Explanation

4^(4x+1) = 1/64

We can start by noticing that 1/64 = 2^(-6) = 4^(-3) (since 4 = 2^2).

So, we have:

4^(4x+1) = 4^(-3)

Since the bases are the same (both are 4), we can equate the exponents:

4x + 1 = -3

Subtracting 1 from both sides gives:

4x = -4

Dividing both sides by -4 gives:

x = -1

Explanation

 Third integer is x + 4 = 11 + 4 = 15. 

Explanation

To solve this, we can start by expressing the given ratio m:n = 3:2 in terms of a variable, let's say x. So, m = 3x and n = 2x.

Now, let's substitute these expressions into the given ratio (4m+5n):(4m-5n):

(4(3x) + 5(2x)) : (4(3x) - 5(2x))

Expanding and simplifying, we get:

(12x + 10x) : (12x - 10x)

22x : 2x

Now, we can divide both terms by 2x to get: 11 : 1

Explanation

9/162=x/306

X=9/162 × 306

X= 17

Explanation

Person A completes the work in 12 days, so their work rate is 1/12 of the work per day.

Person B completes the work in 6 days, so their work rate is 1/6 of the work per day.

When they work together, their combined work rate is the sum of their individual work rates:

(1/12 + 1/6) = (1/12 + 2/12) = 3/12 = 1/4 of the work per day.

Since they can complete 1/4 of the work in a day, they will complete the entire work in: 4 days.

Explanation

Area of a circle =πr2
∴38.5=πr2
∴722​×r2=38.5
⇒r2=38.5×227​
⇒r2=12.25⇒r=12.25​
∴ r=3.5
Now, Circumference of circle =2πr
∴ Circumference of circle =2×722​×1035​
∴ Circumference of circle =22mArea of a circle =πr

2
∴38.5=πr2
∴722​×r2=38.5
⇒r2=38.5×227​
⇒r2=12.25⇒r=12.25​
∴ r=3.5
Now, Circumference of circle =2πr
∴ Circumference of circle =2×722​×1035​
∴ Circumference of circle =22m

Explanation

For distribution between A & B the proportion has to be 2:3

Thus when A gets 2 units, B gets 3 units

So A gets ₹20/- & B gets ₹30/-

Distribution between B & C has to be 2:3

If ₹30 is 2, then 3 has to be ₹45/-

So ₹ 95,000/- to be divided between A, B & C shall have to be in the proportion of

20:30:45

Thus A gets ₹20′000/- B gets₹30′000/- and C gets ₹45000/-

Explanation

First, we need to calculate the number of voters who forget to vote.

7% of 5860 is approximately 410 voters.

Now, let's subtract those voters from the total: 5860 - 410 = 5450. Since the candidate needs to win at least 50% of the remaining votes, we'll divide 5450 by 2.

This gives us 2725 votes.

So, the candidate needs 2725 votes to win the election.

Explanation

Hyperlinks can be used for text, drawing objects, and pictures.

They provide a way to navigate within a document, to a different document, or to a web page.

Explanation

The extension of Notepad files is .txt, which indicates plain text format.

This extension is used for simple text documents without any special formatting.