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what does red and purple make - Imagemakers

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 The $ y $-intercept occurs when $ x = 0 $: $ y = 1 $.

📌 Solution: From $ p + q = 7 $, express $ q = 7 - p $. Substitute into the first equation:

📌 $$Question: A herpetologist is tracking 5 distinct species of frogs and 4 distinct species of snakes in a conservation study. If she records one species per day for 9 days, how many different sequences can she observe if each species is only recorded once?

📌 Solution: The herpetologist is observing 9 distinct species (5 frogs + 4 snakes), and each species is observed exactly once over 9 days. Since all species are distinct and order matters, the number of sequences is simply the number of permutations of 9 distinct items:

📌 Question: A marine engineer is programming an underwater robot to respond to 3 types of underwater signals: sonar pings (S), light flashes (L), and pressure changes (P). If the robot sends a sequence of 8 signals consisting of 3 Ss, 3 Ls, and 2 Ps, how many distinct signal sequences can be created?

📌 Solution: We are arranging 8 signals where there are 3 Ss, 3 Ls, and 2 Ps. Since the total number of signals is 8 and some are repeated, the number of distinct sequences is given by the multinomial coefficient:

📌 Question: A science communicator is creating a 7-part video series on famous scientists, and chooses 3 videos on physicists, 2 on chemists, and 2 on biologists, in any order. How many different schedules can be made for the 7-episode series if videos on the same field are indistinguishable?

📌 Solution: We are arranging 7 episodes where 3 are on physicists (P), 2 on chemists (C), and 2 on biologists (B). Since videos within each field are indistinguishable, the number of distinct arrangements is:

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