To determine which statements are true given Miss Rose's ballet class data, let's analyze each statement using the provided relative frequency table.
### Relative Frequency Table:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
& \text{Beginner} & \text{Intermediate} & \text{Advanced} & \text{Total} \\
\hline
\text{Boys} & 0.15 & 0.2 & 0.05 & 0.4 \\
\hline
\text{Girls} & 0.1 & 0.35 & 0.15 & 0.6 \\
\hline
\text{Total} & 0.25 & 0.55 & 0.2 & 1.0 \\
\hline
\end{array}
\][/tex]
Now, let's verify each statement:
#### Statement A: [tex]$20\%$[/tex] of her students are in the intermediate class.
To determine if this is true, we look at the "Intermediate" column under the "Total" row in the table:
[tex]\[
\text{Intermediate class (Total)} = 0.55 = 55\%
\][/tex]
Thus, [tex]$20\%$[/tex] (or 0.20) of her students are not in the intermediate class. Therefore, Statement A is false.
#### Statement B: [tex]$20\%$[/tex] of her students are in the advanced class.
To verify this, we look at the "Advanced" column under the "Total" row in the table:
[tex]\[
\text{Advanced class (Total)} = 0.20 = 20\%
\][/tex]
This matches the statement precisely. Thus, Statement B is true.
#### Statement C: [tex]$40\%$[/tex] of her students are girls.
To check this, we look at the "Girls" row under the "Total" column in the table:
[tex]\[
\text{Girls (Total)} = 0.60 = 60\%
\][/tex]
Therefore, [tex]$40\%$[/tex] (or 0.40) of her students are not girls. Thus, Statement C is false.
#### Statement D: [tex]$15\%$[/tex] of her students are boys.
To determine this, we look at the "Boys" row under the "Total" column in the table:
[tex]\[
\text{Boys (Total)} = 0.40 = 40\%
\][/tex]
Therefore, [tex]$15\%$[/tex] (or 0.15) of her students are not boys. Thus, Statement D is false.
### Summary
From the analysis, the only true statement is:
- B. [tex]$20\%$[/tex] of her students are in the advanced class.
Thus, the correct and true statement is B.
