a. The plane x = 2 is

b. Which of the following vectors is not perpendicular to vector u =(-5, 2, 1)?

c.Given unit vectors i, j and k, 2j × 3k=

d. If Car A is travelling north at 50 km/h and Car B is travelling south at 60 km/h, the velocity of Car A relative to Car B is

e. Given three vectors, u, v, and w, if u • (v × w) = 0, what geometrical result can be concluded?

f. The plane (x, y, z) = (4, 2, 1) + s(1, 1, -2) + t(2, -1, 3), converted into scalar form, has equation

An aircraft is in level flight at airspeed v(t) m/s with thrust T(t) N at cruising altitude. Suppose that at v0 = 250 m/s, the aerodynamic drag experienced by the aircraft at this altitude is:

Fd(v) = 0.25v 2 . (1)

Then, an extremely simplified model relating v(t) to T(t) is:

mv˙(t) + Fd(v(t)) = T(t), (2)

where m = 25000 kg. Assume v(t) is always positive.

Question 1. Linearize (2) at v0 = 250 m/s, and an appropriate nominal thrust T0. That is, create a new linear system model ˙δv + aδv = bδT that is accurate for small perturbations δv(t) = v(t) − v0, δT = T(t) − T0.

Question 2. Suppose we want the aircraft to fly at v0 = 250 m/s. However, precise modelling of drag is very difficult. Suppose in reality the dynamics are slightly different:

mv˙(t) + 0.23v(t) 2 = T(t). (3)

To control v(t) to be close to the reference 250m/s, you try using a proportional controller to control the thrust:

T(t) = T0 + k(v0 − v(t)), (4) with k = 100.

Here T0 is the value calculated in Question 1, but the controller is applied to the true dynamics (3). Find the final final value of v in: (a) open loop (i.e. just apply T(t) = T0), and (b) closed loop (using (4)). You may need to solve a quadratic equation. Recall that v(t) is assumed to be positive. Which one is better?

CONVERT CODE FROM JAVA TO C# PLEASE AND SHOW OUTPUT

import java.util.*;

public class TestPaperFolds
{
   public static void main(String[] args)
   {
       for(int i = 1; i <= 4; i++)               //loop for i = 1 to 4 folds
       {
           String fold_string = paperFold(i);   //call paperFold to get the String for i folds
           System.out.println("For " + i + " folds we get: " + fold_string);
       }
   }

   public static String paperFold(int numOfFolds)   //recursive function that returns the FoldSequence string
   {
       if(numOfFolds == 1){       //if numOfFolds = 1, the return "v"
           return "v";
       }
       else{                       //Otherwise make a recursive call to the paperFold(numOfFolds - 1)
           String s = paperFold(numOfFolds -1);
           return flipString(reverseString(s)) + "v" + s;    //reverse the string s, then flip it, then append "v" and s
       }

   }

   public static String reverseString(String s)   //this helper function reverses a string
   {
       String out = "";
       for(int i = s.length()-1; i >= 0; i--)
           out = out + s.charAt(i);
       return out;
   }

   public static String flipString(String s)   //this helper function flips a string
   {
       String out = "";
       for(int i = 0; i < s.length(); i++){
           if(s.charAt(i) == 'v'){               //converts v into ^
               out = out + '^';
           }
           else if(s.charAt(i) == '^'){       //converts ^ into v
               out = out + 'v';
           }
       }
       return out;
   }
}

-----------
Sample Output:
For 1 folds we get: v
For 2 folds we get: ^vv
For 3 folds we get: ^^vv^vv
For 4 folds we get: ^^v^^vvv^^vv^vv

1.An analysis that includes all subjects who were randomized to the treatment and comparison groups, regardless of whether they received or completed their assigned study protocol

2.What is the primary objective of any case-control or cohort study?

3Which study design is most appropriate to study multiple outcomes from a single exposure?

4.A case-control study is most efficient design for studying the health effects of rare exposures.

5.The ecological fallacy states that associations seen on the group level will not necessarily be present on the individual level.

6.A major advantage of a randomized clinical trial is that it rules out self-selection of patients to the different treatment groups

7.An experimental study was conducted among adults with Type 2 diabetes in order to determine if a new medication was more effective in reducing blood glucose levels than the currently used medication. What type of experimental study is this?

8.Which of the following techniques used in experimental studies can be directly applied in cohort studies (choose all that apply)?

9A study was done to determine whether the amount of money spent on soft drinks was related to mortality from diabetes. The investigators collected data on per capita (average per person) soft drink consumption in ten US states and examined its relationship to mortality rates from diabetes in those ten states. In order to calculate per capita sales they gathered annual data on soft drink sales from commerce records and then divided these figures by the state’s population from the most recent census. The mortality data were gathered from the vital records department in each state. What type of study is this?

10.What sources can be used to identify controls for a case-control study?

11.When is it desirable to use a case-control study (choose all that apply)?

12.What is the purpose of the control group in a case-control study?

1. Wage and Tax Statement Data on Employer Federal Insurance Contributions Act tax used to finance federal programs for old-age and disability benefits (social security) and health insurance for the aged (Medicare).FICA Tax

   Ehrlich Co. began business on January 2, 20Y8. Salaries were paid to employees on the last day of each month, and social security tax, Medicare tax, and federal income tax were withheld in the required amounts. An employee who is hired in the middle of the month receives half the monthly salary for that month. All required The total amount paid to employees for a certain period.payroll tax reports were filed, and the correct amount of payroll taxes was remitted by the company for the calendar year. Early in 20Y9, before the Wage and Tax Statements (Form W-2) could be prepared for distribution to employees and for filing with the Social Security Administration, the A detailed record of each employee's earnings.employees' earnings records were inadvertently destroyed.

   None of the employees resigned or were discharged during the year, and there were no changes in salary rates. The social security tax was withheld at the rate of 6.0% and Medicare tax at the rate of 1.5%. Data on dates of employment, salary rates, and employees’ income taxes withheld, which are summarized as follows, were obtained from personnel records and payroll records:

   Employee	Date First Employed	Monthly Salary		Monthly Income Tax Withheld
   Arnett	Jan. 2	$3,900		$546
   Cruz	Oct. 1	5,900		1,062
   Edwards	Apr. 16	2,200		275
   Harvin	Nov. 1	2,200		275
   Nicks	Jan. 16	5,800		1,305
   Shiancoe	Dec. 1	3,900		605
   Ward	Feb. 1	6,500		1,398

   Required:

   1. Calculate the amounts to be reported on each employee's Wage and Tax Statement (Form W-2) for 20Y8.

   Note: Round amounts to the nearest whole dollar and enter all amounts as positive values.

   Employee	Gross Earnings		Federal Income Tax Withheld		Social Security Tax Withheld		Medicare Tax Withheld
   Arnett	$		$		$		$
   Cruz
   Edwards
   Harvin
   Nicks
   Shiancoe
   Ward
   					$		$

   2. Calculate the following employer payroll taxes for the year: (a) social security; (b) Medicare; (c) state unemployment compensation at 5.4% on the first $10,000 of each employee’s earnings; (d) federal unemployment compensation at 0.6% on the first $10,000 of each employee’s earnings; (e) total.

   Note: Round amounts to the nearest whole dollar and enter all amounts as positive values.

   (a)	$
   (b)
   (c)
   (d)
   (e)	$

Wage and Tax Statement Data on Employer FICA Tax Ehrlich Co. began business on January 2. Salaries were paid to employees on the last day of each month, and social security tax, Medicare tax, and federal income tax were withheld in the required amounts. An employee who is hired in the middle of the month receives half the monthly salary for that month. All required payroll tax reports were filed, and the correct amount of payroll taxes was remitted by the company for the calendar year. Early in the following year, before the Wage and Tax Statements (Form W-2) could be prepared for distribution to employees and for filing with the Social Security Administration, the employees' earnings records were inadvertently destroyed. None of the employees resigned or were discharged during the year, and there were no changes in salary rates. The social security tax was withheld at the rate of 6.0% and Medicare tax at the rate of 1.5% on salary. Data on dates of employment, salary rates, and employees' income taxes withheld, which are summarized as follows, were obtained from personnel records and payroll records: Employee Date First Employed Monthly Salary Monthly Income Tax Withheld Arnett Nov. 16 $3,900 $577 Cruz Jan. 2 5,100 959 Edwards Oct. 1 2,400 298 Harvin Dec. 1 2,100 260 Nicks Feb. 1 10,400 2,340 Shiancoe Mar. 1 3,200 490 Ward Nov. 16 8,100 1,750 Required: 1. Calculate the amounts to be reported on each employee's Wage and Tax Statement (Form W-2). Enter amounts to the nearest cent if required. Enter all amounts as positive numbers. Employee Gross Earnings Federal Income Tax Withheld Social Security Tax Withheld Medicare Tax Withheld Arnett $ 5,850 $ $ 351 $ 87.75 Cruz 61,200 3,672 918 Edwards 7,200 432 108 Harvin 2,100 260 126 31.50 Nicks 114,400 6,864 1,716 Shiancoe 32,000 1,920 480 Ward 12,150 729 182.25 $ 14,094 $ 3,523.50 2. Calculate the following employer payroll taxes for the year: (a) social security; (b) Medicare; (c) state unemployment compensation at 5.4% on the first $10,000 of each employee's earnings; (d) federal unemployment compensation at 0.8% on the first $10,000 of each employee's earnings; (e) total. Round your answers to two decimal places. (a) $ (b) $ 0 (c) $ 0 (d) $ 0 (e) $ 0 Feedback Consider each employee's date of hire. Remember there is a limit on how much the employer pays for state and federal unemployment taxes per employee.

Dr. Trudeau’s little experiment had a big impact on medical thinking at the time. His experiment offered a rationale for opening his Adirondack Cottage Sanitarium, which offered rich and poor alike a regimen of abundant nourishing food, lots of sunlight, plenty of rest, and as much fresh air as a person could tolerate. Hundreds were helped, and many similar establishments were opened. Perhaps the experiment was so successful because of the care with which Trudeau had designed its components. It is important to identify an interesting and potentially approachable question or set of questions before undertaking an experiment. But it is just as important to devise a clever experimental design. When we design an experiment, we choose the treatments that will be received and we control or manipulate them in appropriate ways. These treatments or manipulations are the independent variable(s). The observed or measurable differences in outcome for the treatment groups are the dependent variable(s). Suppose I want to know how much sunlight is needed to produce the sweetest oranges? Based on what I know about sunlight and photosynthesis, I hypothesize that the greater amount of sunlight an orange plant gets, the sweeter the juice of the orange. To investigate whether this is true, I might place one group of plants in the sun for 2 hours per day, another group for 4 hours per day, and nother group for 8 hours per day. At the end of the experiment, I could test for the amount of sugar in the juice of the oranges. The amount of time in the sun is the independent variable. The sugar in the juice is the dependent variable.

7. What is the dependent variable in the Rabbit Island Experiment? Also, list all of the independent variables you can think of in the experiment. (Hmm, maybe Dr. Trudeau’s experiment was not so simple after all!)

8. Often, scientists like to hold all conditions constant except one. Just varying one thing at a time makes it easier to analyze the results. Select any one of the independent variables you have listed above and design an experiment similar to Dr. Trudeau’s. State your experimental question, i.e., what are you trying to find out. Formulate a hypothesis. Then decide upon and write out a description of how you will manipulate your treatment groups (there needn’t be three; you could have two, or four—just design a good experiment!), and then imagine the possible outcomes, assuming survival is the dependent variable. Now generate two survival curves based on those imagined outcomes—one that supports your hypothesis and one that does not. Give possible percent survival rates for each experimental group under both outcomes.

Depreciation for Partial Periods

Clifford Delivery Company purchased a new delivery truck for $54,600 on April 1, 2016. The truck is expected to have a service life of 10 years or 109,200 miles and a residual value of $4,800. The truck was driven 11,300 miles in 2016 and 12,700 miles in 2017. Clifford computes depreciation to the nearest whole month.

Required:

Compute depreciation expense for 2016 and 2017 using the
For interim computations, carry amounts out to two decimal places. Round your final answers to the nearest dollar.
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

For each method, what is the book value of the machine at the end of 2016? At the end of 2017?
(Round your answers to the nearest dollar.)
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

The book value of the asset in the early years of the asset's service will be under an accelerated method as compared to the straight-line method. The method is appropriate when the service life of the asset is affected primarily by the amount the asset is used.

Bean Delivery Company purchased a new delivery truck for $58,200 on April 1, 2016. The truck is expected to have a service life of 5 years or 122,400 miles and a residual value of $4,800. The truck was driven 9,000 miles in 2016 and 10,700 miles in 2017. Bean computes depreciation to the nearest whole month.

Required:

Compute depreciation expense for 2016 and 2017 using the
For interim computations, carry amounts out to two decimal places. Round your final answer to the nearest dollar.
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

For each method, what is the book value of the machine at the end of 2016? At the end of 2017?
(Round your answers to the nearest dollar.)
Straight-line method

Sum-of-the-years'-digits method

Double-declining-balance method

Activity method

The book value of the asset in the early years of the asset's service will be under an accelerated method as compared to the straight-line method. The method is appropriate when the service life of the asset is affected primarily by the amount the asset is used.