<span>One way to view the "logical geography" of the standard-form categorical propositions is to use diagrams invented by John Venn, a friend of Lewis Carroll.
A. Perhaps, you have been introduced to diagrams used in set theory; the Venn Diagrams are somewhat different.
B. Most descriptions of Venn Diagrams introduce the three symbols used as follows.
1. An empty circle is used to represent a subject class or a predicate class and is generally so labeled with an S or a P. Putting the name of the actual subject or predicate class next to the circle is preferred. The area inside the circle represents members of the class in question, if there are any. The area outside the circle represents all other individuals (the complementary class) if there are any. Note that the label "things" is written outside the circle, even though "things," if there are any, would be inside the circle. things.gif (1122 bytes)
2. Shading or many parallel lines are used to indicate areas which are known to be empty. I.e., there are no individuals existing in that area. E.g., the diagram to the right represents the class of "Yeti."</span>
How often do they pay? If they only pay once a year, 90000/100=900. 900 * .52 = 468
Answer:
a) the 95% confidence interval for the true mean µ is 60.971, 65.629
The exact 95% confidence interval for the true mean µ is 60.971, 65.629
P (x`- ∝ s/√n<u <x`+ ∝ s/√n) = 0.95
Step-by-step explanation:
n= 50
x`= 63.3
s= 8.4 minutes
∝= 95%= ±1.96
The formula for calculating the confidence interval is:
x`± ∝ s/√n
Putting the values
x`± 1.96 s/√n
63.3 ± 1.96(8.4/√50)
63.3± 2.3287
60.971, 65.629
a) the 95% confidence interval for the true mean µ is 60.971, 65.629
b) Putting the values
x`± 1.96 s/√n
63.3 ± 1.96(8.4/√50)
63.3± 2.3287
The exact 95% confidence interval for the true mean µ is 60.971, 65.629
c) The prediction level tells that the drying time of the wall from 60.971 to 65.629 minutes must be in the range 95 % of the time.
And is given by
P (x`- ∝ s/√n<u <x`+ ∝ s/√n) = 0.95
Answer
q1.
Given:
Rewrite this function in the way as;
then;
and
q2.
Given the function:
and
Confirm f and g are inverses by showing f(g(x)) =x and g(f(x)) =x
First show f(g(x)) =x
f(g(x)) = 9(g(x)) + 3
Substitute the function g(x) we have;
or
= x -3 + 3 = x
f(g(x)) =x
Similarly show that: g(f(x)) =x
Substitute the value of function g(x) we have;
Simplify:
hence proved!
Therefore, f and g are inverse of each other after showing f(g(x)) =x and g(f(x)) =x