Question
7 of 157 of 15 Items
Question
Which of the given values 6, 8, or 12 would make the inequality m³ < 325 a true statement? (1 point)
Responses
6 makes the inequality true
6 makes the inequality true
None of the values make the inequality true
None of the values make the inequality true
12 makes the inequality true
12 makes the inequality true
8 makes the inequality true
8 makes the inequality true
Answers
GPT-4o mini
To determine which of the values (6, 8, or 12) makes the inequality \( m^3 < 325 \) true, we can calculate the cubes of each value and see which cubed value is less than 325.
1. For \( m = 6 \):
\[
6^3 = 216
\]
Since \( 216 < 325 \), this value makes the inequality true.
2. For \( m = 8 \):
\[
8^3 = 512
\]
Since \( 512 > 325 \), this value does not make the inequality true.
3. For \( m = 12 \):
\[
12^3 = 1728
\]
Since \( 1728 > 325 \), this value does not make the inequality true.
Therefore, the only value that makes the inequality \( m^3 < 325 \) true is **6**.
The correct response is:
**6 makes the inequality true.**
1. For \( m = 6 \):
\[
6^3 = 216
\]
Since \( 216 < 325 \), this value makes the inequality true.
2. For \( m = 8 \):
\[
8^3 = 512
\]
Since \( 512 > 325 \), this value does not make the inequality true.
3. For \( m = 12 \):
\[
12^3 = 1728
\]
Since \( 1728 > 325 \), this value does not make the inequality true.
Therefore, the only value that makes the inequality \( m^3 < 325 \) true is **6**.
The correct response is:
**6 makes the inequality true.**