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maksim [4K]
3 years ago
13

Factor completely: 9x3 + 9x2y - 4x - 4y

Mathematics
2 answers:
Sholpan [36]3 years ago
4 0

Answer:

(x+y)(3x+2)(3x-2)

Step-by-step explanation:

The given expression is 9x^3+9x^2y-4x-4y

Make group as shown below

(9x^3+9x^2y)+(-4x-4y)

Factor out GCF from each of the group

9x^2(x+y)-4(x+y)

Now, factored out the common term

(x+y)(9x^2-4)

Now, rewrite the expression in perfect square form

(x+y)((3x)^2-2^2)

Apply the difference of squares formula: a^2-b^2=(a+b)(a-b)

(x+y)(3x+2)(3x-2)

Hence, the factored form of the given expression is

(x+y)(3x+2)(3x-2)

belka [17]3 years ago
3 0
9x^3 + 9x^2y - 4x - 4y

= 9x^2(x + y) -4(x + y)

= (x +y)(9x^2-4)

= (x +y)(3x - 2)(3x + 2)
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In a study of red/green color blindness, 700 men and 2850 women are randomly selected and tested. Among the men, 66 have red/gre
olga55 [171]

Answer:

z=\frac{0.0943-0.00281}{\sqrt{0.0208(1-0.0208)(\frac{1}{700}+\frac{1}{2850})}}=15.197  

p_v =P(Z>15.197) \approx 0  

If we compare the p value and using any significance level for example \alpha=0.05 always p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of men with red/green color blindness.is significanlty higher than the proportion of women with red/green color blindness.

Step-by-step explanation:

Data given and notation  

X_{M}=66 represent the number of men with red/green color blindness.

X_{W}=8 represent the number of women with red/green color blindness.

n_{M}=700 sample of male slected

n_{W}=2850 sample of female selected

p_{M}=\frac{66}{700}=0.0943 represent the proportion of male with red/green color blindness.

p_{W}=\frac{8}{2850}=0.00281 represent the proportion of female with red/green color blindness.

z would represent the statistic (variable of interest)  

p_v represent the value for the test (variable of interest)

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportion of men with red/green color blindness. is higher than the proportionof women with red/green color blindness. , the system of hypothesis would be:  

Null hypothesis:p_{M} \leq p_{W}  

Alternative hypothesis:p_{M} > p_{W}  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{M}-p_{W}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{M}}+\frac{1}{n_{W}})}}   (1)

Where \hat p=\frac{X_{M}+X_{W}}{n_{M}+n_{W}}=\frac{66+8}{700+2850}=0.0208

Calculate the statistic

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.0943-0.00281}{\sqrt{0.0208(1-0.0208)(\frac{1}{700}+\frac{1}{2850})}}=15.197  

Statistical decision

For this case we don't have a significance level provided \alpha, but we can calculate the p value for this test.  

Since is a one side test the p value would be:  

p_v =P(Z>15.197) \approx 0  

If we compare the p value and using any significance level for example \alpha=0.05 always p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of men with red/green color blindness.is significanlty higher than the proportion of women with red/green color blindness.

8 0
3 years ago
Is -55 a natural number, whole number, integers, or irrational numbers
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On the first day of school last year, Cody was 148.5 cm tall.
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Answer:

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Step-by-step explanation:

10-1=9

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