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Gwar [14]
3 years ago
13

7- a. What is the radius of the circle with center (3,10) that passes through (12,12)?

Mathematics
1 answer:
loris [4]3 years ago
6 0

Answer: a. Radius of circle = \sqrt{85}

b. The equation of this circle : (x-3)^2+(y-10)^2=85

Step-by-step explanation:

Given : Center of the circle = (3,10)

Circle is passing through (12,12).

a. To find the radius we apply distance formula (∵ Radius is the distance from center to any point ion the circle.)

Radius of circle = \sqrt{(12-3)^2+(12-10)^2}

Radius of circle = \sqrt{(9)^2+(2)^2}=\sqrt{81+4}=\sqrt{85}

i.e. Radius of circle = \sqrt{85}

b. Equation of a circle = (x-h)^2+(y-k)^2=r^2 , where (h,k)=Center and r=radius of the circle.

Put the values of (h,k)= (3,10) and r= \sqrt{85} , we get

(x-3)^2+(y-10)^2=(\sqrt{85})^2

(x-3)^2+(y-10)^2=85

∴  The equation of this circle :(x-3)^2+(y-10)^2=85

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A company is approached by a new warehouse management systems vendor to adopt a new system. The vendor claims that the warehouse
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a

     The null hypothesis  is  H_o  :  \mu  = 180

      The alternative hypothesis is  H_a :  \mu  <  180

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Step-by-step explanation:

From the question we are told that

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     The sample  size is  n =  25

     The excel sheet is show on the first uploaded image

     The level of significance is  \alpha =  0.05

     The null hypothesis  is  H_o  :  \mu  = 180

      The alternative hypothesis is  H_a :  \mu  <  180

Generally the sample mean is mathematically represented as

        \= x  =  \frac{156 + 136 + \cdots  + 181}{25}

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Generally the standard deviation is mathematically represented as

      \sigma  =  \sqrt{\frac{\sum  (x_i - \= x )^2 }{n} }

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Generally the test statistics is mathematically represented as

      t =  \frac{\= x  -  \mu }{\frac{\sigma}{\sqrt{n} } }

=>   t =  \frac{173.2 -  180 }{\frac{24.261}{\sqrt{25} } }

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Generally p-value is mathematically represented as

  p-value  =  P(Z <  z)

=>  p-value  =  P(Z < -1.40)

From the z-table  

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The conclusion

There no sufficient evidence to support the vendor claim  that the warehouse management system reduces the average pick, pack, and ship time to below 3 minutes(180 seconds) per order through bin location and routing optimization

   

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