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Home » Let \( x \) be the original weekly water usage. - Midis

Let \( x \) be the original weekly water usage. - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Now, compute $ 3025 \mod 9 $. Since $ 55 \equiv 1 \mod 9 $, $ 55^2 \equiv 1^2 = 1 \mod 9 $.

📌 Thus, the remainder is $ \boxed{1} $.

📌 Question: What is the base-ten equivalent of the base-seven number $ 321_7 $?

📌 Solution: To convert $ 321_7 $ to base ten, expand using powers of 7:

📌 \cdot 7^2 + 2 \cdot 7^1 + 1 \cdot 7^0 = 3 \cdot 49 + 2 \cdot 7 + 1 = 147 + 14 + 1 = 162

📌 Thus, the base-ten equivalent is $ \boxed{162} $.

📌 Question: What is the greatest common divisor of $ 2^5 \cdot 3^2 \cdot 5 $ and $ 2^3 \cdot 3^4 \cdot 7 $?

📌 Solution: To find the GCD, take the minimum exponent for each common prime factor:

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