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2 years ago

Find the vertical asymptote for y=x^2-5x/x^2-x-2

Mathematics

1 answer:

grigory [225]2 years ago

7 0

Answer:

vertical asymptote at x=2 and x=-1

Step-by-step explanation:

$y= \frac{x^2-5x}{x^2-x-2}$

To find out vertical asymptote we set the denominator =0 and solve for x

$x^2 - x - 2=0$

now factor left hand side

find out two factors whose product is -2 and sum is -1

-2 times 1 = -2

-2+1 = -1

(x-2)(x+1) =0

x-2 =0 so x= 2

x+1 =0 so x=-1

vertical asymptote at x=2 and x=-1

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2 years ago

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In a second grade class containing 13 girls and 9 boys, 2 students are selected at random to give out the math papers. What is t

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13/22 x 9/21 = 0.25

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3.30 Survey response rate. Pew Research reported in 2012 that the typical response rate to their surveys is only 9%. If for a pa

Artist 52 [7]

Answer:

0% probability that at least 1,500 will agree to respond

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 15000, p = 0.09$

$\mu = E(X) = np = 15000*0.09 = 1350$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15000*0.09*0.91} = 35.05$

What is the probability that at least 1,500 will agree to respond

This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1499 - 1350}{35.05}$

$Z = 4.25$

$Z = 4.25$ has a pvalue of 1.

1 - 1 = 0

0% probability that at least 1,500 will agree to respond

6 0

2 years ago

A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18 \pi18π18, pi

Whitepunk [10]

Answer:

$A=81\pi $ m^2$

Step-by-step explanation:

Circumference of the column $=18\pi $ meters$

Circumference of a circle $=2\pi r$

Therefore:

$2\pi r =18\pi $ meters\\2r=18\\r=18 \div 2\\$Radius, r=9 meters$

Area of a Circle $=\pi r^2$

Since radius of the cross section of the column =9 meters

Area of the cross section of the column

$=\pi *9^2\\=81\pi $ m^2$

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2 years ago

2.8, 3.4, 4.0, 4.6, . . . Write an equation for the nth term of the arithmetic sequence. Then find a50.

vova2212 [387]

Answer:

a_n = 2.2 + 0.6 n

a_50 = 32.2

Step-by-step explanation:

What's the common difference of this series?

$a_1 = 2.8$

$a_2 = 3.4$

Common difference = $a_2 - a_1 = 3.4 - 2.8 = 0.6$ .

Expression for the nth term:

$a_n = a_1 + (n - 1) \cdot\text{Common Difference} \\\phantom{a_n } = 2.8 + 0.6 \; (n-1) \\\phantom{a_n} = 2.8 + 0.6 \; n - 0.6\\\phantom{a_n} = 2.2 + 0.6\; n$

n = 50 for the fiftieth term. Therefore

$a_{50} = 2.2 + 0.6 \times 50 = 32.2$ .

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2 years ago