\(\displaystyle (1, 5, 9, 13, 17, 21)\)

The numbers in the set are all odd, meaning that they are not divisble by 2.

While the numbers in the set increase by 4 sequentially, they are not divisible by 4, and therefore are not multiples of 4. 

Thus, the best answer is that they are all odd. 

Additionally, the numbers are not prime because 9 and 21 are both divisible by 3. 

Given that Jill's class starts at 8:00 and that it takes her 15 minutes to walk there, she must leave at 7:45. Since she woke up an hour before class starts, at 7 am, this means that she must leave in 45 minutes. Therefore, the correct answer is:

She must leave in 45 minutes in order to leave at 7:45. 

To find the total number of cookies, add each person's cookies together.

\(\displaystyle 17+6+13=36\)

\(\displaystyle 2y = 30\)

To solve, you will need to get \(\displaystyle y\) alone on the left side of the equation. Do this by dividing both sides by 2.

\(\displaystyle \frac{2y}{2}=\frac{30}{2}\)

The left side cancels.

\(\displaystyle y=\frac{30}{2}\)

Reduce the right side.

\(\displaystyle y=15\)

To simplify, you must rearrange the expression to group like-terms together.

\(\displaystyle 7x+4-4x+3\)

\(\displaystyle 7x-4x+4+3\)

Like-terms can be simplified.

\(\displaystyle 7x-4x=3x\)

\(\displaystyle 4+3=7\)

\(\displaystyle 7x-4x+4+3=3x+7\)

This results in \(\displaystyle 3x+7\), which is the correct answer. 

The average consists of the sum of the number of students tutored for the  6 days, divided by 6. Thus, the average would be calculated with this equation:

\(\displaystyle \frac{\text{total students}}{\text{total days}}\)

\(\displaystyle \frac{3+3+3+5+5+5}{6}\)

\(\displaystyle \frac{24}{6}\)

This is equal to \(\displaystyle 4\).

If 15 students like both the mountains and the beach and 10 like the mountains only that means that the total numbers of students who like mountains will be the sum of these two numbers.

\(\displaystyle 10+15=25\)

The sum is 25, which is the number of students who like mountains. 

To simplify, the first step is to reorder the terms and add the like variables together.

\(\displaystyle 7n+4-2+5n\)

\(\displaystyle 7n+5n+4-2\)

\(\displaystyle (7n+5n)+(4-2)\)

\(\displaystyle 12n+2\)

This gives us \(\displaystyle 12n+2\), which is therefore the correct answer. 

In Mrs. Kermit's painting class, there are three 7-year-olds and two 6-year-olds.

\(\displaystyle 6,6,7,7,7,8,8,9\)

Because 3 plus 2 equals 5, that is the correct answer. 5 total students are age 7 or younger.

Given that the guests ate 8 of the brownie desserts and 7 of the vanilla desserts, a total of 15 desserts were eaten.

\(\displaystyle 7+8=15\)

This means that of the 12 guests, 3 guests must have eaten 2 desserts.

\(\displaystyle 1+1+1+1+1+1+1+1+1+2+2+2=15\)

3 guests is therefore the correct answer.