Explanation

Let's break it down:

A = x% of y = (x/100)y = xy/100

B = y% of x = (y/100)x = yx/100

Since xy = yx, A = B.

Explanation

To solve the equation:

$$x^2 + 16 = 0$$

Step 1: Isolate x^2

$$x^2 = -16$$

Step 2: Take the square root of both sides

$$x = pm sqrt{-16}$$

Since $sqrt{-16}$

involves the square root of a negative number, we use imaginary numbers:

$$x = pm 4i$$x=±4i

Explanation

1/2% means 0.5% or 0.005 in decimal.

So,

Step 1: Find 1/2% of 100  

= 0.005 × 100  

= 0.5

Step 2: Now, find 1/2% of 0.5  

= 0.005 × 0.5  

= 0.0025

Explanation

We are given an arithmetic progression (AP):

10, 7, 4, ...

Step 1: Identify the first term and common difference

First term a = 10

Common difference d = 7 - 10 = -3

Step 2: Use the formula for the nth term of an AP:

Tₙ = a + (n - 1) × d

Find the 30th term (T₃₀):

T₃₀ = 10 + (30 - 1) × (-3)

T₃₀ = 10 + 29 × (-3)

T₃₀ = 10 - 87 = -77

Explanation

This looks like an arithmetic sequence problem.
If the first term $a = 3$ and last term $l = 18$, and there are 4 numbers in between, the total terms $n=6$ (3 + 4 + 18).

The terms:
$a_1 = 3$
$a_6 = 18$
Number of terms $n = 6$

Common difference $d = frac{18 - 3}{6 - 1} = frac{15}{5} = 3$

The 3rd middle number is the 4th term:
$a_4=a_1+3d=3+3\times 3=12$

Explanation

50% of 100 is 50.

50% of 50 is 25.

Explanation

15 ÷ 3 = 5

5 + 20 = 25

Explanation

To find the Arithmetic Mean (Average):

Add the numbers: 10 + 20 + 30 + 40 + 50 = 150

Count the numbers: 5

Divide the sum by the count: 150/5 = 30

Explanation

Equating the two expressions and simplifying gives:

$$x cdot 200 = y cdot 250 Rightarrow frac{y}{x} = frac{200}{250} = frac{4}{5} Rightarrow y : x = 4 : 5$$

⇒y​/x=200/250

=4​/5

⇒y:x=4:5

Explanation

If the common difference $d = 0$, the sequence is constant.

General formula for an arithmetic sequence:
$a_n = a + (n - 1)d$

For $d = 0$
$a_n = 3 + (n - 1) times 0 = 3$

So, the 5th number $$a5=3a_5 = 3