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2 years ago

Can someone help please

Mathematics

1 answer:

Elena L [17]2 years ago

4 0

9514 1404 393

Answer:

4. n = 4

5. P(A|B) = 0.75

Step-by-step explanation:

4. The coefficient of x will depend on n. The expansion is ...

(5 +nx)^2(1 +3/5x)^n = (25 +10nx +n^2·x^2)(1 +3/5nx +...)

So, the x-term of the expansion is ...

25(3/5nx) +(10nx)(1) = 25nx

The problem statement tells us that is 100x, so we have ...

25nx = 100x

n = 100x/(25x) = 4 . . . . . divide by the coefficient of n

The value of n is 4.

5. For the conditional probability formula, we need to know P(A∩B).

P(A∩B) = P(A) +P(B) -P(A∪B)

P(A∩B) = 0.5 +0.4 -0.6 = 0.3

Then the conditional probability is ...

P(A|B) = P(A∩B)/P(B) = 0.3/0.4

P(A|B) = 0.75

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Since the perimeter must not exceed 291.
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x + 87 + 64 < 291
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x < 291 -151.
x < 140. (First)

But for a triangle there is what is called the Triangle Inequality Theorem. That given the two sides of a tringle, the third side of the triangle must greater than the positive difference between the two sides and less than the sum of the two sides.

So for this case. 87 and 64.

x > ( 87 - 64). x > 23.
x < (87 + 64) x < 151. Combine both inequalities.

23 < x < 151 (second).

Combining First and second. Both must be satisfied.
So we have a more accurate answer as:

23 < x < 140. x is greater than 23 and x is less than 140.

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I hope this helps.

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