The number of students who don't have a learning disability is:

\(\displaystyle 30-10 =20\)

Using part over whole we get the percentage of students who don't have a learning disability as:

\(\displaystyle \frac{20}{30}=\frac{2}{3}\)

The value of the stock after the first year is 90% (0.9) of the value of the stock at time 0.

The value of the stock after the second year is 125% (1.25) of the value of the stock at the end of the first year.

The value of the investment today is:

\(\displaystyle 1000\times(1-0.1)\times(1-0.25)=1000\times0.9\times1.25\)

\(\displaystyle =900\times1.25 = 900+\frac{900}{4}= 900+225 =1125\)

Let \(\displaystyle x\) be Rob's salary.

Then, since Tim's salary is 10% less than Rob's salary, we can write Tim's salary as \(\displaystyle 0.9x\).

Since Peggy's salary is 20% less than Tim's salary, we can write Peggy's salary as \(\displaystyle 0.8(0.9x)=0.72x\).

Peggy's salary is 72% of Rob's salary as we can write:

Peggy salary/ Rob salary = \(\displaystyle 0.72x/x =0.72\)

Making the answer into a percent we get,

\(\displaystyle 0.72 \times 100=72\%\).

The number of accountants at the end of last year is:

\(\displaystyle 10000\times0.1=1000\)

The number of accountants at the end of this year is:

\(\displaystyle 9500\times0.06=570\)

The approximate change in the number of accountants from the end of last year to the end of this year is:

\(\displaystyle \frac{570-1000}{1000}=-0.43\)

There was a 43% decrease in the number of accountants over this period.

The number of students who did not vote is:

\(\displaystyle 48-14-12-16=6\)

The percent of students who did not vote is therefore:

\(\displaystyle \frac{6}{48}=\frac{1}{8}=0.125\)

\(\displaystyle 12.5\%\) of the students did not vote.

\(\displaystyle Y\)  is \(\displaystyle 40\%\) of \(\displaystyle Z\), so \(\displaystyle Y = 0.40 Z = \frac{2}{5}Z\).

\(\displaystyle X\) is \(\displaystyle 20\%\) of \(\displaystyle Y\), so \(\displaystyle X = 0.20 Y = \frac{1}{5}Y = \frac{1}{5} \cdot \frac{2}{5} Z = \frac{2}{25} Z\).

For \(\displaystyle X\) to be an integer, \(\displaystyle Z\) must be a multiple of \(\displaystyle 25\). Therefore, the smallest positive integer value of \(\displaystyle Z\) is \(\displaystyle 25\) itself; \(\displaystyle Y\) is \(\displaystyle 40\%\) of \(\displaystyle 25\) is \(\displaystyle 0.40 \cdot 25 = 10\), and \(\displaystyle X\) is \(\displaystyle 20\%\) of \(\displaystyle 10\), or \(\displaystyle 0.20 \cdot 10= 2\).

Add these to get

\(\displaystyle X+Y+Z = 2 + 10 + 25 = 37\)

The correct response is thus "From 31 to 40 inclusive."

\(\displaystyle A\) is \(\displaystyle 24\%\) of \(\displaystyle B\) and \(\displaystyle 72\%\) of \(\displaystyle C\), so

\(\displaystyle A = 0.24 B = \frac{6}{25}B\) and \(\displaystyle A = 0.72 C = \frac{18}{25}C\).

Equivalently, \(\displaystyle B = \frac{25}{6}A\) and \(\displaystyle C = \frac{25}{18}A\)

\(\displaystyle A\) must be the least possible number divisible by both \(\displaystyle 6\) and \(\displaystyle 18\), so 

\(\displaystyle A = LCM (6, 18) = 18\).

If \(\displaystyle M\) is \(\displaystyle 84\%\) of \(\displaystyle N\), then \(\displaystyle M = \frac{84}{100}N = \frac{21}{25}N\).

Equivalently,

\(\displaystyle \frac{25}{21} \cdot \frac{21}{25}N = \frac{25}{21} \cdot M\)

\(\displaystyle N = \frac{25M}{21}\)

The percentage of women who have an income greater than \(\displaystyle \$50,000\) in the sample is simply the product of the percentage of women in the sample and the percentage of these women who earn more than \(\displaystyle \$50,000\).

\(\displaystyle 0.6\times 0.3=0.18\)

The percentage of women who earn more than \(\displaystyle \$50,000\) in the sample is \(\displaystyle 18\%\).

Or, we could assume there are \(\displaystyle 100\) people in the sample. The number of women in the sample would then be \(\displaystyle 100\cdot0.6=60\). And the number of women who earn more than \(\displaystyle 50,000\) in the sample would be \(\displaystyle 60 \cdot 0.3=18\).

The percentage of women who earn more than \(\displaystyle \$50,000\) in the sample is \(\displaystyle \frac{18}{100}=18\%\).

Let's verify this answer by taking another sample size, let's say there are \(\displaystyle 150\) people in the sample.

The number of women who earn more than \(\displaystyle \$50,000\) in the sample would then be \(\displaystyle 150 \cdot 0.6 \cdot 0.3=90 \cdot 0.3=27\).

The percentage of women who earn more than \(\displaystyle \$50,000\) in the sample is \(\displaystyle \frac{27}{150}=18%\).

We still get the same result because the number of people in the sample is not necessary to find that percentage since we are given the percentage of women in the sample and the percentage of these women in the sample who earn more than \(\displaystyle \$50,000\).

Assume there are \(\displaystyle 100\) adults in the city. \(\displaystyle 40\%\) of these adults are unemployed, which means the number of unemployed adults is \(\displaystyle 40\) given there are \(\displaystyle 100\) adults. Also, \(\displaystyle 24\%\) of the adults in the city are unemployed women, so the number of unemployed adult women in the city is \(\displaystyle 24\). We can then find the number of unemployed adult men in that city, which is \(\displaystyle 40-24=16\).

At this point, we can calculate the percentage of unemployed adults in the city who are men: \(\displaystyle \frac{16}{40}\cdot100= \frac{2}{5}\cdot100=\frac{40}{100}=40\%\)

\(\displaystyle 40\%\) of the unemployed adults in that city are men.