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15 + x^3 ≤ 24
A) x > 9
B) x ≤ 3
C) x^2 > 9
D) x < 9

1 Answer

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Final answer:

The solution to the inequality 15 + x^3 ≤ 24 is x ≤ 3. While we solved an inequality, the context of probability was also mentioned, explaining that while x can be less than or equal to 3, probabilities of certain larger values are practically zero.

Step-by-step explanation:

The student is attempting to solve an inequality, specifically finding values for x that satisfy the condition 15 + x^3 ≤ 24. To find the range of possible values for x, we must first isolate x on one side of the inequality. Subtract 15 from both sides to get x^3 ≤ 9. Then we take the cube root of both sides to find the range of values that x can take, which leads to x ≤ 3.

It is important to note that while x is less than or equal to 3, the probability of x being exactly 3 is not zero. However, if we're looking for a probability related to the inequality, such as P(x > 24), this would be practically zero because x cannot exceed 3 for the original inequality to hold true.

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