Explanation

Given: a/b = 3/5 ... (1)

When 2 is added to both numbers, the ratio becomes 2/3, so we can write:

(a+2)/(b+2) = 2/3 ... (2)

Cross-multiplying (2), we get:

3(a+2) = 2(b+2)

Expanding and simplifying, we get:

3a + 6 = 2b + 4

Subtracting 6 from both sides gives:

3a = 2b - 2

Now, substituting (1) in the above equation, we get:

3(3/5)b = 2b - 2

Multiplying both sides by 5, we get:

9b = 10b - 10

Subtracting 10b from both sides gives:

-b = -10

Dividing both sides by -1, we get:

b = 10

So, the correct answer is: 10

Explanation

The Department of Government Efficiency (DOGE) is a U.S. government initiative established by President Donald Trump on January 20, 2025, through an executive order.

DOGE aims to modernize federal technology systems and reduce government spending.

It operates under the Executive Office of the President.

It is led by Elon Musk.

Explanation

Carrying capacity refers to the maximum number of individuals of a species that an environment can support over the long term without degrading the environment.

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

She wished she had bought the new car.

اس کی خواہش تھی کہ اس نے نئی کار خریدی ہو۔

"She wished" refers to a past regret, so the past perfect "had bought" is correct.

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

Given:

Sum of numbers = -8

Product of numbers = 15

The algebraic expression representing this is:

x^2 - (sum)x + (product) = 0

x^2 - (-8)x + 15 = 0

x^2 + 8x + 15 = 0

The correct answer is: x^2 + 8x + 15

Explanation

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

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

4A.M=4*10.5

         =42

Explanation

The 2025 Australian federal election was held on Saturday, 3 May 2025.

All 150 seats in the House of Representatives and 40 of 76 seats in the Senate were up for election.

The Albanese Labor government won a second term with a landslide victory.

The opposition Liberal–National Coalition, led by Peter Dutton, was defeated.

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.