To determine which statement is false based on the given data, let's analyze the table carefully:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
& Biology & Chemistry & \begin{tabular}{c}
Physical \\
Science
\end{tabular} & Total \\
\hline
Freshman & 0.15 & 0.1 & 0.2 & 0.45 \\
\hline
Sophomores & 0.2 & 0.25 & 0.1 & 0.55 \\
\hline
Total & 0.35 & 0.35 & 0.3 & 1.0 \\
\hline
\end{tabular}
\][/tex]
Let's go through each statement one by one and check their validity based on the table:
Statement A: [tex]$20 \%$[/tex] of her students are in physical science.
- The total percentage of students in physical science is provided in the table as [tex]\(0.3\)[/tex] or [tex]\(30\%\)[/tex].
- Comparing this with [tex]\(20\%\)[/tex], we see that [tex]\(20\%\)[/tex] is not equal to [tex]\(30\%\)[/tex].
Statement A is false.
Statement B: [tex]$55 \%$[/tex] of her students are sophomores.
- According to the table, the total percentage of sophomores is [tex]\(0.55\)[/tex] or [tex]\(55\%\)[/tex].
- This matches the statement exactly.
Statement B is true.
Statement C: [tex]$35 \%$[/tex] of her students are in biology.
- The total percentage of students in biology is given as [tex]\(0.35\)[/tex] or [tex]\(35\%\)[/tex].
- This matches the statement exactly.
Statement C is true.
Statement D: [tex]$35 \%$[/tex] of her students are in chemistry.
- The total percentage of students in chemistry is provided as [tex]\(0.35\)[/tex] or [tex]\(35\%\)[/tex].
- This matches the statement exactly.
Statement D is true.
After analyzing all the statements, the false one is:
Statement A: [tex]$20 \%$[/tex] of her students are in physical science.
The correct percentage is [tex]\(30 \%\)[/tex], not [tex]\(20 \%\)[/tex]. Thus, the false statement is statement [tex]\(A\)[/tex].
