In a survey conducted at a software firm, 65% of the developers use Python, 55% use SQL, and 40% use both tools. What percentage of the developers use at least one of these two programming tools?

The correct option is 80%.

To find the percentage of developers who use at least one of the two programming tools, we use the Principle of Inclusion-Exclusion for sets.

Step 1: Identify the given data
Let A be the set of developers who use Python, and B be the set of developers who use SQL.

Percentage of developers using Python:
$P\left(A\right)=65\%$

Percentage of developers using SQL:
$P\left(B\right)=55\%$

Percentage of developers using both Python and SQL:
$P(A\cap B)=40\%$

Step 2: Apply the Principle of Inclusion-Exclusion
The formula to calculate the percentage of developers using at least one tool is:

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

Step 3: Calculate the result
Substituting the given values into the formula:

$P(A\cup B)=65\%+55\%-40\%$

$P(A\cup B)=80\%$

Therefore, 80% of the developers use at least one of these two programming tools.