basically learn this for ease

A=[(1-fa)/(1-fb)] B

fa=fill factor of A fb=fill factor of B

1-fa=80,1-fb=60 80/60=4/3=1.33

So answer is A=1.33 B

In SQL Server, a clustered index organizes the data in a table based on the index key. The fill factor setting determines how much space on each page is left free for future growth, which affects how many rows fit on each page.

Here's how the fill factor affects the number of free rows per page:

Fill Factor: This percentage indicates how full each page should be when data is inserted. For example, a fill factor of 20% means that only 20% of each page will be used for data, leaving 80% of the page free for future growth. Conversely, a fill factor of 40% means that 60% of each page is free.

Calculating the Relationship:

Understanding Fill Factor and Free Space:
    Fill Factor = 20%: This means that 20% of each page is filled with data, leaving 80% of the page free.
    Fill Factor = 40%: This means that 40% of each page is filled with data, leaving 60% of the page free.

Number of Free Rows Per Page:

Let's assume the total number of rows that a page can hold when completely full is RR.
    For a fill factor of 20%, the free space is 80% of the page:
    Free Rows per Page=0.80×R
    Free Rows per Page=0.80×R
    For a fill factor of 40%, the free space is 60% of the page:
    Free Rows per Page=0.60×R
    Free Rows per Page=0.60×R

Relating Free Rows (A and B):

Let AA be the total number of free rows per page for the fill factor of 20%.
Let BB be the total number of free rows per page for the fill factor of 40%.

We can write:
A=0.80×R
A=0.80×R
B=0.60×R
B=0.60×R

To find the relationship between AA and BB:
AB=0.80×R0.60×R=0.800.60=43≈1.33
BA​=0.60×R0.80×R​=0.600.80​=34​≈1.33

Therefore:
A=1.33×B
A=1.33×B

Conclusion

The correct relationship between AA and BB is: A=1.33B A=1.33B

So, the number of free rows per page with a fill factor of 20% (A) is 1.33 times the number of free rows per page with a fill factor of 40% (B).

I think option B

According to Copilot: The fill factor in a database determines the percentage of each page (in a page-organized storage system) to be filled with data, leaving the rest as free space for future growth. In your question, the fill factor is 20% for the first design and 40% for the second design. This means that 80% of each page is left as free space in the first design and 60% in the second design.

If we denote the total number of rows that can fit in a page as R, then the number of free rows per page can be calculated as follows:

For the first design: A = R * 80% For the second design: B = R * 60% If we divide A by B, we get:

A/B = (R * 80%) / (R * 60%) = 80/60 = 1.33

So, A = 1.33B.

This means that the first design, with a lower fill factor, leaves more free rows per page than the second design.

In MS SQL Server, the fill factor determines the percentage of space on each page that is initially allocated to store data. A lower fill factor (e.g., 20%) leaves more space empty on each page, while a higher fill factor (e.g., 40%) allocates less empty space. The purpose of the fill factor is to allow for page splits and data growth without requiring frequent page adjustments, which can be costly in terms of auto performance.

The relationship between A and B can be calculated as follows:

Let's assume that the total number of rows per page is C.

For the first design (20% fill factor): A = 0.20 * C (20% of the page is empty)

For the second design (40% fill factor): B = 0.40 * C (40% of the page is empty)

Now, we want to find the relationship between A and B:

A = 0.20 * C B = 0.40 * C

To find the ratio of A to B, we can divide the equation for A by the equation for B:

A / B = (0.20 * C) / (0.40 * C)

C cancels out, and you get:

A / B = 0.20 / 0.40 = 1/2

So, A is half of B:

A = 0.5 * B

If you want to express the relationship between B and A, you can take the reciprocal:

B = 2 * A

Therefore, the correct relationship between A and B is:

B = 2A