Solve the problem below X-y=1 X+y=3
2 answers:
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Prove:
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Base Step: For n=1:
and
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Induction Hypothesis: Assume true for n=k. Meaning:
assumed to be true.
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Induction Step: For n=k+1:
by our Induction Hypothesis, we can replace every term in this summation (except the last term) with the right hand side of our assumption.
From here, think about what you are trying to end up with.
For n=k+1, we WANT the formula to look like this:
That thing on the right hand side is what we're trying to end up with. So we need to do some clever Algebra.
Combine the (k+1) and 1/2, put the 2 in the bottom,
We want to end up with a 2^k as our final denominator, so our middle term is missing a power of 2. Let's multiply top and bottom by 2,
Distribute the -2 and combine the fractions together,
Combine like-terms,
pull the negative back out,
And ta-da! We've done it!
We can break apart the +3 into +1 and +2,
and the +0 in the bottom can be written as -1 and +1,
____________________________________________
Base Step: For n=1:
and
--------------------------------------------------------------------------
Induction Hypothesis: Assume true for n=k. Meaning:
assumed to be true.
--------------------------------------------------------------------------
Induction Step: For n=k+1:
by our Induction Hypothesis, we can replace every term in this summation (except the last term) with the right hand side of our assumption.
From here, think about what you are trying to end up with.
For n=k+1, we WANT the formula to look like this:
That thing on the right hand side is what we're trying to end up with. So we need to do some clever Algebra.
Combine the (k+1) and 1/2, put the 2 in the bottom,
We want to end up with a 2^k as our final denominator, so our middle term is missing a power of 2. Let's multiply top and bottom by 2,
Distribute the -2 and combine the fractions together,
Combine like-terms,
pull the negative back out,
And ta-da! We've done it!
We can break apart the +3 into +1 and +2,
and the +0 in the bottom can be written as -1 and +1,
Answer:
The percentage of the variability in plant weight is NOT explained by height is
%
Step-by-step explanation:
From the question we are told that
The correlation between height and weight is
Generally the R-Squared between height and weight is mathematically represented as
substituting values
This R-Squared tells us the percentage of plant weight is accounted by height
and from the calculation we see that it is 56.3%
Now the percentage of plant weight that is not accounted by height is
%