To find the value of [tex]\( x \)[/tex] that completes the conditional relative frequency table by column, we need to follow these steps:
1. Understand the Table Setup: The table shows preferences for a new paint color among children and adults. Each cell in the table represents the proportion of individuals who liked or disliked the new paint color.
2. Formulate the Equation: The total for the row "Liked New Paint Color" is given as 0.77. This is the combined preference of both children and adults. We know that 0.6 represents the proportion of children who liked the new paint color, and [tex]\( x \)[/tex] represents the proportion of adults who liked the new paint color.
3. Set Up the Equation: According to the total row value, we have:
[tex]\[
0.6 + x = 0.77
\][/tex]
4. Solve for [tex]\( x \)[/tex]: To find [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]:
[tex]\[
x = 0.77 - 0.6
\][/tex]
5. Perform the Subtraction: When you subtract 0.6 from 0.77, you get:
[tex]\[
x = 0.17
\][/tex]
Thus, the value for [tex]\( x \)[/tex] that completes the conditional relative frequency table by column is 0.17. This means the correct answer is:
[tex]\[
\boxed{0.17}
\][/tex]
