To determine which player has the better batting average, we need to compare Jana's and Tasha's batting averages.
1. Calculate Jana's Batting Average:
- Jana has hit the ball 7 times out of 10 attempts.
- Her batting average is calculated as:
[tex]\[
\text{Jana's Batting Average} = \frac{7}{10} = 0.7
\][/tex]
2. Calculate Tasha's Batting Average:
- Tasha has hit the ball 10 times out of 16 attempts.
- Her batting average is calculated as:
[tex]\[
\text{Tasha's Batting Average} = \frac{10}{16} = 0.625
\][/tex]
3. Compare Their Batting Averages:
- Jana's batting average is [tex]\(0.7\)[/tex].
- Tasha's batting average is [tex]\(0.625\)[/tex].
- Between these, [tex]\(0.7 > 0.625\)[/tex].
Therefore, Jana has the highest batting average.
Now, we analyze the provided options:
- Option 1: "Tasha, because she has the lowest ratio since [tex]\(0.7 < 0.625\)[/tex]."
- This statement is incorrect because [tex]\(0.7\)[/tex] is not less than [tex]\(0.625\)[/tex].
- Option 2: "Tasha, because she has the highest ratio since [tex]\(\frac{56}{80} > \frac{50}{80}\)[/tex]."
- This comparison is factually incorrect as well since [tex]\(0.7\)[/tex] is actually greater than [tex]\(0.625\)[/tex].
- Option 3: "Jana, because she has the highest ratio since [tex]\(\frac{56}{80} > \frac{50}{80}\)[/tex]."
- This is misleading but concludes correctly that Jana has the highest batting average, although the [tex]\(56\)[/tex] and [tex]\(50\)[/tex] do not correctly represent the ratios given earlier.
- Option 4: "Jana, because she has the lowest ratio since [tex]\(0.7 < 0.625\)[/tex]."
- This statement is incorrect because [tex]\(0.7\)[/tex] is not less than [tex]\(0.625\)[/tex].
The correct detailed conclusion from the correct answer is:
Jana, because she has the highest batting average since [tex]\(0.7 > 0.625\)[/tex].
