The total number of survey respondents is equal to \(\displaystyle 100\) percent. Since the common part of the Venn diagram represents the respondents that like both Super Heroes. 

Thus, the solution is: 

\(\displaystyle 100-(34+49)=\)

\(\displaystyle 100-83=17\)

The total number of survey respondents is equal to \(\displaystyle 100\) percent. Since the common part of the Venn diagram represents the respondents that use both of the Social Media sites, the solution is:

\(\displaystyle 100-(36+51)=\)

\(\displaystyle 100-87=13\)

The total number of survey respondents is equal to \(\displaystyle 100\) percent. Since the common part of the Venn diagram represents the respondents that use both social media sites, the solution is:

\(\displaystyle 100-(36+51)=\)

\(\displaystyle 100-87=13\)

\(\displaystyle 13\%=\frac{13}{100}\)

The total number of survey respondents is equal to \(\displaystyle 100\) percent, which equals \(\displaystyle \frac{5}{5}\). 

The total number of respondents that do not like both tacos and tamales: \(\displaystyle \frac{3}{5}+\frac{1}{5}=\frac{4}{5}\).

The remaining amount equals the respondents that like both tacos and tamales. 

Thus, the solution is: 

\(\displaystyle \frac{5}{5}-\frac{4}{5}=\frac{1}{5}\)

The total number of survey respondents is equal to \(\displaystyle 100\) percent, which equals \(\displaystyle \frac{5}{5}\). 

The total number of respondents that do not like both tacos and tamales: \(\displaystyle \frac{3}{5}+\frac{1}{5}=\frac{4}{5}\).

The remaining amount equals the respondents that like both tacos and tamales. 

Thus, the solution is: 

\(\displaystyle \frac{5}{5}-\frac{4}{5}=\frac{1}{5}\)


Now we need to convert the fraction into a percent.

\(\displaystyle \frac{1}{5}=\frac{1}{5}\times \frac{20}{20}=\frac{20}{100}=20\%\) 

In order to find the value of the common area of this Venn diagram, find the sum of \(\displaystyle 56\) percent and \(\displaystyle 21\) percent.

Then find the difference from the sum to \(\displaystyle 100\) percent. 

The solution is:

\(\displaystyle 56+21=77\)

\(\displaystyle 100-77=23\)

The shaded area represents the set of all elements that are both in \(\displaystyle B\) and not in \(\displaystyle A\). This the intersection of \(\displaystyle B\) and the complement of \(\displaystyle A\), or \(\displaystyle \overline{A} \cap B\).

The gray region represents all elements that either are in \(\displaystyle A\), are not in \(\displaystyle B\) - that is, are in \(\displaystyle \overline{B}\) - or both. This is the union of \(\displaystyle A\) and \(\displaystyle \overline{B}\), or \(\displaystyle A \cup \overline{B}\).

The symbol \(\displaystyle \cup\) stands for the union between two sets.  Therefore, \(\displaystyle A\cup B\) means the set of all numbers that are in either A or B.  Looking at our choices, the only number that isn't in either A, B, or both is 23.

The gray area represents the portion of \(\displaystyle B\) that is not in \(\displaystyle A\) - in other words, all multiples of 9 that are not also multiples of 6.

\(\displaystyle 4,572 \div 6 = 762\) 

\(\displaystyle 3,438 \div 6 = 573\) 

\(\displaystyle 8,544 \div 6 =1,424\) 

Therefore, 4,572, 3,438, and 8,544 can be eliminated.

\(\displaystyle 9,349 \div 9 = 1,038 \;R\; 7\), so 9,349 can be eliminated because it isn't a multiple of 9.

\(\displaystyle 4,077 \div 6 = 679 \; R \; 3\) and \(\displaystyle 4,077 \div 9 = 453\), so, as both a nonmultiple of 6 and a multiple of 9, 4.077 is the correct choice.