Explanation

The third class in the frequency distribution corresponds to the class limits 15-19, and its frequency is given as 50.

Therefore, the frequency of the third class is 50.

Explanation

The sum of the values is calculated as the average multiplied by the number of values: 30 * 4 = 120.

Therefore, the sum of the values is 120.

Explanation

To find the length of marks on dust when the wheel completes one rotation, we need to calculate the circumference of the wheel:

Circumference = π × diameter

= π × 35 cm

≈ 3.14 × 35 cm

≈ 109.9 cm

Rounding to the nearest whole number:

≈ 110 cm

Explanation

The area of a trapezium is given by:

Area = (1/2) × (sum of bases) × altitude

Given:

Area = 153 m^2

Altitude = 9 m

One base = 13 m

Let's denote the other base as 'b'. Then:

153 = (1/2) × (13 + b) × 9

Multiply both sides by 2:

306 = (13 + b) × 9

Divide both sides by 9:

34 = 13 + b

Subtract 13 from both sides:

b = 21

Explanation

13 + 12 = 25 is mathematically correct.

Explanation

Given:

x + 1/x = 10

Squaring both sides:

(x + 1/x)^2 = 10^2

x^2 + 2(x)(1/x) + 1/x^2 = 100

x^2 + 2 + 1/x^2 = 100

Subtract 2 from both sides:

x^2 + 1/x^2 = 98

Explanation

Two hundred million = 200,000,000

It has 8 zeros after 2.

Explanation

 Decrease = 25,000 - 24,500 = 500

Percentage decrease = (500 / 25,000) × 100 = 2%

Explanation

A singleton set has only one element (e.g., {a}).

The only proper subset is the empty set (∅), so it has one proper subset.

Explanation

Using the power of a power rule:

(x^3)^5 = x^(3×5)

= x^15