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+ 0.50x = 0.35(3 + x) - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: A box contains 7 green educational badges and 9 digital certificates. If three items are selected at random, what is the probability that exactly 2 are badges?

📌 Solution: The total number of ways to choose 3 items is $\binom{16}{3} = 560$. The favorable cases are $\binom{7}{2} \times \binom{9}{1} = 21 \times 9 = 189$. The probability is $\frac{189}{560} = \frac{27}{80}$. Thus, the answer is $\boxed{\dfrac{27}{80}}$.

📌 Question: A marine conservation initiative tags 10 sea turtles and 15 coral fragments. If four items are randomly selected, what is the probability that at least one sea turtle is chosen?

📌 Solution: The total ways to select 4 items: $\binom{25}{4} = 12650$. The unfavorable case (no turtles) is $\binom{15}{4} = 1365$. The probability of at least one turtle is $1 - \frac{1365}{12650} = 1 - \frac{273}{2530} = \frac{2257}{2530}$. The answer is $\boxed{\dfrac{2257}{2530}}$.

📌 Question: A student designs a bridge with 5 red struts and 7 blue connectors. If all struts and connectors are placed in a line, how many distinct sequences are possible if struts of the same color are indistinct?

📌 Solution: The total items are $5 + 7 = 12$, with 5 red and 7 blue. The number of distinct sequences is $\frac{12!}{5!7!} = 792$. Therefore, the answer is $\boxed{792}$.Question: A robotic engineer is programming a machine to assemble components using exactly 3 different colored

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