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Solution: The minimum depth where both measurements coincide is the LCM of 5 and 7. Since 5 and 7 are prime, LCM(5, 7) = $5 \cdot 7 = 35$. The answer is $\boxed{35}$.
Question: A science journalist recorded 10, 14, and 16 articles published in three months. What is the average number of articles per month?
Solution: The arithmetic mean is calculated by summing the values and dividing by the count: $\frac{10 + 14 + 16}{3} = \frac{40}{3} \approx 13.\overline{3}$. The exact average is $\boxed{\dfrac{40}{3}}$.

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