We appreciate your visit to A construction manager is monitoring the progress of building a new house The scatterplot and table show the number of months since the start of. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We want to find a linear function of the form
[tex]$$
y = m x + b,
$$[/tex]
where [tex]$m$[/tex] is the slope and [tex]$b$[/tex] is the [tex]$y$[/tex]-intercept. The data given is:
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
0 & 100 \\
1 & 86 \\
2 & 65 \\
3 & 59 \\
4 & 41 \\
5 & 34 \\
\end{array}
\][/tex]
Step 1. Compute the slope [tex]$m$[/tex].
The formula for the slope is
[tex]$$
m = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2},
$$[/tex]
where [tex]$\bar{x}$[/tex] and [tex]$\bar{y}$[/tex] are the averages of the [tex]$x$[/tex] and [tex]$y$[/tex] values respectively.
After performing the calculations, the slope is found to be approximately
[tex]$$
m \approx -13.46.
$$[/tex]
Step 2. Compute the [tex]$y$[/tex]-intercept [tex]$b$[/tex].
Once the slope is determined, the [tex]$y$[/tex]-intercept can be calculated using the formula
[tex]$$
b = \bar{y} - m\bar{x}.
$$[/tex]
With the computed values, the intercept is approximately
[tex]$$
b \approx 97.81.
$$[/tex]
Step 3. Formulate the linear equation.
Substituting the values of [tex]$m$[/tex] and [tex]$b$[/tex] into the linear equation gives
[tex]$$
y \approx -13.46\,x + 97.81.
$$[/tex]
Rounding the slope to [tex]$-13.5$[/tex] and the intercept to [tex]$97.8$[/tex], the equation becomes
[tex]$$
y = -13.5\,x + 97.8.
$$[/tex]
Step 4. Identify the correct model.
Comparing with the answer choices:
[tex]\[
\begin{aligned}
\textbf{A: } & y=-13.5 x+97.8 \\
\textbf{B: } & y=-13.5 x+7.3 \\
\textbf{C: } & y=97.8 x-13.5 \\
\textbf{D: } & y=7.3 x-97.8
\end{aligned}
\][/tex]
we see that the equation we obtained, [tex]$y=-13.5 x+97.8$[/tex], corresponds to option A.
Final Answer: Option A.
[tex]$$
y = m x + b,
$$[/tex]
where [tex]$m$[/tex] is the slope and [tex]$b$[/tex] is the [tex]$y$[/tex]-intercept. The data given is:
[tex]\[
\begin{array}{c|c}
x & y \\
\hline
0 & 100 \\
1 & 86 \\
2 & 65 \\
3 & 59 \\
4 & 41 \\
5 & 34 \\
\end{array}
\][/tex]
Step 1. Compute the slope [tex]$m$[/tex].
The formula for the slope is
[tex]$$
m = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2},
$$[/tex]
where [tex]$\bar{x}$[/tex] and [tex]$\bar{y}$[/tex] are the averages of the [tex]$x$[/tex] and [tex]$y$[/tex] values respectively.
After performing the calculations, the slope is found to be approximately
[tex]$$
m \approx -13.46.
$$[/tex]
Step 2. Compute the [tex]$y$[/tex]-intercept [tex]$b$[/tex].
Once the slope is determined, the [tex]$y$[/tex]-intercept can be calculated using the formula
[tex]$$
b = \bar{y} - m\bar{x}.
$$[/tex]
With the computed values, the intercept is approximately
[tex]$$
b \approx 97.81.
$$[/tex]
Step 3. Formulate the linear equation.
Substituting the values of [tex]$m$[/tex] and [tex]$b$[/tex] into the linear equation gives
[tex]$$
y \approx -13.46\,x + 97.81.
$$[/tex]
Rounding the slope to [tex]$-13.5$[/tex] and the intercept to [tex]$97.8$[/tex], the equation becomes
[tex]$$
y = -13.5\,x + 97.8.
$$[/tex]
Step 4. Identify the correct model.
Comparing with the answer choices:
[tex]\[
\begin{aligned}
\textbf{A: } & y=-13.5 x+97.8 \\
\textbf{B: } & y=-13.5 x+7.3 \\
\textbf{C: } & y=97.8 x-13.5 \\
\textbf{D: } & y=7.3 x-97.8
\end{aligned}
\][/tex]
we see that the equation we obtained, [tex]$y=-13.5 x+97.8$[/tex], corresponds to option A.
Final Answer: Option A.
Thanks for taking the time to read A construction manager is monitoring the progress of building a new house The scatterplot and table show the number of months since the start of. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
