1. **State the problem:** We are given the ratio of analysts to field agents as 3:5 and the total number of agents as 40. We need to find the number of analysts. 2. **Understand the ratio:** The ratio 3:5 means for every 3 analysts, there are 5 field agents. 3. **Calculate the total parts:** Total parts in the ratio = 3 + 5 = 8 parts. 4. **Find the value of one part:** Since total agents are 40, one part equals $$\frac{40}{8} = 5$$ agents. 5. **Calculate the number of analysts:** Number of analysts = 3 parts = $$3 \times 5 = 15$$ analysts. **Final answer:** There are 15 analysts.