Prove that Zn Zn is notisomorphic to any subgroup of Zm for any m.
1 answer:
Answer and Step-by-step explanation:
Every group homomorphism ϕ:Zn→Zm extends in a unique way to a linear transformation T:Qn→Qm of vector spaces over Q.
Moreover, ϕ is injective iff T is injective. But T being injective implies n≤m.
Applying this to both ϕ and ϕ−1, we conclude that n≤m≤n.
NOTE:
The proof and step-by-step explanation is in the attachment below
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Answer:
The minimum sample size required to create the specified confidence interval is 2229.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
What is the minimum sample size required to create the specified confidence interval
This is n when
Rounding up
The minimum sample size required to create the specified confidence interval is 2229.
Answer:
13 glue sticks cost $25.22.
Step-by-step explanation:
4 blue sticks cost $7.76, this means that one glue stick costs
$7.76/4 = $1.94.
Let be the cost of the glue sticks, and
be the number of glue sticks; then
We can use this equation to find the cost of 13 glue sticks; we just put into our equation and it gives:
So 13 glue sticks cost $25.22.