Explanation

Z1Z2 = (2 - i)(3 - i)

= 6 - 2i - 3i + i²

= 6 - 5i - 1 (since i² = -1)

= 5 - 5i

Explanation

Papaya is a dioecious plant, meaning male and female flowers are on separate plants, so it relies on cross-pollination.

In contrast, pea and tomato plants usually undergo self-pollination.

Explanation

To hear a distinct echo, the reflecting surface must be at least 17 meters away from the sound source.

This distance allows the sound to travel to the surface and back (total 34 meters) in 0.1 seconds, the minimum time gap for the human ear to perceive an echo.

Explanation

Smallest 5-digit number: 10000

Greatest 4-digit number: 9999

Result = 10000 - 9999= 1

Explanation

10 is a multiple of itself because any number is a multiple of itself.

Explanation

If the sum of all digits of a number is divisible by 3, then the number itself is divisible by 3.

This is a divisibility rule for 3.

Explanation

A band is the correct collective noun for a group of musicians.

"Team" is used for sports players.

"Group" is general.

Explanation

In the word "island", the letter S is silent — it is not pronounced when speaking.

The pronunciation is /ˈaɪ.lənd/, where "S" is not heard.

Explanation

First, find the rate at which the carpenters work:

6 carpenters make 8 chairs in 10 days.

Step 1: Calculate the rate of work per carpenter per day

Rate = 8 chairs / (6 carpenters * 10 days)

= 8 / 60

= 4/30

= 2/15 chairs per carpenter per day

Step 2: Calculate the number of days for 10 carpenters to make 18 chairs

Let the number of days be x.

10 carpenters * x days * (2/15) chairs/carpenter/day = 18 chairs

(20/15)x = 18

(4/3)x = 18

x = 18 * (3/4)

x = 13.5

Explanation

x + 3y = 53

4x - 2y = 2

x = 8

y = 15