If the mean of the scores `x_(1), x_(2), x_(3), x_(4), x_(5) "and" x_(6)` is x, then mean of `5x_(1), 5x_(2), 5x_(3), 5x_(4), 5x_(5), "and" 5x_(6)` is ______.

Answer

To solve the problem, we need to find the mean of the new set of scores given that the mean of the original scores is \( x \).

### Step-by-Step Solution:

1. **Understanding the Mean of the Original Scores**:
The mean of the scores \( x_1, x_2, x_3, x_4, x_5, x_6 \) is given as \( x \).
The formula for the mean is:
\[ \text{Mean} = \frac{\text{Sum of all scores}}{\text{Number of scores}} \]
Therefore, we can express this as:
\[ x = \frac{x_1 + x_2 + x_3 + x_4 + x_5 + x_6}{6} \]
From this, we can find the sum of the scores:
\[ x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 6x \]

2. **Calculating the Mean of the New Scores**:
Now we need to find the mean of the new scores \( 5x_1, 5x_2, 5x_3, 5x_4, 5x_5, 5x_6 \).
Using the mean formula again:
\[ \text{Mean of new scores} = \frac{5x_1 + 5x_2 + 5x_3 + 5x_4 + 5x_5 + 5x_6}{6} \]
We can factor out the 5:
\[ = \frac{5(x_1 + x_2 + x_3 + x_4 + x_5 + x_6)}{6} \]
Substituting the sum we found earlier:
\[ = \frac{5(6x)}{6} \]
Simplifying this gives:
\[ = 5x \]

### Final Answer:
The mean of \( 5x_1, 5x_2, 5x_3, 5x_4, 5x_5, 5x_6 \) is \( 5x \).

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