Final answer:
To find f(16) for the function f(x)=2x+105, substitute x with 16 to get 137. For a function like f(x)=20/20 between 0 and 20, the graph is a horizontal line at y=1. Probability concepts relate to areas under curves and conditional probabilities.
Step-by-step explanation:
The question involves evaluating a function at a given input value and also includes concepts related to the graph of a function within certain intervals. To find f(16) using the function rule f(x) = 2x + 105, you simply substitute 16 for x in the function and perform the arithmetic: f(16) = 2(16) + 105 = 32 + 105 = 137. The function evaluated at 16 yields a value of 137.
For the graphical representation, if we consider f(x) = 20/20 for 0 ≤ x ≤ 20, we should recognize that the output is a constant function. Since 20/20 simplifies to 1, f(x) = 1 for the entire interval. The graph of this function is a horizontal line at y = 1 between x = 0 and x = 20, inclusive.
In probability terms such as P(0 < x < 2) = 0.1, the notation describes the probability of a continuous random variable x being between two values, which can be represented as the area under a probability density function curve for that interval. Similarly, the concept of conditional probability, such as finding the probability that a child eats a doughnut in a specific time frame given they have been eating for a given amount of time, involves adjusting the sample space and recalculating probabilities accordingly.