Let's break down the problem step by step and evaluate the expression correctly.
1. Identify Key Words:
- "a number" will be replaced with [tex]\( n \)[/tex].
- "cubed" indicates raising to the power of 3 ([tex]\( n^3 \)[/tex]).
- "minus" signifies subtraction (-).
- "five" is the number 5.
2. Translate the Phrase to an Expression:
- The phrase "a number cubed minus five" translates to the mathematical expression [tex]\( n^3 - 5 \)[/tex].
3. Substitute the Given Value:
- We are asked to evaluate the expression for [tex]\( n = 3 \)[/tex]. This means we will substitute 3 in place of [tex]\( n \)[/tex] in the expression [tex]\( n^3 - 5 \)[/tex].
4. Evaluate the Expression:
- First, compute the value of [tex]\( 3^3 \)[/tex].
- [tex]\( 3^3 = 3 \times 3 \times 3 = 27 \)[/tex].
- Then subtract 5 from this value:
[tex]\[
27 - 5 = 22
\][/tex]
So, the value of the expression when [tex]\( n = 3 \)[/tex] is 22.
Now let's review the provided options:
- The correct expression derived from the key words is [tex]\( n^3 - 5 \)[/tex].
- Evaluating by substituting 3 for the variable is correct, and we have verified the correct procedure.
- The final value of the expression when [tex]\( n = 3 \)[/tex] is indeed 22.
Correct Answers Checklist:
- The expression is written as [tex]\( n^3 - 5 \)[/tex].
- Evaluating by substituting 3 in for the variable.
- The value of expression is 22.
