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3 years ago

Find a cubic function with the given zeros.

Mathematics

1 answer:

tester [92]3 years ago

5 0

The cubic function is $f(x)=x^3+3x^2-46x-168$

Option D is correct

Step-by-step explanation:

We need to find the cubic function with the given zeros -6,7,-4

If -6,7,-4 are zeros of the function then:

x=-6, x=7 and x=-4

=> x+6=0,x-7=0 and x+4=0

Multiplying these terms to find the cubic function:

(x+6)(x-7)(x+4)

Solving:

$(x+6)(x-7)(x+4)\\=(x+6)(x(x+4)-7(x+4))\\=(x+6)(x^2+4x-7x-28)\\=(x+6)(x^2-3x-28)\\=x(x^2-3x-28)+6(x^2-3x-28)\\=x^3-3x^2-28x+6x^2-18x-168\\Combining\,\,like\,\,terms:\\=x^3-3x^2+6x^2-28x-18x-168\\=x^3+3x^2-46x-168$

So, the cubic function is $f(x)=x^3+3x^2-46x-168$

Option D is correct

Keywords: cubic function

Learn more about cubic function at:

#learnwithBrainly

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Step-by-step explanation:

s1 = 300

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Answer:

The estimation for the proportion for this case is $\hat p = 0.21$

And we know that the 99% confidence interval is given by:

$0.21 \pm 0.045$

So then the margin of error at 99% of confidence is 0.045, and the margin of error is given by this formula:

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

If we decrease the confidence level this margin of error can't be higher than 0.045 so then the correct answer for this case would be:

d. 21% ± 4.8%

Because if the z value decrease from 2.58 to 1.96 not makes sense that the margin of error increase from 0.045(4.5%) to 0.048(4.8%)

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.

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".

Solution to the problem

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

The estimation for the proportion for this case is $\hat p = 0.21$

And we know that the 99% confidence interval is given by:

$0.21 \pm 0.045$

So then the margin of error at 99% of confidence is 0.045, and the margin of error is given by this formula:

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

If we decrease the confidence level this margin of error can't be higher than 0.045 so then the correct answer for this case would be:

d. 21% ± 4.8%

Because if the z value decrease from 2.58 to 1.96 not makes sense that the margin of error increase from 0.045(4.5%) to 0.048(4.8%)

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