Explanation

From equation (1), we can write:

2 = 10^0.3010

Now, take log base 2 on both sides:

log2 2 = log2 (10^0.3010)

1 = 0.3010 log2 10

Now, divide both sides by 0.3010:

log2 10 = 1/0.3010

= 100/30.10

= 1000/301

Explanation

The average marks of four subjects is 120, so the total marks are:

120 x 4 = 480

If 33 was misread as 13, that means the actual total marks should be:

480 - 13 + 33 = 500

Now, let's calculate the correct average:

Correct average = Total marks / Number of subjects

= 500 / 4

= 125

Explanation

We know that:

x × x = x²

Reciprocal of x = 1/x

According to the problem:

(x × x) ÷ (1/x) = 18/26 × 27

Simplifying the equation:

x² ÷ (1/x) = 18/26 × 27

x³ = 18/26 × 27

Now, let's solve for x:

x³ = 486/26

x³ = 18.69 (approximately)

x = ∛(18.69) ≈ 2.67

Explanation

Given that 40% of a number is equal to two-third of another number, we need to find the ratio of the first number to the second number.

Let's assume that the first number is x and the second number is y. 40% of x is equal to 2/3 of y.

We can write this as: 0.4x = 2/3 y To find the ratio of x to y, we can divide both sides by y: 0.4x/y = 2/3

Simplifying further, we get: x/y = (2/3)/(0.4) x/y = 5/3

Therefore, the ratio of the first number to the second number is 5:3.

Explanation

We know:

- Angle of elevation (θ) = 60°

- Distance of the foot of the ladder from the wall (x) = 12.4 m

- We need to find the length of the ladder (hypotenuse)

Using the cosine function:
cos(θ) = adjacent side / hypotenuse
cos(60°) = 12.4 / hypotenuse
To find the hypotenuse (length of the ladder), we can rearrange the equation:
hypotenuse = 12.4 / cos(60°)
Using a calculator:
hypotenuse = 12.4 / 0.5
hypotenuse = 24.8
So, the length of the ladder is 24.8 meters.

Explanation

Explanation

Total weight of (36 + 44) Students,

= (36 × 40 + 44 × 35) kg

= 2980 kg

Therefore average weight of the whole class,

= 298080 kg.

Therefore average weight = 37.25 kg.

Explanation

Total cartons = 5 + 8 = 13

Total cost = 105 + 155 = 260

Total items = 13 x 5 = 65

Average price per item = Total cost / Total items = 260 / 65 = 4

Explanation

Let number of boys are x and then number of girls
= (100 - x)
Thus,
50x + (100 - x) × 40 = 46 × 100
→ x = 60
Number of boys = 60

Explanation

Full tank capacity = Distance ÷ Miles per gallon

= 250 miles ÷ 15 miles/gallon

= 16.67 gallons (approximately)

Now, if the car gets 20 miles per gallon, we can calculate the distance it can travel on a full tank:

Distance = Full tank capacity × Miles per gallon

= 16.67 gallons × 20 miles/gallon

= 333.4 miles