Hello :
all n in N ; n(n+1)(n+2) = 3a a in N or : <span>≡ 0 (mod 3)
1 ) n </span><span>≡ 0 ( mod 3)...(1)
n+1 </span>≡ 1 ( mod 3)...(2)
n+2 ≡ 2 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 0×1×2 ( mod 3) : ≡ 0 (mod 3)
2) n ≡ 1 ( mod 3)...(1)
n+1 ≡ 2 ( mod 3)...(2)
n+2 ≡ 3 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 1×2 × 3 ( mod 3) : ≡ 0 (mod 3) , 6≡ 0 (mod)
3) n ≡ 2 ( mod 3)...(1)
n+1 ≡ 3 ( mod 3)...(2)
n+2 ≡ 4 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 2×3 × 4 ( mod 3) : ≡ 0 (mod 3) , 24≡ 0 (mod3)
Answer:
the correct answer is 1 because it looks like they are doing it by odd numbers.
hope this helps :)
Step-by-step explanation:
A. since they choose 4 people to form the committee and all the people chosen are teachers
from 5 teacher, we choose 4, 5C4
and
from 20 parents, we choose none, 20C0
5C4*20C0= 5
b. from 5 teacher choose 2, 5C2
and
from 20 parents choose 2, 20C2
5C2 * 20C2=1900
c.all parents
from 5 teachers choose 0, 5C0
and
from 20 parents choose 4, 20C4
5C0 * 20C4= 4845
d. from 5 teacher choose 1, 5C1
and
from 20 parents choose 3, 20C3
5C1 * 20C3= 5700
The perimeter is 36 yd.
We set up a proportion to represent this situation. We know that the ratio of the side to the perimeter is the same for every square. This means that the ratio of the first square, 2/8 is the same for the second one. We know that the side length is 9, which gives us:
2/8 = 9/x
Cross multiply:
2*x = 8*9
2x = 72
Divide both sides by 2:
2x/2 = 72/2
x = 36
