To determine how many games fell into the [tex]$51-57$[/tex] points category, follow these steps:
1. Identify the scores from the last 10 games:
The scores are:
[tex]\[
51, 70, 63, 59, 56, 75, 60, 55, 67, 64
\][/tex]
2. Understand the category range:
To be in the [tex]$51-57$[/tex] points category, the score must be between 51 and 57 (inclusive).
3. Count the scores within the range:
- Look at each score one by one and check if it falls in the [tex]$51-57$[/tex] range:
- [tex]\(51\)[/tex] is in the range.
- [tex]\(70\)[/tex] is not in the range.
- [tex]\(63\)[/tex] is not in the range.
- [tex]\(59\)[/tex] is not in the range.
- [tex]\(56\)[/tex] is in the range.
- [tex]\(75\)[/tex] is not in the range.
- [tex]\(60\)[/tex] is not in the range.
- [tex]\(55\)[/tex] is in the range.
- [tex]\(67\)[/tex] is not in the range.
- [tex]\(64\)[/tex] is not in the range.
This gives us the scores [tex]\(51, 56,\)[/tex] and [tex]\(55\)[/tex] which are all within the category [tex]$51-57$[/tex].
4. Count the total number of valid scores:
- We have three games scoring in the range [tex]$51-57$[/tex]. Therefore, the number of games in this category is 3.
So, the correct answer is:
[tex]\[
\boxed{3}
\][/tex]
