Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Select the correct answer.

Which equation best models the set of data in this table?

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
[tex]$y$[/tex] & 32 & 67 & 79 & 91 & 98 & 106 & 114 & 120 & 126 & 132 \\
\hline
\end{tabular}

A. [tex]$y=33 x-32.7$[/tex]

B. [tex]$y=33 x+32.7$[/tex]

C. [tex]$y=33 \sqrt{x}+32.7$[/tex]

D. [tex]$y=33 \sqrt{x-32.7}$[/tex]

Sagot :

GinnyAnswer
Let's break down the problem step-by-step to determine which equation best models the given data.

Given the data:
[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline y & 32 & 67 & 79 & 91 & 98 & 106 & 114 & 120 & 126 & 132 \\ \hline \end{array} \][/tex]

### Step 1: Calculate the differences between consecutive [tex]\( y \)[/tex] values.

Let's look at the differences [tex]\(\Delta y\)[/tex] between consecutive [tex]\( y \)[/tex] values:

[tex]\[ \begin{array}{|c|c|} \hline \Delta y & \\ \hline 67 - 32 & = 35 \\ \hline 79 - 67 & = 12 \\ \hline 91 - 79 & = 12 \\ \hline 98 - 91 & = 7 \\ \hline 106 - 98 & = 8 \\ \hline 114 - 106 & = 8 \\ \hline 120 - 114 & = 6 \\ \hline 126 - 120 & = 6 \\ \hline 132 - 126 & = 6 \\ \hline \end{array} \][/tex]

These differences are [tex]\([35, 12, 12, 7, 8, 8, 6, 6, 6]\)[/tex].

### Step 2: Calculate the mean difference.

To find the mean difference, sum the differences and divide by the number of differences.

[tex]\[ \text{Mean difference} = \frac{35 + 12 + 12 + 7 + 8 + 8 + 6 + 6 + 6}{9} = \approx 11.11 \][/tex]

### Step 3: Check the potential model [tex]\( y = 33x + 32.7 \)[/tex].

Calculate [tex]\( y \)[/tex] values using [tex]\( y = 33x + 32.7 \)[/tex] for each given [tex]\( x \)[/tex]:

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & 33 \cdot 0 + 32.7 = 32.7 \\ \hline 1 & 33 \cdot 1 + 32.7 = 65.7 \\ \hline 2 & 33 \cdot 2 + 32.7 = 98.7 \\ \hline 3 & 33 \cdot 3 + 32.7 = 131.7 \\ \hline 4 & 33 \cdot 4 + 32.7 = 164.7 \\ \hline 5 & 33 \cdot 5 + 32.7 = 197.7 \\ \hline 6 & 33 \cdot 6 + 32.7 = 230.7 \\ \hline 7 & 33 \cdot 7 + 32.7 = 263.7 \\ \hline 8 & 33 \cdot 8 + 32.7 = 296.7 \\ \hline 9 & 33 \cdot 9 + 32.7 = 329.7 \\ \hline \end{array} \][/tex]

The calculated values are [tex]\([32.7, 65.7, 98.7, 131.7, 164.7, 197.7, 230.7, 263.7, 296.7, 329.7]\)[/tex].

### Conclusion

The equation that best models the given data points appears to be:
[tex]\[ y = 33x + 32.7 \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{B. \, y = 33x + 32.7} \][/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.