Explanation

Let, the number be x.

Given, one-third of one-fourth of the number is 15.

Or, (1/3)(1/4)x = 15

So, x = 15*3*4 = 180.

Now, three-tenths of that number will be ,(3/10)x = (3/10)*180 = 18*3 = 54.

Explanation

To find the percentage, divide 25 by 75 and multiply by 100:

25 ÷ 75 = 0.33

0.33 × 100 = 33%

Explanation

Width =p/2-h P=30 H=10 W=30÷2-10=5cm

w=5cm l Length 10 cm P Perimeter 30 cm Using the formula P=2(l+w) Solving forw w=P 2﹣l=30 2﹣10=5cm

Explanation

Here M1 = 30, D1 = 16,
T1 = 9, M2 = 36 and T2 = 8
By formula, M1D1T1 = M2D2T2
30 x 16 x 9 = 36 x D2 x 8
∴ D2 = (30 x 16 x 9)/(36 x 8) = 15 days

Explanation

1 minute= 60 seconds

27 minutes = 1620

Explanation

To find the distance between two points, use the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Given points:

(x₁, y₁) = (2, 3)

(x₂, y₂) = (7, 3)

Substitute the values:

Distance = √((7 - 2)² + (3 - 3)²)

= √((5)² + 0²)

= √(25)

= 5

Explanation

Explanation

We use the relation:

Product of two numbers = LCM × HCF

Given:

Product = 2500

LCM = 125

So,

2500 = 125 × HCF

⇒ HCF = 2500 ÷ 125 = 20

Explanation

To find 25% of 150, multiply 150 by 0.25:

150 × 0.25 = 37.5.

Therefore, 37.5 is 25% of 150.

Explanation

x = 7 — 4√3, we are required to find x + 1/x.

1/x = 1/(7 — 4√3)

Rationalising 1/x,

1/x = {1/(7 —4√3)} × {(7 + 4√3)/7 + 4√3)} = {(7 + 4√3)}/{7² — 4²(√3)²} = (7 + 4√3)/(49 — 48) = 7 + 4√3.

Therefore

x + 1/x = 7 — 4√3 + 7 + 4√3 = 14.