Answer:
A company produces electric insulators. The strength of the insulators is important since a broken insulator may cause a short circuit. Unfortunately, the strength varies significantly due to the material. Because of the expense, only a limited number of insulators could be tested. The engineers sampled 25 insulators (From a production run of 200), and conducted a destructive test to determine the force that was required to break the insulators. The mean value of this force was 1723 lbf with a sample standard deviation of 90 lbf. You may approximate the population standard deviation with the sample standard deviation for the following questions. a. Determine if the population is large enough or if a finite population correction (FPC) factor is needed. If so, what is the FPC factor? b. For 95% confidence, determine the margin of error (+ lbf) c. For these conditions, estimate the range of the probable population mean. Provide lower and upper values. For 95% confidence, determine the margin of error ( Assume the same mean and sample standard deviation. What is one advantage and one disadvantage of using 50 insulators instead of 25 insulators? d. lbf) if 50 insulators were tested.
Step-by-step explanation:
<span> I am assuming you want to prove:
csc(x)/[1 - cos(x)] = [1 + cos(x)]/sin^3(x).
</span>
<span>If we multiply the LHS by [1 + cos(x)]/[1 + cos(x)], we get:
LHS = csc(x)/[1 - cos(x)]
= {csc(x)[1 + cos(x)]/{[1 + cos(x)][1 - cos(x)]}
= {csc(x)[1 + cos(x)]}/[1 - cos^2(x)], via difference of squares
= {csc(x)[1 + cos(x)]}/sin^2(x), since sin^2(x) = 1 - cos^2(x).
</span>
<span>Then, since csc(x) = 1/sin(x):
LHS = {csc(x)[1 + cos(x)]}/sin^2(x)
= {[1 + cos(x)]/sin(x)}/sin^2(x)
= [1 + cos(x)]/sin^3(x)
= RHS.
</span>
<span>I hope this helps! </span>
Answer:
b
Step-by-step explanation:
because that is the correct answer believe me
Answer:
The matching is shown below.
Step-by-step explanation:
The given sets are defined as
A = {x | x < 1}
It means all the values of x which are less than 1.
B = {x | x ≥ 5}
It means all the values of x which are greater than or equal to 5.
C = {x | x = 5}
It means all the value of x is 5.
Union of two sets contains all the elements of both sets.
Intersection of two sets contains only common elements of both sets.
The matching is shown below.
Sets Correct value
1. A ∪ B {x | x < 1 or x ≥ 5}
2. A ∪ C {x | x < 1 or x = 5}
3. B ∪ C {x | x ≥ 5}
4. A ∩ B Ø
5. B ∩ C {x | x = 5}
Minus 3 from the 3 and the 18
