Question

the table below shows the percentage of male and female populations in a certain country employed in the civilian work force in selected years from 1970 to 2005. algebraically, the linear model for the female data is ( y_1 = 0.547x + 27.9 ) and the linear model for the male data is ( y_2 = - 0.610x + 82.1 ), where the 1970 and 2000 ordered pairs are used to compute the slopes. if the percentages continue to follow the linear models, at what point will the lines intersect? what is the significance of the intersection point in terms of employment participation?

the lines will intersect at the point (square).
(type an ordered pair. round to the nearest tenth as needed.)

what is the significance of the intersection point in terms of employment participation? select the correct choice below and fill in the answer box to complete your choice.

a. the linear models suggest that, at the intersection point, female and male participation rates will be different in the year (square)
(round down to the nearest year.)

b. the linear models suggest that, at the intersection point, female and male participation rates will be the same in the year (square)
(round down to the nearest year.)

Explanation:

Step1: Set the two equations equal

Set \(y_1 = y_2\), so \(0.547x+27.9=- 0.610x + 82.1\).

Step2: Solve for \(x\)

Add \(0.610x\) to both sides: \(0.547x+0.610x+27.9=-0.610x + 0.610x+82.1\), which gives \(1.157x+27.9 = 82.1\).
Subtract \(27.9\) from both sides: \(1.157x+27.9 - 27.9=82.1 - 27.9\), so \(1.157x=54.2\).
Divide both sides by \(1.157\): \(x=\frac{54.2}{1.157}\approx46.9\).

Step3: Find \(y\)

Substitute \(x = 46.9\) into \(y_1=0.547x + 27.9\).
\(y=0.547\times46.9+27.9\approx0.547\times47+27.9 = 25.709+27.9=53.609\approx53.6\).

Answer:

The lines will intersect at the point \((46.9,53.6)\).
For the significance:
The linear models suggest that, at the intersection point, female and male participation rates will be the same in the year \(1970 + 46.9\approx2017\). So the answer is B. The linear models suggest that, at the intersection point, female and male participation rates will be the same in the year \(2017\).