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2 years ago

Find (x³+x²-20x+24) divided by (x-3)

Mathematics

1 answer:

Rus_ich [418]2 years ago

3 0

Answer:

$\frac{x^3 + x^2 -20x + 24}{x-3} = x^2 +4x-8$

Step-by-step explanation:

Given;

p(x) = x³ + x²- 20x + 24

factor of p(x) = x-3

Apply long division method;

x² + 4x - 8

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

x - 3 √ x³ + x²- 20x + 24

-( x³ - 3x²)

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

4x² - 20x + 24

-(4x² -12x )

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

-8x + 24

- (-8x + 24)

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

$thus, \ \frac{x^3 + x^2 -20x + 24}{x-3} = x^2 +4x-8$

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Multiple Choice What is the sum of five-sixths + start fraction 2 over 3 end fraction? A. one and one-third B. One and one half

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Answer:

Step-by-step explanation:

$\frac{5}{6} +\frac{2}{3} \\\\=\frac{5}{6}+\frac{2*2}{2*3} \\\\=\frac{5}{6}+\frac{4}{6} \\\\=\frac{5+4}{6} \\\\=\frac{9}{6} \\\\=\frac{3*3}{3*2} \\\\=\frac{3}{2}$

$=\frac{2+1}{2} \\\\=\frac{2}{2}+\frac{1}{2} \\\\=1+\frac{1}{2}$

B.One and one half

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3 years ago

What’s the total value of the 6 in 26,312

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The total value is 6,000

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3 years ago

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Mrs.johnson is working on math with a group of students. she has a total of 15 students. 9 of them are girls. what is the ratio

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Answer:

Step-by-step explanation:

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3 years ago

Ive never did anything like this before, Can someone help?

FromTheMoon [43]

Answer:

Step-by-step explanation:

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Suppose we are interested in analyzing the weights of NFL players. We know that on average, NFL players weigh 247 pounds with a

tigry1 [53]

Answer:

$SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58$

$ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073$

$\bar X - ME = 237- 14.073 = 222.927$

$\bar X + ME = 237+ 14.073 = 251.073$

$n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238$

So the answer for this case would be n=238 rounded up to the nearest integer

Null hypothesis: $\mu \geq 247$

Alternative hypothesis: $\mu$

$z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165$

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is lower than 247 at 10% of significance.

Step-by-step explanation:

For this case we have the following data given:

$\bar X =237$ represent the sample mean

$\sigma = 47$ represent the population deviation

$n =30$ represent the sample size selected

$\mu_0 = 247$ represent the value that we want to test.

The standard error for this case is given by:

$SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58$

For the 90% confidence the value of the significance is given by $\alpha=1-0.9 = 0.1$ and $\alpha/2 = 0.05$ so we can find in the normal standard distribution a quantile that accumulates 0.05 of the area on each tail and we got:

$z_{\alpha/2}= 1.64$

And the margin of error would be:

$ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073$

The confidence interval for this case would be given by:

$\bar X - ME = 237- 14.073 = 222.927$

$\bar X + ME = 237+ 14.073 = 251.073$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

Replacing into formula (b) we got:

$n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238$

So the answer for this case would be n=238 rounded up to the nearest integer

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is lower than 247 pounds, the system of hypothesis would be:

Null hypothesis: $\mu \geq 247$

Alternative hypothesis: $\mu$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165$

P-value

Since is a left tailed test the p value would be:

$p_v =P(z$

Conclusion

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2 years ago

Find (x³+x²-20x+24) divided by (x-3)​

Find (x³+x²-20x+24) divided by (x-3)