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Home » Using the power rule, \( f'(x) = 12x^2 - 18x + 6 \). - Get link 4share

Using the power rule, \( f'(x) = 12x^2 - 18x + 6 \). - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 So, there are 20 ways to choose positions for the 3 A’s such that no two are adjacent.

📌 Step 2: Assign labels to the remaining 5 positions.

📌 Each of the 5 non-A positions can be labeled U, C, or G (3 choices each). So, number of labelings is $3^5 = 243$.

📌 Therefore, total number of valid sequences is:

📌 \times 243 = 4860

📌 Thus, the virologist can observe $\boxed{4860}$ valid genome configurations.

📌 Question: A science fair judge evaluates 7 student projects, each judged on creativity (C), scientific rigor (R), and presentation (P), with each project receiving a score in each category: high (H) or low (L). The judge considers a project Exceptionally Strong if it receives high scores in at least 5 of the 3 categories. Assuming each score is independently high with probability $ \frac{1}{2} $, what is the probability that exactly 3 out of the 7 projects are Exceptionally Strong?

📌 Solution: First, compute the probability that a single project is Exceptionally Strong, i.e., gets H in at least 5 of the 3 categories. But there are only 3 categories, so getting high in at least 5 is impossible.

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