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Home » Diese quadratische Gleichung faktorisiert als: - Malaeb

Diese quadratische Gleichung faktorisiert als: - Malaeb

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 5Question: In a futuristic Mars colony, a scientist must select 3 identical prototype life-support modules from a storage bay containing 7 distinguishable modules and 5 identical backup units. How many distinct ways can the scientist select 3 modules, assuming the backup units are indistinguishable among themselves and all prototypes are unique?

📌 Solution: We are selecting 3 modules where 7 are distinguishable prototypes and 5 are identical backup units. Since the prototype units are unique and the backup units are indistinguishable, we consider combinations based on how many prototypes are selected (from 0 to 3), and how many backup units are used (up to 3, but limited by availability and total draw).

📌 Let $ k $ be the number of prototype modules selected, where $ k = 0, 1, 2, 3 $.

📌 So the total number of distinct selections is:

📌 Thus, there are 64 distinct ways to choose the 3 modules.

📌 Question: A Swedish biotech project involves replacing defective neurons using 4 genetically identical stem cell lines and 6 unique patient-derived neural templates. If a researcher selects 4 components — one stem cell line and three neural templates — and the stem cell lines are indistinguishable, how many distinct experimental sets can be assembled?

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Using the difference of squares in the denominator:
rac{3(\sqrt{7} + \sqrt{2})}{5} = rac{3\sqrt{7} + 3\sqrt{2}}{5}
Final simplified form:
oxed{rac{3\sqrt{7} + 3\sqrt{2}}{5}}
Question: Let $f(x) = 2x^2 - 3x + 1$ and $g(x) = \sqrt{x + 4}$. What i...
Solution: First evaluate $f(2)$:
f(2) = 2(2)^2 - 3(2) + 1 = 8 - 6 + 1 = 3
Now evaluate $g(f(2)) = g(3)$:
g(3) = \sqrt{3 + 4} = \sqrt{7}
oxed{\sqrt{7}}

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