To find the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex], we'll follow these steps:
1. Calculate the total number of males and females surveyed:
- Total number of males = Males who enjoyed the movie + Males who did not enjoy the movie
[tex]\[
47 + 13 = 60
\][/tex]
- Total number of females = Females who enjoyed the movie + Females who did not enjoy the movie
[tex]\[
53 + 3 = 56
\][/tex]
2. Determine the percentage of males who enjoyed the movie ([tex]\( a \)[/tex]):
- The percentage of males who enjoyed the movie is calculated by the formula:
[tex]\[
a = \left( \frac{\text{Males who enjoyed}}{\text{Total males}} \right) \times 100
\][/tex]
Plugging in the numbers:
[tex]\[
a = \left( \frac{47}{60} \right) \times 100 \approx 78\%
\][/tex]
- Rounding this to the nearest percent, [tex]\( a = 78\% \)[/tex].
3. Determine the percentage of females who did not enjoy the movie ([tex]\( b \)[/tex]):
- The percentage of females who did not enjoy the movie is calculated by the formula:
[tex]\[
b = \left( \frac{\text{Females who did not enjoy}}{\text{Total females}} \right) \times 100
\][/tex]
Plugging in the numbers:
[tex]\[
b = \left( \frac{3}{56} \right) \times 100 \approx 5\%
\][/tex]
- Rounding this to the nearest percent, [tex]\( b = 5\% \)[/tex].
So, the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are:
- [tex]\( a = 78\% \)[/tex]
- [tex]\( b = 5\% \)[/tex]
Therefore, none of the given options match the correct values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] based on the provided data. The correct values should be:
[tex]\[ a = 78\%, \, b = 5\% \][/tex]
