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Charra [1.4K]
3 years ago
5

What is 17/18 + 1/20

Mathematics
1 answer:
MrMuchimi3 years ago
8 0

Answer:

179/180

Step-by-step explanation:

<em><u>Step One</u></em>

Find the prime factors of 18 and 20

18:3*3*2

20: 2 * 2 * 5

<em><u>Step Two</u></em>

You need two 2s two 3s and one 5 for the common denominator

The common denominator is 2 * 2 * 3 * 3 * 5 = 180

<em><u>Step Three</u></em>

Put the two fractions over 180

\dfrac{17*10}{10*18} + \dfrac{1*9}{10*18}

\dfrac{170}{180} + \dfrac{9}{180}

179/180

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Answer:

A. (3, 8) and 2\sqrt{2}

B. (2, 4) and 2\sqrt{10}

Step-by-step explanation:

Midpoint formula: (\frac{x1+x2}{2} ,\frac{y1+y2}{2})

Distance formula: \sqrt{(x_{2}-x_{1}) ^2+(y_{2}-y_{1}) ^2 }

A. plug in the points in the formulas

(4, 7) and (2, 9)

Midpoint:

(\frac{4 + 2}{2} , \frac{7+9}{2} )=6/2, 16/2 = (3,8)

Length:

\sqrt{(2-4)^2+(9-7)^2}=\sqrt{4+4} =\sqrt{8} =2\sqrt{2}

B.

(5, 5) and (-1, 3)

Midpoint:

(\frac{5-1}{2} , \frac{5+3}{2} )=4/2,8/2=(2,4)

Length:

\sqrt{(-1-5)^2+(3-5)^2} =\sqrt{-6^2+-2^2} =\sqrt{36+4} =\sqrt{40} = 2\sqrt{10}

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Answer:

Null hypothesis:p_{1} = p_{2}  

Alternative hypothesis:p_{1} \neq p_{2}  

z=\frac{0.179-0.15}{\sqrt{0.17(1-0.17)(\frac{1}{140}+\frac{1}{60})}}=0.500  

p_v =2*P(Z>0.500)=0.617  

So the p value is a very low value and using any significance level for example \alpha=0.05, 0,1,0.15 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions NOT differs significantly.  

Step-by-step explanation:

Data given and notation  

X_{1}=25 represent the number of homeowners who would buy the security system

X_{2}=9 represent the number of renters who would buy the security system

n_{1}=140 sample 1

n_{2}=60 sample 2

p_{1}=\frac{25}{140}=0.179 represent the proportion of homeowners who would buy the security system

p_{2}=\frac{9}{60}= 0.15 represent the proportion of renters who would buy the security system

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 two proportions differs , the system of hypothesis would be:  

Null hypothesis:p_{1} = p_{2}  

Alternative hypothesis:p_{1} \neq p_{2}  

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

z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}   (1)  

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{25+9}{140+60}=0.17  

Calculate the statistic  

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

z=\frac{0.179-0.15}{\sqrt{0.17(1-0.17)(\frac{1}{140}+\frac{1}{60})}}=0.500  

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 two sided test the p value would be:  

p_v =2*P(Z>0.500)=0.617  

So the p value is a very low value and using any significance level for example \alpha=0.05, 0,1,0.15 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions NOT differs significantly.  

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Answer: 1.25664 or if you want in fraction form it's 2π/5

Step-by-step explanation:

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Therefor, the answer is 2π/ 5 or in decimal form 1.25664.

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