Answer:
16 = <u>3x</u>
Step-by-step explanation:
It is an equilateral triangle. The formula for the perimeter of an equilateral triangle is P = 3a.
Answer:
<span>x=6</span>, <span>x=−5</span> or <span>x=9</span>
Explanation:
<span><span>f<span>(x)</span></span>=<span>(x−6)</span><span>(x+5)</span><span>(x−9)</span></span>
If all of the linear factors are non-zero, then so is their product <span>f<span>(x)</span></span>.
If any of the linear factors is zero, then so is their product <span>f<span>(x)</span></span>.
So the zeros of <span>f<span>(x)</span></span> are precisely the values of x which make at least one of the linear factors 0, namely: 6, <span>−5</span> or 9.
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)