Explanation

The standard deviation of a binomial distribution is indeed √npq, where:

• n is the number of trials
• p is the probability of success
• q is the probability of failure (q = 1 - p)

The formula for the standard deviation of a binomial distribution is:

σ = √npq

This represents the spread or dispersion of the distribution.

Explanation

To find the percentage, divide 25 by 75 and multiply by 100:

25 ÷ 75 = 0.33

0.33 × 100 = 33%

 Last updated on 12 NOV 2026

Explanation

To find how many more men are needed, we can use the formula for work:

$$text{Work} = text{Men} times text{Days}$$

Initially, 120 men can complete the work in 90 days. The total work can be represented as:

$$120 times 90 = 10800 text{ man-days}$$

Now, we need to find how many men are needed to complete the work in 40 days:

$$text{Required Men} = frac{10800}{40} = 270 text{ men}$$

Explanation

1. Convert all fractions to a common denominator (8):

   • $\frac{3}{4}=\frac{6}{8}$

   • $\frac{5}{8}=\frac{5}{8}$

   • $\frac{1}{2}=\frac{4}{8}$

2. Perform the calculation:

   • $\frac{6}{8}+\frac{5}{8}-\frac{4}{8}=\frac{7}{8}$

3. Convert $\frac{7}{8}$ to decimal:

   • $\frac{7}{8}=0.875\approx 0.87$

Explanation

1 km = 0.62137119 miles

0.62137119 miles ∼ 0.62 miles

∴ 1 km = 0.62 miles

Additional Information

Miles to Kilometres = Miles × 8/5 (Approximately)

Kilometers to Miles = Km × 5/8 (Approximately)

Explanation

When a square is rotated by 90 degrees, it still remains a square.

The shape of the square does not change because it has equal sides and 90-degree angles, regardless of its orientation.

Explanation

Pythagoras is considered the founder of the basic laws of geometry.

His work, particularly the Pythagorean theorem.

This laid foundational principles for the study of geometry.

Explanation

A group generated by one of its elements is called a cyclic group.

This means that the group can be generated by repeatedly applying the group operation to a single element, called the generator.

In other words, all elements of the group can be expressed as powers of the generator.

Explanation

x + y = 30 ... (Equation 1)

x - y = 8 ... (Equation 2)

We can solve these equations by adding them together, which eliminates y:

2x = 38

Dividing both sides by 2 gives us:

x = 19

Now that we have x, we can find y by substituting x into Equation 1:

19 + y = 30

Subtracting 19 from both sides gives us:

y = 11

Now that we have both x and y, we can find their product:

Product = x * y

= 19 * 11

= 209

Explanation