You have five friends. A serving of ice cream is 3/4 cups. How many cups of ice cream would it take to feed all five of your friends?
Answer:
6*8=48 groups with elements of order 7
Step-by-step explanation:
For this case the first step is discompose the number 168 in factors like this:

And for this case we can use the Sylow theorems, given by:
Let G a group of order
where p is a prime number, with
and p not divide m then:
1) 
2) All sylow p subgroups are conjugate in G
3) Any p subgroup of G is contained in a Sylow p subgroup
4) n(G) =1 mod p
Using these theorems we can see that 7 = 1 (mod7)
By the theorem we can't have on one Sylow 7 subgroup so then we need to have 8 of them.
Every each 2 subgroups intersect in a subgroup with a order that divides 7. And analyzing the intersection we can see that we can have 6 of these subgroups.
So then based on the information we can have 6*8=48 groups with elements of order 7 in G of size 168
Answer:
a) a
b) ab
e) bbbbb
Step-by-step explanation:
We are given the following in the question:


a) a
It is given that 
b) ab

Thus, ab belongs to S.
c) aba
This does not belong to S because we cannot find x for which xb belongs to S.
d) aaab
This does not belong to S because we cannot find x for which xb belongs to S.
e) bbbbb

Thus, bbbbb belongs to S.
3/8 s
It already went 5/8. 8/8 is the whole yard. 8/8 - 5/8 is 3/8
91 is 130% of what number...
91 = 1.3x
91 / 1.3 = x
70 = x
so 91 is 130% of 70 <==