To solve this problem, we need to insert the value 95 into the max-heap and then perform the necessary percolations to maintain the heap property.

Initial Max-Heap Representation:

The tree you've provided can be represented as an array in level order as follows: $100, 90, 80, 70, 85$

Step 1: Insert 95

When we insert 95, it is initially added as the last element in the array: $100, 90, 80, 70, 85, 95$

Step 2: Percolate Up

Since 95 is greater than its parent (80), we need to swap them to maintain the max-heap property. After the swap, the array looks like this: $100, 90, 95, 70, 85, 80$

No further percolation is needed because 95 is less than its new parent (100).

Final Array Representation:

The final array representation of the max-heap after inserting 95 and percolating is: $100, 90, 95, 70, 85, 80$

This is your answer.

Would you like any further details or explanations?

Here are some related questions you might find useful:

1. How do you insert a new element into a max-heap?
2. What is the time complexity of inserting an element into a max-heap?
3. How do you delete the maximum element from a max-heap?
4. What are the advantages of using a max-heap?
5. How is the max-heap property different from the min-heap property?

Tip: Remember that a max-heap is a complete binary tree where each parent node is greater than or equal to its children.