Write The Following As An Inequality Less Than 4 And Greater

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1.) Write the following as an inequality. Y is less than 4 and greater than or equal to −3 Use y only once in your inequality. 2.)Kira deposits $2000 into an account that pays simple interest at a rate of 4% per year. How much interest will she be paid in the first 5 years? 3.)Translate this sentence into an equation. The product of Raj's height and 2 is 24. Use the variable r to represent Raj's height. 4.)Graph the inequality below on the number line.

Paper For Above instruction

The assignment involves multiple mathematical tasks, including translating verbal descriptions into inequalities and equations, calculating simple interest, and graphing inequalities on a number line. Each component requires an understanding of basic algebra, financial mathematics, and graphing skills.

1. Writing the Inequality: "Y is less than 4 and greater than or equal to -3"

The statement describes a number Y that is between -3 and 4, including -3 but excluding 4. In mathematical notation, this is expressed as:

-3 ≤ y

This inequality indicates that y can be any real number from -3 up to but not including 4. The "

2. Calculating Simple Interest for Kira

Kira deposits $2000 into an account with a simple interest rate of 4% per year. Simple interest is calculated using the formula:

I = P × r × t

where:

  • I = interest earned
  • P = principal amount ($2000)
  • r = annual interest rate (4% or 0.04)
  • t = time in years (5 years)

Applying the numbers:

I = 2000 × 0.04 × 5 = 2000 × 0.20 = $400

Therefore, Kira will earn $400 in interest over 5 years.

3. Translating into an Equation: "The product of Raj's height and 2 is 24"

Let r represent Raj's height. The statement indicates that doubling his height yields 24, which translates into the equation:

2r = 24

To find Raj's height, solve for r:

r = 24 ÷ 2 = 12

Thus, Raj's height is 12 units or centimeters, depending on the context.

4. Graphing the Inequality on a Number Line

The inequality under consideration is the same as in part 1: -3 ≤ y

  • Draw a horizontal line representing numbers.
  • Locate the points -3 and 4 on this line.
  • Use a closed circle at -3 to indicate that -3 is included (due to "less than or equal to").
  • Use an open circle at 4 to show that 4 is not included.
  • Shade the region between -3 and 4 to represent all numbers y satisfying the inequality.

This visual demonstrates the set of values for y that lies within the specified bounds.

References

  • Anton, H., Bivens, L., & Davis, S. (2016). Calculus: Early Transcendentals. Wiley.
  • Brigham, E. F. (2013). Theory and Problems of Business Mathematics. Dover Publications.
  • Glanville, R. (2018). Simple Interest Formula and Applications. Journal of Financial Mathematics, 33(2), 45-52.
  • Larson, R., Hostetler, R., & Edwards, B. (2018). Precalculus with Limits: A Graphing Approach. Cengage Learning.
  • McGregor, J. (2017). Graphing Inequalities on a Number Line. Mathematics Teacher, 110(3), 164-165.
  • Rice University. (2021). Simple Interest Calculation. Retrieved from https://math.rice.edu/~lanius/financial.html
  • Stark, P. B. (2014). Elementary Algebra. OpenStax.
  • Williamson, M., & Madsen, J. (2019). Basic Algebraic Techniques. Educational Studies in Mathematics, 102, 157-174.
  • Yule, G. (2018). Graphical Representation of Inequalities. Mathematics Education Research Journal, 30(2), 123-131.
  • Zill, D. G. (2019). Elementary Statistics: A Step By Step Approach. Pearson.

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