1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Setler79 [48]
3 years ago
5

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

+e-02n).
(a) Find the proportion of correct responses after 3 trials.
(b) Find the proportion of correct responses after 7 trials.
(c) use a graphing utility to graph the model.Find the number of trials required for the porportion of correct responses to be 0.75.
(d) Does the porportion of correct responses have a limit as n increase without bound?Explain your reasoning.

Mathematics
1 answer:
elena-s [515]3 years ago
5 0

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.

You might be interested in
Refer to the figure to answer the question.
tresset_1 [31]

Answer:

It's HG

Step-by-step explanation:

The line of intersection is where they cross, and this line is the line HG

7 0
3 years ago
Cora arrived at school at 7:55 am She left for 1 hour for a doctors appointment. She was dismissed from school at 3:15 pm. How l
algol [13]
7 hours and 20 min, hope this helps mark me the brainliest
5 0
3 years ago
Read 2 more answers
Line k is parallel to line l. Lines k and l are parallel. Lines m and n intersect to form 2 triangles. The top triangle has angl
larisa86 [58]

Answer:The line that is congruent to angle 4 is angle 1

hope this helped :)

6 0
3 years ago
Read 2 more answers
Select Parameter or Statistic to classify each statement.
REY [17]

Answer:

Step-by-step explanation:

A parameter describes a population, and a statistic describes a sample.

The first one is a statistic.  A sample was surveyed.

The second one is a parameter.  It describes the entire soccer team.

The third one is a statistic.  A sample was surveyed.

The fourth one is a parameter.  It describes the entire golf team.

6 0
3 years ago
1) When the plumber comes to my house to fix the leaky faucet, he charges a flat rate of
Travka [436]

Answer:

3 hours

Step-by-step explanation:

To find the number of hours the plumber was at the house, we need to solve for x.

22x + 50 = 116

22x = 116 - 50

22x = 66

22x/22 = 66/22

x = 3

4 0
3 years ago
Read 2 more answers
Other questions:
  • Based on the graph below, what are the solutions to the equation f(x) = g(x)? (5 points) graph of function f of x equals 4 times
    15·1 answer
  • is it possible to store a 20 foot long pipe in a rectangular room that is 10 feet by 12 feet by 8 feet?
    8·2 answers
  • A.)5 x 10^-2, B.) 7.5 x 10^3. how many times greater is B compared to A?
    8·1 answer
  • Zeros are never significant digits. <br><br> T<br><br> F
    8·2 answers
  • An lpn earned a gross pay of 650.04 last week. if 21 1/2% of her gross paycheck is taken out in taxes, what is her bring home pa
    9·2 answers
  • A study was conducted on dolphins born in 2016 in a certain region of the ocean. Ten of the 250 dolphins studied were born with
    10·2 answers
  • When you spin a 2D triangle, it looks like a 3D pyramid. true or false
    9·2 answers
  • The function f(x) = 9x +5 is one-to-one.<br> Find an equation for f-'(x), the inverse function.
    5·1 answer
  • Will has used Frog to solve a subtraction, but he thinks that he has got the wrong
    8·1 answer
  • 1. Write an equivalent<br> ratio by multiplying:<br> 1<br> -<br><br> 4
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!