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 N=4 N = 4 ?A. The Correct Expression Is N 3 16 − 2 + 8 \frac{n^3}{16} - 2 + 8 16 N 3 ​ − 2 + 8 .B. The Correct Expression Is $2 -

Introduction

In mathematics, expressions and equations are used to describe various mathematical relationships and operations. When dealing with expressions, it's essential to understand the correct interpretation of the given description to arrive at the correct solution. In this article, we will explore the correct statement about the description "two less than the quotient of a number cubed and sixteen, increased by eight" when $n=4$.

Breaking Down the Description

The given description can be broken down into several parts to understand the correct interpretation. The description states "two less than the quotient of a number cubed and sixteen, increased by eight." Let's analyze each part of the description:

• Two less than: This implies that we need to subtract 2 from the result of the expression.
• The quotient of a number cubed and sixteen: This implies that we need to divide the cube of a number by 16.
• Increased by eight: This implies that we need to add 8 to the result of the expression.

Correct Expression

To find the correct expression, we need to follow the order of operations (PEMDAS):

1. Cube the number: The number is $n$, so we need to cube it: $n^3$.
2. Divide by sixteen: We need to divide the result by 16: $\frac{n^3}{16}$.
3. Subtract 2: We need to subtract 2 from the result: $\frac{n^3}{16} - 2$.
4. Add 8: We need to add 8 to the result: $\frac{n^3}{16} - 2 + 8$.

Evaluating the Correct Expression

Now that we have the correct expression, let's evaluate it when $n=4$:

$\frac{n^3}{16} - 2 + 8$

Substituting $n=4$:

$\frac{4^3}{16} - 2 + 8$

Evaluating the expression:

$\frac{64}{16} - 2 + 8$

Simplifying the expression:

$4 - 2 + 8$

Evaluating the expression:

$10$

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 $\frac{n^3}{16} - 2 + 8$

This expression correctly interprets the given description and evaluates to the correct result when $n=4$.

Discussion

• What is the correct interpretation of the given description?
  • The correct interpretation is that we need to cube the number, divide by 16, subtract 2, and then add 8.
• How does the correct expression evaluate when $n=4$?
  • The correct expression evaluates to 10 when $n=4$.

References

• [1] Khan Academy. (n.d.). Order of Operations. Retrieved from https://www.khanacademy.org/math/algebra/x2f-alg-review/x2f-alg-review-1/x2f-alg-review-1-1
• [2] Mathway. (n.d.). Order of Operations. Retrieved from https://www.mathway.com/subjects/Algebra/Order of Operations

Additional Resources

• [1] Algebra.com. (n.d.). Order of Operations. Retrieved from https://www.algebra.com/algebra/homework/order-of-operations/order-of-operations.html
• [2] Purplemath. (n.d.). Order of Operations. Retrieved from https://www.purplemath.com/modules/orderops.htm
  Frequently Asked Questions about the Correct Statement ===========================================================

Q: What is the correct interpretation of the given description?

A: The correct interpretation is that we need to cube the number, divide by 16, subtract 2, and then add 8.

Q: How does the correct expression evaluate when $n=4$?

A: The correct expression evaluates to 10 when $n=4$.

Q: What is the order of operations in the correct expression?

A: The order of operations in the correct expression is:

1. Cube the number: $n^3$
2. Divide by 16: $\frac{n^3}{16}$
3. Subtract 2: $\frac{n^3}{16} - 2$
4. Add 8: $\frac{n^3}{16} - 2 + 8$

Q: Can you provide an example of how to evaluate the correct expression?

A: Yes, let's evaluate the correct expression when $n=4$:

$\frac{n^3}{16} - 2 + 8$

Substituting $n=4$:

$\frac{4^3}{16} - 2 + 8$

Evaluating the expression:

$\frac{64}{16} - 2 + 8$

Simplifying the expression:

$4 - 2 + 8$

Evaluating the expression:

$10$

Q: What is the significance of the correct expression in real-world applications?

A: The correct expression can be used in various real-world applications, such as:

• Calculating the volume of a cube
• Determining the area of a square
• Finding the perimeter of a rectangle

Q: Can you provide a step-by-step guide on how to evaluate the correct expression?

A: Yes, here is a step-by-step guide on how to evaluate the correct expression:

1. Cube the number: $n^3$
2. Divide by 16: $\frac{n^3}{16}$
3. Subtract 2: $\frac{n^3}{16} - 2$
4. Add 8: $\frac{n^3}{16} - 2 + 8$

Q: What are some common mistakes to avoid when evaluating the correct expression?

A: Some common mistakes to avoid when evaluating the correct expression include:

• Not following the order of operations
• Not simplifying the expression correctly
• Not evaluating the expression correctly

Q: Can you provide additional resources for learning more about the correct expression?

A: Yes, here are some additional resources for learning more about the correct expression:

• [1] Khan Academy. (n.d.). Order of Operations. Retrieved from https://www.khanacademy.org/math/algebra/x2f-alg-review/x2f-alg-review-1/x2f-alg-review-1-1
• [2] Mathway. (n.d.). Order of Operations. Retrieved from https://www.mathway.com/subjects/Algebra/Order of Operations

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 $\frac{n^3}{16} - 2 + 8$

This expression correctly interprets the given description and evaluates to the correct result when $n=4$. We hope this article has provided you with a better understanding of the correct expression and its significance in real-world applications.