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A function is _____ on an open interval, I, if for any (x1) and (x2) in the interval, where (x1) < (x2) then f(x1) = f(x2).

User MountainX
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Final answer:

A function is constant on an open interval, I, if for any x1 and x2 in the interval, where x1 < x2, then f(x1) = f(x2). The probability P(0 < x < 12) for a function f(x) that is equal to 12 for 0 ≤ x ≤ 12 is 144.

Step-by-step explanation:

A function is constant on an open interval, I, if for any x1 and x2 in the interval, where x1 < x2, then f(x1) = f(x2).

In the given question, we have a function f(x) that is equal to 12 for 0 ≤ x ≤ 12. To find the probability P(0 < x < 12), we need to find the area under the graph of f(x) between x = 0 and x = 12. Since the function is a horizontal line with a constant value of 12, the area under the graph is equal to the length of the interval (12 - 0) multiplied by the height (12).

Therefore, P(0 < x < 12) = 12 * (12 - 0) = 144.

User Deng
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