The bag contains a total of 7 + 12 + 17 = 36 socks.

Of these, 7 + 17 = 24 are NOT white.

Plug these two numbers (the number of colored socks and the total number of socks) into the formula for probability:

\(Probability = \frac{Target \;\, Outcomes}{Total \;\, Outcomes} = \frac{24}{36} = \frac{2}{3}\)

Line agoes “down 5, over 8,” so its slope is -⁵⁄₈ Line b is parallel, so it has the same slope and has a y-intercept of –3.

Plug these numbers into the slope-intercept form to get the equation:

y = mx + b

y = -⁵⁄₈x - 3

The ratio of girls to boys was 4 to 5, so write the ratio like this:

\(\frac{Girls}{Boys} = \frac{4}{5}\)

If you let g equal the number of girls on the trip, you know that the number of boys was g + 6.

Plug these values into the ratio:

\(\frac{g}{g + 6} = \frac{4}{5}\)

Cross-multiply and solve for g:

5g = 4(g + 6)

5g = 4g + 24

g = 24

So now you know that 24 girls went on the field trip, and you’re ready to find the number of adults.

The ratio of adults to girls was 1 : 4.

That is, the number of adults was ¹⁄₄ the number of girls, so you know that 6 adults attended the field trip.

The variables v and w are inversely proportional, so for some constant k,the equation vw = k is always true.

Thus, when v = 7 and w = 14:

vw = (7)(14) = 98

So k = 98.

When v = 2, you can find w like this:

vw = 98

2w = 98

w = 49

The two legs of the triangle are of lengths y and 3y, and the hypotenuse is of length y.

Plug these values into the Pythagorean theorem:

a² + b² = c²

y² + (3y)² = x²

Simplify and solve for x in terms of y:

y² + 9y² = x²

10y² = x²

\(\sqrt{10y^{2}} = x \Rightarrow y\sqrt{10} = x\)

To start, find the values of f(4) and g(–1):

f(4) = 42 + 9 = 16 + 9 = 25

g(–1) = 24 + 4(–1) = 24 – 4 = 20

Thus:

\(\frac{f\left ( 4 \right )}{g\left ( -1 \right )} = \frac{25}{20} = 1.25\)

Plug the values (–3, –7) and (1, 8) into the midpoint formula:

\(Midpoint = \left ( \frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2} \right )\) = \(\left ( \frac{-3 + 1}{2} , \frac{-7 + 8}{2} \right ) = \left ( -1 , \frac{1}{2} \right )\)

To begin, isolate the absolute value on one side of the equation:

|5m – 11| – 3m = 9

|5m – 11| = 9 + 3m

Next, split the equation into two separate equations and remove the absolute value bars:

5m – 11 = 9 + 3m ; 5m – 11 = –(9 + 3m)

Solve both equations for m:

5m = 20 + 3m ; 5m – 11 = –9 – 3m

2m = 20 ; 5m = 2 – 3m

m = 10 ; 8m = 2

m = 0.25

The product of these two values is 10 × 0.25 = 2.5.

Any line perpendicular to y = ¹⁄₃x + 9 has a slope of –3.

So you can rule out Choices (A), (B), and (C).

Plug this number into the slope-intercept form, along with the x- and y-coordinates for the point (3, 4):

y = mx + b

4 = –3(3) + b

4 = –9 + b

13 = b

Now plug the slope m = –3 and the y-intercept of 13 into the slope-intercept form to get the formula of the line:

y = –3x + 13

Write “15% of n is 300” as an equation:

0.15n = 300

Now solve for n:

\(n = \frac{300}{0.15} = 2000\)

Twenty-two percent of 2,000 is 440.