Explanation

If 105% of the number = $x$, then the number itself is $frac{x}{1.05}$

Therefore, 42% of the number is:

$$0.42 times frac{x}{1.05} = frac{42}{105} x$$

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

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

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

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

3x:2X

3X=2X+5 3

X-2X=5

X=5

Age of younger one is 2X

 X is 5 that is equal to 5×2=10

ND11-3-2023

SH25-8-2023

Explanation

n(A) = 75% of 600 = 450

n(B) = 45% of 600 = 270 and n(A ∪ B) = 600

∵ n(A∩B) = n (A) + n(B) - n(A∪B) = (450 + 270 - 600) = 120

Explanation

The mean proportional between two numbers a and b is a number x such that: a : x :: x : b

In this case, we want to find the mean proportional between 64 and 81.

Let's set up the proportion: 64 : x :: x : 81

We can rewrite this as: 64/x = x/81

Cross-multiplying, we get: 64 × 81 = x^2

Simplifying, we get: 5184 = x^2

Taking the square root of both sides, we get:

x = √5184

x = 72

So, the mean proportional between 64 and 81 is 72.

Explanation

Arithmetic mean= (18+3)/2=10.5

formula: sum of n A.M= n*A.M

4A.M=4*10.5

         =42