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3 years ago

Write 9− 16x⁴ as the product of two factors.

Mathematics

1 answer:

Marysya12 [62]3 years ago

6 0

Answer:

The two factors will be $=(3+4x^2)\ and\ (3-4x^2)$

Step-by-step explanation:

We have given the equation $9-16x^4$

We know the algebraic equation $a^2-b^2=(a+b)(a-b)$

As $9-16x^4$ can be written as $3^2-(4x^2)^2$ , as square of 3 is 9 and square of $4x^2$ is $16x^4$

So $9-16x^4=3^2-(4x^2)^=(3+4x^2)(3-4x^2)$

So the two factors will be $=(3+4x^2)\ and\ (3-4x^2)$

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4 years ago

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3 years ago

Read 2 more answers

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Rzqust [24]

Answer:

$0.388 - 2.00\sqrt{\frac{0.388(1-0.388)}{500}}=0.344$

$0.388 + 2.00\sqrt{\frac{0.388(1-0.388)}{500}}=0.432$

The 95.5% confidence interval would be given by (0.344;0.432)

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".

The population proportion have the following distribution

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

Solution to the problem

The estimated proportion on this case is given by:

$p = \frac{X}{n}= \frac{194}{500}=0.388$

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 95.5% of confidence, our significance level would be given by $\alpha=1-0.955=0.045$ and $\alpha/2 =0.0225$ . And the critical value would be given by: