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Home » \(2(3w + w) = 48\) - Imagemakers

\(2(3w + w) = 48\) - Imagemakers

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 Proportion with the gene is 80/200 = 0.40.

📌 Expected number in a sample of 50 = 50 × 0.40 = <<50*0.4=20>>20.

📌 A science fiction writer designs a generation ship traveling at 0.1 times the speed of light over 300 years to reach the nearest star. If each generation lasts 30 years, how many generations will live and die on the ship during the journey?

📌 Total time = 300 years.

📌 Generation length = 30 years.

📌 Number of generations = 300 ÷ 30 = <<300/30=10>>10.

📌 A venture capitalist divides a $2 million investment between two clean energy startups: 60% in a wind company and 40% in a green hydrogen firm. If the wind company returns 15% and the hydrogen firm 25% after one year, what is the total value of the portfolio at the end of the year?

📌 Amount in wind = $2,000,000 × 0.60 = $<<2000000*0.6=1200000>>1,200,000.

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We now count the number of outcomes where the sum of the three numbers...
The odd numbers from 1 to 6 are: 1, 3, 5 (3 options), and the even num...
Case 1: All three numbers are even.
Each number has 3 choices (2, 4, 6):
3^3 = 27 \text{ outcomes}
Case 2: Exactly two numbers are odd, one is even.
Choose which two of the three positions are odd:
\binom{3}{2} = 3 \text{ ways}
Each odd number has 3 choices, and the even number has 3 choices:
\cdot (3^2 \cdot 3) = 3 \cdot 27 = 81 \text{ outcomes}

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