Let's evaluate each of the numbers in the set, taking into consideration their exact values:
1. [tex]\(7 \frac{1}{3} = 7 + \frac{1}{3}\)[/tex]
[tex]\[
7 + \frac{1}{3} = 7 + 0.3333\ldots = 7.3333\ldots
\][/tex]
2. [tex]\(\frac{221}{30}\)[/tex]
[tex]\[
\frac{221}{30} \approx 7.3667
\][/tex]
3. [tex]\(7.\overline{36}\)[/tex]
[tex]\[
7. \overline{36} = 7 + 0.363636\ldots = 7.363636\ldots
\][/tex]
4. [tex]\(2.4 \sqrt{3\pi}\)[/tex]
[tex]\[
\sqrt{3\pi} \approx \sqrt{9.42} \approx 3.07
\][/tex]
[tex]\[
2.4 \sqrt{3\pi} \approx 2.4 \cdot 3.07 \approx 7.368
\][/tex]
Now, ordering these numbers from greatest to least:
- [tex]\(2.4 \sqrt{3\pi} \approx 7.368\)[/tex]
- [tex]\(\frac{221}{30} \approx 7.3667\)[/tex]
- [tex]\(7.\overline{36} = 7.363636\ldots\)[/tex]
- [tex]\(7 \frac{1}{3} = 7.3333\ldots\)[/tex]
Thus, the correct order from greatest to least is:
[tex]\[2.4 \sqrt{3\pi}, \frac{221}{30}, 7.\overline{36}, 7 \frac{1}{3}\][/tex]
Therefore, the correct answer is:
[tex]\[2.4 \sqrt{3 \pi}, \frac{221}{30}, 7 . \overline{36}, 7 \frac{1}{3}\][/tex]
