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Home » So previous year: 1020 / 1.15 = 887.0 mm (exact) - IX Labs

So previous year: 1020 / 1.15 = 887.0 mm (exact) - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Final amount paid: $103.50 - $10.35 = $<<103.5-10.35=93.15>>93.15.
#### 93.15
Peter studies algorithm efficiency and compares two sorting methods. M...
We need to solve: 0.05n log₂(n) < 0.01n².
Divide both sides by n (n > 0): 0.05 log₂(n) < 0.01n → log₂(n) < 0.2n.
We test values:
n = 10: log₂(10) ≈ 3.32, 0.2×10 = 2 → 3.32 > 2 → A faster
n = 20: log₂(20) ≈ 4.32, 0.2×20 = 4 → 4.32 > 4
n = 25: log₂(25) ≈ 4.64, 0.2×25 = 5 → 4.64 < 5 → B faster
n = 24: log₂(24) ≈ 4.58, 0.2×24 = 4.8 → 4.58 < 4.8 → B faster

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$ (8-2)\binom{8}{2} = 6 \cdot 28 = 168 $
$ (8-3)\binom{8}{3} = 5 \cdot 56 = 280 $
Total = $8 + 56 + 168 + 280 = 512$
Second sum ($k = 4$ to $8$):
$4\binom{8}{4} = 4 \cdot 70 = 280$
$5\binom{8}{5} = 5 \cdot 56 = 280$
$6\binom{8}{6} = 6 \cdot 28 = 168$
$7\binom{8}{7} = 7 \cdot 8 = 56$
$8\binom{8}{8} = 8 \cdot 1 = 8$
Total = $280 + 280 + 168 + 56 + 8 = 792$

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