If each canoe requires an even number of campers, then it would have been impossible for 6 campers to have paddled across in all 4 canoes.

This is because if 6 campers used the canoes, 2 campers would have gone the first two canoes, while 1 camper would have gone in each of the 2 remaining canoes. Only having 1 camper per canoe would have been an odd number of campers, causing the canoe to be unbalanced.

6 campers:

Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 1, Canoe 4 - 1

In order for each canoe to have an even number of campers, there must be a minimum of 8 campers.

If there were 8 campers:

Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 2, Canoe 4 - 2

If there were 12 campers:

Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 2, Canoe 4 - 6

If there were 14 campers:

Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 4, Canoe 4 - 6

If there were 20 campers:

Canoe 1 - 4, Canoe 2 - 4, Canoe 3 - 6, Canoe 4 - 6

If b is equal to the number of brownies in the batch, the following equation can be used to determine the value of b:

\(\displaystyle \frac{2}{17}=\frac{4}{b}\)

Given that 4 is twice the value of 2, it follows that b will be twice the value of 17. Therefore, the value of b is 17 mutliplied by 2, which is 34. 

We can set up a proportion to solve:

\(\displaystyle \frac{4\ \textup{tea bags} }{x\ \textup{original tea bags}}=\frac{1}{4}\)

Cross-multiply:

\(\displaystyle x\ \textup{original tea bags}=4\times 4=16\ \textup{tea bags}\)

To solve the expression, \(\displaystyle \frac{3(3+5)-6+9}{1+2}\), the key is to reduce it step by step, as shown below:

\(\displaystyle \frac{3(3+5)-6+9}{1+2}\)

\(\displaystyle \frac{3\cdot 8+3}{3}\)

\(\displaystyle \frac{24+3}{3}\)

\(\displaystyle \frac{27}{3}\)

\(\displaystyle 9\)

To solve \(\displaystyle 14-7+(-7-3)+(2+5)-3\), the expression must be reduced step by step, starting with the parentheses. 

\(\displaystyle 14-7+(-10)+(7)-3\)

\(\displaystyle 14-7-10+7-3\)

Negative 7 and positive 7 cancel each other out. 

\(\displaystyle 14-10-3\)

\(\displaystyle 1\)

Therefore, 1 is the correct answer. 

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.