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Home » \( a = -5, b = 20, c = 2 \) - Get link 4share

\( a = -5, b = 20, c = 2 \) - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \( (n+1)^2 - n^2 = 35 \).

📌 \( n^2 + 2n + 1 - n^2 = 35 \).

📌 \( 2n + 1 = 35 \).

📌 \( 2n = 34 \), so \( n = 17 \).

📌 #### 17, 18Question: A palynologist is analyzing the distribution of pollen samples from 5 different plant species labeled A through E. If each sample must be analyzed exactly once and the order of analysis matters, how many distinct sequences are possible if species A must be analyzed before species B?

📌 To solve this, we begin by considering all permutations of the 5 species. Since each species is analyzed exactly once and order matters, the total number of unrestricted permutations is:

📌 Now, we impose the condition that species A must be analyzed before species B. In any permutation of the 5 species, for every pair A and B, A appears either before B or after B, with equal likelihood. Thus, exactly half of all permutations satisfy the condition that A comes before B.

📌 So, the number of valid sequences is:

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