Subtract 3a^2+5ab−4b^2 from 8a^2−6ab+4b^2

Mathematics

1 answer:

liberstina [14]3 years ago

3 0

Answer:

$\large\boxed{(8a^2-6ab+4b^2)-(3a^2+5ab-4b^2)=5a^2-11ab+8b^2}$

Step-by-step explanation:

$(8a^2-6ab+4b^2)-(3a^2+5ab-4b^2)\\\\=8a^2-6ab+4b^2-3a^2-5ab-(-4b^2)\\\\=8a^2-6ab+4b^2-3a^2-5ab+4b^2\qquad\text{combine like terms}\\\\=(8a^2-3a^2)+(-6ab-5ab)+(4b^2+4b^2)\\\\=5a^2-11ab+8b^2$

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If P(A) = 0.2, P(B) = 0.2, and P(A ∪ B) = 0.4, then P(A ∩ B) = _______.

Pavlova-9 [17]

Answer:

P(A ∩ B) = 0.

a) NO

b) YES

Step-by-step explanation:

Thinking about this through Venn diagrams we can sort of understand that:

if P(A) = 0.2 and P(B) = 0.2, and P(A∪B) = 0.4.

there's no overlapping between P(A) and P(B).

(If there was overlapping then P(A∪B) < 0.4, since you'd be excluding the overlapped part from getting counted twice.

Think of it in terms of calculating areas circles A and B, if the circles were disjoint, then the sum of the areas A and B would be 0.2+0.2. But if the circles were overlapping then the sum of the areas would be 0.2+0.2-P(A ∩ B), where P(A ∩ B) is the overlapping part)

since there's no overlapping P(A ∩ B) = 0.

a) NO

events A and B are only independent when P(A ∩ B) > 0 (or overlapping)

b) YES

events A and B are mutually exclusive when P(A ∩ B) = 0 (or disjoint)

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3 years ago

4) BRAINLIEST + 15 + POINTS :)

malfutka [58]

Answer:

Step-by-step explanation:

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