The numbers greater than 4 on a die are 5 and 6. There are 2 favorable outcomes out of 6 total outcomes. Therefore, P(number > 4) = 2/6 = 1/3.

Even numbers on a die are 2, 4, 6. Total outcomes = 6. Probability = Number of even outcomes / Total outcomes = 3/6 = 1/2.

For rolling without slipping, the linear velocity v is equal to the radius r times the angular velocity ω, hence v = rω.

Let the original price be x. After a 15% discount, the selling price is x - (0.15 * x) = 0.85x. Setting this equal to $85 gives 0.85x = $85, so x = $85 / 0.85 = $100.

Probability of not transmitting in one contact = 1 - 0.1 = 0.9. For 3 contacts, it is 0.9^3 = 0.729.

The probability of a false positive is equal to 1 - specificity = 1 - 0.95 = 0.05.

The probability that the disease will not be transmitted = 1 - 0.3 = 0.7.

The probability of a correct diagnosis = 1 - probability of misdiagnosis = 1 - 0.05 = 0.95.

Total infections = R0^n = 2.5^3 = 15.625.

Expected deaths = Case fatality rate × Number of cases = 0.04 × 250 = 10.

Expected new cases = 0.1% of 1,000,000 = 0.001 * 1,000,000 = 100 cases.

Total infected after 3 weeks = 10% + 10% of (100% - 10%) + 10% of (100% - 20%) = 10% + 9% + 8% = 27%.

Using the formula for compound growth: Total infected = 100 × (1 - (1 - 0.03)^4) = 100 × (1 - 0.88) = 12.36%.

Average Speed = Total Distance / Total Time = 120 km / 1.5 h = 80 km/h

Speed = Distance / Time = 150 km / 1.5 h = 100 km/h.

Average Speed = Total Distance / Total Time = 120 km / 2 h = 60 km/h

Due to surface tension, a drop of liquid will take the shape of a sphere, as this shape has the minimum surface area for a given volume.

1200 kg/day * 7 days = 8400 kg

The factory operates 24 hours a day, which totals 168 hours in a week.

Units per hour = Total Units / Total Hours = 500 units / 8 hours = 62.5 units.

A viscosity of 0.5 Pa·s indicates that the fluid is relatively thick and flows less easily compared to fluids with lower viscosity.

50 grams needed / 10 grams per serving = 5 servings.

60 grams / 10 grams per serving = 6 servings.

(5 grams / 25 grams) * 100 = 20%.

Fraction of substitutes = Number of substitutes / Total players = 5 / 22.

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

Each match involves 2 teams, so the total number of matches is (16 teams * 4 matches) / 2 = 32.

The total number of matches is calculated using the formula n(n-1)/2, where n is the number of teams. Here, it is 16(15)/2 = 120.

The horizontal component is calculated as 10 N * cos(30°) = 8.66 N.

Using F = ma, acceleration a = F/m = 10 N / 2 kg = 5 m/s².