Let's compare [tex]\(\sqrt{130}\)[/tex] and [tex]\(\frac{111}{8}\)[/tex].
First, we need to determine the numerical values of [tex]\(\sqrt{130}\)[/tex] and [tex]\(\frac{111}{8}\)[/tex].
1. Calculate [tex]\(\sqrt{130}\)[/tex]:
- The value of [tex]\(\sqrt{130}\)[/tex] is approximately [tex]\(11.40175425099138\)[/tex].
2. Calculate [tex]\(\frac{111}{8}\)[/tex]:
- [tex]\(\frac{111}{8}\)[/tex] equals [tex]\(13.875\)[/tex].
Now we compare these two values:
- [tex]\(\sqrt{130} \approx 11.40175425099138\)[/tex]
- [tex]\(\frac{111}{8} = 13.875\)[/tex]
Looking at these values:
- [tex]\(11.40175425099138\)[/tex] (which is [tex]\(\sqrt{130}\)[/tex]) is less than [tex]\(13.875\)[/tex] (which is [tex]\(\frac{111}{8}\)[/tex]).
Therefore, the correct comparison is:
[tex]\[
\frac{111}{8} > \sqrt{130}
\][/tex]
So, the correct answer from the provided choices is:
[tex]\[
\boxed{\frac{111}{8} > \sqrt{130}}
\][/tex]
