Solve each problem using a math drawing. Write a corresponding math expression.

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Dividing Fractions

1. Use fraction bars to divide fractions. Draw models of your work.

a) 3 1
4 2



b) 3 1
4 3



Solve each problem using a math drawing. Write a corresponding math expression.
2. You have 8 cups of popcorn. Each serving of popcorn takes 3
4 of a cup of popcorn.
How many servings can you make?


3. You have 4 cups of popcorn. Each serving of popcorn takes 5
6 of a cup of popcorn.
How many servings can you make?

4. A recipe calls for ¾ cup of sugar. How many recipes can you make with 31
2 cups of
sugar?
31
2÷3
4=


5. A recipe calls for 1
3 cup of sugar. How many recipes can you make with 11
2 cups of
sugar?
11
2÷1
3=


6. A recipe calls for ¾ cup of sugar. How many recipes can you make with 3 cups of
sugar? 33 4 =


7. A recipe calls for ¾ cup of sugar. How many recipes can you make with 31
2 cups of
sugar?

31
2÷3
4=

State an example of a variable that follows a normal distribution. State one way knowing this is useful in your professional or personal life. Briefly elaborate on your example.

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Normal distribution

https://mediaplayer.pearsoncmg.com/assets/_jGvVe5Jbkm44I2D0TWEMnsz6A6Y7fin
Please read the following carefully. I need a discussion post on the following topic with an example mathematical problem.

This video explains what the normal distribution is and gives examples of normal distributions in the natural and social world. The distribution of the number of heads thrown on 20 coins, the weight of ants, and the age of marathon runners are all approximately normal distributions. Thus, the normal distribution is what often happens when we chart a large number of random events.
Option 2

State an example of a variable that follows a normal distribution.
State one way knowing this is useful in your professional or personal life.
Briefly elaborate on your example.

 Why do most of the sample means differ somewhat from the population mean?  What is this difference called?  What is the mean of the sample means?  What is the standard deviation of the sample means called?  What is the formula for this standard deviation?

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  1.  It is very important to be able to find probabilities for a given z score.  Using software or a Standard Normal Distribution table, determine the following probability for the area (15 points)

    a.    between z = -0.52 and z = 2.33
    b.    z > 1.65
    c.    z < 1.85
    d.    z < 0
    e.    between z = 0 and z = 1

    2.    Answer the following: (15 points)

    a.    If samples of a specific size are selected from a population and the means are computed, what is the distribution of the means called?
    b.    Why do most of the sample means differ somewhat from the population mean?  What is this difference called?
    c.    What is the mean of the sample means?
    d.    What is the standard deviation of the sample means called?  What is the formula for this standard deviation?
    e.    What does the central limit theorem say about the shape of the distribution of sample means?

    3.    A pediatrician obtains the heights of her 200 three-year-old female patients.  The heights are normally distributed with a mean of 37.8 and a standard deviation of 3.14.  What percent of the three-year-old females have a height less than 34 inches? (15 points)

    4.    The local news reported that 6% of U.S. drivers text on their cell phones while driving.  If 300 drivers are selected at random, find the probability that exactly 25 say they text while driving.   Be sure and use the continuity correction for the normal approximation to the binomial distribution. (15 points)

    5.    Suppose you are asked to toss a coin 16 times and calculate the proportion of the tosses that were heads. (10 points)

    a.    What shape would you expect this histogram to be and why?
    b.    Where you do expect the histogram to be centered?
    c.    How much variability would you expect among these proportions?
    d.    Explain why a Normal model should not be used here.

    6.    The average cholesterol content of a certain brand of eggs is 210 milligrams, and the standard deviation is 14 milligrams.  Assume the variable is normally distributed.  If two eggs are selected, find the probability that the cholesterol content will be greater than 230 milligrams. (10 points)

 What is the probability that all 12 will be available to serve on the jury?  What is the probability that 6 or more will not be available to serve on the jury?  Find the expected number of those available to serve on the jury.  What is the standard deviation?

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The following assignment will allow you to master the concepts you have learned on discrete probability distributions.

1.  Answer the following questions based on rolling a single six-sided die. (2 points for each part)

a)    If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes?  Are the outcomes equally likely?
b)    Assign probabilities to the outcomes of the sample space of part (a).  Do the probabilities add up to 1?  Should they add up to 1?  Explain.
c)    What is the probability of getting a number less than 4 on a single throw?
d)    What is the probability of getting a 3 or 4 on a single throw?

2.  You draw two cards while playing Blackjack from a standard deck of 52 cards without replacing the first one before drawing the second. (2 points for each part)

a)    Are the outcomes on the two cards independent?  Why?
b)    Find P(ace on first card and king on second)
c)    Find P(king on first card and ace on second)
d)    Find the probability of drawing an ace and a king in either order

3.    You have three pancakes.  One is golden on both sides, one is brown on both sides and one is golden on one side and brown on the other.  You choose one pancake at random and see that one side is brown. Find the probability that the other side of the pancake is brown. (4 points)

4.    You wish to play a three-number lottery with your favorite data 8, 2 and 5.  After a number is drawn, the number is placed back in the container for the next draw.  What is the probability that the three winning numbers will be 8, 2 and 5?  Are the numbers independent of each other? How would the probability change if no repetition is allowed? (4 points)

5.    Have you ever tried to get out of jury duty?  About 25% of those called will find an excuse to avoid it.  If 12 people are called for jury duty, (2 points for each part)

a)    What is the probability that all 12 will be available to serve on the jury
b)    What is the probability that 6 or more will not be available to serve on the jury
c)    Find the expected number of those available to serve on the jury.  What is the standard deviation

6.    Create a probability distribution for a coin flipping game.  That is, toss a coin at least 25 times and keep up with the number of heads and the number of tails.  (8 points for each part)

a.    Compile your data into a probability distribution.  Be sure to show that your distribution meets the properties for a probability distribution.
b.    Use a bar graph to graph the distribution.
c.    Explain the random variables for your data.
d.    Did the values come out as you would expect?  Explain what you would expect to happen with the outcome of the game versus the actual expected value of your distribution.

7.    Use your example from question 6 to set up a binomial distribution. Find the probability based on your data that if the coin is flipped 25 times, what is the probability that a heads would appear 10 times or less.  (10 points)

8.    The following information has been given that shows the highest level of education received by employees of a company. (2 points for each part)

# Employees
Ph.D. 8
Master’s 21
Bachelor’s 33
Associate 18
High School Diploma 7
Other 2

Answer the following questions based on the data in the table:
a.    Find the probability an employee chosen at random has a Ph.D.
b.    Find the probability an employee chosen at random has an Associate degree.
c.    Find the probability an employee chosen at random does not have a Ph.D.
d.    Are the events independent?  Explain.

 

Explain why you want to study Financial Mathematics at graduate level. Why you want to study Financial Mathematics at UCL. What particularly attracts you to this programme?

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Financial Mathematics

 

Course link:

Personal Statement requirement of UCL:

why you want to study Financial Mathematics at graduate level

why you want to study Financial Mathematics at UCL

what particularly attracts you to this programme

how your academic background meets the demands of a challenging programme

where you would like to go professionally with your degree

Write the PS according to the above requirement. State a clear career plan for the future after completing this programme.

Identify the set ̃A ∩ ̃B using roster notation. Construct a truth table and identify the truth value of the statement

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Exam 1: Written Name:Math110 Spring 2021

1.(10 points.) Consider the following sets
A = {x|x ∈N and 25 ≤x ≤75 and x is an even number}
B = {x|x ∈N and x ≤50 and x is an odd number}
U = {x|x ∈N and x ≤100}
where U is the universal set under consideration. Identify the set ̃A ∩ ̃B using roster
notation.
2.(10 points.) Let P and Q be two true statements. Construct a truth table and
identify the truth value of the statement
(P ∧ ̃Q) ∨( ̃P ∧Q)
Complete all of your work on a separate sheet of paper (no need to print this page) and
email a photograph of the page to rrtromacek@dmacc.edu with the subject ”Math 110
Exam 1”.

How long does it take approximately (in years) for Supercomputer Fugaku to complete a LU factorization for a square matrix with n = 108? How about n = 109, n = 1010?

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Finish 3 math question

MATH 3510 FALL 2021 HOMEWORK 4
(DUE IN CLASS OCTOBER 6)
Instructions: For proof-based questions, write your answers on your own papers. For pro-gramming questions, submit your codes using MATLAB Grader. Hand in your homework (written part) on Wednesday, October 6 in class.

1. Write a MATLAB function to perform the LU factorization (without pivoting). Your input should be a nonsingular n×n matrix A. Your output should be a lower triangular matrix L and an upper triangular matrix U such that A = LU. See detailed description in MATLAB Grader.

2. We discussed in class that Gaussian Elimination/LU factorization is an O(n3) algorithm. This means that for a n ×n matrix, LU factorization needs approximately n3 flops. The top supercomputer today is Supercomputer Fugaku in Japan. This machine can execute, theoretically, 4.42 ×1017 flops per second.

a. How long does it take approximately (in years) for Supercomputer Fugaku to complete a LU factorization for a square matrix with n = 108? How about n = 109, n = 1010?

b. Suppose we have an O(n) algorithm to solve the linear system Ax = b, how long does it take for Supercomputer Fugaku to solve the system with size n = 108? How about n = 109, n = 1010? Remark 1. From the results you should see why we need fast algorithms.

3. (Pivoting) In class, we find the LUP factorization of the following matrix

In other words, we have PA = LU.
Use this LUP factorization to solve the system Ax = b by hand where b =

2 (DUE IN CLASS OCTOBER 6)
Remark 2. You need to use forward substitution and back substitution.

4. (Vector Norms)
a. Let x =

Compute the norms ‖x‖1 and ‖x‖2.

b. Define a vector ∞-norm ‖x‖∞ for any x ∈Rnas follows,‖x‖∞ = maxk|xk|.
Prove the following properties for ‖·‖∞:
1. ‖x‖∞ ≥0. ‖x‖∞ = 0 if and only if x = 0.
2. ‖αx‖∞ = |α|‖x‖∞, where α ∈R.
3. ‖x + y‖∞ ≤‖x‖∞ + ‖y‖∞.

Find an article that mentions a new drug that promises an improved survival rate. Identify whether this rate represents the mean or the median of the data set.

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Discussion Week 3

This video focuses on when to use a mean and when to use a median. When data all have similar values, such as housing prices of similar-sized houses on the same block, then the mean is an appropriate measure, but if the value of one residence is 50 times as high as the others, then the median gives a better description of a typical value than the mean.

https://mediaplayer.pearsoncmg.com/assets/cWSUSyFyf2fjOGj5lEJQ_w73ZBZdo4JW

However, you want to get away from the idea that the data, and only the data, drives the choice of descriptive statistics. The example is given that, if you wanted to buy all the houses in Brooklyn, if you took the median, and multiplied by the number of houses, you wouldn’t have enough cash. So, the median is a useful descriptive statistic, but the mean is essential for planning and making decisions.

Option 1: Find an article that mentions a new drug that promises an improved survival rate.

Identify whether this rate represents the mean or the median of the data set.
Assess whether that is ideally what you’d want to know for this data.
Provide a specific reason for your answer.

Provide one specific, real-life example of how either financial accounting helps external stakeholders make informed decisions or how managerial accounting helps managers to improve operational and financial performance.

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Compare and contrast financial and managerial accounting

Instructions
Write a 750 – 1250 word paper on the following topic:

Compare and contrast financial and managerial accounting. Provide one specific, real-life example of how either financial accounting helps external stakeholders make informed decisions or how managerial accounting helps managers to improve operational and financial performance.

Your paper must be formatted according to APA 6th edition guidelines, and you need to use at least three external references. Save your file as “LastnameFirstinitial-ACCT105-8.

Provide one specific, real-life example of how either financial accounting helps external stakeholders make informed decisions or how managerial accounting helps managers to improve operational and financial performance.

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Compare and contrast financial and managerial accounting

Compare and contrast financial and managerial accounting. Provide one specific, real-life example of how either financial accounting helps external stakeholders make informed decisions or how managerial accounting helps managers to improve operational and financial performance.

Your paper must be formatted according to APA 6th edition guidelines, and you need to use at least three external references. Save your file as “LastnameFirstinitial-ACCT105-8.”

Submit your work by midnight ET on Day 7 (Sunday).

Note that your attached paper will automatically be submitted to Turnitin, and an Originality Report should be sent back to the classroom within around 15 minutes. The Originality report does not actually recommend changes. It does point out where you may need to add a citation or quotation marks (if not already cited). Once you use it a few times, you will appreciate this tool, as it will assist you in improving quality and content, as well as avoid plagiarism. Your goal is to keep direct quotations to a minimum and to make sure that you do not just cut and paste material. Ensure that all your references are cited. A report with a similarity index less than 25% is acceptable for undergraduate level work.

Your paper will be evaluated according to the Writing Assignment Grading shown below. To maximize your grade, be sure to use the proper organization (intro, body, conclusion) and follow APA style. Your paper should have a title page and reference page, but you do not need an abstract for this assignment. See the PowerPoint presentation attached for APA assistance.