Whats (8x+10) please help me T-T

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.

5 0

3 years ago

22. Use your model to determine when the volume of oil will get down to 500 gallons.

Helen [10]

Answer:

21. y = 75000·0.935^t

22. after 74.6 days

23. y = 27.8112·1.18832^t

24. 18.8% per month

25. 1748

Step-by-step explanation:

22. It is convenient to use the graphing calculator to solve this problem. The number of days is where the exponential curve has the value 500. It is about 74.55 days. (see the first attachment)

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23. y = 27.8112·1.18832^t (see the second attachment)

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24. The rate of change is the difference between the base of the exponential and 1, often expressed as a percentage. The time period is the units of t.

(1.18832 -1) × 100% ≈ 18.8% . . . . per month

__

25. Evaluating the function for t=24 gives y ≈ 1748.30425259 ≈ 1748.

_____

<em>Comment on graphing calculator</em>

A graphing calculator can make very short work of problems like these. It is worthwhile to get to know how to use one well.

8 0

3 years ago

Which shows the best use of the associative and commutative properties to

OlgaM077 [116]

Answer:

D

Step-by-step explanation:

So the associative and commutative properties basically say That you can change the orders of the numbers and the answer won't change (for multiplication and addition).

Your answer would be D because they added the numbers with a decimal place together, it makes it easier to look at, and add in your head.

5 0

3 years ago

Find the area of the trapezoid

daser333 [38]

Answer:

52√3 ft^2

Step-by-step explanation:

The area of a trapezoid is the average of the bases times the height

We have enough information to find these parts.

The average of the bases is 11+15 /2 =13

The height is 4√3

So the answer is 13 * 4√3 = 52√3

Please vote me for brainliest i really need it, i hope i helped you. :)

4 0

3 years ago

Which expression is equivalent to 5(9 + 7). I will mark brainliest if you answer. DatGuy323 I like You! Answer please

Virty [35]

Answer: 80

Step-by-step explanation:

$5(9+7)\\\\Parenthesis\\\\5(16)\\\\Multiply\\\\80$

Hope it helps <3

4 0

3 years ago