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spayn [35]
3 years ago
15

A rectangle has an area of 112 square yards. Its width is nine yards less than the length. Write an equation that models this pr

oblem
Mathematics
1 answer:
Troyanec [42]3 years ago
4 0

Step-by-step explanation:

L = length

W = width

L = W + 9

A = 112 = LW = (W+9)W

So,

W2 + 9W = 112

W2 + 9W - 112 = 0

Factoring

(W-7)(W+16) = 0

W = 7, -16

We discard W = -16, since a measurement cannot be negative.

W = 7

And since L = W + 9, then L = 7 + 9 = 16

This is a 16x7 rectangle

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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
Ludmilka [50]

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
All the angles in a rectangle are right angles. ABCD is a rectangle. Using deductive reasoning, what can we conclude?
svet-max [94.6K]
The answer is C, "ABCD are right angles", because rectangles only have 90 degree angles.
7 0
3 years ago
Cindy can read in different amounts of time 10 pages in 8minutes, 15 pages in 12 minutes and 25 pages in 20 minutes what is the
babunello [35]

Answer:

5/4

Step-by-step explanation:

10/8 = 5/4

15/12 = 5/4

25/20 = 5/4

They all simplify to 5/4.

Hope this helps!

5 0
3 years ago
Peter paid $79.80 for renting a tricycle for 6 hours. What was the rate per hour for renting the tricycle? (Input only numeric v
ElenaW [278]

Answer:

13.3

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What is the area of the parallelogram with a base of 1.75 cm and a height of 1.5 cm? 2.75 cm2 3.625 cm2 2.625 cm2 3.25 cm2
choli [55]

Answer:

Step-by-step explanation:

Area of parallelogram=base*height

So 1.75*1.5=2.625cm²

8 0
3 years ago
Read 2 more answers
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