Explanation

Explanation

For projectile motion, two complementary angles θ and 90° - θ give the same range if the initial velocity is constant.

Since 10° + 80° = 90°, the angles 10° and 80° are complementary and will have equal ranges.

Explanation

Explanation

The total time of flight (T) for a projectile is given by:

T = 2v₀sin(θ) / g

The maximum height (H) is:

H = (v₀sin(θ))² / (2g)

Using T = 2v₀sin(θ) / g, we can express v₀sin(θ) = gT/2. Substituting this into the height equation gives:

H = (gT/2)² / (2g) = g²T² / 8g = gT² / 8

Explanation

Median is the middle value when data is arranged in order.

Ordered data: 63, 65, 66, 67, 69 → middle value is 66.

Explanation

Explanation

Specific death rate refers to the death rate calculated for a particular segment or subgroup of the population (e.g., by age, sex, cause).

It helps in understanding mortality patterns more precisely than the overall crude death rate.

Explanation

To find Σ(x - 1), first calculate (x - 1) for each value:

(3 - 1) + (1 - 1) + (7 - 1) + (4 - 1)

= 2 + 0 + 6 + 3

= 11

Explanation

The formula ∑x/n calculates the arithmetic mean of a set of numbers, where:

∑x = sum of all values

n = number of values

This formula provides the average value of the dataset.

Explanation

For a leptokurtic distribution, β₂ > 3:

β₂ = μ₄ / μ₂² > 3

Given μ₂ = 3.5:

μ₄ / (3.5)² > 3

μ₄ > 3 × 12.25

μ₄ > 36.75