If an ice cream container has 4 servings and each serving is equal to 2 ounces, the total number of ounces in the container can be found by multiplying 2 by 4.

$\displaystyle 2\times4=8$

This results in 8 ounces. 

We know that one-third of the pie is 2 slices. We can set up an equation:

$\displaystyle \frac{1}{3}(\text{total pie})=2$

In other words, one-third times the total slices in the pie will be equal to 2 slices.

Multiply both sides of the equation by 3.

$\displaystyle \frac{1}{3}\times3\times(\text{total pie})=2\times3$

The fraction on the left side cancels.

$\displaystyle (\text{total pie})=2\times3=6$

There are a total of 6 slices in the pie.

If the class eats $\displaystyle \frac{2}{3}$ of the cookies and $\displaystyle 5$ remain, this means that $\displaystyle 5=\frac{1}{3}$. Therefore, $\displaystyle \frac{2}{3}$ of the batch will be equal to $\displaystyle 10$ cookies, as $\displaystyle \frac{2}{3}$ is twice the value of $\displaystyle \frac{1}{3}$, and $\displaystyle 10$ is twice the value of $\displaystyle 5$. 

The entire batch of cookies will be equal to $\displaystyle 5+10=15$.

Thus, $\displaystyle 15$ is the correct answer. 

The first step is to convert the coins into their values in cents. 

If we look at the combination of $\displaystyle 1$ quarter, $\displaystyle 2$ dimes, $\displaystyle 3$ nickels, and $\displaystyle 6$ pennies, the following expression can be used to determine the coins' value in cents:

$\displaystyle 1\cdot 25+2\cdot 10+3\cdot 5+6\cdot 1$

$\displaystyle 25+20+15+6$

$\displaystyle 66$

Therefore, the correct answer is $\displaystyle 1$ quarter, $\displaystyle 2$ dimes, $\displaystyle 3$ nickels, and $\displaystyle 6$ pennies.

As for the incorrect answers, $\displaystyle 1$ quarter, $\displaystyle 2$ dimes, $\displaystyle 3$ nickels, and $\displaystyle 1$ penny adds up to $\displaystyle 61$ cents; $\displaystyle 2$ quarters, $\displaystyle 2$ dimes, $\displaystyle 3$ nickels, and $\displaystyle 6$ pennies adds up to $\displaystyle 91$ cents; and $\displaystyle 1$ quarter, $\displaystyle 3$ dimes, $\displaystyle 4$ nickels, and $\displaystyle 6$ pennies adds up to $\displaystyle 81$ cents.

If the sales tax is $\displaystyle 8\%$, then this means that for every purchase of $\displaystyle \$100$, an $\displaystyle 8\%$ tax will be charged. 

Given that the shoes are $\displaystyle \$50$ (half of $\displaystyle \$100$), half the sales tax of $\displaystyle \$8$ should be charged, which is a value of $\displaystyle \$4$. 

Since $\displaystyle 50+4=54$, the shoes will cost $\displaystyle \$54$ after sales tax. 

If Anita bought a pair of boots for $\displaystyle \$100$ that was on sale for $\displaystyle \%40$$\displaystyle 40\%$ off, this means she would get $\displaystyle \$40$ off. But if she was taxed at $\displaystyle 8\%$ on the full price, this would be equal to $\displaystyle 100\cdot.08=8$. 

Therefore, the total she would have to pay would be equal to $\displaystyle \$68$, because $\displaystyle 100-40+8=68$.

If Arnold made $\displaystyle \$120$ tutoring, that means that he gave $\displaystyle 4$ tutoring sessions because $\displaystyle \$120$ divided by $\displaystyle \$30$ (his rate per tutoring session) is equal to $\displaystyle 4$. 

Given that Arnold must spend half an hour preparing for each session, the total number of hours it took him to earn $\displaystyle \$120$ is equal to:

$\displaystyle 4+(4\cdot \frac{1}{2})=4+2=6$

If Joe has one third of his assignment to complete after finishing $\displaystyle 14$ problems, that means that $\displaystyle 14$ is equal to two-thirds of the entire set. Knowing this, we can write out the equation $\displaystyle \frac{2}{3}=\frac{14}{x}$ and solve for $\displaystyle x$ in order to find how many problems make up Joe's homework assignment.

We can solve this equation by cross-multiplying to get $\displaystyle 3\cdot14=2\cdot x$, which simplifies to $\displaystyle 42=2x$.

To find $\displaystyle x$, we can divide each side of the equation by $\displaystyle 2$. This gives us $\displaystyle 21=x$, so there are $\displaystyle 21$ problems in Joe's homework assignment.

Given that there are 3 birds in the tree who are then joined by their mates, there are 6 total birds in the tree. If two-thirds of the birds fly away, 4 birds leave, and 2 birds are left in the nest

To find out how many students are in the class, we first need to find the number of girls in the class. For every $\displaystyle 3$ boys, there will be $\displaystyle 1$ girl. There are $\displaystyle 4$ groups of $\displaystyle 3$ in a group of $\displaystyle 12$ (or, put another way, $\displaystyle 12\div3=4$), so the class has $\displaystyle 4$ groups of $\displaystyle 3$ boys. That means we also have $\displaystyle 4$ groups of $\displaystyle 1$ girl. $\displaystyle 1\times4$ is $\displaystyle 4$, so altogether we have $\displaystyle 12$ boys and $\displaystyle 4$ girls. $\displaystyle 12+4=16$, so the correct answer is $\displaystyle 16$.