Given two vectors
they are parallel if they are a multiple of each other:
You can easily test this by checking if
they are orthogonal if their dot product is null:
For example, in the first case, we have
So, they aren't parallel. Similarly, you have
So, they aren't orthogonal.
In the second case, we have
So, they aren't parallel, and
So, they are orthogonal.
Finally, we have
So, they are parallel (and thus can't be orthogonal)
Part a: For variable X using z score you have (x-30)/10, replace X for this expression in (a), i mean Z=2+10((x-30)/10) = 2+x-30= put this in the way of z score = (x-18)/1, so the mean is 18 and standard deviation is 1.
Part b: Z=X+Y= (x-30)/10 + (x-20)/8 = solve adding fractions = (18x-440)/80 now divide all the numbers between 18 (because you need to show as z score way) = (x-24.4)/4.4, so the mean is 24.4 and standard deviation is 4.4.
For part c,do the same.
The answer to this is (0,6).
So do
25x16=400
this shows how many raffle tickets were sold all together
Then do 400x$15 =$6000
So all together they raised $6000
P=12T
Q=66T
-----------
Toys added to each bag:
P=12T+nT
Q=66T+nT
Therefore, 66T+nT=3(12T+nT)
------------
66T+nT=36T+3nT
T(66+n)=T(36+3n)
66+n=36+3n
3n-n=66-36
2n=30
Therefore, n=30/2=15
-------------
*She added 15 toys to each bag.
