Question

For the inequality __________ is less than or equal to x is less than or equal to _______. Is the correct answer: 12 is less than or equal to x less than or equal to 36?

Answer 1

Yes, the given inequality 12 is less than or equal to x, which is less than or equal to 36, is correct.

Step-by-step explanation:

The inequality states that the value of x falls within a specific range, bounded by two numbers: 12 and 36.

It specifies that x must be greater than or equal to 12 (meaning it can be 12 or any number larger than 12).

It also specifies that x must be less than or equal to 36 (meaning it can be 36 or any number smaller than 36).

Therefore, the possible values of x lie within the inclusive range from 12 to 36.

Mathematical Notation:

The inequality can be written concisely as 12 ≤ x ≤ 36.

Answer 2

The student's question pertains to validating an inequality which seems to be related to setting up conditions for probability calculations. The reference information suggests the use of a graphing calculator for binomial distributions and conditional probabilities.

Step-by-step explanation:

Regarding the inequality question, the student asks for confirmation on whether "12 is less than or equal to x less than or equal to 36" is correct. To address this, we look at different instances of inequalities provided in the reference information. A continuous probability function f(x) is mentioned to be equal to 12 and restricted between 0 and 12, suggesting that the probability P(0 < x < 12) is being assessed. In one case, to find P(x > 12|x > 8), we consider the conditional probability which adapts the sample space. On the other hand, when finding P(x ≤ 12), a graphing calculator’s distribution menu is typically used to calculate the binomial distribution probability, which can be time-consuming without technological assistance.