(c) [2] For which of the following functions are the level curves linear?  

(I) f(x, y) = tan(x + y)

(II) g(x, y) = e^y/x (e to the power of y over x)

(III) h(x, y) = ln(xy)

(A) none (B) I only (E) I and II (F) I and III

(C) II only (G) II and III

(D) III only (H) all three

A partial table of values for a function f(x,y) is given below. Which of the following are positive?

(I) fy(4, 1)

(II) fx(4, 1) (III) fxx(4, 1)

Code using JAVA:

must include a "Main Method" to run on "intelliJ".

Hint: Use a hash table. You can use either Java HashTable or Java HashMap. Refer to Java API for the subtle differences between HashTable and HashMap.

Determine if a 9 x 9 Sudoku board is valid. Only the filled cells need to be validated according to the following rules:

1. Each row must contain the digits 1-9 without repetition.
2. Each column must contain the digits 1-9 without repetition.
3. Each of the nine 3 x 3 sub-boxes of the grid must contain the digits 1-9 without repetition.

class Solution {
public boolean isValidSudoku(char[][] board) {
  
}
}

Note:

• A Sudoku board (partially filled) could be valid but is not necessarily solvable.
• Only the filled cells need to be validated according to the mentioned rules.

Example 1:

Input: board = 
[["5","3",".",".","7",".",".",".","."]
,["6",".",".","1","9","5",".",".","."]
,[".","9","8",".",".",".",".","6","."]
,["8",".",".",".","6",".",".",".","3"]
,["4",".",".","8",".","3",".",".","1"]
,["7",".",".",".","2",".",".",".","6"]
,[".","6",".",".",".",".","2","8","."]
,[".",".",".","4","1","9",".",".","5"]
,[".",".",".",".","8",".",".","7","9"]]
Output: true

Example 2:

Input: board = 
[["8","3",".",".","7",".",".",".","."]
,["6",".",".","1","9","5",".",".","."]
,[".","9","8",".",".",".",".","6","."]
,["8",".",".",".","6",".",".",".","3"]
,["4",".",".","8",".","3",".",".","1"]
,["7",".",".",".","2",".",".",".","6"]
,[".","6",".",".",".",".","2","8","."]
,[".",".",".","4","1","9",".",".","5"]
,[".",".",".",".","8",".",".","7","9"]]
Output: false
Explanation: Same as Example 1, except with the 5 in the top left corner being modified to 8. Since there are two 8's in the top left 3x3 sub-box, it is invalid.

Constraints:

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit or '.'.

Find solutions to the following ODEs:

• y¨ − y˙ − 2y = t, y(0) = 0, y˙(0) = 1

• y¨ − 2 ˙y + y = 4 sin(t), y(0) = 1, y˙(0) = 0

• y¨ = t 2 + t + 1 (find general solution only)

• y¨ + 4y = t − 2 sin(2t), y(π) = 0, y˙(π) = 1

Consider the two dependent discrete random variables X and Y . The
variable X takes values in {−1, 1} while Y takes values in {1, 2, 3}. We observe that

P(Y =1|X=−1)=1/6
P(Y =2|X=−1)=1/2
P(Y =1|X=1)=1/2
P(Y =2|X=1)=1/4
P(X = 1) = 2/ 5
(a) Find the marginal probability mass function (pmf) of Y .
(b) Sketch the cumulative distribution function (cdf) of Y .
(c) Compute the expected value E(Y ) of Y .
(d) Compute the conditional expectation E[Y |X = 1].

The shape of indifference curves tells you something about the relationship between consumption goods.

A. Define (in your own words) the meaning of MRS_SB where S indicates steaks and B indicates beer. What does the MRS have to do with the construction of indifference curves? (4)

B. Suppose an individual’s marginal rate of substitution of steak for beer (MRS_SB) is 2:1. Suppose also that the price of steak is $ 4 and the price of beer is $ 1. In order to increase the individual’s level of utility, should he/she buy more steak, buy more beer, or purchase the same consumption bundle? Explain. (4)

C         If we have the utility function U (X₁,X₂) = X₁^1/3 X₂^2/3 , what is the marginal rate of substitution between X₁ and X₂ if X₁ = 1 and X₂ = 1? What is MRS if X₁ = 2 and X₂ = 1? Would the indifference curves generated from this utility function exhibit diminishing marginal rates of substitution as X₁ increases? (4

1. Solve the initial value problem below using the method of Laplace transforms.

56w′′−4w′+4w=16t+56​, w(−3)=2​, w'(-3)=2

2. Solve for​ Y(s), the Laplace transform of the solution​ y(t) to the initial value problem below.

ty′′−6y′+9y=cos5t−sin5t​, y(0)=4​, y'(0)=4

Write a Java program to 1. read in the size of a square boolean matrix A 2. read in the 0-1 matrix elements 3. read in a positive integer n 4. display A^n Multiplying that matrix to the nth power. Like A^2 = matrix A * matrix A. Elements ONLY can be 0 or 1.

Show your work!

2.   We did a poll of students in a BUS 232 class. The students were asked to name their favorite color. The result is shown in Table 2.

Table 2

     Favorite Color

Number of E whoare∈favorof F

Hint: Conditional Probability Rule: P (F | E) =

Totalnumberof E

Suppose that one student is selected at random from the group. (4 points) What is the probability as a fraction in the simplest form that:

1. it will be a male? P (male) =
2. it will be a female who likes red? Hint: This is NOT a conditional probability.
   16. (a female who likes red) =
3. it will be someone who likes blue given that we know that it is a male?
   16. (someone who likes blue | male) =
4. it will be someone who likes red given that we know that it is a female?

.

16. (someone who likes red | female) =

3.   Suppose you roll a fair die three times. What would be the probability of getting ONE three times? Hint: Use the law of large number, which is the theoretical probability. Show the answers as a fraction in the simplest form. (2 point)

P (1 for the first roll, 1 for the second roll and 1 for the third roll roll) =

(25 pts) A coffee enthusiast would like to test whether the coffee preference of young consumers living in Brooklyn is affected by the perceived brand. He recruits 18 volunteers and divides them into 3 groups: one group gets coffee in a starbucks cup, another group gets coffee in a McDonalds cup, and a third group gets coffee in a cup labeled “new Fair-Trade Organic no GMO Rainforest” coffee. The catch is that everyone receives the same brewed coffee. The participants are asked to drink as much coffee as they can tolerate out of an 8oz serving. Below is the number of ounces consumed by each of the 18 people. Test the hypothesis that perceived brand affects preference for coffee (use alpha = .05).

1. (2 pts) Find the critical value:
2. (4 pts) Calculate the obtained statistic (DO THIS BY HAND HERE):
3. (2 pts) Make a decision
4. (2 pts) What does your decision mean?
5. (3 pts) Perform this test in SPSS and paste the proper output here:
6. (3 pts) Explain in words which part of the output specifically indicates which decision to make about the null hypothesis.
7. (4 pts) Is a post-hoc test appropriate here? Why or why not? If it is, run the post-hoc and explain the results: