Question
Which is a correct statement about the description “two less than the quotient of a number cubed and nine, increased by twelve” when n = 3? Select the three correct answers..
The correct expression is 6 minus StartFraction n cubed Over 9 EndFraction + 12.
The correct expression is StartFraction n cubed Over 9 EndFraction minus 6 + 12.
One of the steps to determining the value when n = 3 is 3 minus 6 + 12.
One of the steps to determining the value when n = 3 is 6 minus 3 + 12.
The value when n = 3 is 11.
The value when n = 3 is 13.
The value when n = 3 is 15.
The value when n = 3 is 17.
The correct expression is 6 minus StartFraction n cubed Over 9 EndFraction + 12.
The correct expression is StartFraction n cubed Over 9 EndFraction minus 6 + 12.
One of the steps to determining the value when n = 3 is 3 minus 6 + 12.
One of the steps to determining the value when n = 3 is 6 minus 3 + 12.
The value when n = 3 is 11.
The value when n = 3 is 13.
The value when n = 3 is 15.
The value when n = 3 is 17.
Answers
GPT-4o mini
To analyze the description “two less than the quotient of a number cubed and nine, increased by twelve” and evaluate it for \( n = 3 \), we need to translate the description into a mathematical expression.
1. "the quotient of a number cubed and nine" translates to \( \frac{n^3}{9} \).
2. "two less than" indicates we subtract 2, resulting in \( \frac{n^3}{9} - 2 \).
3. "increased by twelve" means we then add 12, resulting in:
\[
\frac{n^3}{9} - 2 + 12
\]
which simplifies to:
\[
\frac{n^3}{9} + 10.
\]
Now, substituting \( n = 3 \):
\[
n^3 = 3^3 = 27,
\]
therefore:
\[
\frac{27}{9} + 10 = 3 + 10 = 13.
\]
Now let's check the statements provided:
1. **"The correct expression is \( 6 - \frac{n^3}{9} + 12 \)."** - **False.** The expression is \( \frac{n^3}{9} + 10 \).
2. **"The correct expression is \( \frac{n^3}{9} - 6 + 12 \)."** - **False.** The expression does not match; it should include \( -2 \) not \( -6 \).
3. **"One of the steps to determining the value when \( n = 3 \) is \( 3 - 6 + 12 \)."** - **False.** This step does not apply to our expression.
4. **"One of the steps to determining the value when \( n = 3 \) is \( 6 - 3 + 12 \)."** - **False.** Incorrect arithmetic expression.
5. **"The value when \( n = 3 \) is 11."** - **False.** We calculated the value is 13.
6. **"The value when \( n = 3 \) is 13."** - **True.** This matches our calculation.
7. **"The value when \( n = 3 \) is 15."** - **False.** This does not match our calculation.
8. **"The value when \( n = 3 \) is 17."** - **False.** This does not match our calculation.
The only true statement about the given description is:
- The value when \( n = 3 \) is 13.
### Correct answers:
- The value when n = 3 is 13.
1. "the quotient of a number cubed and nine" translates to \( \frac{n^3}{9} \).
2. "two less than" indicates we subtract 2, resulting in \( \frac{n^3}{9} - 2 \).
3. "increased by twelve" means we then add 12, resulting in:
\[
\frac{n^3}{9} - 2 + 12
\]
which simplifies to:
\[
\frac{n^3}{9} + 10.
\]
Now, substituting \( n = 3 \):
\[
n^3 = 3^3 = 27,
\]
therefore:
\[
\frac{27}{9} + 10 = 3 + 10 = 13.
\]
Now let's check the statements provided:
1. **"The correct expression is \( 6 - \frac{n^3}{9} + 12 \)."** - **False.** The expression is \( \frac{n^3}{9} + 10 \).
2. **"The correct expression is \( \frac{n^3}{9} - 6 + 12 \)."** - **False.** The expression does not match; it should include \( -2 \) not \( -6 \).
3. **"One of the steps to determining the value when \( n = 3 \) is \( 3 - 6 + 12 \)."** - **False.** This step does not apply to our expression.
4. **"One of the steps to determining the value when \( n = 3 \) is \( 6 - 3 + 12 \)."** - **False.** Incorrect arithmetic expression.
5. **"The value when \( n = 3 \) is 11."** - **False.** We calculated the value is 13.
6. **"The value when \( n = 3 \) is 13."** - **True.** This matches our calculation.
7. **"The value when \( n = 3 \) is 15."** - **False.** This does not match our calculation.
8. **"The value when \( n = 3 \) is 17."** - **False.** This does not match our calculation.
The only true statement about the given description is:
- The value when \( n = 3 \) is 13.
### Correct answers:
- The value when n = 3 is 13.