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Home » L = 100 \times 1.74900625 = 174.900625 - Sterling Industries

L = 100 \times 1.74900625 = 174.900625 - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 Total number of arrangements without restriction:

📌 There are 6 distinct experiments, so:

📌 Number of arrangements where A and B are adjacent:

📌 Treat A and B as a single block. Then we have 5 blocks to arrange: (AB), and the other 4 experiments.

📌 Subtract to get valid (non-adjacent) arrangements:

📌 Choose 2 non-consecutive positions out of 6 for A and B.

📌 Number of ways to choose 2 non-consecutive positions from 6:

📌 On a line of 6, the number of ways to choose 2 non-consecutive positions is:

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\( x = \pm 4 \): \( 9(16) = 144 \Rightarrow 25y^2 = 81 \Rightarrow y^2...
\( x = \pm 5 \): \( 9(25) = 225 \Rightarrow 25y^2 = 0 \Rightarrow y =...
Total lattice points: \( (0, \pm3), (\pm5, 0) \) → 4 points.
Thus, the number of lattice points is \( \boxed{4} \).
Question:** How many of the 150 smallest positive integers are congrue...
Solution:** We want integers \( n \) such that \( 1 \leq n \leq 150 \)...
Such numbers are of the form \( n = 7k + 3 \).
Find the smallest and largest such \( n \) in range:
Smallest: \( k = 0 \Rightarrow n = 3 \)
Largest: solve \( 7k + 3 \leq 150 \Rightarrow 7k \leq 147 \Rightarrow...

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