Given t is a transversal crossing parallel line m and n, m a. 60° b. 160° c. 100° d. 40° e. 140°

The number of female faculty in the Department with a PhD is 8.

Step-by-step explanation:

There are 14 + 30 = 44 faculty members.

Of those, x are male and y are female.

Then

x + y = 44.

The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.

y = z + w

z is the number of females with PhD.

w is the number of females without PhD.

w = z + 10

If a third of the male faculty in the Department have a PhD

Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.

The objective is:

To find z from the first equation, that is:

To do this, we have to write x and y as functions of z.

Writing x and y as functions z.

And

In which

So

Replacing:

The number of female faculty in the Department with a PhD is 8.