Amount donated = 10% of 2500 = 0.1 * 2500 = $250.

Amount spent on books = 20% of 5000 = 0.2 * 5000 = $1000. Amount left = 5000 - 1000 = $4000.

Banana has the highest count (8), so the mode is Banana.

Speed = Distance / Time = 200 meters / 120 seconds = 1.67 m/s. To convert to km/h, multiply by 3.6: 1.67 * 3.6 = 6 km/h.

Time = Total Volume / Rate = 500 liters / 25 liters/min = 20 min

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

Departure time = 2 PM, travel time = 3 hours. Arrival time = 2 PM + 3 hours = 5 PM.

Total time = (120/60) + (180/90) = 2 + 2 = 4 hours. Total distance = 120 + 180 = 300 km. Average speed = Total distance / Total time = 300/4 = 75 km/h.

Total distance = 60 + 90 = 150 km. Time for first part = 60/30 = 2 hours. Time for second part = 90/60 = 1.5 hours. Total time = 2 + 1.5 = 3.5 hours. Average speed = Total distance / Total time = 150 / 3.5 = 42.86 km/h, which rounds to 45 km/h.

Distance = Speed × Time. Therefore, distance = 60 km/h × 2.5 h = 150 km.

Distance = Speed × Time. Therefore, distance = 60 km/h × 2.5 h = 150 km.

Distance = Speed * Time = 90 km/h * 2.5 h = 225 km.

Time = Distance / Speed = 270 km / 90 km/h = 3 hours.

Time = Distance / Speed = 300 km / 75 km/h = 4 hours.

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625, which is equal to 25^2. Therefore, it is a right triangle.

If the vaccine is 80% effective, then 20% will still contract the disease. Therefore, expected cases = 20% of 1000 = 200.

Using the formula s = ut + (1/2)at²; s = 0 + (1/2)(2)(10²) = 100 m.

Using the lens formula 1/f = 1/v - 1/u, where u = -30 cm and f = 15 cm, we find v = 10 cm.

Using the formula h = (u²)/(2g) = (20²)/(2 × 10) = 20 m.

Distance = Speed × Time = 10 m/s × 15 s = 150 m.

Distance = Speed × Time = 30 m/s × 15 s = 450 m.

At the equinox, the sun is directly overhead at the equator, which is at 0 degrees latitude.

Each hour corresponds to 15 degrees. Therefore, 3 hours ahead means 3 * 15 = 45 degrees east of GMT, which is 45°E.

The area under the curve is given by ∫(from 1 to 4) (2x + 1) dx = [x^2 + x] from 1 to 4 = (16 + 4) - (1 + 1) = 20.

The area under the curve is given by ∫(from 0 to 2) x^3 dx = [x^4/4] from 0 to 2 = (16/4) - (0) = 4.

The determinant of J is calculated as 1*(1*1 - 0*3) - 2*(0*1 - 0*2) + 1*(0*3 - 1*2) = 1 - 0 - 2 = -1.

Using the distance formula: d = √[(1 - 1)² + (5 - 2)²] = √[0 + 9] = √9 = 3.

Using the distance formula: d = √[(2 - 6)² + (3 - 8)²] = √[16 + 25] = √41.

Using the fact that sin(x) ~ x as x approaches 0, we find that lim (x -> 0) (x^3)/(sin(x)) = 0.

Dividing numerator and denominator by x^2 gives lim (x -> ∞) (3 + 2/x^2)/(5 - 4/x^2) = 3/5.