The only way 3 digits can have product 24 is
1 x 3 x 8 = 241 x 4 x 6 = 242 x 2 x 6 = 242 x 3 x 4 = 24
So the digits comprises of 1,3,8 or 1,4,6, or 2,2,6, or 2,3,4
To be divisible by 3 the sum of the digits must be divisible by 3.
1+ 3+ 8=12, 1+ 4+ 6= 11, 2 +2 + 6=10, 2 +3 + 4=9Of those sums of digits, only 12 and 9 are divisible by 3.
So we have ruled out all but integers whose digits consist of1,3,8, and 2,3,4.
Meanwhile they must be odd they either must end in 1 or 3.
The only ones which can end in 1 are 381 and 831.
The others must end in 3.
They must be greater than 152 which is 225. So the
First digit cannot be 1. So the only way its digits can contain of1,3,8 and close in 3 is to be 813.
The rest must contain of the digits 2,3,4, and the only way they can end in 3 is to be 243 or 423.
So there are precisely five such three-digit integers: 381, 831, 813, 243, and 423.
Answer:
Sample Space = {SSS,SSF,SFF,SFS,FSS,FSF,FFS,FFF}
Step-by-step explanation:
Given a sale representative makes presentations about a product in three homes per day.
In each home, Sale is denoted by S and No Sale is denoted by F.
Now the cases for required sample space will be :
- Sale in first home, Sale in second home and Sale in third home.
- Sale in first home, Sale in second home and No Sale in third home.
- Sale in first home, No Sale in second home and No Sale in third home.
- Sale in first home, No Sale in second home and Sale in third home.
- No Sale in first home, Sale in second home and Sale in third home.
- No Sale in first home, Sale in second home and No Sale in third home.
- No Sale in first home, No Sale in second home and Sale in third home.
- No Sale in first home, No Sale in second home and No Sale in third home.
So our Required sample space for the experiment
= {SSS,SSF,SFF,SFS,FSS,FSF,FFS,FFF}.
The area is 20.5632 cm sq.
Lets break it down:
Triangle- the area of a triangle is bh/2 (base×height÷2). If we plug in the numbers, the base is 4.8 and the height is 4.8. 4.8×4.8= 23.04÷2= 11.52
Semi circle- the area of the semi circle is pi×radius×radius. We have the diameter (4.8) so we would need to divide 4.8 by 2 to get 2.4. 2.4×2.4×3.14= 18.0864. We need to divide that by 2 because its a semi circle so 18.0864÷2= 9.0432
11.52+9.0432= 20.5632 cm sq.
hope this helps!
