Identify the restrictions on the domain of f(x) = x+5/x-2

What are the zeros of the function?

cluponka [151]

The function is:

f ( x ) = x² - x - 72

This is a quatdratic function. So we can find the zeroes of the function with the formula:

x 1/2 = ( - b +/- √(b² - 4 ac) ) / ( 2a )

And we have: a = 1, b = - 1 and c = - 72

x 1/2 = ( 1 +/- √((-1)² - 4 · 1· ( - 72 )) ) / 2

x 1/2 = ( 1 +/- √( 1 + 288 ) ) / 2

x 1/2 = ( 1 +/- √289 ) / 2

x 1/2 = ( 1 +/- 17 ) / 2

x 1 = ( 1 - 17 ) 2 = - 16 / 2 = - 8

x 2 = ( 1 + 17 ) / 2 = 18 / 2 = 9

Answer: The zeroes are - 8 and 9.

7 0

3 years ago

A $104,000 selling price with $24,000 down at 81⁄2% for 25 years results in a monthly payment of

Katena32 [7]

Okay so first I am taking it that you have to subtract 24k from the 104k which brings it to 80,000.
I am also taking it that the 8.5% is suppose to be in decimal form which makes it .085%
Take the 80,000 and use the monthly payment formula, which is really easy to use.
Monthly payment should be 644.18

8 0

3 years ago

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Suppose you just purchased a digital music player and have put 9 tracks on it. After listening to them you decide that you like

ioda

a) consider the first song played . The probability of its being liked is 4/9.

And for second song, we have 3 liked songs and 8 remaining songs.

Hence probability of second being liked is 3/8.

Overall probability = (4/9)*(3/8) = 1/6 = 0.167 hence it is almost unusual.

b) First song being not liked is 5/9.

And for second song being not liked is 4/8.

Hence overall probability = (5/9)*(4/8) = 5/18.

c) To like exactly one of them, it has 2 possibilities. First song may be liked and second song disliked = (4/9)*(5/8) = (5/18)

First song may be disliked and second song liked = (5/9)*(4/8) = (5/18)

Hence overall probability = (5/18)+(5/18) = 5/9

d) a)Probability of 2 songs liked by me with replacement means in both cases i have to select a song from 4 liked songs.

Hence probability = (4/9)*(4/9) = 16/81

b) probability of both being not liked by me is = (5/9)*(5/9) = (25/81)

c) probability of exactly one being liked = (4/9)*(5/9)+(5/9)*(4/9) = 40/81

8 0

3 years ago

A random sample of 150 men found that 88 of the men excercise regularly, while a random sample 200 women found that 130 of the w

melamori03 [73]

Answer:

The hypothesis is:

H₀: $p_{X}-p_{Y}=0$ .

Hₐ: $p_{X}-p_{Y}$ .

Step-by-step explanation:

Let X = number of men who exercise regularly and Y = number of women who exercise regularly.

The information provided is:

$n_{X}=150\\X=88\\n_{Y}=200\\Y=130$

Compute the sample proportion of men and women who exercise regularly as follows:

$\hat p_{X}=\frac{X}{n_{X}}=\frac{88}{150}=0.587$

$\hat p_{Y}=\frac{Y}{n_{Y}}=\frac{130}{200}=0.65$

The random variable X follows a Binomial distribution with parameters n = 150 and $\hat p_{X}=0.587$ .

The random variable Y also follows a Binomial distribution with parameters n = 200 and $\hat p_{Y}=0.65$ .

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

$\hat p=p$

The standard deviation of this sampling distribution of sample proportion is:

$\sigma_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}$

So, the sampling distribution of the proportion of men and women who exercise regularly follows a Normal distribution.

A two proportion z-test cab be performed to determine whether the proportion of women is more than men who exercise regularly.

The hypothesis for this test cab be defined as:

H₀: The proportion of women is same as men who exercise regularly, i.e. $p_{X}-p_{Y}=0$ .

Hₐ: The proportion of women is more than men who exercise regularly, i.e. $p_{X}-p_{Y}$ .

6 0

3 years ago

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Melissa cut 2 and 1/4 feet of tape. How much is this in inches?

taurus [48]

1 ft = 12 inches

so 2 ft = (2 * 12) = 24 inches
and 1/4 ft = 1/4 * 12 = 12/4 = 3 inches

for a total of 27 inches

5 0

3 years ago

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