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.

Answer 1

For the statement 'two less than the quotient of a number cubed and nine, increased by twelve,' when n = 3, the correct expression is ((n³) / 9) - 2 + 12, and the correct value when n = 3 is 13.

Step-by-step explanation:

To determine which statements are correct for the description “two less than the quotient of a number cubed and nine, increased by twelve” when n = 3, let's break down the statement step by step.

The quotient of a number cubed and nine is n³ / 9. If we say “two less than” this amount, we subtract two: (n³ / 9) - 2. Then, to “increase by twelve”, we add twelve to this expression: (n³ / 9) - 2 + 12.

Now let's plug in n = 3 into the expression:
((3³) / 9) - 2 + 12, which simplifies to (27 / 9) - 2 + 12 = 3 - 2 + 12 = 13.

So the second statement is correct, and the value when n = 3 is indeed 13. The other two correct statements would be steps in this calculation process.