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2 years ago

Sketch a graph of the following rational function: h(x)= x²-1/ x³-2x²-x+2

Mathematics

1 answer:

Naddika [18.5K]2 years ago

4 0

Note that

$\frac{x^2-1}{x^3 - 2x^2 -x+2}=\frac{x^2 -1}{x^2 (x-2)-(x-2)}=\frac{x^2 -1}{(x^2 -1)(x-2)}$

So, for all $x \neq \pm 1$ , $f(x)=\frac{1}{x-2}$ .

So, the graph looks like something like as following in the image.

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Suppose we have a population whose proportion of items with the desired attribute is p = 0:5. (a) If a sample of size 200 is tak

crimeas [40]

Answer:

a. If a sample of size 200 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 41.26%.

b. If a sample of size 100 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 30.5%.

Step-by-step explanation:

This problem should be solved with a binomial distribution sample, but as the size of the sample is large, it can be approximated to a normal distribution.

The parameters for the normal distribution will be

$\mu=p=0.5\\\\\sigma=\sqrt{p(1-p)/n} =\sqrt{0.5*0.5/200}= 0.0353$

We can calculate the z values for x1=0.47 and x2=0.51:

$z_1=\frac{x_1-\mu}{\sigma}=\frac{0.47-0.5}{0.0353}=-0.85\\\\z_2=\frac{x_2-\mu}{\sigma}=\frac{0.51-0.5}{0.0353}=0.28$

We can now calculate the probabilities:

$P(0.47$

If a sample of size 200 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 41.26%.

b) If the sample size change, the standard deviation of the normal distribution changes:

$\mu=p=0.5\\\\\sigma=\sqrt{p(1-p)/n} =\sqrt{0.5*0.5/100}= 0.05$

We can calculate the z values for x1=0.47 and x2=0.51:

$z_1=\frac{x_1-\mu}{\sigma}=\frac{0.47-0.5}{0.05}=-0.6\\\\z_2=\frac{x_2-\mu}{\sigma}=\frac{0.51-0.5}{0.05}=0.2$

We can now calculate the probabilities:

$P(0.47$

If a sample of size 100 is taken, the probability that the proportion of successes in the sample will be between 0.47 and 0.51 is 30.5%.

8 0

2 years ago

1/3 divided by 8??????????

Serga [27]

Answer: 1/24

Step-by-step explanation: if you take 8 and change it to 1/8, you can multiply it by 1/3 and 1x1 is 1 and 8x3 is 24 so it’s 1 over 24 or 1/24

8 0

3 years ago

Suppose T= {-8,-4,0,4,8,12,16,20} and K= {-3,-2,-1,0,1,2,3,4,5,6}. What is T U K?

Ivanshal [37]

T U K = { -8,-4, -3, -2, -1, 0, 1,2,3,4, 5,6,8,12,16,20}

3 0

2 years ago

The arc length

Zina [86]

Answer:

s = rθ
2.5 radians
143.24°

Step-by-step explanation:

The applicable formula is ...

s = rθ

where s is the arc length, r is the circle's radius, and θ is the central angle in radians.

Filling in the given values, we find ...

15 = 6θ

θ = 15/6 = 2.5 . . . radians

Pi (π) radians is 180°, so the angle in degrees is ...

2.5(180°/π) ≈ 143.24°

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3 years ago

Please help me Asp Please

Sati [7]

Answer:

it will make a cube

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2 years ago

Read 2 more answers

Sketch a graph of the following rational function: h(x)= x²-1/ x³-2x²-x+2​

Sketch a graph of the following rational function: h(x)= x²-1/ x³-2x²-x+2