Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To fill in the missing values of [tex]\( y \)[/tex] for the given [tex]\( x \)[/tex] values in the table, we need to determine the linear relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex]. Through regression analysis, this relationship can be expressed in the form of a linear equation [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
For our data points, the best fit line is given by the equation:
[tex]\[ y = -6.8x + 22.1 \][/tex]
We will use this equation to calculate the values of [tex]\( y \)[/tex] for each [tex]\( x \)[/tex].
1. When [tex]\( x = 3 \)[/tex]:
[tex]\[ y = -6.8 \cdot 3 + 22.1 = -20.4 + 22.1 = 1.7 \][/tex]
2. When [tex]\( x = 6 \)[/tex]:
[tex]\[ y = -6.8 \cdot 6 + 22.1 = -40.8 + 22.1 = -18.7 \][/tex]
3. When [tex]\( x = 9 \)[/tex]:
[tex]\[ y = -6.8 \cdot 9 + 22.1 = -61.2 + 22.1 = -39.1 \][/tex]
4. When [tex]\( x = 10 \)[/tex]:
[tex]\[ y = -6.8 \cdot 10 + 22.1 = -68 + 22.1 = -45.9 \][/tex]
With these calculations, we can fill in the missing values in the table as follows:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 3 & 1.7 \\ \hline 6 & -18.7 \\ \hline 9 & -39.1 \\ \hline 10 & -45.9 \\ \hline \end{tabular} \][/tex]
For our data points, the best fit line is given by the equation:
[tex]\[ y = -6.8x + 22.1 \][/tex]
We will use this equation to calculate the values of [tex]\( y \)[/tex] for each [tex]\( x \)[/tex].
1. When [tex]\( x = 3 \)[/tex]:
[tex]\[ y = -6.8 \cdot 3 + 22.1 = -20.4 + 22.1 = 1.7 \][/tex]
2. When [tex]\( x = 6 \)[/tex]:
[tex]\[ y = -6.8 \cdot 6 + 22.1 = -40.8 + 22.1 = -18.7 \][/tex]
3. When [tex]\( x = 9 \)[/tex]:
[tex]\[ y = -6.8 \cdot 9 + 22.1 = -61.2 + 22.1 = -39.1 \][/tex]
4. When [tex]\( x = 10 \)[/tex]:
[tex]\[ y = -6.8 \cdot 10 + 22.1 = -68 + 22.1 = -45.9 \][/tex]
With these calculations, we can fill in the missing values in the table as follows:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 3 & 1.7 \\ \hline 6 & -18.7 \\ \hline 9 & -39.1 \\ \hline 10 & -45.9 \\ \hline \end{tabular} \][/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.