Final answer:
The smallest value that can be generated from the expression (int)(Math.random() * 100) + 3 is 3, as Math.random() produces a value between 0.0 and 99.999 before it is cast to an integer and has 3 added to it.
Step-by-step explanation:
The expression (int)(Math.random() * 100) + 3 is used to generate random numbers in programming. The function Math.random() generates a random double between 0.0 (inclusive) and 1.0 (exclusive). When it is multiplied by 100, the result is a random double between 0.0 and 99.999. Casting to an integer using (int) truncates the decimal part, resulting in a whole number between 0 and 99. Adding 3 to the result produces a number between 3 and 102. Therefore, the smallest value that can be generated from this expression is 3.