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Home » To find the \( y \)-intercept, set \( x = 0 \) in the equation: - Nelissen Grade advocaten

To find the \( y \)-intercept, set \( x = 0 \) in the equation: - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \binom{7}{4} \cdot \binom{4}{2} \cdot 4! = 35 \cdot 6 \cdot 24 = 5040.

📌 But if the "order" refers only to the application of the operation (i.e., 2 positions are distinct for pumping), the count is $ \binom{7}{4} \cdot \binom{4}{2} \cdot \frac{4!}{2!} = 35 \cdot 6 \cdot 12 = 2520 $. Clarifying the problem's intent, the most plausible interpretation leads to $\boxed{2520}$.

📌 Question: A nanotechnology engineer is designing a solar-powered water harvesting system with 5 identical microfilters. How many distinct ways can 8 unique water source samples be distributed into the filters if each filter can hold any number of samples?

📌 Solution: Since the filters are identical and samples are distinguishable, this is equivalent to partitioning 8 distinct elements into up to 5 indistinct subsets. The total number of ways is the sum of Stirling numbers of the second kind for $ k = 1 $ to $ 5 $:

📌 S(8, 1) + S(8, 2) + S(8, 3) + S(8, 4) + S(8, 5).

📌 Using known values:

📌 + 127 + 966 + 1701 + 1050 = 3845.

📌 Thus, the number of ways is $\boxed{3845}$.Question: If $ f(x) = 3x^2 - 4x + 7 $ and $ g(x) = 2x - 5 $, what is the value of $ g(f(-2)) $?

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