Answered

Which set of numbers is correctly ordered from greatest to least?

A. [tex]\( 7 \frac{1}{3}, \frac{221}{30}, 7 . \overline{36}, 2.4 \sqrt{3 \pi} \)[/tex]

B. [tex]\( 7 \frac{1}{3}, 7 . \overline{36}, \frac{221}{30}, 2.4 \sqrt{3 \pi} \)[/tex]

C. [tex]\( 2.4 \sqrt{3 \pi}, 7.36, \frac{221}{30}, 7 \frac{1}{3} \)[/tex]

D. [tex]\( 2.4 \sqrt{3 \pi}, \frac{221}{30}, 7 . \overline{36}, 7 \frac{1}{3} \)[/tex]



Answer :

GinnyAnswer
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]