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howard johnson by wyndham san diego sea world - NBX Soluciones

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 On Mars, a new settlement uses a timekeeping system where a Martian day (sol) is divided into 28 Mars-hours. Each Mars-hour is further divided into 75 Mars-minutes. How many total Mars-minutes are there in a Martian day?

📌 To determine the total number of Mars-minutes in a Martian day, we start by analyzing the structure of a sol:

📌 We multiply the number of Mars-hours by the number of Mars-minutes per hour to find the total number of Mars-minutes in a sol:

📌 A venture capitalist is evaluating 12 clean technology startups, each working on a unique renewable energy solution. She plans to invest in exactly 4 of them, but wishes to ensure that no two selected startups are in the same environmental category. If there are exactly 4 categories—solar, wind, geothermal, and hydro—and each startup belongs to one category—how many ways can she choose 4 startups, one from each category?

📌 Since each category has exactly 3 startups, and we must pick one from each, the number of valid combinations is:

📌 This counts one startup selected from each category, with no restriction on order (but since we are choosing one per category, each combination is uniquely determined by category selection).

📌 Therefore, the number of ways she can make such an investment is:

📌 A Mars colony module has 8 identical life-support units, each labeled with a unique letter from A to H. To activate the system, a command sequence must consist of 5 units such that no two identical letters are adjacent and exactly two units are repeated (i.e., two letters appear twice, and one other letter appears once). How many valid 5-unit activation sequences are possible?

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