Explanation

To find the probability that a pair of books will always be together, we need to count the number of arrangements where the pair is together and divide it by the total number of arrangements.

Let's consider the pair of books as a single unit. Then, we have 9 units (the pair and the remaining 8 books) to arrange on the shelf. The number of ways to arrange these 9 units is 9!.

However, within the pair, the two books can be arranged in 2! ways (either book can be on the left or right).

So, the total number of arrangements where the pair is together is 9! × 2!.

Now, we divide the number of favorable arrangements (where the pair is together) by the total number of arrangements:

Probability = (9! × 2!) / 10!

= (9! / 10!) × 2

= (1/10) × 2

= 1/5

Explanation

The mode is the digit that appears most frequently in the data set.

Let's count the occurrences of each digit:

• 0: 3 times
• 1: 2 times
• 2: 1 time
• 3: 2 times
• 5: 1 time
• 6: 2 times
• 7: 1 time
• 9: 1 time

The digit 0 appears most frequently, 3 times. Therefore, the mode is 0.

Explanation

The equation $text{IQ} = frac{text{Mental Age (M.A.)}}{text{Chronological Age (C.A.)}} times 100$ was developed by Alfred Binet and Theodore Simon.

This formula was part of the Binet-Simon scale, designed to measure intelligence in children.

It was later adapted and popularized in various forms, such as the Stanford-Binet IQ test.

Explanation

From the above-shown logic tables, we can say that for the NAND and NOR gate, we will get the output '0' when both the inputs are 1.

Explanation

• To find the mean of a set of numbers, you add up all the numbers and then divide by the total count of numbers.
• For the scores 1, 2, 3, 4, 5:
• (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3
• So, the mean of the scores is 3.

Explanation

To find the interest earned using the simple interest formula, use:

Simple Interest = 𝑃 × 𝑟 × 𝑡

where:

P is the principal amount ($1200),

r is the annual interest rate (5% or 0.05),

t is the time in years (2 years).

Substitute the values into the formula:

Simple Interest=1200×0.05×2

Calculate:

Simple Interest=1200×0.05=60

Simple Interest=60×2=120

Explanation

Stratified Sampling is a probability sampling method where the population is divided into subgroups (strata), and random samples are drawn from each stratum to ensure representation.

Other types of probability sampling include Simple Random Sampling, Cluster Sampling, and Systematic Sampling.

Explanation

To find the 3rd term of the sequence 

𝑎𝑛 =n+3, substitute .n=3 into the formula:

𝑎3 = 3 + 3 = 6

Thus, the 3rd term of the sequence is 6.

Explanation

When there is a profit, the selling price (SP) is greater than the cost price (CP).

This means the seller sells the product for more than what it cost them to purchase or produce it, resulting in a profit.

Explanation

The cost price is the original price at which a product is purchased, excluding any markup or profit.

It represents the expense incurred by a seller to acquire the product before selling it to customers.