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Home » From Silence to Stardom: How PKSM Captured Millions in a Week—Give It Up! - Leaselab

From Silence to Stardom: How PKSM Captured Millions in a Week—Give It Up! - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Solution: The smallest 4-digit number divisible by 11 is $ 1001 $ (since $ 1001 \div 11 = 91 $), and the largest is $ 9999 $ (since $ 9999 \div 11 = 909 $). The count is $ 909 - 91 + 1 = 819 $.

📌 The answer is $ \boxed{819} $.Question: A digital literacy advocate is organizing a workshop with 8 distinct tech tutorials and 5 community centers. How many distinct ways can the tutorials be assigned to centers if each center can receive any number of tutorials?

📌 Solution: Each of the 8 distinct tutorials can be assigned to any of the 5 centers. Since assignments are independent, the total number of ways is $5^8 = 390625$. Thus, the answer is $\boxed{390625}$.

📌 Question: A middle school student is building a model bridge with 6 unique metal rods and 3 distinct connector bars. How many distinct configurations are possible if each rod can be paired with any connector?

📌 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?

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-\frac{108}{6} + d = 3 \implies -18 + d = 3 \implies d = 21
Thus, the polynomial is:
f(x) = -\frac{7}{6}x^3 + \frac{21}{2}x^2 - \frac{82}{3}x + 21
\boxed{-\frac{7}{6}x^3 + \frac{21}{2}x^2 - \frac{82}{3}x + 21}
Let \( a \) and \( b \) be complex numbers such that \( a + b = 4 + 2i...
We start with the identity for the square of a sum:
Rearranging gives:
a^2 + b^2 = (a + b)^2 - 2ab
Substitute the given values \( a + b = 4 + 2i \) and \( ab = 5 + 3i \)...
a^2 + b^2 = (4 + 2i)^2 - 2(5 + 3i)

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