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stealth61 [152]
1 year ago
7

What are the solution(s) to the quadratic equation 9x² = 4?

Mathematics
2 answers:
UkoKoshka [18]1 year ago
6 0

Answer:

x = ± \frac{2}{3}

Step-by-step explanation:

9x² = 4 ( divide both sides by 9 )

x² = \frac{4}{9} ( take square root of both sides )

x = ± \sqrt{\frac{4}{9} } = ± \frac{\sqrt{4} }{\sqrt{9} } = ± \frac{2}{3}

x = - \frac{2}{3} , x = \frac{2}{3}

vagabundo [1.1K]1 year ago
5 0

Answer:

x= 2/3, -2/3

Step-by-step explanation:

9x² = 4

To solve this quadratic, divide each side by 9

x^2 = 4/9

Take the square root of each side

sqrt(x^2) = sqrt(4/9)

x = ±2/3

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Answer:

a) n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401  

And rounded up we have that n=2401

b) n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22  

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

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Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

Part a

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.02 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't have prior information about the population proportion we can use ase estimator \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401  

And rounded up we have that n=2401

Part b

For thi case the estimator for p is \hat p =0.07

n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22  

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

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Step-by-step explanation:

When graphing, you take the opposite if there is a number in the absolute value bars. If there is, then you will be going towards the x axis. If there is a number outside of the absolute value bars, assume that this will be the y axis

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