Question

Hello help me with math please

Answer 1

Answers: Everything except the $\frac{76}{11}$

So there are four answers to pick:

$\sqrt{19}+2\\\\6.\overline{3}\\\\5\pi-9\\\\2\sqrt{11}$

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Explanation:

There are several approaches to problems like this. Perhaps the easiest way is to use a calculator to convert the given expressions into decimal form.

Let's start with the two original numbers, which are the endpoints of our interval:

$\frac{25}{4} = 6.25\\\\\sqrt{47} \approx 6.86$

So we're looking for numbers that are between exactly 6.25 and approximately 6.86

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Next, convert each of the answer choices into decimal form as well.

$\sqrt{19}+2 \approx 6.36\\\\6.\overline{3} \approx 6.33\\\\\frac{76}{11} \approx 6.91\\\\5\pi-9 \approx 6.71\\\\2\sqrt{11} \approx 6.63$

Again, we're looking to see which values are between 6.25 and 6.86

Of those five decimal values in the list above, only 6.91 is outside the interval mentioned.

So effectively, we'll select nearly every item except for the $\frac{76}{11}$ choice.