Which Is A Correct Statement About The Description two Less Than The Quotient Of A Number Cubed And Sixteen, Increased By Eight When $n=4$?A. The Correct Expression Is $\frac{n^3}{16} - 2 + 8$.B. The Correct Expression Is

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When it comes to mathematical expressions, it's essential to understand the description and evaluate the statements correctly. In this article, we will explore the description "two less than the quotient of a number cubed and sixteen, increased by eight" and determine the correct statement when $n=4$.

Breaking Down the Description

The description "two less than the quotient of a number cubed and sixteen, increased by eight" can be broken down into several parts:

  • "a number cubed" means the number raised to the power of 3.
  • "the quotient of" means the result of dividing one quantity by another.
  • "two less than" means subtracting 2 from the result.
  • "increased by eight" means adding 8 to the result.

Evaluating the Statements

Now that we have broken down the description, let's evaluate the statements:

A. The correct expression is $\frac{n^3}{16} - 2 + 8$

This statement can be evaluated by substituting $n=4$ into the expression:

4316−2+8\frac{4^3}{16} - 2 + 8

6416−2+8\frac{64}{16} - 2 + 8

4−2+84 - 2 + 8

1010

However, this expression does not accurately represent the description "two less than the quotient of a number cubed and sixteen, increased by eight".

B. The correct expression is $\frac{n^3}{16} + 8 - 2$

This statement can be evaluated by substituting $n=4$ into the expression:

4316+8−2\frac{4^3}{16} + 8 - 2

6416+8−2\frac{64}{16} + 8 - 2

4+8−24 + 8 - 2

1010

This expression accurately represents the description "two less than the quotient of a number cubed and sixteen, increased by eight".

Conclusion

In conclusion, the correct statement about the description "two less than the quotient of a number cubed and sixteen, increased by eight" when $n=4$ is:

  • The correct expression is $\frac{n^3}{16} + 8 - 2$.

This expression accurately represents the description and can be evaluated by substituting $n=4$ into the expression.

Understanding the Importance of Mathematical Expressions

Mathematical expressions are essential in mathematics and are used to represent relationships between variables. Understanding the description and evaluating the statements correctly is crucial in mathematics and has many real-world applications.

Real-World Applications of Mathematical Expressions

Mathematical expressions have many real-world applications, including:

  • Science: Mathematical expressions are used to model and analyze scientific phenomena, such as the motion of objects and the behavior of populations.
  • Engineering: Mathematical expressions are used to design and optimize systems, such as bridges and electronic circuits.
  • Economics: Mathematical expressions are used to model and analyze economic systems, such as supply and demand.

Conclusion

In conclusion, understanding the description and evaluating the statements correctly is crucial in mathematics and has many real-world applications. The correct statement about the description "two less than the quotient of a number cubed and sixteen, increased by eight" when $n=4$ is:

  • The correct expression is $\frac{n^3}{16} + 8 - 2$.

In this article, we will answer some frequently asked questions related to the description "two less than the quotient of a number cubed and sixteen, increased by eight" and the correct statement when $n=4$.

Q: What is the correct expression for the description "two less than the quotient of a number cubed and sixteen, increased by eight"?

A: The correct expression is $\frac{n^3}{16} + 8 - 2$.

Q: Why is the expression $\frac{n^3}{16} - 2 + 8$ incorrect?

A: The expression $\frac{n^3}{16} - 2 + 8$ is incorrect because it does not accurately represent the description "two less than the quotient of a number cubed and sixteen, increased by eight". The correct expression should be $\frac{n^3}{16} + 8 - 2$.

Q: What is the value of the expression $\frac{n^3}{16} + 8 - 2$ when $n=4$?

A: The value of the expression $\frac{n^3}{16} + 8 - 2$ when $n=4$ is $10$.

Q: How do I evaluate the expression $\frac{n^3}{16} + 8 - 2$ when $n=4$?

A: To evaluate the expression $\frac{n^3}{16} + 8 - 2$ when $n=4$, you can substitute $n=4$ into the expression and simplify:

4316+8−2\frac{4^3}{16} + 8 - 2

6416+8−2\frac{64}{16} + 8 - 2

4+8−24 + 8 - 2

1010

Q: What is the importance of understanding mathematical expressions?

A: Understanding mathematical expressions is crucial in mathematics and has many real-world applications. Mathematical expressions are used to represent relationships between variables and are essential in science, engineering, and economics.

Q: Can you provide more examples of mathematical expressions?

A: Yes, here are a few more examples of mathematical expressions:

  • 2x+32x + 3

  • x2−1\frac{x}{2} - 1

  • x2+4x−5x^2 + 4x - 5

These expressions can be evaluated by substituting values for $x$ and simplifying.

Conclusion

In conclusion, understanding the description and evaluating the statements correctly is crucial in mathematics and has many real-world applications. The correct statement about the description "two less than the quotient of a number cubed and sixteen, increased by eight" when $n=4$ is:

  • The correct expression is $\frac{n^3}{16} + 8 - 2$.

This expression accurately represents the description and can be evaluated by substituting $n=4$ into the expression.

Additional Resources

For more information on mathematical expressions, you can refer to the following resources:

  • Mathematics textbooks: Many mathematics textbooks provide examples and exercises on mathematical expressions.
  • Online resources: Websites such as Khan Academy and Mathway provide interactive lessons and exercises on mathematical expressions.
  • Mathematical software: Software such as Mathematica and Maple can be used to evaluate and manipulate mathematical expressions.

Conclusion

In conclusion, understanding mathematical expressions is crucial in mathematics and has many real-world applications. The correct statement about the description "two less than the quotient of a number cubed and sixteen, increased by eight" when $n=4$ is:

  • The correct expression is $\frac{n^3}{16} + 8 - 2$.

This expression accurately represents the description and can be evaluated by substituting $n=4$ into the expression.