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:
7/40
Step-by-step explanation:
There are 3 girls+9 boys = 12 students in the 7th grade
P (girl in 7th grade) = girls/ total
= 3/12 = 1/4
There are 7 girls+3 boys = 10 students in the 8th grade
P (girl in 8th grade) = girls/ total
= 7/10
P(7th grade girl, 8th grade girl) = 1/4 * 7/10 = 7/40
The cost of labour per hour is $90.56
The total amount paid by Austin is the sum of the total cost of labour and the cost of the parts
Total amount paid = total cost of labour + cost of parts
$553.50 = total cost of labour + $126
total cost of labour = $533.50 - $126
= $407.50
The total cost of labour = cost of labour per hour x total time worked
$407.50 = xx × 4.5
xx = $407.50 / 4.5
xx = $90.56
A similar question was solved here: brainly.com/question/21400699?referrer=searchResults
Answer:
at most she can spend $22 on flowers
Step-by-step explanation:
hope this helped :)
