What is the solution of the equation?<br> 4.7c + 3.8 = 13.2

s x – 5 a factor of the function f(x) = x3 – 5x2 + 7x – 35? Use the Remainder Theorem to justify your answer.

Assoli18 [71]

By using the remainder theorem we found that ( x - 5 ) is the factor of function f(x) = x³ – 5x² + 7x – 35.

<h3>What is factorization?</h3>

Factorization is defined as splitting the polynomial into its most simplified form. This factor satisfies the polynomials from which it is extracted.

The factorization by using the Remainder theorem.

x - 5 ) x³ – 5x² + 7x – 35.( x ² + 7

x³ - 5x²

______________

00 7x - 35

7x - 35

-------------------------

00

Here the function is completely divided by the factor x - 5 therefore

by using the remainder theorem we found that ( x - 5 ) is the factor of function f(x) = x³ – 5x² + 7x – 35.

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2 years ago

Suppose a lawn and garden company wants to determine the current percentage of customers who use fertilizer on their lawns. How

marishachu [46]

Answer:

n=601

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".

The population proportion have the following distribution

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

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:

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

The confidence interval for the mean is given by the following formula:

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

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 $ME =\pm 0.04$ 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 a prior estimation for the proportion we can use 0.5 as estimation. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.96})^2}=600.25$