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3 years ago

Given the line of best fit for a data set of data points with the equation y=5x-2.5,what is the residual for the point (4,13)

Mathematics

1 answer:

BlackZzzverrR [31]3 years ago

7 0

Answer:

-4.5

Step-by-step explanation:

The predicted value from the model is calculated by substituting x with 4 in the regression equation;

y = 5(4) - 2.5

y = 17.5

The actual value when x is 4 is given as 13. The residual is simply the difference between the actual and the predicted value;

residual = actual value - predicted value

residual = 13 - 17.5

residual = -4.5

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Learning Thoery In a learning theory project, the proportion P of correct responses after n trials can be modeled by p = 0.83/(1

elena-s [515]

Answer:

a) $P(n=3) = \frac{0.83}{1+e^{-0.2(3)}}= \frac{0.83}{1+ e^{-0.6}} = 0.536$

b) $P(n=7) = \frac{0.83}{1+e^{-0.2(7)}}= \frac{0.83}{1+ e^{-1.4}} = 0.666$

c) $0.75 =\frac{0.83}{1+e^{-0.2n}}$

$1+ e^{-0.2n} = \frac{0.83}{0.75}= \frac{83}{75}$

$e^{-0.2n} = \frac{83}{75}-1= \frac{8}{75}$

$ln e^{-0.2n} = ln (\frac{8}{75})$

$-0.2 n = ln(\frac{8}{75})$

And then if we solve for t we got:

$n = \frac{ln(\frac{8}{75})}{-0.2} = 11.19 trials$

d) If we find the limit when n tend to infinity for the function we have this:

$lim_{n \to \infty} \frac{0.83}{1+e^{-0.2t}} = 0.83$

So then the number of correct responses have a limit and is 0.83 as n increases without bound.

Step-by-step explanation:

For this case we have the following expression for the proportion of correct responses after n trials:

$P(n) = \frac{0.83}{1+e^{-0.2t}}$

Part a

For this case we just need to replace the value of n=3 in order to see what we got:

$P(n=3) = \frac{0.83}{1+e^{-0.2(3)}}= \frac{0.83}{1+ e^{-0.6}} = 0.536$

So the number of correct reponses after 3 trials is approximately 0.536.

Part b

For this case we just need to replace the value of n=7 in order to see what we got:

$P(n=7) = \frac{0.83}{1+e^{-0.2(7)}}= \frac{0.83}{1+ e^{-1.4}} = 0.666$

So the number of correct responses after 7 weeks is approximately 0.666.

Part c

For this case we want to solve the following equation:

$0.75 =\frac{0.83}{1+e^{-0.2n}}$

And we can rewrite this expression like this:

$1+ e^{-0.2n} = \frac{0.83}{0.75}= \frac{83}{75}$

$e^{-0.2n} = \frac{83}{75}-1= \frac{8}{75}$

Now we can apply natural log on both sides and we got:

$ln e^{-0.2n} = ln (\frac{8}{75})$

$-0.2 n = ln(\frac{8}{75})$

And then if we solve for t we got:

$n = \frac{ln(\frac{8}{75})}{-0.2} = 11.19 trials$

And we can see this on the plot attached.

Part d

If we find the limit when n tend to infinity for the function we have this:

$lim_{n \to \infty} \frac{0.83}{1+e^{-0.2t}} = 0.83$

So then the number of correct responses have a limit and is 0.83 as n increases without bound.

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Lisa made a shirt using 1/3 m of blue fabric and 3/5 m of red fabric how many meters of fabric did she use in all

Marysya12 [62]

Answer: 14/15 of a meter

Step-by-step explanation:

5 and 3 LCM is 15.

3/5 x 3 + 1/3 x 5= 9/15 + 5/ 15 = 14/15

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Jessie works at a car manufacturing plant. One day she installed a total of 46 axles, 2 in each car she worked on. She wants to

shtirl [24]

Answer:

Step-by-step explanation:

total number of cars: x

the total number of axles: 46

and the number of axles installed per car: 2

2 axles in each car, then total instaled axles: 2•x

2•x = 46

x = 46÷2

x = 23

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Step-by-step explanation:

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