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3 years ago

Which of the following represents the zeros of f(x) = 2x3 − 5x2 − 28x + 15?

Mathematics

2 answers:

likoan [24]3 years ago

5 0

$\mathrm{Use\:the\:rational\:root\:theorem}$

$a_0=15,\:\quad a_n=2$

$\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:3,\:5,\:15,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2$

$\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:3,\:5,\:15}{1,\:2}$

$-\frac{3}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+3$

$\mathrm{Compute\:}\frac{2x^3-5x^2-28x+15}{x+3}\mathrm{\:to\:get\:the\:rest\:of\:the\:eqution:\quad }2x^2-11x+5$

$=\left(x+3\right)\left(2x^2-11x+5\right)$

$Factor: 2x^2-11x+5$

$2x^2-11x+5=\left(2x^2-x\right)+\left(-10x+5\right)$

$=x\left(2x-1\right)-5\left(2x-1\right)$

$2x^3-5x^2-28x+15=\left(x+3\right)\left(x-5\right)\left(2x-1\right)$

$\left(x+3\right)\left(x-5\right)\left(2x-1\right)=0$

$\mathrm{Using\:the\:Zero\:Factor\:Principle:}$

thus zeros of f(x) is

$x=-3,\:x=5,\:x=\frac{1}{2}$

abruzzese [7]3 years ago

4 0

Answer:

I think it is 5, -3, 1/2.

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Because of staffing decisions, managers of the Gibson-Marion Hotel are interested in the variability in the number of rooms occu

olchik [2.2K]

Answer:

a) $s^2 =30^2 =900$

b) $\frac{(19)(30)^2}{30.144} \leq \sigma^2 \leq \frac{(19)(30)^2}{10.117}$

$567.28 \leq \sigma^2 \leq 1690.224$

c) $23.818 \leq \sigma \leq 41.112$

Step-by-step explanation:

Assuming the following question: Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 20 days of operation shows a sample mean of 290 rooms occupied per day and a sample standard deviation of 30 rooms

Part a

For this case the best point of estimate for the population variance would be:

$s^2 =30^2 =900$

Part b

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The degrees of freedom are given by:

$df=n-1=20-1=19$

Since the Confidence is 0.90 or 90%, the significance $\alpha=0.1$ and $\alpha/2 =0.05$ , the critical values for this case are:

$\chi^2_{\alpha/2}=30.144$

$\chi^2_{1- \alpha/2}=10.117$

And replacing into the formula for the interval we got:

$\frac{(19)(30)^2}{30.144} \leq \sigma^2 \leq \frac{(19)(30)^2}{10.117}$

$567.28 \leq \sigma^2 \leq 1690.224$

Part c

Now we just take square root on both sides of the interval and we got:

$23.818 \leq \sigma \leq 41.112$

5 0

3 years ago

How to factor the algebraic expression 24a + 28

bonufazy [111]

So use undistributive properyt]
ab+ac=a(b+c)
so factor 24a dadn 28 to find 'a' the common factor
24=2 times 2 times 2 times 3 tiems a
28=2 times 2 times 7
common one is 2 itmes 2=4
a=4
4(2 times3 times a)+4(7)=4(6a)+4(7)=4(6a+7)

7 0

3 years ago

Help please and make sure the answer is right! Please :(

likoan [24]

You see how these 2 angles marked are both inside the 2 parallel lines?

And they are on opposite side of the transversal, the line crossing the 2 parallel lines?

These 2 angles are alternate interior angles and they are equal, I think you can do the last part by yourself.

8 0

3 years ago

2/3A=-24 this the last one that I need help on.

pychu [463]

You can answer this question in numerous ways but one simple way is by multiplying fractions.

2/3 of 24 is also 2/3 of 24/1 
To get the answer, you must multiply 2/3 by 24/1 

To do this, you multiply the numerator (the top number) by the other numerator. That is, 2 x 24 . The answer is 48. 

Then, multiply the denominators (the bottom numbers) by each other. That is, 3 x 1. The answer is 3. 

The answer is 48/3. But you must continue simplifying. 

What is 48 divided by 3? 16. 

If you do not understand it that way, think of it in a simpler way. 

Say there are 24 slices of pieces. 

What is one third of those 24 slices? 

24 divided by 3 = 8. 

Now you want TWO thirds. So all you do is multiply 8 by 2. 

That gives you 16.

I hope i helped, and, if so, please mark as brainliest :P

3 0

3 years ago

Read 2 more answers

PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS!! WHAT IS M∠1?

TEA [102]

Answer:

angle 1= $135$ °