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The average number of students per classroom at Central High School from 2000 to 2010 can be modeled by the equation y = 0.56x + 27.2, where x represents the number of years since 2000, and y represents the average number of students per classroom. Which of the following best describes the meaning of the number 0.56 in the equation?
  • a)
    The total number of students at the school in 2000
  • b)
    The average number of students per classroom in 2000
  • c)
    The estimated increase in the average number of students per classroom each year
  • d)
    The estimated difference between the average number of students per classroom in 2010 and in 2000
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The average number of students per classroom at Central High School fr...
Meaning of the number 0.56 in the equation:

The equation given is y = 0.56x + 27.2, where x represents the number of years since 2000 and y represents the average number of students per classroom at Central High School from 2000 to 2010. We need to determine the meaning of the number 0.56 in the equation.

c) The estimated increase in the average number of students per classroom each year.

Explanation:

1. Understanding the equation:
- The equation y = 0.56x + 27.2 is in slope-intercept form, y = mx + b, where m represents the slope of the line and b represents the y-intercept.
- In this equation, the slope (0.56) represents the rate of change of y with respect to x.
- Since x represents the number of years since 2000 and y represents the average number of students per classroom, the slope indicates how y changes as x increases.

2. Analyzing the slope (0.56):
- The slope of 0.56 indicates that for every increase of 1 year since 2000 (x), the average number of students per classroom (y) is estimated to increase by 0.56.
- This means that the average number of students per classroom is expected to increase by 0.56 every year from 2000 to 2010 according to the model.

3. Eliminating other options:
- Option a) states that 0.56 represents the total number of students at the school in 2000, which is not supported by the equation.
- Option b) states that 0.56 represents the average number of students per classroom in 2000, which is not accurate as the y-intercept (27.2) represents the average number of students per classroom in 2000, not the slope.
- Option d) states that 0.56 represents the estimated difference between the average number of students per classroom in 2010 and in 2000, which is not supported by the equation.

4. Conclusion:
- The best description of the number 0.56 in the equation is that it represents the estimated increase in the average number of students per classroom each year from 2000 to 2010.
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The average number of students per classroom at Central High School fr...
Choice C is correct. In the equation y = 0.56x + 27.2, the value of x increases by 1 for each year that passes. Each time x increases by 1, y increases by 0.56 since 0.56 is the slope of the graph of this equation. Since y represents the average number of students per classroom in the year represented by x, it follows that, according to the model, the estimated increase each year in the average number of students per classroom at Central High School is 0.56.
Choice A is incorrect because the total number of students in the school in 2000 is the product of the average number of students per classroom and the total number of classrooms, which would appropriately be approximated by the y-intercept (27.2) times the total number of classrooms, which is not given. Choice B is incorrect because the average number of students per classroom in 2000 is given by the y-intercept of the graph of the equation, but the question is asking for the meaning of the number 0.56, which is the slope. Choice D is incorrect because 0.56 represents the estimated yearly change in the average number of students per classroom. The estimated difference between the average number of students per classroom in 2010 and 2000 is 0.56 times the number of years that have passed between 2000 and 2010, that is, 0.56 × 10 = 5.6.
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The average number of students per classroom at Central High School from 2000 to 2010 can be modeled by the equation y = 0.56x + 27.2, where x represents the number of years since 2000, and y represents the average number of students per classroom. Which of the following best describes the meaning of the number 0.56 in the equation?a)The total number of students at the school in 2000b)The average number of students per classroom in 2000c)The estimated increase in the average number of students per classroom each yeard)The estimated difference between the average number of students per classroom in 2010 and in 2000Correct answer is option 'C'. Can you explain this answer?
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