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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

The seventh-grade students at Charleston Middle School are choosing one girl and one boy for the student council. Their choices for girls are Michaela (M), Candice (C), and Raven (R). Complete the table and the sentence beneath it.

\begin{tabular}{|c|c|c|c|}
\hline & & \multicolumn{3}{|c|}{Boys} \\
\hline & & Neil & Barney & Ted \\
\hline \multirow{3}{*}{Girls} & Michaela & [tex]$N - M$[/tex] & & [tex]$T - M$[/tex] \\
\hline & Candice & [tex]$N - C$[/tex] & [tex]$\cdot$[/tex] & [tex]$T - C$[/tex] \\
\hline & Raven & [tex]$N - R$[/tex] & & [tex]$T - R$[/tex] \\
\hline
\end{tabular}

If instead of three girls and three boys, there were four girls and four boys to choose from, the new sample size would be [tex]$\square$[/tex].



Answer :

GinnyAnswer
Alright, let's go through the steps required to complete the table and the sentence beneath it.

1. Complete the Table:
- Each cell in the table should show the pairs of girls and boys.
- In each pair, a girl is represented by her initial (M for Michaela, C for Candice, R for Raven), and a boy is also represented by his initial (N for Neil, B for Barney, T for Ted).

Here is the completed table:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline & & \multicolumn{3}{|c|}{\text{Boys}} \\ \hline & & \text{Neil} & \text{Barney} & \text{Ted} \\ \hline \multirow{3}{*}{\text{Girls}} & \text{Michaela} & \text{N-M} & \text{B-M} & \text{T-M} \\ \hline & \text{Candice} & \text{N-C} & \text{B-C} & \text{T-C} \\ \hline & \text{Raven} & \text{N-R} & \text{B-R} & \text{T-R} \\ \hline \end{array} \][/tex]

2. Calculate the Number of Pairings:
- Originally, there are 3 girls and 3 boys.
- The number of different pairs that can be formed from 3 girls and 3 boys is given by multiplying the number of girls by the number of boys: \(3 \times 3 = 9\).

3. New Sample Size:
- If there are now 4 girls and 4 boys, the number of pairs will be:
- Multiply the number of girls by the number of boys: \(4 \times 4 = 16\).

So the new sample size would be [tex]\(16\)[/tex].

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