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Since the determinant is non-zero ($ -576 - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \]**Question:** A soil scientist measures two samples of soil compaction, obtaining values of 1.2 kg/m\(^3\) and 3.8 kg/m\(^3\). What is the average soil compaction, in kg/m\(^3\), of these samples?

📌 To find the average soil compaction, sum the two measurements and divide by the number of samples. The formula for the average \( \bar{x} \) is:

📌 \bar{x} = \frac{x_1 + x_2}{2}

📌 where \( x_1 = 1.2 \) kg/m\(^3\) and \( x_2 = 3.8 \) kg/m\(^3\).

📌 \bar{x} = \frac{1.2 + 3.8}{2} = \frac{5.0}{2} = 2.5

📌 Thus, the average soil compaction is \(\boxed{2.5}\) kg/m\(^3\).

📌 Question:** An archaeologist uncovers two ancient pottery fragments with volumes measured at 12 liters and 27 liters. Find the least common multiple (LCM) of the volumes in liters.

📌 To find the least common multiple of 12 and 27, first determine their prime factorizations:

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