If $$ n \in \mathrm{n}, \mathrm{n}

Question

If $$ n \in \mathrm{n}, \mathrm{n}<\sqrt{26}<\mathrm{n}+1 $$, then $$ n=\ldots $$ The arithmetic mean of the set of values : $$ 3-x, 5+x, 4 $$ equals

UpStudy AI · Accepted Answer

Let's address each part of your question step by step.

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**1. Finding $$ n $$ such that $$ n < \sqrt{26} < n + 1 $$:**

First, calculate the approximate value of $$ \sqrt{26} $$.

- $$ 5^2 = 25 $$
- $$ 6^2 = 36 $$

Since $$ 25 < 26 < 36 $$, it follows that:
$$ 5 < \sqrt{26} < 6 $$

Therefore, the integer $$ n $$ that satisfies the inequality is:
$$ n = 5 $$

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**2. Calculating the Arithmetic Mean of the Set $$ \{ 3 - x, \; 5 + x, \; 4 \} $$:**

The arithmetic mean (average) of a set of numbers is given by:
$$ \text{Mean} = \frac{\text{Sum of all elements}}{\text{Number of elements}} $$

Compute the sum of the elements:
$$
(3 - x) + (5 + x) + 4 = 3 - x + 5 + x + 4 = 12
$$

There are 3 elements in the set, so:
$$
\text{Mean} = \frac{12}{3} = 4
$$

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**Final Answers:**
- $$ n = 5 $$
- The arithmetic mean is $$ 4 $$
$$ n = 5 $$ and the arithmetic mean is 4.

If , then
The arithmetic mean of the set of values : equals