Question

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?
The correct expression is StartFraction n cubed Over 16 EndFraction minus 2 + 8.
The correct expression is 2 minus StartFraction n cubed Over 16 EndFraction + 8.
One of the steps to determining the value when n = 4 is 1 minus 2 + 8.
One of the steps to determining the value when n = 4 is 2 minus 1 + 8.
The value when n = 4 is 6.
The value when n = 4 is 7.
The value when n = 4 is 9.
The value when n = 4 is 10.

Answer 1

To analyze the description “two less than the quotient of a number cubed and sixteen, increased by eight,” we first need to translate this description into a mathematical expression.

Let \( n \) be the number.

1. The quotient of a number cubed and sixteen can be expressed as \( \frac{n^3}{16} \).
2. "Two less than" this quantity means we subtract 2: \( \frac{n^3}{16} - 2 \).
3. "Increased by eight" means we add 8 to the previous amount: \( \frac{n^3}{16} - 2 + 8 \).

Putting this all together, we have:

\[
\frac{n^3}{16} - 2 + 8 = \frac{n^3}{16} + 6
\]

Now, substituting \( n = 4 \):

\[
\frac{4^3}{16} + 6 = \frac{64}{16} + 6 = 4 + 6 = 10
\]

Now we can analyze the options:

1. **The correct expression is \( \frac{n^3}{16} - 2 + 8 \).** (This is correct)
2. **The correct expression is \( 2 - \frac{n^3}{16} + 8 \).** (This is incorrect)
3. **One of the steps to determining the value when \( n = 4 \) is \( 1 - 2 + 8 \).** (This is incorrect)
4. **One of the steps to determining the value when \( n = 4 \) is \( 2 - 1 + 8 \).** (This is incorrect)
5. **The value when \( n = 4 \) is 6.** (This is incorrect)
6. **The value when \( n = 4 \) is 7.** (This is incorrect)
7. **The value when \( n = 4 \) is 9.** (This is incorrect)
8. **The value when \( n = 4 \) is 10.** (This is correct)

The correct statements are that **the correct expression is \( \frac{n^3}{16} - 2 + 8 \)**, and **the value when \( n = 4 \) is 10.**