To analyze the relationship between the number of questions correct and the score on the test, we need to address several components:
1. Independent and Dependent Variables:
- The independent variable is the number of questions correctly answered, [tex]\( x \)[/tex]. This means [tex]\( x \)[/tex] can vary independently.
- The dependent variable is the score on the test, [tex]\( V \)[/tex]. This score depends directly on the number of questions [tex]\( x \)[/tex] that are answered correctly.
2. Function Relating the Variables:
Since each question answered correctly is worth 3 points, the function [tex]\( V(x) \)[/tex] that relates the number of correct answers to the test score can be given by:
[tex]\[
V(x) = 3x
\][/tex]
This equation indicates that for every correct question, the score increases by 3 points.
3. Specific Example Calculation:
Let's consider [tex]\( x = 7 \)[/tex] as a specific example, which means Mila correctly answered 7 questions. Using the function [tex]\( V(x) \)[/tex]:
[tex]\[
V(7) = 3 \times 7 = 21
\][/tex]
Therefore, when Mila answers 7 questions correctly, her score on the test is 21 points.
Summarizing all this, we can fill in the blanks as follows:
The independent variable, [tex]\( x \)[/tex], represents the number of questions correct, and the dependent variable is the score on the test, because the score on the test depends on the number of questions correct.
A function relating these variables is [tex]\( V(x) = 3x \)[/tex].
[tex]\( V(7) \)[/tex], meaning 21 points.
