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Kisachek [45]
3 years ago
6

Help! Math Perimeter!

Mathematics
1 answer:
Butoxors [25]3 years ago
5 0
Area= 3x0.8 =2.4

Perimeter= 3+3=6
0.8+0.8=1.6
6+1.6=7.6

Pls mark brainliest
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Complete Question

The complete question is shown on the first and second  uploaded image

Answer:

Part 1

 The correct option is  B

Part 11

   The correct option is  H

Step-by-step explanation:

From the question we are told that

     The sample size is  n  =  15

Generally the sample mean for the input temperature is mathematically represented as

        \= x _1 =  \frac{\sum x_i}{n}

        \= x _1 =  \frac{57.6 + 68.9 \cdots +60.4 }{15}

      \= x _1 =  62.57

Generally the sample mean for the output temperature is mathematically represented as

        \= x _2 =  \frac{\sum x_i}{n}

        \= x _2 =  \frac{65.1 + 74.4 \cdots +67.3 }{15}

      \= x _2 =  55.97

Generally the difference between the mean of the input temperature and that of the output temperature is

      d =  \= x_1 - \= x_2

=>    d =  62.57 - 55.97

=>    d = 6.6

Generally the standard deviation of the difference between the input temperature and the output temperature is mathematically represented as

     s_d  = \sqrt {\frac{1}{n-1 }  \sum [d_i - d]^2}

=>   s_d = \sqrt{\frac{[(57.6 - 65.1) - 6.6]^2+[(68.9 - 74.4) - 6.6]^2+ \cdots +[(68.1 - 74.7) - 6.6]^2  }{15-1} }

=>   s_d = 1.732

The null hypothesis is  H_o  :  \mu_1 -\mu_2 =  6

The alternative hypothesis is  H_a :  \mu _1 - \mu_2\ne 6

Generally the test statistics is mathematically represented as

           t  =  \frac{d - 6}{ \frac{s_d}{ \sqrt{n} } }

          t  =  \frac{6.6- 6}{ \frac{1.732}{ \sqrt{15} } }

          t  =  1.342

Generally the p-value is mathematically represented as

    p-value  =  2 *  P(t > 1.342)

From the student t distribution table( reference - danielsoper(dot)com(slash)statcalc(slash)calculator) at a degree of freedom of  df = n-1 =  15-1 = 14

       P(t >  1.342) =  t_{1.342 , 14} =  0.100478

So    

     p-value  =  2 *   0.100478)

     p-value  =  0.201

From the values obtained we see that the p-value >  \alpha hence the decision rule is  fail to reject the null hypothesis

The  conclusion is  

The cooling system changes the temperature of the water by 6 degrees.  

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