Final answer:
The 3-digit even numbers that can be created from the tiles 5, 8, and 2 are 582, 852, 528, and 258, as the last digit must be 2 or 8 to ensure the number is even.
Step-by-step explanation:
The question is asking us to list all the 3-digit even numbers that can be created by rearranging the number tiles 5, 8, and 2. Since we want even numbers, the units place must be an even number. Thus, our number must end with 2 or 8. The combinations we can form for the hundreds and tens place with the remaining numbers are 58, 85, 52, and 25. Combining these with our even number units, we get the following 3-digit even numbers: 582, 852, 528, and 258. Note that although '2' is an even number, it cannot be used in the hundreds place as this would only form a 2-digit number. Therefore, these are the only four valid combinations for creating 3-digit even numbers with the tiles provided.