Explanation

a = 3, r = 2

5th term:

3, 6, 12, 24, 48

Explanation

The number of ways to choose 2 elements from 5 is 5C2 = 5! / (2! × 3!) = 10.

This represents the combinations where order does not matter.

Explanation

The number of arrangements of 4 distinct books is 4! = 4 × 3 × 2 × 1 = 24.

This represents all possible permutations of the books on the shelf.

Explanation

Mode = 11, Mean = 12

Using:

Mean - Mode ≈ 3(Mean - Median)

12 - 11 = 3(12 - Median)

1 = 36 - 3Median

3Median = 35

Median = 35/3

= 11.67

Explanation

When class frequencies vary widely, weighting each class by its frequency gives a more accurate central tendency.

Weighted mean accounts for differences in data distribution across classes.

Explanation

A mile is a unit of distance.

It is equal to 5,280 feet or exactly 1.609344 kilometers.

1 km = 0.62137119 miles

0.62137119 miles ∼ 0.62 miles

∴ 1 km = 0.62 miles

Additional Information

Miles to Kilometres = Miles × 8/5 (Approximately)

Kilometers to Miles = Km × 5/8 (Approximately)

Explanation

Factors of 48: 2^4 × 3

Factors of 180: 2^2 × 3^2 × 5

Common: 2^2 × 3 = 12

Explanation

4 workers finish in 6 days

1 worker will finish in 4 × 6 = 24 days

3 workers will finish in 24/3 = 8 days

Explanation

The volume of a cube is given by:

V = side³

= 5³

= 5 × 5 × 5

= 125 cm³

Explanation

Compound interest (CI) is always more than simple interest (SI) when interest is calculated more than once or for multiple periods.

This is because CI earns interest on both principal and accumulated interest.

The difference between CI and SI increases with higher rates and longer time periods.