How many times wider is 2ft than the width of 2in
2 answers:
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Answer:
See the proof below.
Step-by-step explanation:
What we need to proof is this: "Assuming X a vector space over a scalar field C. Let X= {x1,x2,....,xn} a set of vectors in X, where . If the set X is linearly dependent if and only if at least one of the vectors in X can be written as a linear combination of the other vectors"
Proof
Since we have a if and only if w need to proof the statement on the two possible ways.
If X is linearly dependent, then a vector is a linear combination
We suppose the set is linearly dependent, so then by definition we have scalars
in C such that:
And not all the scalars are equal to 0.
Since at least one constant is non zero we can assume for example that , and we have this:
We can divide by c1 since we assume that and we have this:
And as we can see the vector can be written a a linear combination of the remaining vectors
. We select v1 but we can select any vector and we get the same result.
If a vector is a linear combination, then X is linearly dependent
We assume on this case that X is a linear combination of the remaining vectors, as on the last part we can assume that we select and we have this:
For scalars defined in C. So then we have this:
So then we can conclude that the set X is linearly dependent.
And that complet the proof for this case.
First, let's create the ratios of sweetened to unsweetened. To do this, you would have to subtract the number of people that preferred unsweetened from the total.
Westside mall: 15:30 or
Eastside mall: 13:26 or
Now, you would divide to both ratios.
15 ÷ 30 = 0.5
13 ÷ 26 = 0.5
They have the same sum, meaning, they are the same.
Westside Mall shoppers are just as likely to prefer unsweetened tea as Eastside Mall shoppers.
I hope this helps!
Westside mall: 15:30 or
Eastside mall: 13:26 or
Now, you would divide to both ratios.
15 ÷ 30 = 0.5
13 ÷ 26 = 0.5
They have the same sum, meaning, they are the same.
Westside Mall shoppers are just as likely to prefer unsweetened tea as Eastside Mall shoppers.
I hope this helps!