Answered

Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

A student believes there is a correlation between the number of texts sent during class and GPA. The student collected data and found that the line of fit can be modeled by the equation [tex]\rho = 3.9 - 0.1x[/tex].

Identify and interpret the slope in this scenario.

A. The slope is 3.9. Starting at 0.1, the GPA will increase by 3.9 for every text sent in class.
B. The slope is 3.9. Starting at 0.1, the GPA will decrease by 3.9 for every text sent in class.
C. The slope is -0.1. Starting at 3.9, the GPA will increase by 0.1 for every text sent in class.
D. The slope is -0.1. Starting at 3.9, the GPA will decrease by 0.1 for every text sent in class.

Sagot :

GinnyAnswer
To address the student's question about the correlation between the number of texts sent during class and GPA, let's carefully examine the given equation [tex]\(\rho = 3.9 - 0.1x\)[/tex].

In this equation:
- [tex]\(\rho\)[/tex] stands for the GPA.
- [tex]\(x\)[/tex] represents the number of texts sent during class.
- The term [tex]\(3.9\)[/tex] is the y-intercept, which is the GPA when no texts are sent.
- The term [tex]\(-0.1\)[/tex] is the slope, which indicates the change in GPA for each additional text sent during class.

Step-by-Step Explanation:

1. Identify the Slope and Intercept:
- The slope (represented as [tex]\(m\)[/tex] in linear equations) is [tex]\(-0.1\)[/tex].
- The y-intercept is [tex]\(3.9\)[/tex].

2. Interpret the Slope:
- The slope of [tex]\(-0.1\)[/tex] means that for every additional text sent during class, the GPA decreases by [tex]\(0.1\)[/tex].
- A negative slope indicates a negative relationship between the number of texts sent and the GPA; as one increases, the other decreases.

3. Interpret the Full Equation:
- When no texts are sent ([tex]\(x = 0\)[/tex]), the GPA ([tex]\(\rho\)[/tex]) starts at [tex]\(3.9\)[/tex].
- For each additional text sent ([tex]\(x\)[/tex] increases by 1), the GPA ([tex]\(\rho\)[/tex]) decreases by [tex]\(0.1\)[/tex].

Conclusion:
Given the correct slope and interpretation:
The slope is [tex]\(-0.1\)[/tex]. Starting at [tex]\(3.9\)[/tex], the GPA will decrease by [tex]\(0.1\)[/tex] for every text sent in class.

Therefore, the correct answer is:
"The slope is [tex]\(-0.1\)[/tex]. Starting at [tex]\(3.9\)[/tex], the GPA will decrease by [tex]\(0.1\)[/tex] for every text sent in class."
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.