Explanation

Explanation

Let x = 0.888... (repeating).

Multiply by 10: 10x = 8.888...

Subtract: 10x - x = 8.888... - 0.888...

→ 9x = 8

Solve for x: x = 8/9.

Explanation

The cube roots of unity are 1, ω, and ω², where ω = -1 + √3i / 2 and ω² = -1 - √3i / 2.
Their product is 1 × ω × ω² = 1.

Explanation

The Roman numeral "XVI" represents the number 16.

"X" stands for 10.

"V" for 5.

"I" for 1.

Roman numerals for the given numbers:

• 1 - I
• 5 - V
• 10 - X
• 50 - L
• 100 - C
• 500 - D

Explanation

A.M=Sum/total

A.M. of 75 numbers = 35

Sum of 75 numbers = 75 * 35 = 2625

Total increase = 75 * 5 = 375

Increased sum = 2625 + 375 = 3000

Increased average = 3000/75 = 40

Explanation

8.73³ = 665.6

4.27³ = 171.4

Total = 665.6 + 171.4 = 837.0

Explanation

Step 1: Find A'

A' = I - A = {a, b, c, e, f, g} - {b, e, f} = {a, c, g}.

Step 2: Find B'

B' = I - B = {a, b, c, e, f, g} - {a, b, c} = {e, f, g}.

Step 3: Find A' ∩ B'

A' ∩ B' = {a, c, g} ∩ {e, f, g} = {g}.

Explanation

The set { 0, +, - } contains three distinct elements:

0, +, and −

Explanation

Multiplying by 100 shifts the decimal 2 places to the right.

Example: 3.45 × 100 = 345.

Explanation

To convert millimeters to centimeters, divide by 10:

0.6 mm ÷ 10 = 0.06 cm.