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Home » So 21 sequences with no two consecutive 3s. - Simpleprint

So 21 sequences with no two consecutive 3s. - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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$$ rac{t^2 + 5t + 6}{t + 2} = rac{(t + 2)(t + 3)}{t + 2} = t + 3 \qu...
eq -2 ext{)}. $$
Substituting $ t = 4 $:
$$ 4 + 3 = 7. $$
The simplified value is $ oxed{7} $.
Question: A linguist uses a polynomial $ P(n) = n^3 + 3n^2 - 2n + 1 $...
Solution: By the Remainder Theorem, substitute $ n = 1 $ into $ P(n) $...
$$ P(1) = 1^3 + 3(1)^2 - 2(1) + 1 = 1 + 3 - 2 + 1 = 3. $$
The remainder is $ oxed{3} $.Question: A linguist is studying the evo...
We are asked to count the number of ways to partition 5 distinguishabl...

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