A point charge q1 = 4.00 nC is placed at the origin, and a second point charge q2 = -3.10 nC is placed on the x-axis at x=+ 20.0 cm . A third point charge q3 = 1.95 nC is to be placed on the x-axis between q1 and q2. (Take as zero the potential energy of the three charges when they are infinitely far apart.)

1:What is the potential energy of the system of the three charges if q3 is placed at x=+ 11.0 cm ?

2:Where should q3 be placed between q1 and q2 to make the potential energy of the system equal to zero?

Jacob Lee is a frequent traveler between Los Angeles and San Francisco. For the past month, he wrote down the flight times on three different airlines.

Goust Jet Red Cloudtran

51 50 54

51 54 55

54 52 60

51 49 44

47 58 42

60 54

64 40

80

A. Use the 0.05 significance level to check ifbvthere is a different in the mean fliht times among the three airlines

B. Is there different between goulf and Couldtran (use 0.05 significant level)

1. For light moving from left to right through a lens, describe the paths of the three principal rays used to locate the image formed by the lens. Using the three principal rays, draw two ray diagrams for object sitting in front of (a) concave lens (b）convex lens. Please indicate the focus points clearly on your ray diagrams.
2. Describe the difference between the shapes of converging and diverging lens , as well as the difference between the images formed by converging and diverging lens.
3. What is the lens equation? What are the sign converntions for the distances f, 0, and i in it?

Suppose that you are thinking about buying a car and have narrowed down your choices to two options.

The new car option: the new car costs $26,000 and can be financed with a four-year loan at 7.54%.

The used car option: a three-year old model of the same car costs $14,000 and can be financed with a three-year loan at 7.07%.

What is the difference in monthly payments between financing the new car and financing the used car? Use PMT formula

The difference in monthly payments between financing the new car and financing the used car is $____.

To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.

1. Construct an analysis of variance table (to 2 decimals, if necessary). Round p-value to four decimal places.
   

   Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
   Treatments
   Error
   Total

   
   
2. Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process.
   
   The p-value is Select: less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10
   
   What is your conclusion?
   Select: Conclude that the mean yields for the three temperatures are not all equal, Conclude that the mean yields for the three temperatures are all equal

Sainsbury's is the second largest chain of supermarkets in the United Kingdom. The have expanded internationally and have recently also opened stores in Egypt. However, Sainsbury has since experienced a variety of issues with the Egyptian market. As business development analyst you only see the three follow- ing options for Sainsbury’s business in Egypt:

Today is December 31, 2000. Suppose you have the following information about the financial implications of Sainsbury’s three strategic options.

Option 1: Scale down operations
Sainsbury’s immediately starts to scale down its operations and plans to eventually leave the Egyptian market effective as of Jan. 01, 2006 (i.e. after 5 more years). At the end of 2001, Sainsbury’s operations in Egypt are projected to generate a loss of £6 million. However, due to the effects of scaling down operations and a number of efficiency increases, Sains- bury’s estimates a profit of £7,2 million at the end of 2002, which is then expected to decrease by 3% on a yearly basis until Dec. 31, 2005. All fore- casts for this option are based on assumptions and considered as risky.

Option 2: New local partners
The NPV of acquiring new local partners has already been calculated for you: £12 million

Option 3: Sell business entirely
Sainsbury’s immediately sells its Egyptian operations to a local investor. The local investor is willing to pay a total £15 million, in three parts of £10 million (today) and £4 million (on Dec. 31, 2001) and £1 million (on Dec. 31, 2002). Since the local investor has also presented a bank guarantee for the whole acquisition price (issued by a well-known British bank), op- tion 3 is considered to be risk-free.

The risk-free interest rate is 1% EAR. Sainsbury’s continuing operations in Egypt are seen as risky and the appropriate risk premium is 8%.

1. Calculate the net present values (NPVs) of options 1 and 3 indicated above. (4 pts)

2. Clearlyindicatewhichoption(Option1,Option2orOption3)shouldbe chosen by Sainsbury’s management, and explain the reasons for your choice in two or three sentences – use technical terminology as needed. (1 pts)

Students Born in USA

MEAN GPA: 3.05 STD DEVIATION: .511

MEAN AGE: 27 STD DEVIATION: 10

MEAN HOURS SPEND ON HW: 8.50 STD DEVIATION: 4.72

STUDENTS BORN OUTSIDE USA

MEAN GPA: 3.26 STD DEVIATION: .428

MEAN AGE: 31 STD DEVIATIONS: 10.5

MEAN HOURS SPENT ON HW: 14.13 STD DEVIATION: 10.4

1. If one student is randomly selected from the USA born group, find the probability of getting someone with a GPA greater than 3.88.

2. If one student is randomly selected from the Non-USA born group, find the probability of getting someone with a GPA greater than 3.88.

3. If one student is randomly selected from the USA born group, find the probability of getting someone between the ages of 20 and 25. 4. If 9 students are randomly selected from the Non-USA born group, find the probability that their mean age is between 22 and 37. 5. If 25 students are randomly selected from the USA born group, find the probability that their mean GPA is between 2.50 and 3.50.

Part II. Student’s t-Test 2. A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Ten older adults (over the age of 70) and younger adults (between 20 and 30) were given a life satisfaction test. Scores on the measure range from 0-60 with high scores indicative of high life satisfaction.

Older Adults Younger Adults

45 34

38 22

52 15

48 27

25 37

39 41

51 24

46 19

55 26

46 36

Sample 1 Mean = 44.50 Sample 2 Mean = 28.10 Sample 1 SD = 8.68 Sample 2 SD = 8.54 Sample 1 N = 10 Sample 2 N = 10

a. Write out the null and research hypothesis for the above question.

b. Calculate the t value.

c. What is the critical value for t?

d. Is there a significant difference between the two groups?

e. What probability level did you choose and why?

f. Interpret your answer.

The table below lists measured amounts (mg) of tar, carbon monoxide (CO), and nicotine in king size cigarettes of different brands. Tar 25 27 20 24 20 20 21 24 CO 18 16 16 16 16 16 14 17 Nicotine 1.5 1.7 1.1 1.6 1.1 1.0 1.2 1.4 Use the amounts of nicotine and carbon monoxide (CO).

1.Find the value of the linear correlation coefficient between amounts of nicotine and carbon monoxide.

2.Use the data and determine whether there is sufficient evidence to support a claim of a linear correlation between amounts of nicotine and carbon monoxide. Find the P-value.

3.Based on the P-value, is there a linear correlation between the amounts of nicotine and carbon monoxide?

4.Using the data, and letting y represent the amount of carbon monoxide and letting x represent the amount of nicotine, find the regression equation.

5.Referring to the data in Question 16, The Raleigh brand king size cigarette is not included in the table, and it has 1.3 mg of nicotine. What is the best predicted amount of carbon monoxide?

The purpose of the program is to play the game of M.A.S.H. (Mansion, Apartment, Shack, House). This program asks the user multiple questions and then randomly generates answers based on the answers to predict the user’s future. By the time you finish this program, you will have learned how to make a menu based program, use switch statements, validate user input with loops, allow a program to run multiple times until user wants to quit, and mix cin>> and getline() intermittently in a program.

1. Names of three people (2 they like & one they don’t like)

1. Three integer numbers between 1 and 100
2. Three locations including city & state (2 they like & one they don’t like)
3. Three job titles (2 they like & one they don’t like)
4. Three companies or restaurants (2 they like & one they don’t like)
5. Three integer numbers between 10000 and 500000
6. Three types of cars (2 they like & one they don’t like

7. You will be predicting the user’s future by selecting one of their three choices randomly. You will need to create a random number for each “category” – this means there should be in total 7 numbers randomly generated between 1 and 3. So for example, you will generate a random number between 1 and 3 for the names of people.

   You will also generate one more random number (this would make 8 total) between 1 and 4 which will indicate if the user will live in a mansion (1), apartment (2), shack (3), or house(4).

8. Indent and comment your code properly.
10. MENU - You will have a main menu that will ask the user to either
    
    1) Play MASH or
    2) End the program.
    
    You must have a switch statement to figure out which choice the user selected. The program should run over and over until the user selects to end the program using a do-while loop. Use a Boolean variable to help with this!
12. You MUST validate user input with while loops if the input is a number to ensure the number is in the specified range. You may assume the user will enter in a number (not a character or string), but you can’t assume they enter a number within the specified range.
13. You MUST allow spaces to be included in all string input.
14. For housing you are not asking the user for the data. The acronym MASH stands for the different types of housing. There are four choices (Mansion, Apartment, Shack or House). You will need to generate a number between 1 and 4. If it is a 1, you will print out that the user will live in a mansion. If it is a 2, you will print out that the user will live in an apartment……and so on.
    
15. For all the other “categories” you have three choices, not four. So you will need to generate a number between 1 and 3. If it is a 1, you print out the first one, 2 the second one, and 3 the third one. For example, for spouse – generate a number between 1 and 3. If it is a 1, then print out the first person that the user said they like. If it is a 2, then print out the second person that the user said they like. If it is a 3, then print out the third person that the user dislikes.    Before printing out the spouse, you should say “You will be happily married to “ and then print out the name.
    
16. For the answers you should say something like:
    • You will live in ….
    • You will be happily married to …
    • You and your spouse will have ….. children.
    • You will live in …..      (name city, state here)
    • You will work at ……. (place) as a ……… (job title) making $ ……… (salary) a year.
    • You will drive a ……