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The average number of pages in 1940 was 30. Twice this amount is $2 \times 30 = 60$ pages.
Check each year:
- 1940: 30 pages (not $\geq 60$) ✗
- 1950: 55 pages (not $\geq 60$) ✗
- 1960: 82 pages ($\geq 60$) ✓
- 1970: 70 pages ($\geq 60$) ✓
- 1980: 74 pages ($\geq 60$) ✓
Three years (1960, 1970, and 1980) had at least twice the 1940 average.
A class has 5 girls and 7 boys. Teams of 2 girls and 3 boys are to be formed. However, two specific boys A and B cannot both be on the same team. How many valid teams can be formed?
Total teams (no restriction): $\binom{5}{2}\binom{7}{3} = 10 \times 35 = 350$
Teams where both A and B are included: Choose remaining 1 boy from 5 others: $\binom{5}{2}\binom{5}{1} = 10 \times 5 = 50$
Valid teams $= 350 - 50 = \mathbf{300}$
Extension $\Delta L = \frac{FL}{AY} = \frac{FL}{\pi (d/2)^2 Y} \propto \frac{L}{d^2}$ [cite: 482, 484].
- New extension $\Delta L' \propto \frac{2L}{(2d)^2} = \frac{2L}{4d^2} = \frac{1}{2} \Delta L$
- $\Delta L' = \frac{1}{2} \times 0.04 = 0.02\text{ m}$[cite: 484].
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