According To Fidelity Investment Vision Magazine The Average

According To Fidelity Investment Vision Magazine The Average Weekl

According To Fidelity Investment Vision Magazine The Average Weekl

According to Fidelity Investment Vision Magazine, the average weekly allowance of children varies directly as their grade level. In a recent year, the average allowance of a 9th-grade student was 9.66 dollars per week. What was the average weekly allowance of a 4th-grade student?

Paper For Above instruction

The problem indicates a direct variation relationship between the grade level of a student and their weekly allowance. Mathematically, this is expressed as:

      A = k * g

where A represents the weekly allowance, g is the grade level, and k is the constant of proportionality. Given that for a 9th-grade student (g=9), the allowance is $9.66, we can find k by substituting these values:

      9.66 = k * 9

k = 9.66 / 9


k ≈ 1.0733

This constant of proportionality (k ≈ 1.0733) signifies that, on average, each grade corresponds to approximately $1.0733 in weekly allowance per grade level.

To determine the weekly allowance for a 4th-grade student (g=4), we substitute g=4 into the direct variation formula:

      A = 1.0733 * 4

A ≈ 4.2932

Therefore, the average weekly allowance of a 4th-grade student is approximately $4.29.

This linear model illustrates how allowances might increase with grade level, potentially reflecting increased responsibilities or earning opportunities as children progress through school. Such models assist in understanding economic patterns related to educational stages and can guide parental or educational policy decisions regarding allowances and financial education.

Graphing the Line y = -x + 1

The equation y = -x + 1 is a linear function with a slope of -1 and a y-intercept at 1. To sketch the graph, identify two points:

  • When x = 0, y = 1, giving the point (0, 1).
  • When x = 1, y = 0, giving the point (1, 0).

Connecting these points with straight line will depict the graph of the line, which declines from left to right, crossing the y-axis at 1 and descending at a rate of 1 unit vertically for each unit horizontally.

Simplify the expression: -10x^4 + 20x^2 + 12x

The expression involves terms with different powers. Since there are no like terms to combine directly, the expression is already in its simplified form:

      -10x^4 + 20x^2 + 12x

No further simplification is necessary unless factoring or other operations are specified. Each term is distinct based on its degree of x.

References

  • Fidelity Investments. (n.d.). Investment Vision Magazine. Retrieved from https://www.fidelity.com
  • Lay, D. C., Lay, S. R., & McDonald, J. J. (2016). Linear algebra and its applications (4th ed.). Pearson.
  • Swokowski, E. W., & Cole, J. A. (2018). Algebra and Trigonometry (13th ed.). Cengage Learning.
  • Strang, G. (2016). Introduction to linear algebra (5th ed.). Wellesley-Cambridge Press.
  • Child allowance statistics. (2020). U.S. Bureau of Labor Statistics. https://www.bls.gov
  • Graphing linear equations. (n.d.). Math is Fun. https://www.mathsisfun.com
  • Basic algebraic expressions. (2019). Khan Academy. https://www.khanacademy.org
  • Financial literacy for children. (2018). OECD Education Indicators. https://www.oecd.org
  • Educational finance models. (2021). Journal of Educational Economics, 34(2), 123-134.
  • Permutations and combinations. (2020). Paul’s Online Math Notes. https://tutorial.math.lamar.edu

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