To determine which player has a better batting average, we need to compare their ratios of hits to attempts.
First, let's find Jana's batting average:
Jana's hits to attempts ratio is [tex]\( \frac{12}{15} \)[/tex].
Next, we simplify this ratio to get Jana's batting average. Dividing the numerator and the denominator by their greatest common divisor, which is 3, we get:
[tex]\[ \frac{12 \div 3}{15 \div 3} = \frac{4}{5} \][/tex]
[tex]\[ \frac{4}{5} = 0.8 \][/tex]
So, Jana's batting average is 0.8.
Now, let's find Tasha's batting average:
Tasha's hits to attempts ratio is [tex]\( \frac{9}{10} \)[/tex].
We simplify this ratio to get Tasha's batting average (note that this is already in simplified form):
[tex]\[ \frac{9}{10} = 0.9 \][/tex]
So, Tasha's batting average is 0.9.
Next, to compare their ratios accurately, we can convert both batting averages to the same common denominator. We'll convert both ratios to be out of 30 attempts:
For Jana:
[tex]\[ 0.8 \times 30 = 24 \][/tex]
For Tasha:
[tex]\[ 0.9 \times 30 = 27 \][/tex]
So, Jana's batting average ratio out of 30 is [tex]\( \frac{24}{30} \)[/tex] and Tasha's batting average ratio out of 30 is [tex]\( \frac{27}{30} \)[/tex].
Comparing these two ratios, [tex]\( \frac{27}{30} \)[/tex] is greater than [tex]\( \frac{24}{30} \)[/tex].
Thus, Tasha has a better batting average with a ratio higher than Jana's.
So the correct answer is:
- Tasha, because she has the highest ratio since [tex]\( \frac{27}{30} > \frac{24}{30} \)[/tex].
