Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72. 

x + (x + 2) + (x + 4) = 72

3x + 6 = 72

3x = 66

x = 22.

This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728. 

The answer is 13728.

$\displaystyle \textup{Look for a pattern. Each term in the sequence is three times the previous term.}$

$\displaystyle 18\ast3=54$

Since we are given the mean, we need to find the sum of the numbers. From there we can figure out $\displaystyle x$. We know

$\displaystyle \text{mean}= \frac{\text{sum of observations}}{\text{number of observations}}$  

We can use this to find the sum by plugging in 

$\displaystyle 12=\frac{\text{Total Sum}}{8}$

So our sum is 96.

So we know that our total sum minus the sum of the given numbers is equal to $\displaystyle x$. 

So, $\displaystyle 96-(1+14+3+15+16+21+10) = x = 96-80 =16$.

2 men can be selected:

$\displaystyle C\binom{5}{2 } = 10$

2 women can be selected out of 4 women:

$\displaystyle C\binom{4}{2} = 6$

Finally, after the selection process, these men and women can fill the executive body in $\displaystyle 4!=24$ ways.

This gives us a total of $\displaystyle 10\times 6\times 24 = 1440$

This is a sequence that features every other positive, odd integers.  The missing number in this case is 9.  

Find the missing number:

$\displaystyle 7,-,33,46,59,72$

To find the missing number, we need to find the pattern.

If we look closely, our numbers are going up by the same number each time: 13

To check this, find the difference between neighboring numbers

$\displaystyle 46-33=13$

$\displaystyle 59-46=13$

You get the idea.

So, to find the missing number, simply do the following:

$\displaystyle 7+13=20$

You need to evaluate the terms in the sequence to determine the pattern that is shown. In this case, the first term is multiplied by 2 and the second term is found by adding 3.

$\displaystyle 6\times2=12$

$\displaystyle 12+3=15$

$\displaystyle 15\times2=30$

$\displaystyle 30+3=33$

$\displaystyle 33\times2=66$

$\displaystyle 66+3=n$

$\displaystyle n\times2=138$

Notice that the world parabolic is given.  This means that our parent function will be in the form:   $\displaystyle y=ax^2+bx+c$

The terms resemble a pattern where the parent function $\displaystyle y=x^2$ is centered at $\displaystyle (0,0)$, and the first term starts at $\displaystyle x=-2$ and so forth.

We can find the two missing terms by substituting $\displaystyle x=2,3$ to determine the missing numbers.

The first number is:

$\displaystyle y=2^2=4$

The second number is:  

$\displaystyle y=3^2=9$

The respective numbers are:  $\displaystyle 4,9$

Notice that the second and third terms in the set of numbers can be subtracted to determine the displacement of each number in the set.

Subtract negative three from one.  Enclose the negative number with parentheses.

$\displaystyle 1-(-3)=4$

Each number is spaced four units.

Subtract four from negative three to find the first number.

$\displaystyle -3-4 = -7$

Add four to one to find the number for the second question mark.

$\displaystyle 1+4=5$

This number is also four units from nine.

The answer is:  $\displaystyle -7,5$

Determine the distance between each number.

$\displaystyle \frac{1}{4}-\frac{1}{5} = \frac{5}{20}-\frac{4}{20}= \frac{1}{20}$

The second and the third number are spaced $\displaystyle \frac{1}{20}$ units.

Check the third and fourth number if this is also has the same displacement.

$\displaystyle \frac{1}{5}- \frac{3}{20} = \frac{4}{20}- \frac{3}{20}=\frac{1}{20}$

Since this is true, this means that the numbers are also spaced at $\displaystyle \frac{1}{20}$ units.

Notice the fractions are in decreasing order.

Add $\displaystyle \frac{1}{20}$ units to the second term to obtain the first term.

$\displaystyle \frac{1}{20}+\frac{1}{4} = \frac{1}{20}+\frac{5}{20} = \frac{6}{20}$

Reduce this fraction.

The first term is:  $\displaystyle \frac{3}{10}$

Subtract $\displaystyle \frac{1}{20}$ units from $\displaystyle \frac{3}{20}$ to obtain the fifth term.

$\displaystyle \frac{3}{20}- \frac{1}{20} = \frac{2}{20}$

Reduce this fraction.

The fifth term is:  $\displaystyle \frac{1}{10}$

The correct answer is:  $\displaystyle \frac{3}{10} , \frac{1}{10}$