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AveGali [126]
3 years ago
14

A survey conducted by the American Automobile Association showed that a family of four spends an average of $215.60 per day whil

e on vacation. Suppose a sample of 64 families of four vacationing at Niagara Falls resulted in a sample mean of $252.45 per day and a sample standard deviation of $77.50.
a. Develop a 95% confidence interval estimate of the mean amount spent per day by a family of four visiting Niagara Falls (to 2 decimals). ( , )

b. Based on the confidence interval from part (a), does it appear that the population mean amount spent per day by families visiting Niagara Falls differs from the mean reported by the American Automobile Association?
Mathematics
1 answer:
Naddika [18.5K]3 years ago
4 0

Answer:

a) (233.09,271.80)

b) Yes  

Step-by-step explanation:

We are given the following information:

Population mean = $215.60

Sample mean = $252.45

Sample standard deviation = $77.50.

n = 64

Formula:

\bar{x} \pm t_{critical}\frac{s}{\sqrt{n}}

Putting the values, we get,

t_{critical}\text{ at degree of freedom 63 and}~\alpha_{0.05} = 1.998

252.45 \pm 1.998(\frac{77.50}{\sqrt{64}} ) = 252.45 \pm 19.355 = (233.09,271.80)

b) The mean amount spent per day by families visiting Niagara Falls differs from the mean reported by the American Automobile Association because the confidence interval lies above  $215.60

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Complete Question

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for x = 3 and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ​?

Answer:

The  generally expression for the slope of y  = 2x^2 + 4x is  y' =  4x +4

The graph is shown on the first uploaded image

The  generally expression for the slope of y=2x^2+4 is   y' =  4x

Step-by-step explanation:

From the question we are told that

  The  equation of the curve is y  = 2x^2 + 4x

First we differentiate the equation

So  

     y' =  4x +4

Therefore the generally expression for the slope tangent to the curve y=2x^2+4x is   y' =  4x +4

The  next step is to substitute for x =  3 and  x =  0.5

So  for x_1 =  3

    y' =  4(3) +4

     y' =m_1=  16

And  for  x_2 =  0.5

      y' =  4(0.5) +4

       y' =m_2=  6

Here m_1  and  m_2 are slops of the curve

Next we obtain the coordinates of the tangent lines

So  at x_1 =  3

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  y_1  =  21

So the coordinate for the first tangent line is  

    (x_1 , y_1 ) =  (3 ,  21)

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So the coordinate for the second  tangent line is  

    (x_2 , y_2 ) =  (0.5 ,  2.5)

Next we obtain the equation for the tangent lines

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       16 =  \frac{y -21 }{x-3)}

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     y' =  4x

     

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