Answer:
We take v in the vector space V different from 0. Since v is not 0, then
Lets take k>0 such that
Now, we take any vector w. We want to show that .
Since v is any non-zero vector, then this will prove that for any vectors a,b. The reason is that for any vector different from 0, lets name it x, there will exist a constant such that for any y (this is for the same reason a constant exists for v). Since y can be anything, then it can be v. But that means that , because v also has its constant k.
Now, lets show that . Lets take a constant c such that . We have that
Thus
Which means that
Which means that . As a consequence
Which proves what we were looking for.
This refers to the actual value. Therefore you can plug it into the calculator:
Sin of 30= 1/2
Cos30=√3/2
Answer:
15 dog heights;
Step-by-step explanation:
The formula to be used here is where:
- is the confidence level
- is the margin of error for a confidence level
- is the critical value for the confidence level
- is the population standard deviation
- is the sample size
We are given that:
To determine the minimum sample size, , we plug our given values into the formula and solve for
Don't forget to round up here! This means that actually.
Therefore, if we want to be 95% confident that the sample mean is within 1 inch of the true population mean, the minimum sample size that can be taken is 15 dog heights.
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25% of 200 is 50.
25% is also 1/4. So we can do 200(1/4) or 200/4 which is 50.