Answer:
(E) None of these above are true.
Step-by-step explanation:
Married = 74% or 0.74
College graduates = 42% or 0.42
pr(married | college graduates) = 0.56
(A) These events are pairwise disjoint. This is false. Pairwise disjoint are also known as mutually exclusive events. Here we can see that both events are occurring at same time.
(B) These events are independent events. This is also false.
(C) These events are both independent and pairwise disjoint. False
(D) A worker is either married or a college graduate always. False
Here Probability(A or B) shall be 1
= Pr(A) + Pr(B) - Pr( A and B) = 0.74 + 0.42 - 0.56 * 0.42 = 0.9248
This is not equal to 1.
(E) None of these above are true. This is true.
Answer:
0.999 units
Step-by-step explanation:
D=

D=0.9994930426
4.133 kilometers
2.063 + 2.07 = 4.133
a.

By Fermat's little theorem, we have


5 and 7 are both prime, so
and
. By Euler's theorem, we get


Now we can use the Chinese remainder theorem to solve for
. Start with

- Taken mod 5, the second term vanishes and
. Multiply by the inverse of 4 mod 5 (4), then by 2.

- Taken mod 7, the first term vanishes and
. Multiply by the inverse of 2 mod 7 (4), then by 6.


b.

We have
, so by Euler's theorem,

Now, raising both sides of the original congruence to the power of 6 gives

Then multiplying both sides by
gives

so that
is the inverse of 25 mod 64. To find this inverse, solve for
in
. Using the Euclidean algorithm, we have
64 = 2*25 + 14
25 = 1*14 + 11
14 = 1*11 + 3
11 = 3*3 + 2
3 = 1*2 + 1
=> 1 = 9*64 - 23*25
so that
.
So we know

Squaring both sides of this gives

and multiplying both sides by
tells us

Use the Euclidean algorithm to solve for
.
64 = 3*17 + 13
17 = 1*13 + 4
13 = 3*4 + 1
=> 1 = 4*64 - 15*17
so that
, and so 