Arduino Project -

Part 1

• Connect 3 LEDs on 3 digital pins

• Blink LEDs at: – 1 at 1 Hz – 2 at 4 Hz – 3 at 5 Hz

• Blink LEDs at: – 1 Hz – 3 Hz – 5 Hz 36

What to submit

• 2 Arduino files – one for 1,4,5 Hz blinking – one for 1,3,5 Hz blinking

1)Select all that applies to the Fourth-order Runge-Kutta (RK4) method K subscript

1 equals f left parenthesis t subscript k comma y subscript k right parenthesis K subscript

2 equals f left parenthesis t subscript k plus h over 2 comma space y subscript k plus h over 2 space K subscript 1 right parenthesis K subscript

3 equals f left parenthesis t subscript k plus h over 2 comma space y subscript k plus h over 2 space K subscript 2 right parenthesis K subscript

4 equals f left parenthesis t subscript k plus h comma space y subscript k plus h space K subscript 3 right parenthesis

2) y subscript k plus 1 end subscript equals ? Select one or more:

A. - It has four function evaluations - and y subscript k plus 1 end subscript equals y subscript k plus space left parenthesis 1 third space K subscript 1 plus 2 over 3 space K subscript 2 plus 2 over 3 space K subscript 3 plus 1 third space K subscript 4 right parenthesis space h over 2

B. - It is a fourth-order accurate method - and it has seven function evaluations

C. All of the above.

D. K subscript 1 comma space K subscript 2 comma space K subscript 3 space a n d space K subscript 4 are also called slopes of the solution curve or integral curve.

E. The method is named after two German Mathematicians Runge and Kutta.

A school psychologist is interested in the effect a popular new cognitive therapy on anxiety. The psychologist collects a sample of 13 students and gives them the cognitive therapy once a week for two months. Afterwards the students fill out an anxiety inventory in which their average score was 46.21. Normal individuals in the population have an anxiety inventory average of 49 with a standard deviation of 2.7. What can be concluded with α = 0.10?

a) What is the appropriate test statistic?'

1. na 2. z-test 3. one-sample test 4. independent-samples t-test 5. related-samples t-test

b1)
Population: (choose one of the following)

1. normal individuals 2. new hypnosis technique 3. two months 4. students receiving hypnosis

b2)
Sample: (choose one of the following)

1. normal individuals 2. new hypnosis technique 3. two months 4. students receiving hypnosis

c) Obtain/compute the appropriate values to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value = ________ ; test statistic = ___________
Decision: ***(choose one)*** 1. Reject H0 or 2. Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[ ], [ ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and select "na" below.
d = ___________ ;   *(choose one)1. na 2. trivial effect 3. small effect 4. medium effect 5. large effect
r² = ___________ ;   *(choose one)1. na 2. trivial effect 3. small effect 4. medium effect 5. large effect

f) Make an interpretation based on the results. (Choose one)

1.) The population has significantly lower anxiety than students that underwent cognitive therapy.

2.) The population has significantly higher anxiety than students that underwent cognitive therapy.  

3.) The new cognitive therapy technique does not significantly effect anxiety.

6. The researcher can choose how wide a bin of a histogram can be-True or false?

16. Suppose that three book publishers were interested in the number of fiction paperbacks adult consumers purchase per month. Each publisher conducted a survey. In the survey, adult consumers were asked the number of fiction paperbacks they had purchased the previous month. The results are as follows:

Publisher A

  Publisher B

Publisher C

1. Find the relative frequencies for each survey. Write them in the charts.
2. Using either a graphing calculator, computer, or by hand, use the frequency column to construct a histogram for each publisher's survey. For Publishers A and B, make bar widths of one. For Publisher C, make bar widths of two.
3. In complete sentences, give two reasons why the graphs for Publishers A and B are not identical.
4. Would you have expected the graph for Publisher C to look like the other two graphs? Why or why not?
5. Make new histograms for Publisher A and Publisher B. This time, make bar widths of two.
6. Now, compare the graph for Publisher C to the new graphs for Publishers A and B. Are the graphs more similar or more different? Explain your answer.

18. Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows.

Table 2.67

1. Construct a histogram of the data.
2. Complete the columns of the chart.

A physical therapist developed a new yoga regimen specifically for treating knee pain. He collected a random sample of chronic knee pain patients from the hospital that underwent the new regimen for 20 days. For each day of the study, the patients are asked to rate their knee pain on a scale from 0-10; no pain to extreme pain, respectively. Chronic knee pain sufferers typically report a 5 on the pain scale. Below are the average knee pain scores for the patients over the study. What can be concluded with an α of 0.01?

b)
Population: (Choose one)
1)pain 2)patients on the regimen 3)the hospital 4)chronic knee pain sufferer 5) 20 days

Sample:
1)pain 2)patients on the regimen 3)the hospital 4)chronic knee pain sufferer 5) 20 days

c) Input the appropriate value(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ;

Decision: Reject H0 or Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =____________ ; (Choose one) 1)na 2)trivial effect 3)small effect 4)medium effect 5)large effect
r² =____________ ; (Choose one) 1)na 2)trivial effect 3)small effect 4)medium effect 5)large effect

e) Make an interpretation based on the results.  (Choose one)

1)The new yoga regimen significantly worsens knee pain.

2)The new yoga regimen significantly improves knee pain.   

3) The new yoga regimen is not significantly effective at treating knee pain.

For the some unknown Hamiltonian, we will use a trial wave function ?? = ??₁??₁ + ??₂??₂ . Where ??1 ?????? ??2 are known functions

a. What are the variational parameters of this trial wave function (2 points)?

b. Minimizing the average energy will lead to a secular Determinant.Write down an expression for the Secular Determinant for this system using the following symbols (4 points)

??_11, ??₁₂ = ??_21, ??₂₂, ??_11, ??₁₂ = ??_21, ??_22, E.

c. Write a mathematical expression using ??₁, ??₂, and any necessary operators to define (2 points)

??₂₂=

??₂₁=

Mathlab

Q1. Instruction Text

% For loop code:

vec = [45, -1, 7, 0, -37, 4, -3];

newvec = zeros(1,numel(vec)); % pre-allocate newvec with zeros

for idx = 1:numel(vec)

if vec(idx) > 1 & vec(idx) < 0

numerator = 3*vec(idx)^3;

denominator = 9*vec(idx)^2 + 3;

else

numerator = 2*vec(idx)^3 - 2*vec(idx);

denominator = 2*vec(idx)^2 - 2/vec(idx);

end

newvec(idx) = numerator/denominator;

end

Let's return to Interstates 80 and 680 in rural Iowa, courtesy of Google Earth. (Open Google Earth using the same file as in the Pre-Lab, Interstate_80_in_Iowa.kmz. (Do it the same way you did in the Chapter 1 lab. If you are using Chrome, there should be a button for this file in the lower left corner of your screen after you download it. If you are using other browsers, this file is probably in your Downloads folder.)
Starting from a complete stop, a car gets on I-80 at the I-80 and I-680 interchange, then drives to Stuart and continues east. After starting to move, the car accelerates over a distance of 1/4 mile, until reaching 55 miles per hour and continuing to Stuart at that constant speed. So between the I-680 interchange and Stuart, the time and distance can be considered to be composed of two time/distance parts:

(link) Interstate_80_in_Iowa.kmz (Google maps shows it is 65.5 miles from I680 to stuart)

time(1): the time taken accelerating from 0 mph to 55 mph during the first 1/4 mile

distance(1): the first 1/4 mile over which the car was accelerating

time(2) the time taken to cover the rest of the distance to Stuart going at the constant speed 55 mph

distance(2): the rest of the distance to Stuart after the 1st 1/4 mile

5.A. What is distance(2), the distance to Staurt after the 1^st ¼ mile? _______________

5.B.   What is the time time(1) spent accelerating, in units of hours?___________

5.C. What is the time time(2) spent driving at the constant speed after the 1^st ¼ mile to Stuart? ____________

5.D. - What percentage of the total distance of the trip (distance(1) + distance(2)) between I-680 interchange and Stuart was spent accelerating?

5.E.   What percentage of the total time of this trip (time(1) + time(2)) was spent accelerating?

7. (Sec. 3.2) Two fair six-sided dice are tossed independently. Let M = the minimum of the two tosses. For example, M(2, 5) = 2, M(4, 4) = 4, etc.

(a) What is the PMF of M? [Hint: just work out each probability individually by counting the number of outcomes which result in a specific value for M, i.e. find p(1), then p(2), and so on up to p(6)].

(b) Determine the CDF of M. (

c) Graph the CDF of M.

1. The JM Partnership was formed to acquire land and subdivide it as residential housing lots. On March 1, 2019, Jessica contributed land valued at $472,000 to the partnership in exchange for a 50% interest. She had purchased the land in 2011 for $330,400 and held it for investment purposes (capital asset). The partnership holds the land as inventory.

   On the same date, Matt contributed land valued at $472,000 that he had purchased in 2009 for $566,400. He became a 50% owner. Matt is a real estate developer, but he held this land personally for investment purposes. The partnership holds this land as inventory.

   In 2020, the partnership sells the land contributed by Jessica for $495,600. In 2021, the partnership sells the real estate contributed by Matt for $448,400.

   a. What is each partner's initial basis in his or her partnership interest?

   Jessica's initial basis is $ . Matt's initial basis is $ .

   b. What is the amount of gain or loss recognized on the sale of the land contributed by Jessica? What is the character of this gain or loss?

   The amount of the (gain/loss)  recognized on the sale of the land contributed by Jessica is $ , and the type is (ordinary income/capital gains/ordinary loss/ capital loss).

   c. What is the amount of gain or loss recognized on the sale of the land contributed by Matt? What is the character of this gain or loss?

   The amount of the (gain/loss) recognized on the sale of the land contributed by Matt is $ , and the type is (ordinary income/capital gains/ part capital gain part ordinary income/ordinary loss/capital loss/ part capital loss part ordinary loss).

2. d. How would your answer in (c) change if the property was sold in 2026?

   The amount of the (gain/loss) recognized on the sale of the land contributed by Matt is $ , and the type is  (ordinary income/capital gains/ part capital gain part ordinary income/ordinary loss/capital loss/ part capital loss part ordinary loss)..