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Home » project 2025 document - DevRocket

project 2025 document - DevRocket

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Question: A cartographer measures two points on a map with coordinates $(2, 5)$ and $(8, 11)$. What is the slope of the line connecting them?

📌 Question: An angel investor splits $x$ and $y$ between two biotech startups. If $x + y = 120,000$ and $x - y = 20,000$, find $x$.

📌 Question: A venture capitalist invests a total of $500,000 in two cleantech projects. If the second project receives $150,000 more than the first, how much is invested in the first?

📌 A paleobotanist is examining fossilized leaf samples from two distinct geological periods. Each sample is analyzed for vein patterns, and the patterns are either monocotyledonous (M) or dicotyledonous (D). How many 5-sample sequences can the paleobotanist create if each sequence must contain at least one pair of consecutive samples with the same type?

📌 Next, calculate the number of sequences with no consecutive samples of the same type. A sequence with alternating types can start either with M or D. Consider:

📌 Starting with M: The sequence is M, D, M, D, M. There is 1 such sequence.

📌 Starting with D: The sequence is D, M, D, M, D. There is 1 such sequence.

📌 The number of sequences with at least one pair of consecutive samples with the same type is the total number of sequences minus the number of sequences with no consecutive same types:

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