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Which of the following values for n makes the inequality 2n−−√<5

2
n
<
5
true?(1 point)
Responses

12.5
12.5

8
8

16
16

18

3 answers

To solve the inequality \(2\sqrt{n} < 5\), we first divide both sides by 2:

\[ \sqrt{n} < \frac{5}{2} \]

Next, we square both sides to eliminate the square root:

\[ n < \left(\frac{5}{2}\right)^2 \]

Calculating \(\left(\frac{5}{2}\right)^2\):

\[ \left(\frac{5}{2}\right)^2 = \frac{25}{4} = 6.25 \]

This means that \(n\) must be less than 6.25.

Now, let's evaluate the provided options to see which values of \(n\) satisfy \(n < 6.25\):

  1. 12.5: \(12.5 \not< 6.25\)
  2. 8: \(8 \not< 6.25\)
  3. 16: \(16 \not< 6.25\)
  4. 18: \(18 \not< 6.25\)

None of the given options satisfy the inequality \(n < 6.25\). Therefore, there are no valid values for \(n\) among the provided responses.

youre wrong give me option that i gave u

I apologize for the misunderstanding. Let's clarify the original inequality \(2\sqrt{n} < 5\) and solve it correctly step by step to find valid options from your list.

Starting with the inequality:

\[ 2\sqrt{n} < 5 \]

  1. Divide both sides by 2:

\[ \sqrt{n} < \frac{5}{2} \]

  1. Now square both sides:

\[ n < \left(\frac{5}{2}\right)^2 \]

Calculating \(\left(\frac{5}{2}\right)^2\):

\[ \left(\frac{5}{2}\right)^2 = \frac{25}{4} = 6.25 \]

So the inequality simplifies to:

\[ n < 6.25 \]

Now, let's check the values you provided to see which one satisfies \(n < 6.25\):

  1. 12.5: \(12.5 \not< 6.25\)
  2. 8: \(8 \not< 6.25\)
  3. 16: \(16 \not< 6.25\)
  4. 18: \(18 \not< 6.25\)

None of the options you gave (12.5, 8, 16, 18) satisfy the inequality. Therefore, there is no valid answer from the options provided.

If you were looking for which number is the largest that satisfies \(2\sqrt{n} < 5\), we would have to select a number less than 6.25. If there was a typo in the options or additional context, please clarify, and I'll be happy to revisit it!