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Home » Final answer: $ \boxed{\pi \sqrt89} $ - Moon Smoking

Final answer: $ \boxed{\pi \sqrt89} $ - Moon Smoking

📅 May 13, 2026 👤 scraface

May 13, 2026

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📌 The shortest altitude is $\boxed{7.2}$.

📌 Question: A micropaleontologist studies a microfossil shaped like a hemisphere with radius $3x$ and a spherical fossil with radius $x$. What is the ratio of their volumes?

📌 Solution: Volume of hemisphere: $\frac{2}{3}\pi (3x)^3 = \frac{2}{3}\pi \cdot 27x^3 = 18\pi x^3$.

📌 Volume of sphere: $\frac{4}{3}\pi x^3$.

📌 Ratio: $\frac{18\pi x^3}{\frac{4}{3}\pi x^3} = \frac{18}{\frac{4}{3}} = \frac{54}{4} = \frac{27}{2}$. $\boxed{\dfrac{27}{2}}$**Question:

📌 A hydrologist is studying the flow of groundwater and models the rate of flow through a porous medium using the equations \(y = 2x + 3\) and \(y = -x + 5\). Find the intersection point of these two lines.

📌 To find the intersection point of the lines \(y = 2x + 3\) and \(y = -x + 5\), we set the equations equal to each other:

📌 2x + 3 = -x + 5

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Since the choices are independent, the probability that all three sele...
\left( \frac{80}{101} \right)^3
Therefore, the probability that **at least one** of the three integers...
- \left( \frac{80}{101} \right)^3
Compute the value:
\left( \frac{80}{101} \right)^3 = \frac{512000}{1030301}
- \frac{512000}{1030301} = \frac{518301}{1030301}
Thus, the probability that the product is divisible by 5 is:
\boxed{\frac{518301}{1030301}}
Question: A geotechnical engineer is analyzing soil samples from three...

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