Explanation

A probability of 1 means that the event is certain to occur.

Probability ranges from 0 (impossible) to 1 (certain).

Explanation

Given the direct variation between x² and y, we can write:

x² = ky

where k is the constant of variation.

Step 1: Find the constant of variation k

When x = 7 and y = 49:

7² = k * 49

49 = k * 49

k = 1

Step 2: Write the equation of variation

x² = y

Step 3: Find x when y = 100

x² = 100

x = ±√100

x = ±10

The answer is: 10, -10.

Explanation

2⅔ can be written as 2^(2/3), which equals ∛(2²) = ∛4 = ³√4.

Explanation

Let daughter's age be x → Iqra's age = 4x

After 12 years:

→ Daughter's age = x + 12, Iqra's age = 4x + 12

→ Total = (x + 12) + (4x + 12) = 5x + 24 = 69

→ 5x = 45 → x = 9

→ Iqra’s age = 4 × 9 = 36 years

Explanation

The expression is 2x² + 8x + 8. First, factor out 2:

→ 2(x² + 4x + 4)

Now factor the quadratic:

→ x² + 4x + 4 = (x + 2)(x + 2)

So the full factorization is 2(x + 2)(x + 2).

Explanation

Since P ∝ 1/V, it means P × V = constant.

So, 10 × 25 = P × 20

Solving:

250 = 20P ⇒ P = 12.5 N/m²

Explanation

Let's find the unknown value x using the proportion x : 5 :: 6 : 15.

We can set up the proportion as x/5 = 6/15.

Step 1: Cross-multiply

15x = 6 * 5

Step 2: Simplify

15x = 30

Step 3: Solve for x

x = 30 / 15

x = 2

Explanation

Given:

x : y = 3 : 4

y : z = 6 : 7

To combine, equalize y in both ratios (LCM of 4 and 6 is 12):

x : y = 9 : 12

y : z = 12 : 14

Combine to get: x : y : z = 9 : 12 : 14

Explanation

Outer rectangle area = 45 × 35 = 1575 m²

Inner rectangle dimensions = (45 – 6) × (35 – 6) = 39 × 29 = 1131 m²

(3 m removed from each side → total 6 m from length & width)

Area of path = 1575 – 1131 = 444 m²

Explanation

Let's solve the equation x/2 - x/3 = 8.

To do this, find a common denominator for the fractions, which is 6.

This gives us (3x - 2x)/6 = 8, simplifying to x/6 = 8.

Multiplying both sides by 6 gives x = 48.

So, the solution is x = 48.