Answer:
<h3>For two events A and B show that P (A∩B) ≥ P (A)+P (B)−1.</h3>
By De morgan's law

which is Bonferroni’s inequality
<h3>Result 1: P (Ac) = 1 − P(A)</h3>
Proof
If S is universal set then

<h3>Result 2 : For any two events A and B, P (A∪B) = P (A)+P (B)−P (A∩B) and P(A) ≥ P(B)</h3>
Proof:
If S is a universal set then:

Which show A∪B can be expressed as union of two disjoint sets.
If A and (B∩Ac) are two disjoint sets then
B can be expressed as:

If B is intersection of two disjoint sets then

Then (1) becomes

<h3>Result 3: For any two events A and B, P(A) = P(A ∩ B) + P (A ∩ Bc)</h3>
Proof:
If A and B are two disjoint sets then

<h3>Result 4: If B ⊂ A, then A∩B = B. Therefore P (A)−P (B) = P (A ∩ Bc) </h3>
Proof:
If B is subset of A then all elements of B lie in A so A ∩ B =B
where A and A ∩ Bc are disjoint.

From axiom P(E)≥0

Therefore,
P(A)≥P(B)
Answer:
- The function f(x) = 9,000(0.95)^x represents the situation.
- After 2 years, the farmer can estimate that there will be about 8,120 bees remaining.
- The range values, in the context of the situation, are limited to whole number
Step-by-step explanation:
The "growth" rate is -5%, so the growth factor, the base in the exponential equation, is 1.00-5% =0.95.
Using x=2, we find the population in 2 years is expected to be about ...
f(2) = 9000·0.95^2 ≈ 8123 . . . . about 8120
Using x=4, we find the population in 4 years is expected to be about ...
f(4) = 9000·0.95^4 ≈ 7331 . . . . about 7330
Since population is whole numbers of bees, the range of the function is limited to whole numbers.
The domain of the function is numbers of years. Years can be divided into fractions as small as you want, so the domain is not limited to whole numbers.
The choices listed above are applicable to the situation described.
Answer:
The time spent by a physician with a patient
Step-by-step explanation:
Option C is the answer