Explanation

(1 + 1/x)(1 + 1/(x+1))(1 + 1/(x+2))(1 + 1/(x+3))

= ((x+1)/x)((x+2)/(x+1))((x+3)/(x+2))((x+4)/(x+3))

Notice that the denominators and numerators cancel out:

= (x+4)/x

Explanation

China and Pakistan broke ground on the Allama Iqbal Industrial City (AIIC) in Faisalabad on January 3, 2020

The AIIC is a Special Economic Zone (SEZ) that is being developed as part of the China-Pakistan Economic Corridor (CPEC)

Explanation

Explanation

Three years ago, the total age of the 5 family members was:

5 x 17 = 85 years

Now, the total age of the 5 family members, considering the 3 years that have passed, is:

85 + 5 x 3 = 100 years

The total age of the 6 family members (including the baby) is:

100 + baby's age

Since the average age remains the same (17 years), we can set up the equation:

(100 + baby's age) / 6 = 17

Multiply both sides by 6:

100 + baby's age = 102

Subtract 100 from both sides:

baby's age = 2

Explanation

• The volume of a sphere (V) is given by V = (4/3)πr^3, and the surface area (A) is given by A = 4πr^2.
• If V = A, then: (4/3)πr^3 = 4πr^2
• Simplifying, we get: r = 3 units

Explanation

Explanation

Let's break it down step by step:

Let the principal amount be P.

According to the problem, the amount becomes 3 times itself in 20 years, so the interest earned is 2P (since 3P = P + 2P).

The simple interest formula is: Interest = (Principal × Rate × Time)/100

We know that Interest = 2P and Time = 20 years. Let's denote the rate as R.

So, 2P = (P × R × 20)/100

Simplifying, we get: R = 10%

Now, let's find the time it takes for the amount to become double (i.e., interest = P):

P = (P × 10 × Time)/100

Time = 10 years

Explanation

Given |n - 2| = 10:

We have two cases:

1. n - 2 = 10 => n = 12

2. n - 2 = -10 => n = -8

The sum of the two possible values of n:

12 + (-8) = 4

Explanation

Let "x" be the number.

Three-fourths of the number is (3/4)x.

When we multiply the number by three-fourths of itself,

we get: x * (3/4)x = 10700.

This simplifies to (3/4)x² = 10700.

Solving for x, we get x = 70. 

Explanation

A circle can have an infinite number of tangents.

Since a circle is defined as a set of points equidistant from a fixed point,

And each point on the circle can have a tangent line, there are infinitely many possible tangent lines.