1. Each question on a math quiz is worth 5 points. The equation p = 5n relates the number of questions answered correctly, 1, and the points earned on the quiz. p. Which of the following is true?
Answer: A
The dependent variable is the number of points scored.
In the equation p = 5n, p represents the total points earned, making it the dependent variable, as its value relies on the number of correctly answered questions (n).
A) The dependent variable is the number of points scored.
This statement is correct because, in the equation p = 5n, the variable p (points scored) depends on the number of questions answered correctly, represented by n. As n changes, p will change accordingly, indicating that p is the dependent variable.
B) The dependent variable is the number of questions answered correctly.
This option is incorrect because the number of questions answered correctly (n) is the independent variable in the equation. The value of n influences the points scored, but it does not depend on the points.
C) The dependent variable is the 5 points scored for each question.
This statement is misleading. While the equation involves a multiplier of 5, this value is a constant and does not represent a variable. The dependent variable must be something that changes based on the independent variable, which in this case is p.
D) The dependent variable is the 1/5 question answered per scored point.
This option is incorrect and nonsensical in the context of the given equation. The equation does not imply a relationship where points are divided by a fraction of questions answered; rather, it shows that points are calculated as a function of the number of correct answers.
Conclusion
The correct answer is definitive as it accurately identifies p as the dependent variable that changes based on the independent variable n. All other options either misinterpret the relationship in the equation or incorrectly define the variables involved, showcasing a misunderstanding of dependent and independent variables in mathematical equations.