Suppose that in a certain population of married couples, 30% of the husbands smoke, 20% of the wives smoke, and in 8% of the cou
1 answer:
Answer:
Not independent
Step-by-step explanation:
Given that in a certain population of married couples, 30% of the husbands smoke, 20% of the wives smoke, and in 8% of the couples both the husband and the wife smoke.
Let A be the event that husbands smoke and B the event that wives smoke
Give that
To check whether A and B are independent it is sufficient to check
P(A\bigcap B)=P(A)P(B)
Right side=
Left side = 0.08
Since two sides do not equal the two events are not independent.
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With 
, the Fourier series expansion of 
is
where the coefficients are obtained by computing
You should end up with
(both due to the fact that is odd)
Now the problem is that this expansion does not match the given one. As a matter of fact, since is odd, there is no cosine series. So I'm starting to think this question is missing some initial details.
One possibility is that you're actually supposed to use the even extension of, which is to say we're actually considering the function
and enforcing a period of
. Now, you should find that
The value of the sum can then be verified by choosing
, which gives
as required.
where the coefficients are obtained by computing
You should end up with
(both due to the fact that
Now the problem is that this expansion does not match the given one. As a matter of fact, since
One possibility is that you're actually supposed to use the even extension of
and enforcing a period of
The value of the sum can then be verified by choosing
as required.
Circle A is missing, so i have attached it.
Answer:
∠XYZ = 35°
Step-by-step explanation:
We want to find the angle ∠XYZ in the image attached.
To solve that, we will use the formula in the theorem for angle formed by secants or tangents. Thus;
∠XYZ = ½(arc WZ - arc XZ)
From the image, arc WZ = 175° and arc XZ = 105°
Thus;
∠XYZ = ½(175 - 105)
∠XYZ = ½(70)
∠XYZ = 35°
