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SpyIntel [72]
3 years ago
11

Shelbie has been asked to construct as many unique triangles as she can that have all sides of integer length, one side of lengt

h 5 cm, and a perimeter less than or equal to 16 cm.
Mathematics
1 answer:
Yuliya22 [10]3 years ago
5 0

Answer:

TOTAL NO TRIANGLE = 15 ;

Step-by-step explanation:

Here one side is fixed as 5 cm.

And the Perimeter is ≤ 15 .

PERIMETER = SUM OF ALL SIDES.

By keeping one side fixed and varying other two, we can get 15 no of triangles.

(5 cm,5 cm,6 cm) , (5 cm,5 cm,5 cm) ,( 4 cm,5 cm, 7 cm) (4 cm,5 cm,5 cm), (4 cm,5 cm,6 cm) , (3 cm,4 cm,5 cm) , (3 cm,5 cm,5 cm) , (3 cm,5 cm,6 cm) , (3 cm,5 cm,7 cm) , (4 cm,4 cm,5 cm) , (1 cm,5 cm,5 cm) , (2 cm,4 cm,5 cm) , (2 cm,5 cm,5 cm) , (2 cm,5 cm,6 cm) , (3 cm,3 cm,5 cm)

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The two trains the same distance from Buffalo is 20
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4 years ago
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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Answer:

a

     The null hypothesis  is  H_o  :  \mu  = 180

      The alternative hypothesis is  H_a :  \mu  <  180

b

The decision rule is  fail to reject the null hypothesis

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

Step-by-step explanation:

From the question we are told that

     The population mean is  \mu  =  3 \  minutes =  180 \  seconds

     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}

=>      \= x  = 173.2

Generally the standard deviation is mathematically represented as

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

=>    \sigma  =  \sqrt{\frac{  (156 - 173.2 )^2 + (136 - 173.2 )^2  + \cdots + (181- 173.2 )^2  }{25} }

=>    \sigma  =  24.261

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} } }

=>   z = -1.40    

Generally p-value is mathematically represented as

  p-value  =  P(Z <  z)

=>  p-value  =  P(Z < -1.40)

From the z-table  

   P(Z < -1.40) =  0.080757

=>   p-value  = 0.080757

From the obtained value we that  p-value >  \alpha

The decision rule is  fail to reject the null hypothesis

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

   

5 0
3 years ago
The endpoints of the diameter of a circle have the coordinates (3, 8) and (9, 16).
Alexxx [7]
The coordinates of the center of this circle will be the average between the extreme points


C = ( (xo+x1)/2 , (yo+y1)/2)

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xo = 3 and x1 = 9

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Then us stay with"


C = ( (3+9)/2 , (8+16)/2)

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Answer:

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5x + 1 - 1 = 36 - 1

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5x/5 = 35/5

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7 0
4 years ago
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