Answer:
a)
And if we solve for we got:
b) False
The reason is because we don't satisfy the following relationship:
We have that:
c) False
In order to satisfy independence we need to have the following condition:
And for this case we don't satisfy this relation since:
Step-by-step explanation:
For this case we have the following probabilities given:
Part a
We want to calculate the following probability:
And we can use the total probability rule given by:
And if we solve for we got:
Part b
False
The reason is because we don't satisfy the following relationship:
We have that:
Part c
False
In order to satisfy independence we need to have the following condition:
And for this case we don't satisfy this relation since:
Answer:
See proof below
Step-by-step explanation
cot^2(x) - csc^2(x) = -1
In trigonometry identity
cot^2x = cos²x/sin²x
Csc²x = 1/sin²x
Substitute into the original expression
cos²x/sin²x - 1/sin²x
Find the LCM
(Cos²x-1)/sin²x .... *
Recall that sin²x+cos²x = 1
Sin²x = 1-cos²x
-sin²x = -1+cos²x
-sin²x = cos²x-1 .... **
Substitute ** into *
(Cos²x-1)/sin²x
-sin²x/sin²x
= -1 (RHS)
Therefore cot^2(x) - csc^2(x) = -1 (Proved!)
Assuming that this is a compounding interest rate, we use the future value formula which is expressed as: F = P ( 1 + i )^n where F is the future value, P is the present value, i is the interest rate and n is the compounding periods. We do as follows:
F = P ( 1 + i )^n
8000 = 4000 ( 1 + 0.0553)^n
n = 12.88 yrs or about 13 years
Therefore, option D is the answer.
Answer:
x+z=m
Step-by-step explanation:
Answer:
7x+21
Step-by-step explanation:
hope this helps! :)