Question 1

The GCD is the greatest common denominator. Euclid found that if A=Bx +R then GCD(A,B)=GCD(A,R). Prove this is true. Show working

Question 2

The approach Euclid in calculating the GCD used was novel as it was an ________process to solve a complex problem, hence formed the first _______.

Question 3

The difference between a breadth first search (BFS) and a depth first search (DFS) is that in the DFS you traverse all the first branch before proceeding to the next branch.

a) True

b) False

1. Question 4 If a Graph is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles, OR a diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc, which is correct?

   1. The first definition as graphs need axes

   2. The second definition as more general so covers all graphs

   3. Neither as they are too vague

Question 5

Find a c such that f(n) is O(n2) when f(n) = 1/4 n2 + 15 n + 115. Justify this answer.

Question 6

If f(n)= 10* log n then Big-O of f(n) is O(n)

a) True

b) False

Suppose we are given an arbitrary digraph G = (V, E) that may or may not be a DAG. Modify the topological ordering algorithm so that given an input G, it outputs one of the two things:

a. A topological ordering thus establishing that G is a DAG.

b. A cycle in G thus establishing that it is not a DAG.

The runtime of your algorithm should be O(m+n) where m = |E| and n = |V|

Which of the following statements is (are) correct?
(x) A choice by Molly to buy more muffins at $2 per muffin than at the price of $3 per muffin is an example of
the law of demand and it is illustrated as a movement along Molly’s demand curve for muffins.
(y) A choice by Albert to buy more Tony’s pizza because of a recent increase in the price of Polly’s pizza is
illustrated as a shift to the right of Albert’s demand curve for Tony’s pizza and reflects an increase in
demand for Tony’s pizza.
(z) If George has a change in behavior and is now willing to buy less apple pie at every price, then his
demand curve for apple pie will shift to the left.
A. (x), (y) and (z)
B. (x) and (y) only
C. (x) and (z) only
D. (y) and (z) only
E. (y) only

Which of the following statements is (are) correct?
(x) Assume pizza and soda are complements. If the price of pizza decreases, then both the demand for soda
will increase and the demand curve for pizza will shift to the right.
(y) Assume Lipton green tea and Arizona green tea are close substitutes. If the price of Lipton tea decreases,
then the quantity demanded of Lipton tea will increase and the demand for Arizona tea will decrease.
(z) Assume Hershey chocolate bars and Mars chocolate bars are substitutes. If the price of Hershey chocolate
bars decreases, then the demand curve for Mars chocolate bars will shift to the left.
A. (x), (y) and (z)
B. (x) and (y) only
C. (x) and (z) only
D. (y) and (z) only
E. (y) only

Which of the following is NOT a determinant of demand?
A. the expected price of the good next month
B. the price of a resource that is used to produce the good
C. the price of a complementary good
D. the price of a substitute good
E. A and B, only

R PROGRAMMING QUESTION

- Below I have code. For each double hashtag (##) can you comment on the code below it (Describe what is happening in the code below it next to each ##)

- Run the code and compare the confidence intervals

- I have to submit the confidence intervals, comments, and the code with the ## filled out

Leaps.then.press.plot.2<-function(xmat0,yvec,xpred,ncheck=20)

{

#

#input quadratic matrix with less than 30 columns eg. the result of x.auto2a<-matrix.2ndorder.make(xmat[,-7],F)

#also, no need for plotting, just pull out best, xpred is one of the row vectors from x.auto2a, but all terms with weight are divided by 2

#

   ##

   leaps.str<-leaps(xmat,yvec)

   ##

   z1<-leaps.str$Cp-leaps.str$size

   ##

   o1<-order(z1)

   matwhich<-(leaps.str$which[o1,])[1:ncheck,]

   MPSEvec<-NULL

   ##

   for(i in 1:ncheck){

       ls.str0<-regpluspress(xmat[,matwhich[i,]],yvec)

       ##

       parvec<-matwhich[i,]

       npar<-sum(parvec)

       ## (WHY npar+1)

       MPSE<-ls.str0$press/(length(yvec)-(npar+1))

       MPSEvec<-c(MPSEvec,MPSE)

   }

   ##

   I1<-(MPSEvec==min(MPSEvec))

   ##

   i<-c(1:ncheck)[I1]

   ##

   xmat.out<-xmat[,matwhich[i,]]

   ##

   xpred.out<-xpred[matwhich[i,]]

   ##

   list(xmatout=xmat.out,yvec=yvec,xpredout=xpred.out)

}

Bootreg<-function(xmat,yvec,xpred,nboot=10000,alpha=0.05)

{

   ##

   lstr0<-leaps.then.press.plot2(xmat,yvec,xpred)

   xmat0<-lstr0$xmat.out

   yvec0<-lstr0$yvec

   xpred0<-lsstr0$xpredout

   ##

   rprd.list<-regpred(xpred0,xmat0,yvec0)

   ypred0<-rprd.list$pred

   sdpred0<-rprd.list$sd

   df<-rprd.list$df

   ##

   bootvec<-NULL

   nobs<-length(yvec0)

   for(i in 1:nboot){

       ##

       vboot<-sample(c(1:nobs),replace=T)

       xmatb<-xmat0[vboot,]

       yvecb<-yvec0[vboot]

       ##

       lstrb<-leaps.then.press.plot2(xmatb,yvecb,xpred)

       ##

       xmatb0<-lstrb$xmat.out

       yvecb0<-lstrb$yvec

       xpredb0<-lsstrb$xpredout

       ##

       rprd.list<-regpred(xpred0,xmat0,yvec0)

       ypredb<-rprd.list$pred

       sdpredb<-rprd.list$sd

       dfb<-rprd.list$df

       ##

       bootvec<-c(bootvec,(ypredb-ypred0)/sdpredb)

}

##

lq<-quantile(bootvec,alpha/2)

uq<-quantile(bootvec,1-alpha/2)

##

LB<-ypred0-(sdpred0)*uq

UB<-ypred0-(sdpred0)*lq

##

NLB<-ypred0-(sdpred0)*qt(1-alpha/2,df0)

NUB<-ypred0+(sdpred0)*qt(1-alpha/2,df0)

list(bootstrap.confidence.interval=c(LB,UB),normal.confidence.interval=c(NLB,NUB))

}

> regpred<-

function(xpred,xmat,y){

##

ls.str<-lsfit(xmat,y)

#calculate prediction

ypred<-ls.str$coef%*%c(1,xpred)

#use ls.diag to extract covariance matrix

ycov<-ls.diag(ls.str)$cov.unscaled

#use ls.diag to extract std deviation

std.dev<-ls.diag(ls.str)$std.dev

#variance of data around line

v1<-std.dev^2

#variance of prediction

vpred<-v1*c(1,xpred)%*%ycov%*%c(1,xpred)

df=length(y)-length(diag(ycov))

list(pred=ypred,sd=sqrt(vpred),df=df)

}

On January 1, Pulse Recording Studio (PRS) had the following account balances.

The following transactions occurred during January.

1. Received $2,490 cash on 1/1 from customers on account for recording services completed in December.
2. Wrote checks on 1/2 totaling $4,380 for amounts owed on account at the end of December.
3. Purchased and received supplies on account on 1/3, at a total cost of $200.
4. Completed $3,900 of recording sessions on 1/4 that customers had paid for in advance in December.
5. Received $4,750 cash on 1/5 from customers for recording sessions started and completed in January.
6. Wrote a check on 1/6 for $4,080 for an amount owed on account.
7. Converted $1,030 of cash equivalents into cash on 1/7.
8. On 1/15, completed EFTs for $1,420 for employees’ salaries and wages for the first half of January.
9. Received $2,880 cash on 1/31 from customers for recording sessions to start in February.

Required:

1. Prepare journal entries for the January transactions. Review the 'General Ledger' and the unadjusted 'Trial Balance' Tabs to see the effect of the transactions on the account balances.
2. Prepare journal entries for items (j)–(n) from the bank reconciliation.
   j. The bank deducted $500 for an NSF check from a customer deposited on January 5.
   k. The check written January 6 has not cleared the bank, but the January 2 payment has cleared.
   l. The cash received and deposited on January 31 was not processed by the bank until February 1.
   m. The bank added $3 cash to the account for interest earned in January.
   n. The bank deducted $3 for service charges.
3. Prepare adjusting journal entries on 1/31 in 'General Journal' Tab. (these are shown as items 15-21).
   o. Depreciation for the month is $170.
   p. Salaries and wages totaling $1,900 have not yet been recorded for January 16–31.
   q. Prepaid Rent will be fully used up by March 31.
   r. Supplies on hand at January 31 were $500.
   s. Received $200 invoice for January electricity charged on account to be paid in February but is not yet recorded.
   t. Interest on the promissory note of $48 for January has not yet been recorded or paid.
   u. Income tax of $1,200 on January income has not yet been recorded or paid.
4. Review the adjusted 'Trial Balance' as of January 31.
5. Prepare an income statement for the period ended January 31 in the 'Income Statement' Tab.
6. Prepare a bank reconciliation in the 'Bank Reconciliation' Tab.
7. Prepare a classified balance sheet as of January 31 in the 'Balance Sheet' Tab.
8. Using the information from the requirements above, complete the 'Analysis' tab.

REQUIREMENTS:

1. General Journal tab - Prepare the journal entries to record the transactions that occurred from January 1-31. Review the accounts as shown in the General Ledger and Trial Balance tabs. Then prepare the necessary adjusting entries at January 31 to correctly report net income for the period.

2. General Ledger tab - Each journal entry is posted automatically to the general ledger. Use the drop-down button to view the unadjusted and adjusted balances in the General Ledger.

3. Trial Balance tab - You may view either the unadjusted and adjusted trial balance by choosing from the drop-down.

4. Income Statement tab - Use the drop-down to select the accounts properly included on the income statement. The unadjusted and adjusted balances will appear for each account based on your selection.

5. Statement of Retained Earnings tab - Prepare the bank reconcilation for the year ended January 31.

6. Balance Sheet tab - Use the drop-down to select the accounts to properly included on the balance sheet. The unadjusted and adjusted balances will appear for each account, based on your selection.

7. Analysis tab - Using the information from the requirements above, complete the 'Analysis' tab.

Discuss how x-inefficiencies arise and how they explain why the measure of the deadweight loss of a monopoly (i.e., Harberger’s) may be too low? Include a graph in your answer that shows the increase in deadweight welfare loss due to x-inefficiencies.

4. Suppose from our class (with 25 students), we find the average GPA is 2.7, with standard deviation
0.4. Regard our class as a random sample from the whole university. Based on the information from our
class, can we believe at significance level 0.05, that the average GPA for all students can be at least 2.8?

2D Car Collision

Car Collision in 2D (c7p50) A 900- kg car collides with a 1400- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 10.0 km/h in a direction of 35 degrees with respect to the positive x axis. The heavier car moves at 13 km/h at -41 degrees with respect to the positive x axis.

A) What was the initial speed of the lighter car (in km/h)? ____Tries 0/7

B) What was the initial direction (as measured counterclockwise from the x-axis)? ___Tries 0/7

Biochemical Tests crossword puzzle:

Across

5 Anaerobic metabolism
6 Crusty growth on broth
8 Cloudy growth in broth
10 Smooth growth on slant
11 Another name for glucose
13 Hydrolyzed collagen
15 Possible sole carbon source
16 Bacterial movement
17 Test use of milk nutrients (2wds)
20 Hydrolyzes starch
22 Bacteria settled to bottom of broth
23 Milk sugar
27 Test for acetoin
28 Produces clear zones in skim milk agar
29 pH indicator in sugar fermentation tubes (2wds)

Down

1 Produced from tryptophan 2 Group of 4 tests
3 Red when acidic (2wds)
4 Turns SIM black
7 Catalysts secreted by the cell
9 Inverted tube to trap gas
12 Tests for lipase
14 Common liquid medium (2wds)
16 Sticky surface growth on broth
18 Breaking macromolecules with addition of water 19 Snowy appearance in broth culture
21 E. coli produces this from glucose (3wds)
24 Spiky growth on slant
25 Breaks down hydrogen peroxide
26 Product of amino acid degradation

what are legal requirements and ethical issues in capturing and analyzing digital images in health sector

Consider a monopolist with a linear demand curve: q = a − bp, where a;b > 0. It produces at constant marginal cost c and has no fixed cost. Assume that 0 < c < a b.
(a) Find the monopoly price, quantity, and profits. (b) Derive the inverse demand curve P(q). Draw P(q), the MRcurve, and the MC-curve in a diagram. Explain why we need the assumption c < a b. (c) Does it matter that the monopolist sets price instead of quantity? (d) Calculate the deadweight loss of monopoly. (e) A change in b results in two opposing effects on the deadweight loss. Calculate the effect of a change in b on the deadweight loss. (f) Derive the price elasticity of demand η for any price. How does η change with p? (g) Show mathematically as well as graphically that the price elasticity of demand η > 1 at the monopoly price.

At t=0 a grinding wheel has an angular velocity of 27.0 rad/s . It has a constant angular acceleration of 25.0 rad/s2 until a circuit breaker trips at time t = 2.00 s . From then on, it turns through an angle 430 rad as it coasts to a stop at constant angular acceleration.

Through what total angle did the wheel turn between t=0 and the time it stopped?At what time did it stopWhat was its acceleration as it slowed down?

Independent Sample T Test (Student Height)

Open College Student Data

Research Question: Is there a significant difference between genders on average student height?

Record the following:

1)What test will you run to answer this research question? Why?

2)Is Assumption One: Equal Variances met? How do you know?

3)Is Assumption Two: Normality met? How do you know?

4)Is Assumption Three: Independency met? How do you know?

5)What are the means? (Male and Female)

6)Answer the research question. How do you know?

7)Which gender is statistically taller? How do you know?

8)Is there an effect size (Cohen’s D)? If so what is it? How did you arrive at the effect size? Is it small, medium, large or very large? How do you know?

DATA SET

height   gender (1 - male, 2 - female)
67.00   2
72.00   1
61.00   2
71.00   1
65.00   2
67.00   1
69.00   1
75.00   1
62.00   2
61.00   2
64.00   2
64.00   1
70.00   1
63.00   2
64.00   2
63.00   2
65.00   2
71.00   1
72.00   1
68.00   2
75.00   1
67.00   2
69.00   1
67.00   1
64.00   2
64.00   2
70.00   1
64.00   1
70.00   1
72.00   1
64.00   2
71.00   1
67.00   2
63.00   2
69.00   1
68.00   1
64.00   2
70.00   1
71.00   1
72.00   1
60.00   2
65.00   2
72.00   1
63.00   2
75.00   1
71.00   1
65.00   2
69.00   1
63.00   2
67.00   2

Researchers conducted a study to investigate the effectiveness of two different treatments for depression (Lithium or Imipramine). A sample of individuals diagnosed with bipolar depression were divided into three groups - one group received Lithium, one group received Imipramine, and the last group was given a placebo. After a specified length of time, patients are evaluated for a recurrence of depression. Use StatCrunch to conduct a chi-square test to determine if recurrence is related to the treatment prescribed. In StatCrunch, select Stat > Tables > Contingency > With Data. Select one of the variables of interest for the row variable and the second variable as the column variable. Then click Compute.

• Select the appropriate hypotheses:
  • HoHo: recurrence of depression is related to the treatment prescribed
    HaHa: recurrence of depression is not related to the treatment prescribed
  • HoHo: recurrence of depression is not related to the treatment prescribed
    HaHa: recurrence of depression is related to the treatment prescribed
• TS: χ2χ2 =   (round to 4 decimal places)
• probability =    (round to 4 decimal places)
• Conclusion: At the 0.10 level, there Select an answer is is not  significant evidence to conclude recurrence of depression Select an answer is not is  related to the treatment prescribed.

Throwback Question: Suppose we know that the risk of liver cancer among alcoholics without cirrhosis of the liver is 29.8%. A researcher conjectures that the risk of cancer among alcoholics with cirrhosis of the liver is higher. Suppose we sample 81 alcoholics with cirrhosis of the liver and determine 29 have liver cancer. Use this information to answer the following:

1. For each person in the sample, what variable is recorded?
   • number of years diagnosed with cirrhosis
   • level of alcoholism
   • percentage of individuals with liver cancer
   • if the individual has liver cancer
2. Completely describe the sampling distribution for the sample proportion of alcoholics with cirrhosis who have liver cancer when samples of size 81 are selected (assuming there is no difference in occurrence between those with and without cirrhosis).
   • mean: μˆpμp^  =
   • standard deviation: σˆpσp^ =  (round to 4 decimal places)
   • shape: the distribution of the sample proportion is Select an answer not normally distributed normally distributed   
     • Checks: np =  and n(1 - p) =
3. Test the appropriate claim using the data collected at a significance level of 0.10.
   • HoHo : p ? < > = ≠     HaHa : p ? = < > ≠  
   • αα =
   • TS: z =   (round your final answer to 2 decimal places; carry 4 decimal places throughout your calculation)
   • probability =   (round to four decimal places)
   • Decision: Select an answer fail to reject H₀ reject H₀
   • Interpretation:At the 0.10 level, there Select an answer is is not   significant evidence to support the claim that the incidence rate of liver cancer is Select an answer lower higher different than   in alcoholics diagnosed with cirrhosis.

Java only !!! Please write the following method that sorts an ArrayList of numbers: public static void sort(ArrayList < Integer > list)

Prompts user to enter 5 ints stores them into an array list and display them in increasing order