Answer:
Example 1 Find the inverse transform of each of the following.
F
(
s
)
=
6
s
−
1
s
−
8
+
4
s
−
3
H
(
s
)
=
19
s
+
2
−
1
3
s
−
5
+
7
s
5
F
(
s
)
=
6
s
s
2
+
25
+
3
s
2
+
25
G
(
s
)
=
8
3
s
2
+
12
+
3
s
2
−
49
Show All Solutions
Answer: sec (75) or csc (15)
Step-by-step explanation:
255 is in the 3rd quadrant where the secant is. Here, the tangent and cotangent is positive.
Reference angle for 255 is,
255 - 180 = 75 degrees.
Therefore, sec (255) = sec (75)
= csc (90 - 75) = csc (15)
Answer:
The appropriate probability model for X is a Binomial distribution,
X
Bin (<em>n</em> = 5, <em>p</em> = 1/33).
Step-by-step explanation:
The random variable <em>X</em> can be defined as the number of American births resulting in a defect.
The proportion of American births that result in a birth defect is approximately <em>p</em> = 1/33.
A random sample of <em>n</em> = 5 American births are selected.
It is assumed that the births are independent, i.e. a birth can be defective or not is independent of the other births.
In this experiment the success is defined as a defective birth.
The random variable <em>X</em> satisfies all criteria of a Binomial distribution.
The criteria are:
- Number of observations is constant
- Independent trials
- Each trial has only two outcomes: Success and Failure
- Same probability of success for each trial
Thus, the appropriate probability model for X is a Binomial distribution, Bin (<em>n</em> = 5, <em>p</em> = 1/33).