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maria [59]
3 years ago
15

Find the difference.

Mathematics
1 answer:
Vsevolod [243]3 years ago
5 0

5.\\12\dfrac{3}{10}-7\dfrac{7}{10}=11\dfrac{10+3}{10}-7\dfrac{7}{10}=11\dfrac{13}{10}-7\dfrac{7}{10}=4\dfrac{6}{10}=4\dfrac{6:2}{10:2}=\boxed{5\dfrac{3}{5}}\\\\11-7=4\\\\\dfrac{13}{10}-\dfrac{7}{10}=\dfrac{13-7}{10}=\dfrac{6}{10}\\\\6.\\8\dfrac{1}{6}-3\dfrac{5}{6}=7\dfrac{6+1}{6}-3\dfrac{5}{6}=7\dfrac{7}{6}-3\dfrac{5}{6}=(7-3)+\dfrac{7-5}{6}=4\dfrac{2}{6}=4\dfrac{2:2}{6:2}=\boxed{4\dfrac{1}{3}}

9.\\7\dfrac{1}{6}-2\dfrac{5}{6}=6\dfrac{6+1}{6}-2\dfrac{5}{6}=6\dfrac{7}{6}-2\dfrac{5}{6}=(6-2)+\dfrac{7-5}{6}=4\dfrac{2}{6}=\boxed{4\dfrac{1}{3}}\\\\10.\\9\dfrac{3}{12}-4\dfrac{7}{12}=8\dfrac{12+3}{12}-4\dfrac{7}{12}=8\dfrac{15}{12}-4\dfrac{7}{12}=(8-4)+\dfrac{15-7}{12}=4\dfrac{8}{12}\\\\=4\dfrac{8:4}{12:4}=\boxed{4\dfrac{2}{3}}

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Answer:

a

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b

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d

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Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  200

     The number of defective is  k =  18

The null hypothesis is  H_o  :  p  =  0.08

The  alternative hypothesis is  H_a  :  p > 0.08

Generally the sample proportion is mathematically evaluated as

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Given that the confidence level is  95% then the level  of significance is mathematically evaluated as

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Next we obtain the critical value of  \frac{ \alpha }{2} from the normal distribution table, the value is  

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Generally the standard of error is mathematically represented as

          SE   =  \sqrt{\frac{\r p (1 -  \r p)}{n} }

substituting values

         SE   =  \sqrt{\frac{0.09  (1 -  0.09)}{200} }

        SE   =0.020

The  margin of error is  

       E =  Z_{\frac{ \alpha }{2} }  * SE

=>    E =  1.96  *  0.020

=>   E =  0.0397

The  95% confidence interval is mathematically represented as

     \r p  -  E  <  \mu <  p <  \r p  + E

=>   0.09 - 0.0397  <  \mu <  p < 0.09 + 0.0397

=>  0.0503  <   p < 0.1297

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