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college students' approval of donald trump - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 #### 15Question: An angel investor decides to fund a startup every month, choosing one of three sectors: AI, biotech, or clean energy. If the investor randomly selects a sector each month with equal probability, what is the probability that over the next 6 months, she funds exactly two AI startups, two biotech startups, and two clean energy startups?

📌 We are selecting one of 3 sectors each month for 6 months, with equal probability for each. We are to find the probability of exactly 2 AI, 2 biotech, and 2 clean energy selections.

📌 We want the number of sequences with exactly 2 of each type. This is a multinomial coefficient:

📌 Question: A robotics engineer is programming a surgical robot that selects one of 4 tools at random for each of 5 procedures, with equal probability. What is the probability that the robot uses each tool at least once over the 5 procedures?

📌 We count the number of sequences of length 5 using 4 tools where each tool appears at least once. This is given by the inclusion-exclusion principle:

📌 If a car travels 150 miles in 3 hours, what is its average speed in miles per hour, and how far will it travel in 7 hours at that speed?

📌 A cylindrical tank has a radius of 5 meters and a height of 10 meters. What is its volume in cubic meters?

📌 The diameter of the circle is 10 units, so the radius is 5 units.

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