Area = length × width = 100 m × 64 m = 6400 square meters.

Perimeter = 2(Length + Width) = 2(100 m + 64 m) = 2 * 164 m = 328 m.

The fraction of the match played is 60 minutes out of 90 minutes, which is 60/90 = 2/3.

Distance = Speed × Time. Time in hours = 90/60 = 1.5 hours. Distance = 8 km/h × 1.5 h = 12 km.

Distance = Speed × Time. Time in hours = 90/60 = 1.5 hours. Distance = 8 km/h × 1.5 h = 12 km.

Matches won = 40% of 30 = 0.4 * 30 = 12.

Number of matches won = 60% of 50 = 0.6 * 50 = 30 matches.

Matches won = 70% of 30 = 0.7 * 30 = 21 matches.

Work done (W) = Force (F) × Distance (d) = 10 N × 5 m = 50 J.

Work done (W) = Force (F) × Distance (d) × cos(θ). Here, θ = 0° (force and displacement are in the same direction). W = 10 N × 5 m × cos(0°) = 10 N × 5 m = 50 J.

Work done = Force × Distance = 10 N × 5 m = 50 J

Horizontal component = F × cos(θ) = 15 N × cos(30°) = 15 N × √3/2 ≈ 12.99 N.

Work done (W) = F × d × cos(θ) = 15 N × 4 m × cos(60°) = 15 N × 4 m × 0.5 = 30 J.

Horizontal component = Fcos(θ) = 50 N × cos(30°) = 50 N × (√3/2) ≈ 43.3 N.

Horizontal component = F × cos(θ) = 50 N × cos(60°) = 50 N × 0.5 = 25 N.

Total parts = 1 + 2 + 3 + 4 = 10. Third project's share = (3/10) * 5000 = $1500.

Work done (W) = PΔV = 100 kPa * (2 m³ - 1 m³) = 100 kPa * 1 m³ = 100 kJ = 20 kJ.

Total duration = (4 sessions * 2 hours) + (3 breaks * 0.5 hours) = 8 hours + 1.5 hours = 9 hours.

Profit Margin = ((Revenue - Cost) / Revenue) * 100 = ((600 - 500) / 600) * 100 = 16.67%.

20% of 1,000,000 = 0.20 * 1000000 = 200,000 trees.

Total expenditure = ₹2000 * 1500 families * 12 months = ₹36,000,000 or ₹36 lakhs.

Each family will receive ₹1,20,000 / 8 = ₹15,000.

Fraction = ₹50,000 / ₹2,00,000 = 1/4.

Amount reserved for administrative costs = 10% of ₹5,00,000 = ₹50,000.

The total age of the original group is 20 * 15 = 300. Adding the new student gives 300 + 22 = 322. The new average age is 322 / 16 = 20.125, which rounds to 20.6.

Let the number of students be n. Total height = 150n. After one leaves, total height = 148(n - 1). Setting the equations gives 150n - 148(n - 1) = height of student.

Total height = 160 * 10 = 1600 cm. New total = 1600 - 170 = 1430 cm. New average = 1430 / 9 = 158.89 cm, approximately 159 cm.

Total score = 75 * 10 = 750. New total = 750 - 90 = 660. New average = 660 / 9 = 73.33.

The mode is 2, as it appears four times in the data set.

The mode is 3, as it appears 3 times, which is more than any other number.