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2 years ago

Express f(x) =3\x²- 1 in partial fraction

1 answer:

7 0

3/(x ² - 1) = 3/((x - 1) (x + 1)) = a/(x - 1) + b/(x + 1)

==> 3 = a (x + 1) + b (x - 1)

==> 3 = (a + b) x + a - b

==> a + b = 3 and a - b = 0

==> a = b

==> a + b = 2a = 3 ==> a = 2/3 and b = 2/3

So you have

3/(x ² - 1) = 2/(3(x - 1)) + 2/(3(x + 1))

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A bag contains 6 red apples and 5 yellow apples. 3 apples are selected at random. Find the probability of selecting 1 red apple

tester [92]

Answer: The required probability of selecting 1 red apple and 2 yellow apples is 36.36%.

Step-by-step explanation: We are given that a bag contains 6 red apples and 5 yellow apples out of which 3 apples are selected at random.

We are to find the probability of selecting 1 red apple and 2 yellow apples.

Let S denote the sample space for selecting 3 apples from the bag and let A denote the event of selecting 1 red apple and 2 yellow apples.

Then, we have

$n(S)=^{6+5}C_3=^{11}C_3=\dfrac{11!}{3!(11-3)!}=\dfrac{11\times10\times9\times8!}{3\times2\times1\times8!}=165,\\\\\\n(A)\\\\\\=^6C_1\times^5C_2\\\\\\=\dfrac{6!}{1!(6-1)!}\times\dfrac{5!}{2!(5-2)!}\\\\\\=\dfrac{6\times5!}{1\times5!}\times\dfrac{5\times4\times3!}{2\times1\times3!}\\\\\\=6\times5\times2\\\\=60.$

Therefore, the probability of event A is given by

$P(A)=\dfrac{n(A)}{n(S)}=\dfrac{60}{165}=\dfrac{4}{11}\times100\%=36.36\%.$

Thus, the required probability of selecting 1 red apple and 2 yellow apples is 36.36%.

4 0

2 years ago

A container has 1 pink block and 3 green blocks. Juan wants to make the probability of randomly selecting a black block equal to

alex41 [277]

Answer:

Step-by-step explanation:

He should add 4 black blocks because there are a total of 4 other blocks, and in order to have a probability of 50%, the number of black blocks needs to be equal to the total number of the other colored blocks.

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3 years ago

Simplify the expression: - 4t+ - 7t+3–10t

Gekata [30.6K]

Answer:t+3

Step-by-step explanation:

4t+7t+3-10t

11t+3-10t

t+3

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2 years ago

What is the slope intercept form for this graph ? Please answer !!

Dmitry_Shevchenko [17]

$y = \frac{3}{2} x + 3$

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2 years ago

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I need the answer to this systems word problem. Step by step explanation please

algol [13]

Answer:

25 miles, and the cost will be $37.50.

Step-by-step explanation:

Mose's charge can be represented by f(x) = 0.5x + 25, Holly's charge can be represented by g(x) = 0.3x + 30.

Set the equations equal to each other: 0.5x + 25 = 0.3x + 30.

0.2x = 5

x = 25

Substitute 25 for x: f(x) = 0.5(25) + 25 = 37.5, g(x) = 0.3(25) + 30 = 37.5.

So f(x) = g(x) at x = 25, and the output will be 37.5.

6 0

1 year ago

Express f(x) =3\x²- 1 in partial fraction​

Express f(x) =3\x²- 1 in partial fraction