Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To solve this problem, we need to use the given linear model [tex]\( y = 14.2992x - 4.5199 \)[/tex], where [tex]\( y \)[/tex] represents the revenue and [tex]\( x \)[/tex] represents the number of patrons attending. We are asked to predict the revenue when 121 patrons attend.
Here's a step-by-step breakdown:
1. Identify the linear model and the parameters:
- The linear model is given by [tex]\( y = 14.2992x - 4.5199 \)[/tex].
- The slope ([tex]\( m \)[/tex]) is 14.2992.
- The y-intercept ([tex]\( b \)[/tex]) is -4.5199.
2. Substitute the given value of [tex]\( x \)[/tex] (the number of patrons) into the linear model:
- The number of patrons [tex]\( x \)[/tex] is 121.
3. Calculate the revenue [tex]\( y \)[/tex] by substituting [tex]\( x \)[/tex] into the linear equation:
- Substitute [tex]\( x = 121 \)[/tex] into the equation [tex]\( y = 14.2992 \cdot x - 4.5199 \)[/tex]:
[tex]\[ y = 14.2992 \cdot 121 - 4.5199 \][/tex]
4. Evaluate the expression:
- First, multiply the slope by the number of patrons:
[tex]\[ 14.2992 \cdot 121 = 1730.2032 \][/tex]
- Then, subtract the y-intercept:
[tex]\[ 1730.2032 - 4.5199 = 1725.6833 \][/tex]
5. State the final result:
- Therefore, the revenue predicted for 121 patrons attending is [tex]\( 1725.6833 \)[/tex].
So, the predicted revenue when 121 patrons attend is $1725.68 (rounded to two decimal places).
Here's a step-by-step breakdown:
1. Identify the linear model and the parameters:
- The linear model is given by [tex]\( y = 14.2992x - 4.5199 \)[/tex].
- The slope ([tex]\( m \)[/tex]) is 14.2992.
- The y-intercept ([tex]\( b \)[/tex]) is -4.5199.
2. Substitute the given value of [tex]\( x \)[/tex] (the number of patrons) into the linear model:
- The number of patrons [tex]\( x \)[/tex] is 121.
3. Calculate the revenue [tex]\( y \)[/tex] by substituting [tex]\( x \)[/tex] into the linear equation:
- Substitute [tex]\( x = 121 \)[/tex] into the equation [tex]\( y = 14.2992 \cdot x - 4.5199 \)[/tex]:
[tex]\[ y = 14.2992 \cdot 121 - 4.5199 \][/tex]
4. Evaluate the expression:
- First, multiply the slope by the number of patrons:
[tex]\[ 14.2992 \cdot 121 = 1730.2032 \][/tex]
- Then, subtract the y-intercept:
[tex]\[ 1730.2032 - 4.5199 = 1725.6833 \][/tex]
5. State the final result:
- Therefore, the revenue predicted for 121 patrons attending is [tex]\( 1725.6833 \)[/tex].
So, the predicted revenue when 121 patrons attend is $1725.68 (rounded to two decimal places).
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.