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andreev551 [17]
3 years ago
11

What is the length of MN

Mathematics
1 answer:
Irina-Kira [14]3 years ago
6 0

Answer: D. 4

Step-by-step explanation:

In the given picture , we have given a triangle ΔMLN in which

ML= 4x and MN= x+3

∠L=∠N=50°

⇒ MN=ML   [∵ Basically by Isosceles triangle property :sides opposite to equal angles of a triangle area equal.]

\Rightarrow\ x+3=4x

Subtract x from both sides , we get

3=3x

Divide bothe sides by x , we get

1= x  or x =1

Then, the length of MN = x+3=1+3=4 units

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The decision rule is  

Reject the null hypothesis  

Step-by-step explanation:

From the question we are told that

    The population mean is \mu =  5.6  \ pounds/inch^2

     The  sample size is  n =  160

      The sample mean is  \=  x =  5.7  \  pounds/ inch^2

     The variance is \sigma ^2 =  0.25

       The level of significance is  \alpha   =  0.01

The null hypothesis is  H_o  :  \mu  =  5.6

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=>         \sigma =  \sqrt{0.25  }  

=>         \sigma =  0.5  

Generally the test statistics is mathematically represented as

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

=>     z =  \frac{5.7  - 5.6  }{ \frac{0.5 }{\sqrt{ 160 }  } }  

=>     z =  2.53

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From the value obtained we see that the p-value  < \alpha hence

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to conclude that the believe  that the valve performs above the specifications is true

 

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