A bag contains 7 black socks, 12 white socks, and 17 red socks. If you pick one sock at random from the bag, what is the probability that it will NOT be white?

Solution
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:
\(Probability = \frac{Target \;\, Outcomes}{Total \;\, Outcomes} = \frac{24}{36} = \frac{2}{3}\)
In the following figure, line a and line b are parallel and pass through the points shown. What is the equation for line b?

Solution
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 yintercept of –3.
Plug these numbers into the slopeintercept form to get the equation:
y = mx + b
y = ^{5}⁄_{8}x  3
The ratio of adults to girls to boys on a class field trip was 1 : 4 : 5. If the trip included 6 more boys than girls, how many adults were with the group?

Solution
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:
\(\frac{g}{g + 6} = \frac{4}{5}\)
Crossmultiply 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.
Two variables, v and w,are inversely proportional such that when v = 7, w = 14. What is the value of w when v = 2?

Solution
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
In the following figure, what is the value of x in terms of y?

Solution
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:
a^{2} + b^{2} = c^{2}
y^{2} + (3y)^{2} = x^{2}
Simplify and solve for x in terms of y:
y^{2} + 9y^{2} = x^{2}
10y^{2} = x^{2}
\(\sqrt{10y^{2}} = x \Rightarrow y\sqrt{10} = x\)
If f(x) = x^{2} + 9 and g(x) = 24 + 4x,what is the value of \(\frac{f\left ( 4 \right )}{g\left ( 1 \right )}\)?

Solution
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:
\(\frac{f\left ( 4 \right )}{g\left ( 1 \right )} = \frac{25}{20} = 1.25\)
In the following figure, what is the midpoint of \(\overline{UV}\)?

Solution
Plug the values (–3, –7) and (1, 8) into the midpoint formula:
\(Midpoint = \left ( \frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2} \right )\) = \(\left ( \frac{3 + 1}{2} , \frac{7 + 8}{2} \right ) = \left ( 1 , \frac{1}{2} \right )\)
Two values of m satisfy the equation 5m – 11 – 3m = 9. What is the result when you multiply these two values together?

Solution
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.
What is the formula of a line that is perpendicular to y = ^{1}⁄_{3}x + 9 and includes the point (3, 4)?

Solution
Any line perpendicular to y = ^{1}⁄_{3}x + 9 has a slope of –3.
So you can rule out Choices (A), (B), and (C).
Plug this number into the slopeintercept form, along with the x and ycoordinates 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 yintercept of 13 into the slopeintercept form to get the formula of the line:
y = –3x + 13
If 15% of n is 300, what is 22% of n?

Solution
Write “15% of n is 300” as an equation:
0.15n = 300
Now solve for n:
\(n = \frac{300}{0.15} = 2000\)
Twentytwo percent of 2,000 is 440.