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Home » Set up the equation: \( 8w = 48 \). - Tacotoon

Set up the equation: \( 8w = 48 \). - Tacotoon

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 + 12085 + 12087 + 12089 = (12083 + 12089) + (12085 + 12087) = 24172 + 24172 = 48344

📌 Now compute $ 48344 \mod 8 $. Since 1000 is divisible by 8, only the last three digits matter:

📌 \div 8 = 43 \text{ with remainder } 0

📌 Question: What is the sum of all positive divisors of $ 2^3 \cdot 3^2 $?

📌 Solution: The sum of the divisors of $ 2^3 \cdot 3^2 $ is given by:

📌 Thus, the sum of all positive divisors is $ \boxed{195} $.

📌 Question: What is the remainder when $ 7^5 + 7^6 $ is divided by 6?

📌 Solution: First, note that $ 7 \equiv 1 \mod 6 $, so $ 7^k \equiv 1^k = 1 \mod 6 $ for any positive integer $ k $.

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Question: A palynologist collects pollen samples from three layers of...
Solution: We compute $ \frac{3}{8} + \frac{5}{12} + \frac{7}{16} $. Th...
\frac{3}{8} = \frac{18}{48}, \quad \frac{5}{12} = \frac{20}{48}, \quad...
\frac{18 + 20 + 21}{48} = \frac{59}{48}
Since $ \frac{59}{48} > 1 $, the total is $ \frac{59}{48} $ kg, which...
$\boxed{\frac{59}{48}}$
Question: A climate researcher in New York City analyzes energy usage...
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x = \frac{147}{7} = 21
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