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4 years ago

Which of the following are factors of x^4 − 81? Select all that apply.

Mathematics

2 answers:

vova2212 [387]4 years ago

5 0

Answer:

The factors are

$\text{A. } x^2 + 9$

$\text{D. } x + 3$

Step-by-step explanation:

$x^4- 81$

$(x^2)^2-9^2$

Once $x^2-y^2=\left(x+y\right)\left(x-y\right)$

$\left(x^2\right)^2-9^2 = \left(x^2+9\right)\left(x^2-9\right)$

Now we can factor $x^2-9$ again using difference of two squares:

Therefore,

$\left(x^2+9\right)\left(x+3\right)\left(x-3\right)$

The factors are

$\text{A. } x^2 + 9$

$\text{D. } x + 3$

Mrrafil [7]4 years ago

3 0

Answer:

Step-by-step explanation:

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An SRS of 350 high school seniors gained an average of x¯=21 points in their second attempt at the SAT Mathematics exam. Assume

Lynna [10]

Answer:

a) $21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

b) $ME=2.58\frac{52}{\sqrt{350}}=7.17$

c) $ME=2.58\frac{52}{\sqrt{100}}=13.42$

d) D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

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".

Part a

$\bar X=21$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=52$ represent the population standard deviation

n=350 represent the sample size

99% confidence interval

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

Now we have everything in order to replace into formula (1):

$21-2.58\frac{52}{\sqrt{350}}=13.83$

$21+2.58\frac{52}{\sqrt{350}}=28.17$

So on this case the 99% confidence interval would be given by (13.83;28.17)

Part b

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{350}}=7.17$

Part c

The margin of error is given by:

$ME=2.58\frac{52}{\sqrt{100}}=13.42$

Part d

As we can see when we reduce the sample size we increase the margin of error so the best option for this case is:

D. Decreasing the sample size increases the margin of error, provided the confidence level and population standard deviation remain the same.

6 0

3 years ago

I need help, don’t get it

Mashutka [201]

B is correct. Substitute the week number for w in the function. Follow order of operations and you should get you N, the number of fruit flies for that week. For instance week 2:
N= 2(5)^2-1
N=2(5)^1
N=2(5)
N= 10
N= 10 corresponds to the table

7 0

3 years ago

Determine the equation of the circle graphed below. <br> Please help, thanks

marusya05 [52]

Answer:

If you are finding the equation using two points then the answer is

y = −2 x + 1

If this does not help, just ignore honestly.

4 0

3 years ago

Find the volume of a rectangular prism that is 8 inches high, 12 inches long, and 5 inches wide.

icang [17]

Answer:

B 480 in.³

Step-by-step explanation:

Volume of a rectangular prism is given by

V = l*w*h

V = 8*12*5

V =480 in ^3

3 0

3 years ago

Read 2 more answers

Number 13 explain......

Marat540 [252]

The slope is 2 and the equation of the line is y = mx+b with m =2

Then the equation becomes: y = 2x+b. How to calculate b?
Since this line passes through the point (-3 , 4), we replace x with -3 and y=4

4= 2.(-3) + b
4 = - 6 + b
and b= 10. The final equation is : y = 2x + 10 (answer a)

3 0

3 years ago