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.