Answer:
- <u>D. Fundamental Principle of Counting</u>
- <u>D. 32</u>
- <u>B. 12 ways</u>
- <u>D. 24</u>
- <u>B. 18</u>
Step-by-step explanation:
<u>Q1</u>
- The Fundamental Principle of Counting states that we can find the total number of ways that two or more separate tasks can happen by multiplying the number of ways each task can happen separately.
<u>Q2</u>
<u>Q3</u>
- No. of ways = 4 x 3 = 12 ways
<u>Q4</u>
- ⁴P₃ = 4! / 1! = 4 x 3 x 2 = 24
<u>Q5</u>
- No. of ways = 2 x 3 x 3 = 18
Answer:
First make mixed
4 x 5 = 20
20 + 2 = 22
22/5 = 4 2/5
1 x 5 = 5
5 + 1 = 6
6/5= 1 1/5
Multiply the reciprocal. The reciprocal is the fraction flipped over like 1/2 becomes 2/1
22/5 / 6/5 = 22/5 x 5/6
Multiply
22 x 5 = 110
5 x 6 = 30
110/30
Simplify
110/10=11
30/10=3
Answer is
11/3 = 3 2/3
Step-by-step explanation:
To determine any area of a shape we need to know the formula for the area of that particular shape which is for a regular hexagon is
Area of hexagon = (3 √3) a^2 / 2
where a is the length of the side of the hexagon
So, first, we determine the length of the side of the smaller hexagon from the given area.
3 in^2 = (3 √3) a^2 / 2
6 in^2 = (3 √3) a^2
a^2 = 2 √3 / 3
a = 1.0746 in
The length of the side of the bigger hexagon is twice that of the smaller so,
A = 2a = 2 (1.0746 in ) = 2.1491 in
Area of the bigger hexagon = (3 √3) a^2 / 2
= (3 √3) 2.1491^2 / 2 = 12 in^2
