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icang [17]
3 years ago
13

Christopher wants to estimate the mean amount of carbon dioxide that is emitted by burning 1\text{ L}1 L1, start text, space, L,

end text of a new type of gasoline. He plans on burning 1\text{ L}1 L1, start text, space, L, end text at a time and measuring the resulting emissions. He'll repeat this process for a sample of nnn attempts and construct a confidence interval for the mean. He wants the margin of error to be no more than 202020 grams at a 90\%90%90, percent level of confidence. Preliminary data suggests that \sigma=50σ=50sigma, equals, 50 grams is a reasonable estimate for the standard deviation of the emissions from burning 1\text{ L}1 L1, start text, space, L, end text of this type of gasoline. Which of these is the smallest approximate sample size required to obtain the desired margin of error?
Mathematics
1 answer:
levacccp [35]3 years ago
6 0

Answer:

The smallest sample size required to obtain the desired margin of error is of 17.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

Which of these is the smallest approximate sample size required to obtain the desired margin of error?

The desired margin of error is 20, so M = 20

We have that \sigma = 50.

The smallest sample size is n. So

M = z*\frac{\sigma}{\sqrt{n}}

20 = 1.645*\frac{50}{\sqrt{n}}

20\sqrt{n} = 50*1.645

\sqrt{n} = \frac{50*1.645}{20}

(\sqrt{n})^2 = (\frac{50*1.645}{20})^2

n = 16.9

Rounding up

The smallest sample size required to obtain the desired margin of error is of 17.

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What is the inverse of the function f(x)=4x+8
Leno4ka [110]

Answer:

f  ( x )  − 1  = ( 1/ 4  x )  − 2.

Step-by-step explanation:        

For inverse function, the x and y interchanges and then make y the subject again of the equation. See the working out below:

f  ( x )  =  4 x  +  8

 f  ( x )  =  y

y    =  4 x  +  8

 x  =  4 y  + 8  ----- interchanging  y  and  x

Now make  y  the subject of the equation:

x  =  4 y  +  8

 − 4 y  =  -   x  +  8

 y  =  ( − 1/ 4  ) .  −  x   +  ( − 1/ 4  )  .8

 y  =  ( 1/ 4  x )  − 2

So the inverse function is:

f (x)  − 1  =  ( 1/ 4  x )  − 2

7 0
4 years ago
If it is 11:15
soldi70 [24.7K]
My god, this is tricky but it's between D and E. 

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4 years ago
4.5x – 2y = 15<br> 3x - y =10<br><br> (answer as a combined pair)
prisoha [69]

Answer:

x = 10/3 , y = 0

Step-by-step explanation:

Solve the following system:

{4.5 x - 2 y = 15

3 x - y = 10

In the first equation, look to solve for x:

{4.5 x - 2 y = 15

3 x - y = 10

4.5 x - 2 y = (9 x)/2 - 2 y:

(9 x)/2 - 2 y = 15

Add 2 y to both sides:

{(9 x)/2 = 2 y + 15

3 x - y = 10

Multiply both sides by 2/9:

{x = (4 y)/9 + 10/3

3 x - y = 10

Substitute x = (4 y)/9 + 10/3 into the second equation:

{x = (4 y)/9 + 10/3

3 ((4 y)/9 + 10/3) - y = 10

3 ((4 y)/9 + 10/3) - y = ((4 y)/3 + 10) - y = y/3 + 10:

{x = (4 y)/9 + 10/3

y/3 + 10 = 10

In the second equation, look to solve for y:

{x = (4 y)/9 + 10/3

y/3 + 10 = 10

Subtract 10 from both sides:

{x = (4 y)/9 + 10/3

y/3 = 0

Multiply both sides by 3:

{x = (4 y)/9 + 10/3

y = 0

Substitute y = 0 into the first equation:

Answer:  {x = 10/3 , y = 0

7 0
3 years ago
John has 8/9 of a gallon of apple cider vinegar. If it takes 1/7 of a gallon of vinegar to make a batch of collard greens, how m
kumpel [21]
1/7 gallon  = 1 batch 

<em>[multiply by 7 through]</em>
1 gallon = 7 batches

<em>[multiply by 8/9 through]</em>
8/9 gallon = 7 x 8/9
8/9 gallon = 6 2/9 

<em>[Good enough to make 6 batches, not enough to make 7 batches]</em>

So he can make 6 batches of collard green


5 0
3 years ago
How many dimensions does a polygon have?
Verdich [7]
A polygon is a 2-dimension figure....
3 0
3 years ago
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