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olga2289 [7]
2 years ago
12

Michael reads 12 pages of a book in 18 minutes, 8 pages in 12 minutes,and 20 pages in 30 minutes. Is this a proportional relatio

nship? If so, what is the constant of proportionality? What does it represent? Write an equation to represent this situation.
Mathematics
1 answer:
maria [59]2 years ago
7 0

Answer:

  • y = 2/3x

Step-by-step explanation:

<u>Reading rate is y pages per x minutes and proportional relationship formula is:</u>

  • y = kx

<u>The coefficient is:</u>

  • k = y/x

<u>Let's verify if the given numbers fit into the same relationship:</u>

  • 12/18 = 2/3
  • 8/12 = 2/3
  • 20/30 = 2/3

We confirm all same and it means k = 2/3

<u>Required equation is:</u>

  • y = 2/3x

This represents that Michael reads 2 pages per 3 minutes and for x minutes he reads 2/3x pages

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Answer:

a

 The  90% confidence interval that  estimate the true proportion of students who receive financial aid is

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Step-by-step explanation:

Considering question a

From the question we are told that

      The sample size is  n = 200

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Generally the sample proportion is  

      \^ p = \frac{k}{n}

=>   \^ p = \frac{118}{200}

=>   \^ p = 0.59

From the question we are told the confidence level is  90% , hence the level of significance is    

      \alpha = (100 - 90 ) \%

=>   \alpha = 0.10

Generally from the normal distribution table the critical value  of \frac{\alpha }{2}  is  

   Z_{\frac{\alpha }{2} } =  1.645

Generally the margin of error is mathematically represented as  

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Generally 90% confidence interval is mathematically represented as  

      \^ p -E <  p <  \^ p +E

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Considering question b

From the question we are told that

    The margin of error  is  E = 0.03

From the question we are told the confidence level is  99% , hence the level of significance is    

      \alpha = (100 - 99 ) \%

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Generally from the normal distribution table the critical value  of   is  

   Z_{\frac{\alpha }{2} } = 2.58

Generally the sample size is mathematically represented as      

        [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )

=>      n = [\frac{2.58}{0.03} ]^2 * 0.59 (1 - 0.59 )

=>      n = 1789

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