Final answer:
The time frame for a department to acknowledge a complaint varies and can average around forty-five days, as historical sources mention.
Step-by-step explanation:
When a department receives a complaint, the time frame for beginning an investigation and sending a written acknowledgment can vary. Historical documentation, such as the quote you provided, suggests that it is part of the duties of executive departments to provide opinions in writing upon any subject relating to their offices. Although the specific time frame for acknowledgment is not provided in the excerpt, it has been reported in various sources, such as Willcocks (1913) and Barois (2010), that the average time for such procedures can be around forty-five days or differ based on the context and the specific department's protocols.