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Surveyed about whether they enjoyed the movie or not:

Males:
- Enjoyed: 47
- Did not enjoy: 13

Females:
- Enjoyed: 53
- Did not enjoy: 3

Survey on Movie:

\begin{tabular}{|c|c|c|c|}
\hline
& Enjoyed & \begin{tabular}{c} Did Not \\ Enjoy \end{tabular} & Total \\
\hline
Males & [tex]$a$[/tex] & [tex]$11 \%$[/tex] & \\
\hline
Females & [tex]$46 \%$[/tex] & [tex]$b$[/tex] & \\
\hline
Total & & & [tex]$100 \%$[/tex] \\
\hline
\end{tabular}

Complete the table for the survey results. Round answers to the nearest percent.

A. [tex]$a = 40 \%, b = 4 \%$[/tex]
B. [tex]$a = 41 \%, b = 3 \%$[/tex]
C. [tex]$a = 47 \%, b = 3 \%$[/tex]
D. [tex]$a = 41 \%, b = 19 \%$[/tex]



Answer :

GinnyAnswer
To solve the problem of filling out the table with the correct percentages, let's break down the steps systematically:

1. Calculate Total Respondents:
- Males who enjoyed the movie: 47
- Males who did not enjoy the movie: 13
- Females who enjoyed the movie: 53
- Females who did not enjoy the movie: 3

Total males = 47 (enjoyed) + 13 (did not enjoy) = 60
Total females = 53 (enjoyed) + 3 (did not enjoy) = 56
Total respondents = 60 (males) + 56 (females) = 116

2. Calculate Percentages:
- Percentage of males who enjoyed the movie:
[tex]\[ \text{Males Enjoyed Percentage} = \left( \frac{47}{116} \right) \times 100 \approx 40.52\% \][/tex]
Rounded to the nearest percent: 41%

- Percentage of females who did not enjoy the movie:
[tex]\[ \text{Females Did Not Enjoy Percentage} = \left( \frac{3}{116} \right) \times 100 \approx 2.59\% \][/tex]
Rounded to the nearest percent: 3%

3. Fill the Table with Given Values:
- The percentage of males who did not enjoy the movie: Given as 11%
- The percentage of females who enjoyed the movie: Given as 46%

4. Verify the Values:
- The value for "Total" should sum up to 100%

So, the values for \(a\) and \(b\) are already calculated and rounded. Based on the options provided:

The correct answers are \(a = 41\%\) and \(b = 3\%\).

Thus, the correct choice is:

[tex]\(a = 41\%, b = 3\%\)[/tex]

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