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Explanation

To find the amount of sugar needed for 1 cup of flour, we set up a proportion based on the given ratio:

Explanation

The given ratio 3:5 can be simplified by multiplying both numbers by 10, which results in:

3 × 10 = 30

5 × 10 = 50

So, the ratio 3:5 is equal to the fraction 30:50.

Explanation

Explanation

To solve for x, we can set up a proportion based on the given ratio:

2/3 = x/12

We can then cross-multiply:

2 × 12 = 3 × x

24 = 3x

Next, we can divide both sides by 3:

x = 24 ÷ 3

x = 8

So, the value of x is 8.

Explanation

Given that two numbers are in the ratio of 6:7 and their sum is -52, we can determine the numbers as follows:

 let the two numbers be 6x and 7x.

The sum of these numbers should be -52:

6x + 7x = -52

13x = -52

Solving for x:

x = -52/13

x = -4

Therefore, the two numbers are 6x and 7x:

6 (-4) = -24

7 (-4) = -28

The numbers in the ratio 6:-7 that sum up to -52 are -24 and -28.

Explanation

L'Hospital's Rule is a technique used to evaluate limits of indeterminate forms, such as 0/0 or ∞/∞. The rule states that if the limit of the ratio of the derivatives of the numerator and denominator exists, then the original limit exists and is equal to that ratio.

The conditions for L'Hospital's Rule to work are:

• The function must be indeterminate, meaning it has the form 0/0 or ∞/∞.
• The derivative of the numerator and denominator must exist.
• The derivative of the denominator must be non-zero at the point being evaluated.

Explanation

Step 1: Determine the total parts in the ratio

The ratio is 1:2:3, so the total parts are 1 + 2 + 3 = 6

Step 2: Calculate Noor's share

Noor's share is 1 out of 6 parts, so his share of the profit is (1/6) * 600

Step 3: Calculate the amount

(1/6) * 600 = 100

Explanation

Explanation

If 1/3 of the tank holds 80 litres, we can set up a proportion to find the total capacity of the tank:

1/3 × Total Capacity = 80 litres

To find the total capacity, we can multiply both sides by 3:

Total Capacity = 80 litres × 3

= 240 litres

Now, we can find the quantity of water that 1/2 tank holds:

1/2 × Total Capacity = 1/2 × 240 litres

= 120 litres

Explanation

1: The ratio of boys to girls is 4:5.

This means that for every 9 parts (4 parts boys + 5 parts girls), 4 parts are boys.

2: Calculate the total number of parts: 

 4+5=9 parts

3: Find the value of one part:

Total students=36

One part = 

36/9 = 4

4: Calculate the number of boys:

Number of boys=4×4=16 boys