4 – The following 32-bit binary word written in hexadecimal format represents a single RISC-V assembly instruction. What is the RISC-V instruction format and specific assembly language instruction?

0x00156A33

Let (G,+) be an abelian group and U a subgroup of G. Prove that G is the direct product of U and V (where V a subgroup of G) if only if there is a homomorphism f : G → U with    f|U = IdU

Animal Rights Law and Politics: What might have allowed the Sierra Club to have standing in Sierra Club v. Morton?

Case: Sierra Club v. Morton, 405 U.S. 727 (1972)

For this problem you must write the functions in a recursive manner (i.e. the function must call itself) – it is not acceptable to submit an iterative solution to these problems.

A. Complete the recursive function gcd(m, n) that calculate the greatest common denominator of two numbers with the following rules:

# If m = n, it returns n

# If m < n, it returns gcd(m, n-m)

# If m > n, it returns gcd(m-n, n) #

def gcd(m,n):
    return None  # Replace this with your implementation

B. Complete the following function that uses recursion to find and return the max (largest) value in the list u.

# find_max([1, 7, 4, 5] returns 7
# find_ max ([1, 7, 4, 5, 9, 2] returns 9
#
def find_max(u):

    return None  # Replace this with your implementation

C. Complete the following recursive function that returns the zip of two lists u and v of the same length. Zipping the lists should place the first element from each into a new array, followed by the second elements, and so on (see example output).

# zip([1, 2, 3], [4, 5, 6]) returns [1, 4, 2, 5, 3, 6]
#
def zip(u, v):

    return None  # Replace this with your implementation

D. Complete the following recursive function that removes all occurrences of the number x from the list nums.

# remove_number(5, [1, 2, 3, 4, 5, 6, 5, 2, 1]) returns [1, 2, 3, 4, 6, 2, 1]
#
def remove_number(x, nums):

    return None  # Replace this with your implementation

E. Write a recursive function removeLetter(string, letter) that takes a string and a letter as input, and recursively removes all occurrences of that letter from the string. The function is case sensitive.

Some example test cases are below:

>>> removeLetter("test string", "t")
es sring

>>> removeLetter("mississipi", "i")
mssssp

>>> removeLetter("To be or not to be is a question.", "t")

To be or no o be is a quesion.

In PyCharm

A group of 70 college students from a certain liberal arts college were randomly sampled and asked about the number of alcoholic drinks they have in a typical week. The purpose of this study was to compare the drinking habits of the students at the college to the drinking habits of college students in general. In particular, the dean of students, who initiated this study, would like to check whether the mean number of alcoholic drinks that students at his college in a typical week differs from the mean of U.S. college students in general, which is estimated to be 4.73.

The group of 70 students in the study reported an average of 4.45 drinks per with a standard deviation of 3.92 drinks.

Find the p-value for the hypothesis test.

The p-value should be rounded to 4-decimal places.

It is known that 20% of the computer engineering students use the library during the e"xam week. A random sample of 25 students (from computer engineering) is selected. Assume that studies at library are made independently, and let x represent number of students who studied in the library during the e"xam week.Important note: Show your work. Provide the expressions and your approach on answering the questions. Results without supporting work will not be credited.(a) What is the probability that exactly 4 students studied in the library? ______________(b) What is the probability that no more than 5 students studied in the library?______________(c) What is the probability that at least 3 students studied in the library?______________(d) What is the probability that between 2 and 7 students, inclusively, studied in the library?

The registrar needs to assign section numbers to a group of 10 sophomores, 20 juniors, and 30 seniors. There are three sections with available seats, say section A, B, C. Each section has room for up to 60 students. We will assume that the registrar randomly and independently assigns the students to the sections.

a) What is the probability that all ten sophomores will be assigned to the same section?

b) What is the probability that exactly 15 students will be assigned to section B?

c) Given that exactly 15 students are assigned to section B, what is the probability that these 15 students are all juniors?

d) Given that exactly 15 students are assigned to section B, what is the probability that these 15 students consist of 5 sophomores, 5 juniors, and 5 seniors?

It is estimated that 30% of university students are taking five or more classes this semester (let us call them full-load students). Among the full-load students, 20% are working part-time. On the other hand, among the non-full-load students, 60% are working part-time.

a) When a university student is randomly selected, what is the probability that one is a full-load student and working part-time? [2]

Define event A as: university students taking five or more classes (or being full-load students).

Define event B as: university students working part-time.

b) When a university student is randomly selected, what is the probability that one is working part-time but not taking full-load? [2]

At a Midwestern business school, historical data indicates that 70% of admitted MBA students ultimately join the business school’s MBA program. In a certain year, the MBA program at the University admitted 200 students.

a. Find the probability that at least 150 students ultimately join the MBA program.

b. Find the probability that no less than 135 and no more than 160 students finally join the MBA program.

c. How many students should the MBA program expect to join the program?

d. What is the standard deviation of the number of students who will join the MBA program? e. Let X be the number of students out of 200 who will join the program. Would the empirical rule apply to the probability distribution of X in this case?