Answer:
Solution : 6 + 6i
Step-by-step explanation:
This is the expression we have to solve for. Now normally we could directly apply trivial identities and convert this into standard complex form, but as the expression is too large, it would be easier to convert into trigonometric form first ----- ( 1 )
( Multiply both expressions )
( Simplify for both and )
=
( Substitute )
Now that we have this in trigonometric form, let's convert into standard form by applying the following identities ----- ( 2 )
sin(π / 4) = √2 / 2 = cos(π / 4)
( Substitute )
= =
= =
= - Therefore our solution is option a.
Answer: 10
Step-by-step explanation:
The formula used for standard error is :-
, where is population standard deviation and n is the sample size.
Given: n = 4
Then, the difference would expected between the sample mean and the population mean will be :
Hence, the expected difference between the sample mean and the population mean = 10
Answer: she worked 8 hours at Job A
She worked 16 hours at Job B
Step-by-step explanation:
Let x represent the number of hours that she worked job A.
Let y represent the number of hours that she worked job B.
Kathy works two part-time jobs for a total of 24 hours a week. This means that
x + y = 24
Job A pays $6.00 per hour, and Job B pays $7.30 per hour and she made $164.80 for the week. it means that
6x + 7.3y = 164.80 - - - - - - -1
Substituting x = 24 - y into equation 1, it becomes
6(24 - y) + 7.3y = 164.80
144 - 6y + 7.3y = 164.80
- 6y + 7.3y = 164.80 - 144
1.3y = 20.8
y = 20.8/1.3 = 16
x = 24 - y = 24 -16
x = 8