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To make the given expression easier to read and correct any errors, I will format it properly:

[tex]\[
\begin{array}{l}
C = \sqrt{\frac{\chi^2}{N + \chi^2}} \\
C = \sqrt{\frac{29,881}{282 + 29,881}} = 0.31
\end{array}
\][/tex]

This provides a clear and accurate representation of the mathematical expressions given.

Sagot :

GinnyAnswer
Alright, let’s solve the given problem step-by-step in detail.

You are given the expression for [tex]\( C \)[/tex]:
[tex]\[ C = \sqrt{\frac{\chi^2}{N + \chi^2}} \][/tex]

The given values are:
[tex]\[ \chi^2 = 29,881 \][/tex]
[tex]\[ N = 282 \][/tex]

Now, let's compute the fraction inside the square root step-by-step:

1. Sum the denominator:
[tex]\[ N + \chi^2 = 282 + 29,881 = 30,163 \][/tex]

2. Form the fraction:
[tex]\[ \frac{\chi^2}{N + \chi^2} = \frac{29,881}{30,163} \][/tex]

3. Simplify the fraction numerically:
[tex]\[ \frac{29,881}{30,163} \approx 0.9906507973344827 \][/tex]

4. Compute the square root:
[tex]\[ C = \sqrt{0.9906507973344827} \][/tex]

5. Final value of [tex]\( C \)[/tex]:
[tex]\[ C \approx 0.9953144213435685 \][/tex]

Thus, the fraction [tex]\(\frac{\chi^2}{N + \chi^2}\)[/tex] simplifies to approximately 0.9906507973344827, and the value of [tex]\( C \)[/tex] is approximately 0.9953144213435685.
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