Suppose Sam bought 1 ticket of CA SupperLotto. The details of how to play and how to win is listed in the two tables below.

Let’s use X to denote the net gain from 1 ticket.

Net gain is defined by Net Gain = Prize (if any) – Cost

Find the expected value of X.

How to Play

Pick 5 different numbers between 1 and 47

Pick 1 Mega numbers between 1 and 27

Cost per ticket $1

Please show the steps

1) Radio waves travel at the speed of light, 300,000 km/s. The wavelength of a radio wave received at 100 megahertz is            1) _______

A) 3.0 m.

B) 300 m.

C) 0.3 m.

D) 30 m.

E) none of these

22) Two charged particles repel each other with a force F. If the charge of one of the particles is doubled and the distance between them is also doubled, then the force will be    22) ______

A) F/4.

B) 2 F.

C) F/2.

D) F.

E) none of these

23) Two charged particles attract each other with a force F. If the charges of both particles are doubled, and the distance between them also doubled, then the force of attraction will be            23) ______

A) 2 F.

B) F/4.

C) F.

D) F/2.

E) none of these

1. Assume that 7% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places: a. There are some lefties ( ≥ 1) among the 5 people. b. There are exactly 3 lefties in the group. c. There are at least 4 lefties in the group. d. There are no more than 2 lefties in the group. e. How many lefties do you expect? f. With what standard deviation?

2. According to government data, 35% of employed women have never been married. Rounding to 4 decimal places, if 15 employed women are randomly selected:

a. What is the probability that exactly 2 of them have never been married?

b. That at most 2 of them have never been married?

c. That at least 13 of them have been married?

The following data give the number of hours 5 students spent studying and their corresponding grades on their midterm exams.

Step 1 of 5: Calculate the sum of squared errors (SSE). Use the values b0=53.9167 and b1=9.5833 for the calculations. Round your answer to three decimal places.

Step 2 of 5: Calculate the estimated variance of errors, . Round your answer to three decimal places.

Step 3 of 5: Calculate the estimated variance of slope, . Round your answer to three decimal places.

Step 4 of 5: Construct the 80% confidence interval for the slope. Round your answers to three decimal places.

Step 5 of 5: Construct the 90%confidence interval for the slope. Round your answers to three decimal places.

Partial Differential Equations

(a) Find the general solution to the given partial differential equation and (b) use it to find the solution satisfying the given initial data.

Exercise 1. 2∂u ∂x − ∂u ∂y = (x + y)u

u(x, x) = e −x 2

Exercise 2. ∂u ∂x = −(2x + y) ∂u ∂y

u(0, y) = 1 + y 2

Exercise 3. y ∂u ∂x + x ∂u ∂y = 0

u(x, 0) = x 4

Exercise 4. ∂u ∂x + 2y ∂u ∂y = e −x − u

u(0, y) = arctan y

Exercise 5. ∂u ∂x+v ∂u ∂y = −ru

(here r and v 6= 0 are constants) u(x, 0) = sin x x

A 10-slit aperture, with slit spacing five times the slit width of 10^-4 cm, is used to produce a Fraunhofer diffraction pattern with light of wavelength

435.8 nm. Determine the light intensity of the principal interference maxima of orders 1, 2, 3, 4 and 5 relative to the central fringe of zeroth order.

Write an ESSAY on what you understand about:

1. Anti- Ice and De-ice

2. Type of Ice

3. Type of ice accretion detectors

4. Areas need for protections

5. 4 principle of Anti-ice

6. Rain protection.

MAKE YOUR OWN WORDINGS. Same content 60%

Suppose you are provided with an array of integer values. Write pseudocode for a program to determine how many unique values are in the array. Your solution should require time that is linearithmic in the size of the array.

(For example, if the array contains the values {1,3,4,1,2}, the answer is "4", because the array contains the values 1, 2, 3, and 4)

1.) In cell H9 create a VLOOKUP to indicate the description Expensive for pups priced $2,000 or more, Moderate for pups priced $1,000 or more but below $2,000, Good Dealfor pups priced $500 or more but less than $1,000 and Cheapfor all pups priced less than $500.  Begin the lookup table in cell E1.  Copy the VLOOKUP in cell H9 to cells H10:H202. 2.) In cell I9 create a Nested IF to duplicate the results of #1 above.  Copy the nested If in cell I9 to cells I10:I202. 3.) Sort the database by AKC Group and within AKC Group by Breed and within Breed by Color (all ascending order).  Create a Subtotal report showing the average price by AKC Group and the total number of pups available for each dog breed. Change to outline level 3.  Right-mouse click on the Sheet 1worksheet tab. Select “Move or Copy” and check mark “Create a copy” and click on (move to end).  Name the newly created worksheet tab, “Subtotal.”   Return to Sheet1and remove the subtotal report by clicking on the “Remove All” button in the Data/Subtotal menu. 4.) Use the “unique records only” feature of the Advanced Filter to indicate the unique varieties of dog colors and breeds.  Start the unique dog breeds in K1 and the unique dog colors in M1. Place the unique dog breed and dog color combinations starting in cell O1.  (You will have to do three separate Unique Advanced Filters.) 5.) Note that none of the filters in #4 require a criterion.  To demonstrate a Unique Filter witha Criteria output the unique breeds with a price of $2,500 or more.  Start your criteria in R1.  Start your output in R4. Output just the Breed names that meet the criteria.  (Check figure: 8) 6.) Insert a new worksheet.  On Sheet 3, create a one variable data table that indicates the total number of pups available for each breed and the average price for each breed.  (Copy/paste the Unique dog breeds extracted in #4.)  Place the northwest corner of the table in cell A5. Begin the required criteria range in cell A1.7.) Insert a new worksheet.  On Sheet 4, create a two variable data table that indicates the total number of pups available by dog breed and by dog color.  (Use the unique dog breeds & unique colors extracted in #4. Use the copy & paste special / transpose to copy vertical text as horizontal text.) Place the northwest corner of the table in cell A5.  Begin the required criteria range in cell A1. 8.) Turn off the display of zeroes in Sheet 4.  File ribbon / Excel Options/Advanced (scroll down to Display Options for this Worksheet: Sheet 4)  Remove the check mark in front of:   Show a zero in cells that have a zero value. 9.) Create a pivot table that indicates the total number of pups available by breed and the average price for each breed.  Place the northwest corner of the pivot table in cell E4 on Sheet 3. 10.) Create a pivot table that indicates the total number of pups available by dog breed and by dog color.  Place the pivot table as a new worksheet.  

1. You have developed a new assessment tool to assess the quality of life in elderly individuals.  The tool contains 7 items and each item is based on an ordinal scale of 1-4 (1: poor, 2: fair, 3: good, 4: excellent).  You have assessed 40 older adults using this new assessment tool and you would like to establish the reliability of this instrument.  The results generated by SPSS are as follows:

Reliability Statistics

Inter-Item Correlation Matrix

                                                               Item-Total Statistics

1. Interpret the Cronbach’s alpha value (0.688) in the “Reliability Statistics” table (1 mark).

2. In the “Item total statistics” table, interpret/explain the number 0.829 for item 1 (highlighted) and discuss its implications .

3. Name the study design (1 mark) and describe the experimental procedures and statistical analysis (1 mark) if you are to establish the concurrent validity of this new quality of life measure using the same sample of 40 older adults.