \) that models the number of employed males as a function of the number of years after 1940.**

We can choose two data points to calculate the slope of the linear model.

Let's use the years 1948 and 2013 (years since 1940: 8 and 73), with the corresponding male employee numbers: 47.370 million and 108.706 million.

The linear equation is of the form:
\[
y = mx + b
\]

1. **Slope Calculation (m):**
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{108.706 - 47.370}{73 - 8} = \frac{61.336}{65} \approx 0.9437
\]

2. **Find the y-intercept (b):**
Using the point \( (8, 47.370) \), substitute into the equation:
\[
47.370 = 0.9437(8) + b
\]
\[
b \approx 47.370 - 7.5496 \approx 39.820
\]

Thus, the linear model for male employment is:
\[
y = 0.9437x + 39.820
\]
where \( x \) is the number of years after 1940.

---

### Question 2:
**Find the quadratic function \( y = g(x) \) that models the number of employed females as a function of the number of years after 1940.**

For this, you need three points. Using the data for 1948, 1980, and 2013, we can set up a quadratic model.

Let’s take the points (8, 22.725), (40, 80.826), and (73, 109.956) to fit a quadratic function of the form:
\[
y = ax^2 + bx + c
\]
We’ll solve the system of equations formed by these three points to find the coefficients \( a \), \( b \), and \( c \).

---

### Question 3:
**Graph the unrounded functions \( y = f(x) \) and \( y = g(x) \) and graphically find when the number of female employees reaches the number of male employees.**

Plotting the functions \( f(x) \) and \( g(x) \) would require generating graphs. You can use graphing tools to plot the two functions and see where they intersect.

---

### Question 4:
**When do these models predict that the number of male employees will again exceed the number of female employees?**

After graphing, find where \( f(x) = g(x) \), which will give the approximate year.

---

### Question 5:
**Calculate the female-to-male earnings ratio for each of the given years.**

The ratio is given by:
\[
\text{Ratio} = \frac{\text{Female Earnings}}{\text{Male Earnings}}
\]

For example, in 1948:
\[
\text{Ratio} = \frac{8523}{20239} \approx 0.421
\]
Repeat this for each year in the table.

---

Would you like to proceed with any specific calculations or explanations from these questions?

### Relative Questions:
1. How would changes in the workforce or population impact the models created?
2. How accurate would a linear model be over a long period, considering population growth?
3. Could there be other factors influencing the employment rates that these models don't account for?
4. What do the trends suggest about the workforce's gender composition over time?
5. What factors besides gender discrimination might explain the persistent earnings gap?

**Tip:** When creating models, always validate them with real-world data to check if the assumptions hold over time.

The table gives numbers of male and female employees in millions in the U.S. and median earnings for selected years from 1940 through 2013. You are asked to model employment trends and earnings gaps using linear and quadratic functions, calculate the female-to-male earnings ratio, and analyze factors influencing wage equality.

Learn how to model U.S. male and female workforce employment trends from 1948 to 2013 using linear and quadratic functions. Analyze the earnings gap by calculating the female-to-male earnings ratio. Understand when female employment will match male employment, and investigate factors behind wage inequality.

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