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?
The dependent variable is the number of points scored.
In the equation p = 5n, 'p' represents the points scored on the quiz, which is dependent on the number of questions answered correctly, denoted by 'n'. Hence, the points scored can vary based on how many questions are answered correctly, making 'p' the dependent variable.
This statement accurately reflects the relationship defined by the equation p = 5n. Since the points scored (p) depend on the number of correctly answered questions (n), 'p' is the dependent variable, influenced directly by 'n'.
This choice incorrectly identifies the dependent variable. In the given equation, 'n' (the number of questions answered correctly) is the independent variable, as it determines the value of 'p' (points scored). The dependent variable must be the one that changes in response to the independent variable.
This option misinterprets the equation. The '5' is a constant multiplier that signifies how many points are awarded per question, not a variable. The dependent variable should be the total points scored (p), which changes based on the number of questions answered correctly.
This statement is inaccurate because it describes a ratio rather than identifying a variable. The equation relates points to questions answered correctly, but it does not establish the number of questions per point as a dependent variable. Instead, it simply shows how many points are awarded based on the number of questions.
Understanding the relationship between independent and dependent variables is crucial in mathematical equations. In the context of the given problem, the points scored on the quiz (p) are directly influenced by the number of questions answered correctly (n), confirming that the dependent variable is indeed the number of points scored. Other choices either misidentify the dependent variable or misinterpret the components of the equation, underlining the importance of clarity in mathematical relationships.
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