studentworld

For the following ratings given to items by the users, perform the tasks below:
 
           Item 1 Item 2 Item 3 Item 4 Item 5 
User 1   ?           3         ?         3          4 
User 2   4           ?         ?         2          ? 
User 3   ?           ?         3         ?          ? 
User 4   3          ?         4        ?           3 
User 5   4          3         ?        4          4

Note: '?' means user has not rated that item.

For all of these tasks, use Pearson Correlation Coefficient as similarity measure and mean-centered prediction function.
Show your working clearly for :
a) Find nearest neighbors of user 1 for k=2.
b) Apply user-based Collaborative Filtering to predict R(U1, I3) (read: rating for user 1 and item 3).
c) Apply item-based Collaborative Filtering to predict R(U3, I2) and R(U4, I4). (HINT: USE CASCADING)
d) Say we had an option of using mode-centered prediction function instead of using mean. What do you think would be the effect of using mode as a baseline instead of average? Can using mode ever improve the performance of recommender system?

Changing Application Problems into Equations:

1. Alberto’s salary was $2000 greater than 4 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y.

Select a variable to represent one quantity and state what the variable represents. Express the second quantity in terms of the variable selected.

2. On a 540-mile trip, Cheng and Elsie shared the driving.

Write the indicated expression.

3. At a 25% off everything sale, Bill purchased a new shirt. If c represents the original cost, write an expression for the sale price of the shirt.

Write the indicated expression. You will need to select the variable to use.

4.For two consecutive odd integers, the sum of 3 times the smaller and the larger is 14.

Solving Application Problems: Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.

5. One number is 5 less than 3 times a second number. Their sum is 43. Find the numbers.

6.According to Wikipedia, the best-selling album in 2005 was Mariah Carey’s The Emancipation of Mimi. The best-selling album in 2004 was the album Confession by Usher. Confession sold 0.94 million copies less than twice the amount The Emancipation of Mimi sold. The sum of these two albums was 13.97 million copies. Determine the sales of both albums.

7. Ruth is having hardwood floors installed in her living room. The cost for the material is $2840 plus an installation charge of $1.90 per square foot. If the total cost for the material plus installation is $5120, determine the area of her living room.

8. Sean is deciding whether to select a satellite receiver or cable for his television programming. The satellite receiver costs $298.90 and the monthly charge is $68.70. With cable, there is no initial cost to purchase equipment, but the monthly charge for comparable channels is $74.80. After how many months will the total cost of the two systems be equal?

Geometric Problems:

9. An equilateral triangle is a triangle that has three sides of the same length. The perimeter of an equilateral triangle is 48.6 centimeters. Use an equation to find the length of each side.
10. When two lines cross, the opposite angles are called vertical angles. Vertical angles have equal measures. Use an equation to determine the measure of the vertical angles if one equals 3x + 38 and the other is 5x + 20.

11. The perimeter of a rectangle is 120 feet. Use an equation to find the length and width of the rectangle if the length is twice the width. Use P = 2W + 2L.

12. A bookcase is to have four shelves, including the top. The height of the bookcase is to be 2 feet more than the width and only 20 feet of lumber is available. Use an equation to determine the width and height of the bookcase.

Money and Mixture Problems:

13.Jerry invested $7000, part at 8% simple interest and the rest at 5% simple interest for a period of 1 year. If he received a total annual interest of $476 from both investments, how much did he invest at each rate?

14. Violet knows that her subscription rate for the basic tier of cable television increased from $18.20 to $19.50 at some point during the calendar year. She paid a total of $230.10 for the year to the cable company. Determine the month of the rate increase.

15. Suppose Wal-Mart stock is selling at $59 a share and Mattel stock is selling at $28 a share. Amy has a maximum of $6000 to invest. She wishes to purchase four times as many shares of Wal-Mart as of Mattel. Only whole shares of stock can be purchased.

a. How many shares of each will she purchase?

b. How much money will be left over?

16. Nick has two cans of white paint, one with a 2% yellow pigment and the other with a 5% yellow pigment. He wants to mix the two paints to get paint with a 4% yellow pigment. How much of the 5% yellow pigment paint should be mixed with 0.4 gallon of the 2% yellow pigment paint to get the desired paint?