To find the value of [tex]\( k \)[/tex] in the relative frequency table, we need to determine the relative frequency of the cell corresponding to [tex]\( T \)[/tex] and [tex]\( V \)[/tex] (which is 2 from the frequency table) and then convert that frequency to a percentage.
1. Identify the frequency: From the given frequency table, the frequency for [tex]\( T \)[/tex] and [tex]\( V \)[/tex] is 2.
2. Identify the total number of observations: The total number of observations in the frequency table is 19.
3. Calculate the relative frequency: To get the relative frequency, divide the frequency of [tex]\( T \)[/tex] and [tex]\( V \)[/tex] by the total number of observations.
[tex]\[
\text{Relative Frequency} = \frac{\text{Frequency of } T \text{ and } V}{\text{Total number of observations}} = \frac{2}{19}
\][/tex]
4. Convert the relative frequency to a percentage: Multiply the relative frequency by 100.
[tex]\[
\text{Percentage} = \left(\frac{2}{19}\right) \times 100
\][/tex]
5. Round to the nearest percent:
[tex]\[
\text{Percentage} \approx 10.53\% \implies 11\%
\][/tex]
When rounding 10.53% to the nearest percent, we get 11%.
Therefore, the value of [tex]\( k \)[/tex] in the relative frequency table is [tex]\( 11\% \)[/tex].
So, the final answer is:
[tex]\[
\boxed{11\%}
\][/tex]
