Explanation

To express 2.08 as a percentage:

2.08 × 100 = 208%

Explanation

Given that log10 2, log10(2x - 1), and log10(2x + 3) are in AP:

2 * log10(2x - 1) = log10 2 + log10(2x + 3)

log10(2x - 1)^2 = log10(2 * (2x + 3))

(2x - 1)^2 = 2 * (2x + 3)

4x^2 - 4x + 1 = 4x + 6

4x^2 - 8x - 5 = 0

(2x + 1)(2x - 5) = 0

2x = 5 or 2x = -1 ( rejected since 2x > 0 for log(2x-1) and log(2x+3) to be defined)

2x = 5

x = log2 5

Explanation

Given:

A1 = 28 (first term)

d = -4 (common difference)

n = 7 (number of terms)

To find the nth term (an), use the formula:

an = a + (n-1)d

an = 28 + (7-1)(-4)

= 28 + 6(-4)

= 28 - 24

= 4

Explanation

The sequence of savings is:

4, 13, 22, ... with a common difference of 9.

Let's find the week when savings reach 130:

4 + (n-1)9 = 130

(n-1)9 = 126

n-1 = 14

n = 15

The savings will reach Rs 130 in the 15th week.

Explanation

Given:  

y = 5  

Expression: 10y × √(y³ − y²)

Step-by-step:

1. y³ = 5³ = 125  

2. y² = 5² = 25  

3. y³ − y² = 125 − 25 = 100  

4. √(100) = 10  

5. 10y = 10 × 5 = 50  

6. Final result: 50 × 10 = 500

Explanation

Original price = 500

New price = 400

Decrease = 500 - 400 = 100

Percentage decrease = 100/500 × 100 = 1/5 × 100 = 20%

Explanation

We can simplify the expression using the identity:  

a³ + b³ = (a + b)(a² - ab + b²)

Here,  

a = 8.73, b = 4.27  

a + b = 13  

a² = 8.73² = 76.2129  

b² = 4.27² = 18.2329  

ab = 8.73 × 4.27 = 37.2671  

Now,  

a³ + b³ = (13)(76.2129 - 37.2671 + 18.2329)  

= 13 × (57.1787)  

≈ 743.3

Explanation

 We are given:

To find $q$, divide both sides by 0.87:

Explanation

 We are given:

Average of 6 numbers = 10

So, total sum = 10 × 6 = 60

If each number is multiplied by 3, then the new total becomes:

New total = 60 × 3 = 180

Number of values = still 6

New average = 180 ÷ 6 = 30

Explanation

To find the number of hours 10 men will take:

First, find the total work hours for 6 men:

6 men * 15 hours = 90 man-hours

Now, divide the total work hours by 10 men:

90 man-hours / 10 men = 9 hours