We appreciate your visit to A construction manager is monitoring the progress of a new house build 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 :
To determine which function best models the data, we need to find the relationship between the number of months since the start of the build (x) and the percentage of the house left to build (y). The data points provided are:
- Month 0: 100% left
- Month 1: 86% left
- Month 2: 65% left
- Month 3: 59% left
- Month 4: 41% left
- Month 5: 34% left
The relationship between these two variables appears to be linear, so we can use a linear regression model to represent this relationship in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
### Step-by-Step Solution
1. Identify the Variables:
- Independent variable (x): Number of months since the start of the build.
- Dependent variable (y): Percentage of the house left to build.
2. Determine the Slope (m) and Intercept (b):
- From the data, we can fit a line that best models this relationship.
- The slope [tex]\( m \)[/tex] represents the change in percentage left to build per month.
- The intercept [tex]\( b \)[/tex] represents the percentage of the house left at [tex]\( x = 0 \)[/tex].
3. Calculate Slope and Intercept:
- Through linear regression analysis, the calculated slope [tex]\( m \)[/tex] is approximately [tex]\(-13.46\)[/tex].
- The calculated intercept [tex]\( b \)[/tex] is approximately [tex]\(97.81\)[/tex].
4. Match the Function:
- Based on the calculations, the function that best matches the data is:
[tex]\[
y = -13.5x + 97.8
\][/tex]
- This function closely matches the given options and represents the decrease in the percentage of the house left to build as time progresses.
Thus, the correct choice among the given functions is [tex]\( y = -13.5x + 97.8 \)[/tex]. This linear function accurately models the relationship between the number of months since construction began and the percentage of the house still left to build.
- Month 0: 100% left
- Month 1: 86% left
- Month 2: 65% left
- Month 3: 59% left
- Month 4: 41% left
- Month 5: 34% left
The relationship between these two variables appears to be linear, so we can use a linear regression model to represent this relationship in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
### Step-by-Step Solution
1. Identify the Variables:
- Independent variable (x): Number of months since the start of the build.
- Dependent variable (y): Percentage of the house left to build.
2. Determine the Slope (m) and Intercept (b):
- From the data, we can fit a line that best models this relationship.
- The slope [tex]\( m \)[/tex] represents the change in percentage left to build per month.
- The intercept [tex]\( b \)[/tex] represents the percentage of the house left at [tex]\( x = 0 \)[/tex].
3. Calculate Slope and Intercept:
- Through linear regression analysis, the calculated slope [tex]\( m \)[/tex] is approximately [tex]\(-13.46\)[/tex].
- The calculated intercept [tex]\( b \)[/tex] is approximately [tex]\(97.81\)[/tex].
4. Match the Function:
- Based on the calculations, the function that best matches the data is:
[tex]\[
y = -13.5x + 97.8
\][/tex]
- This function closely matches the given options and represents the decrease in the percentage of the house left to build as time progresses.
Thus, the correct choice among the given functions is [tex]\( y = -13.5x + 97.8 \)[/tex]. This linear function accurately models the relationship between the number of months since construction began and the percentage of the house still left to build.
Thanks for taking the time to read A construction manager is monitoring the progress of a new house build 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
