Answer:
,
Step-by-step explanation:
First, the vector must be transformed into its polar form:
Let assume that vector is rotated counterclockwise. The new angle is:
Which is coterminal with . The reflection across y-axis is:
The equivalent vector in rectangular coordinates is:
Answer:
For the critical value we need to calculate the degrees of freedom given by:
And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:
Step-by-step explanation:
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=test value with right arm , y = test value with left arm
The system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis:
The first step is calculate the difference
The second step is calculate the mean difference
The third step would be calculate the standard deviation for the differences, and we got:
The 4 step is calculate the statistic given by :
For the critical value we need to calculate the degrees of freedom given by:
And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:
1. Points M and N have coordinates (-4,0) and (4,2), respectively.
Then vector is perpendicular to the neede line.
2. Write the equation of line that passes through the point P(2,-4) and is perpendicular to vector
3. Find the point on x-axis, that lies on the perpendicular line.
When y=0, then 4x-4=0, x=1 and point (1,0) lies on perpendicular line.
Answer: correct choice is C.