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Fittoniya [83]
3 years ago
7

Does secondhand smoke increase the risk of a low weight birth? A baby is “low birth weight” if it weighs less than 5.5 pounds at

birth. According to the National Center of Health Statistics, about 7.8% of all babies born in the U.S. are categorized as low birth weight. Researchers randomly select 1200 babies whose mothers had extensive exposure to secondhand smoke during pregnancy. 10.4% of the sample are categorized as low birth weight. Which of the following are the appropriate null and alternative hypotheses for this research question. H 0 : p = 0.078; H a : p ≠ 0.078 H 0 : p = 0.078; H a : p > 0.078 H 0 : p = 0.104; H a : p ≠ 0.104 H 0 : μ = 0.104; H a : μ > 0.104
Mathematics
1 answer:
11111nata11111 [884]3 years ago
7 0

Answer:

H0: p = 0.078

Ha: p ≠ 0.078

Step-by-step explanation:

The researchers say that the rate is about 7.8%, or 0.078 as a decimal.  That makes that the null hypothesis because using "is" in math is the same as saying "equals" and the null hypothesis always has the statement of equality in it.  The reason there is a not equals to sign in the alternate is for this reason as well.  The researchers say it is about that amount, not more or less than that amount.  So it makes this a 2 tailed test.  If the amount is significantly higher or lower, then we might have to reject the null hypothesis depending on the outcome of the test.

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Answer:

The function is  P(x) =  \frac{1}{2} e^{-x^2} +0.016

Step-by-step explanation:

From the question we are told that

    The rate of growth  is  P'(x) =  xe^{x} - x^2

     The total profit is P(2)  =$25,000

      The time taken to make the profit is x =  2 \ years

         

From the question

     P'(x) =  xe^{-x^2}  is the rate of growth

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       P(x) =  \int\limits {P'(x)} \,  =   \int\limits {xe^{-x^2}} \,

So using substitution method

   We have that

                      u =  - x^2

                      du =  2xdx

  So  

        p(x) =  \int\limits {\frac{1}{2} e^{-u}} \, du

       p(x) =  {\frac{1}{2} [ e^{-u}} +c ]

       p(x) =  {\frac{1}{2}  e^{-x^2}} + \frac{1}{2} c      recall  u =  - x^2   and  let  \frac{1}{2} c =  Z

       

At  x =  2 years  

     P(x)  =$25,000

So

       Since the profit rate is in million

    P(x)  =$25,000 = \frac{25000}{1000000} =$0.025 millon dollars

So  

       0.025 =  {\frac{1}{2}  e^{-2^2}} + Z  

=>    Z = 0.025 - {\frac{1}{2}  e^{-2^2}}  

       Z = 0.016  

So the profit function becomes

         P(x) =  \frac{1}{2} e^{-x^2} +0.016

     

       

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Answer:

He and each of his sisters will recieve 1/4 of the pizza

Step-by-step explanation:

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