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Nostrana [21]
4 years ago
8

Suppose that the functions and are defined for all real numbers as follows. r(x)=3x^(2) s(x)=2x write the expressions for (r-s)(

x) and (r+s)(x) and evaluate (r*s)(-1).
Mathematics
1 answer:
nirvana33 [79]4 years ago
7 0
The expression for (r-s)(x) is found by subtracting s from r.  That difference is 3 x^{2} -2x.  The expression for (r+s)(x) is found by adding them, which is 3 x^{2} +2x.  Now we are told to evaluate (r*s)(x) which means they want us to multiply those and state the "new" expression that results.  (3 x^{2} )(2x)=6x^3.  There you go!
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Step-by-step explanation:

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Step-by-step explanation:

first, we need to find the slope

slope = (y2 - y1) / (x2 - x1)

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now sub

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3 years ago
Two random samples are taken, with each group asked if they support a particular candidate. A summary of the sample sizes and pr
Minchanka [31]

Answer:

And we got \alpha/2 =0.01 so then the value for \alpha=0.02 and then the confidence level is given by: Conf=1-0.02=0.98[/tex[ or 98%Step-by-step explanation: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.  Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  [tex]p_1 represent the real population proportion for 1

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p_2 represent the real population proportion for 2

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z represent the critical value for the margin of error  

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})  

The confidence interval for the difference of two proportions would be given by this formula  

(\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}  

For this case we have the confidence interval given by: (-0.0313,0.2753). From this we can find the margin of erro on this way:

ME= \frac{0.2753-(-0.0313)}{2}=0.1533

And we know that the margin of erro is given by:

ME=z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}

We have all the values except the value for z_{\alpha/2}

So we can find it like this:

0.1533=z_{\alpha/2} \sqrt{\frac{0.768(1-0.768)}{92} +\frac{0.646 (1-0.646)}{95}}

And solving for z_{\alpha/2} we got:

z_{\alpha/2}=2.326

And we can find the value for \alpha/2 with the following excel code:

"=1-NORM.DIST(2.326,0,1,TRUE)"

And we got \alpha/2 =0.01 so then the value for \alpha=0.02 and then the confidence level is given by: Conf=1-0.02=0.98 or 98%

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