Explanation

Mean = (9 + 8 + 10 + x + 12) / 5 = 15

39 + x = 75 → x = 75 - 39 = 36

Explanation

Given:

Copper : Silver = 3 : 7

Step 1: Find total parts

3+7= 10

Step 2: Silver = 7 parts

Silver percentage= 7/10 x100

$$=70\%$$

Explanation

The factors of -4 that add up to -3 are -4 and +1.

So, x² - 3x - 4 = (x - 4)(x + 1).

Explanation

Given data:

The seller sells 40% of his apples.
After selling, he still has 420 apples.
Concept/Formula:

The concept used to solve this problem is related to "percentage". The seller was left with 60% of his apples (100% - 40% = 60%) when he had 420 apples left.

Solution:

⇒ the 420 apples represent 60% of his original stock (since he sold 40%).

⇒ If 60% of the original stock equals 420 apples, then 1% can be calculated by dividing 420 by 60.

Hence, 1% = 420 ÷ 60 = 7 apples.

⇒ Now, to find the total original stock (100%), the amount per 1% is multiplied by 100.

Therefore, the original amount = 7 × 100 = 700 apples.

Therefore, originally, he had 700 apples.

Explanation

Given x + 1/x = 10:

Step 1: Square both sides

(x + 1/x)² = 10²

x² + 2(x)(1/x) + 1/x² = 100

x² + 2 + 1/x² = 100

Step 2: Solve for x² + 1/x²

x² + 1/x² = 100 - 2

x² + 1/x² = 98

Explanation

Subtracting a negative is the same as adding: (-0.9) - (-0.9) = -0.9 + 0.9.

The result is 0.

Explanation

Let's use the quadratic formula to find the roots:

x = (-b ± √(b² - 4ac)) / 2a

For the given equation x² - 3x + k + 1 = 0:

a = 1, b = -3, c = k + 1

The roots differ by unity, so:

√(b² - 4ac) = 1

(-3)² - 4(1)(k + 1) = 1

9 - 4k - 4 = 1

5 - 4k = 1

-4k = -4

k = 1

Explanation

15 ÷ 3 = 5

5 + 20 = 25

Explanation

15 ÷ 3 = 5

5 + 20 = 25

Explanation

Given:

Time taken by 6 men to complete work= 10 days

Solution:

Time taken by 1 man = 6 x 10 = 6o hours

The time taken by 4 men to complete the work:

60/ 4 = 15 hours.