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fiasKO [112]
4 years ago
11

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:

<em>A and D</em>

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
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