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Home » These Eighties TV Shows Shook America—What They’re Still Hiding Today! - Abbey Badges

These Eighties TV Shows Shook America—What They’re Still Hiding Today! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Solution: For each of the 6 rods, there are 3 choices of connectors. The total configurations are $3^6 = 729$. Therefore, the answer is $\boxed{729}$.

📌 Question: A marine conservation educator collects 4 sea turtle shell images and 6 starfish photos for a sustainability project. How many distinct arrangements can be made in a row if all turtle shells must appear before any starfish?

📌 Solution: First, choose 4 positions out of 10 for the turtle shells, and the remaining 6 will hold starfish. The number of arrangements is $\binom{10}{4} = 210$. Hence, the answer is $\boxed{210}$.

📌 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?

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A = 250,000 × (1 + 0.18/4)^(4×3) = 250,000 × (1.045)^12
A ≈ 250,000 × 1.69588 = 423,970
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A drone flies over a circular crop field with a radius of 200 meters....
Using the perpendicular from center to chord: split chord in half → 15...
Radius = 200 m, half-chord = 150 m
Using Pythagorean theorem: distance = √(200² - 150²) = √(40,000 - 22,5...
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A startup’s revenue grows according to the function R(t) = 5000(1.12)^...
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