Explanation

Co-primes (or relatively prime numbers) are pairs of numbers whose greatest common divisor (GCD) is 1.

Let's check the GCD for each pair:

(23, 92): GCD = 23 (not co-prime).

(21, 35): GCD = 7 (not co-prime).

(12, 28): GCD = 4 (not co-prime).

(18, 25): GCD = 1 (they are co-prime).

Explanation

To find the average:

First 5 multiples of 11:

11, 22, 33, 44, 55

Add the multiples:

11 + 22 + 33 + 44 + 55 = 165

Divide by the number of multiples:

165 ÷ 5 = 33

Explanation

Given: A : B = 3 : 1 and B : C = 1 : 2.

To find A : B : C, make the ratio of B the same in both expressions.

A : B = 3 : 1 means A = 3B.

B : C = 1 : 2 means C = 2B.

So, A : B : C = 3B : B : 2B, which simplifies to 3 : 1 : 2.

Now, multiply the entire ratio by 5 to make the B value in all ratios equal: 3 : 5 : 10.

Explanation

The angle of depression is formed between a horizontal line and the line of sight to an object that is below the horizontal.

It is measured from the observer's eye level down to the object.

Explanation

To find the third proportion:

First term: a²b²

Second term: abc

The proportion is in the form:

a²b² : abc :: abc : x

To find x, set up a proportion equation:

a²b² / abc = abc / x

Simplify:

ab / c = abc / x

x = c²

Explanation

A histogram is a type of vertical bar graph used to represent frequency distributions, where the bars touch each other to indicate continuous data.

Unlike bar graphs, histograms do not have space between the bars, reflecting intervals of data.

Explanation

We are given:

5^a = 3125

Now, let's express 3125 as a power of 5:

3125 = 5^5

So, a = 5

Now we need to find:

5^(a - 3) = 5^(5 - 3) = 5^2 = 25

**********************

3125 = 5⁵ ⇒ a = 5

So, 5^(a - 3) = 5² = 25

Explanation

To find the fraction that is less than 7/8 and greater than 1/3, we need to compare the given options:

• Convert all fractions to equivalent decimals:

    - 7/8 = 0.875

    - 1/3 = 0.333

    - 17/24 = 0.708

    - 1/4 = 0.25

    - 23/24 = 0.958

    - 11/12 = 0.917

• Identify the fraction that falls between 0.333 and 0.875:

    - 17/24 = 0.708 (this is the only fraction that meets the condition)

So, the correct answer is: 17/24

Explanation

When two successive discounts are given, use the formula:

Overall Discount (%) = A + B - (A × B) / 100

Where:

A = first discount = 10%

B = second discount = 14%

So:

= 10 + 14 - (10 × 14) / 100

= 24 - 1.4

= 22.6%

Explanation

To simplify the given expression:

6/8 + 2 1/2 + 4/12

Simplify each fraction:

6/8 = 3/4

2 1/2 = 5/2

4/12 = 1/3

Now, add the simplified fractions:

3/4 + 5/2 + 1/3