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Home » Question: Compute \( \sin 225^\circ $. - Sterling Industries

Question: Compute \( \sin 225^\circ $. - Sterling Industries

📅 April 15, 2026 👤 scraface

Apr 15, 2026

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📌 \binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6

📌 Hence, there are \(\boxed{6}\) different pairs of startups that can be chosen for investment.

📌 Question:** A bioengineer is developing a sequence of 7 engineered microbial strains to be used in a bioremediation project. If there are 3 distinct functional groups of microbes, and each strain must belong to exactly one group, how many distinct sequences of microbial strains can be created?

📌 Solution:** Each of the 7 microbial strains can be assigned to one of the 3 functional groups. Therefore, for each strain, there are 3 choices, and the total number of sequences is \(3^7\).

📌 3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187

📌 Thus, there are \(\boxed{2187}\) distinct sequences of microbial strains possible.

📌 Question:** In a futuristic city, a transportation system uses pods that can be painted in 5 different colors. If a route requires a sequence of 4 pods, and adjacent pods cannot share the same color, how many valid color sequences exist for the route?

📌 Solution:** For the first pod, there are 5 possible color choices. For each subsequent pod, since it cannot match the previous one, there are 4 choices. Thus, the total number of valid sequences is:

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