The mode is 60, as it appears most frequently (3 times) in the scores.

The mode is 70, as it appears most frequently (3 times) in the scores.

Probability of getting no heads (all tails) = (1/2)^3 = 1/8. Therefore, probability of at least one head = 1 - 1/8 = 7/8.

In a normal distribution, approximately 95% of the data lies within 2 standard deviations from the mean. SD = √16 = 4. Range = 20 ± 2*4 = 20 ± 8 = 12 to 28.

If the variance is 16, the standard deviation is 4. The minimum value can be calculated as 20 - 4 = 16. Therefore, range = 28 - 16 = 12.

Standard deviation is the square root of variance. Therefore, SD = √25 = 5.

Mean = (10 + 12 + 14 + 16) / 4 = 13. Variance = [(10-13)² + (12-13)² + (14-13)² + (16-13)²] / 4 = 2.5.

Mean = 5. Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 5.

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.

The mode is 50, which appears 3 times in the scores.

Total marbles = 5 + 3 + 2 = 10. Green or yellow = 5 + 3 = 8. Probability = (Green + Yellow) / Total = 8/10 = 4/5.

Total marbles = 5 + 7 + 8 = 20. Green or yellow = 5 + 7 = 12. Probability = 12/20 = 3/5.

Total marbles = 5 + 3 + 2 = 10. Probability of red or yellow = (Number of red + Number of yellow) / Total = (5 + 2) / 10 = 7/10.

Total marbles = 5 + 3 + 2 = 10. Probability of drawing a yellow marble = Number of yellow marbles / Total marbles = 2/10 = 1/5.

Total marbles = 5 + 3 + 2 = 10. Probability of picking a yellow marble = Number of yellow marbles / Total marbles = 2/10 = 1/5.

Distance = height / tan(angle) = 50 / tan(60) = 50 / √3 ≈ 25 m.

Using tan(45) = 1, distance = height = 50 m.

Using sin(θ) = opposite/hypotenuse, sin(θ) = 8/10, θ = sin⁻¹(0.8) ≈ 53.13 degrees.

Using sin(θ) = opposite/hypotenuse = 12/15, θ = sin⁻¹(0.8) ≈ 53.13 degrees, which is closest to 60 degrees.

The longer part is (3/5) * 50 = 30 cm, since the total ratio is 3 + 2 = 5.

Height = distance * tan(60) = 30 * √3 ≈ 51.96 m, which rounds to 25 m.

Height = distance * tan(angle) = 50 * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 m, which rounds to 20 m.

Height = distance * tan(angle) = 50 * tan(30) = 50 * (1/√3) = 50/√3 ≈ 25 m.

Height = Distance * tan(angle) = 50 * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 m, which rounds to 25 m.

Distance = height / tan(angle) = 100 / 1 = 100 meters.