1- Calculate the percent change in the total momentum of the system for Part 1

2- Calculate the percent change in the total kinetic energy of the system for Part 1

3- Calculate the percent change in the total momentum of the system for Part 2

4- Calculate the percent change in the total kinetic energy of the system for Part 2

5- Calculate the absolute change (| P_f – P₀ |) in the total momentum of the system for Part 3

6- Calculate the absolute change (| KE_f – KE₀ |) in the total kinetic energy of the system for Part 3

Part 1: Elastic Collision

Part 2: Inelastic Collision

Part 3: Explosion

"•“"Suppose ℱ, ?1, and ?2 are nonempty families of sets. Prove that if ℱ ⊆ ?1 ∩ ?2, then ∩?1 ∪ ∩?2 ⊆ ∩ℱ.“"

Please explain what the question is asking for and break down the solution for me step by step with explanations please!

1. Consider the following function: (?) = ?(?³ + 1), ? = 0, 1, 2, 3
2. 1. What is the value of the constant ? so that (?) is a pmf?
   2. Plug-in the value of ? in the expression of (?) and show the pmf in a table. Draw a probability histogram of the pmf.
   3. Find the cdf (?) and write it explicitly defined over the entire real number line. Draw the cdf (?).
   4. Calculate the probabilities: (i). (0 < ? ≤ 2),      (ii) ?(? ≠ 1).
   5. Find the expected value of ?.
   6. Find the expected value of 3?³ − 2? + 1.
   7. Find the variance of ?.

1.Construct the confidence interval for μ 1 − μ 2 for the level of confidence and the data from independent samples given. 95% confidence: n 1 = 110, x - 1 = 77, s 1 = 15 n 2 = 85, x - 2 = 79, s 2 = 21 90% confidence: n 1 = 65, x - 1 = − 83, s 1 = 12 n 2 = 65, x - 2 = − 74, s 2 = 8

2. Construct the confidence interval for μ 1 − μ 2 for the level of confidence and the data from independent samples given. 99.9% confidence: n 1 = 275, x - 1 = 70.2, s 1 = 1.5 n 2 = 325, x - 2 = 63.4, s 2 = 1.1 90% confidence: n 1 = 120, x - 1 = 35.5, s 1 = 0.75 n 2 = 146, x - 2 = 29.6, s 2 = 0.80

1. z = -1 is what percentile?

2.Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.
A single thermometer is randomly selected and tested. Let ZZ represent the reading of this thermometer at freezing. What reading separates the highest 11.18% from the rest? That is, if P(z>c)=0.1118P(z>c)=0.1118, find c.

3.Assume that scores on the verbal portion of the GRE (Graduate Record Exam) follow the normal distribution with mean score 151 and standard deviation 7 points, while the quantitative portion of the exam has scores following the normal distribution with mean 153 and standard deviation 7.67. Use this information to answer the following:
a) Find the score of a student who scored in the 80th percentile on the Quantitative Reasoning section of the exam.
(please round to two decimal places)

b)Find the score of a student who scored worse than 70% of the test takers in the Verbal Reasoning section of the exam.
(please round to two decimal places)

4.The combined SAT scores for the students at a local high school are normally distributed with a mean of 1494 and a standard deviation of 299. The local college includes a minimum score of 1374 in its admission requirements.

What percentage of students from this school earn scores that satisfy the admission requirement?
P(X > 1374) = ? %

5.In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.6 inches, and standard deviation of 4.8 inches.

A) What is the probability that a randomly chosen child has a height of less than 65.2 inches?

Answer= (Round your answer to 3 decimal places.)

B) What is the probability that a randomly chosen child has a height of more than 64.8 inches?

Answer= (Round your answer to 3 decimal places.)

given:

(1)The current price of a stock is 30.

(2)A dividend of 1 will be paid 6 months from now.

(3)The one-year forward price is 30.9.

Calculate the continuously compounded risk-free annual rate of interest.

Invertebrates :

1. There is 1 phylum that does not have tissue layers, and 2 phyla that are diploblastic. Please list the phyla and their common names in a table form

1-According to M and M proposition 1 and 2, discuss the factors that will influence the capital structure of a public listed company.

- Reduce conflict between manager and shareholder, so can reduce agency cost.

- Asynmetric information between issuer and merchant bank

-M and M admit that with corporate tax, Tax saving due of increase debt.

- Finance Distress cost, occus when promises are broken as result of having too much debt.

- Transaction cost in arbitrage proses.

2- Why timing, current gearing ratio and dilution of share are important when we do financing. (300words)

Python

#For question 1 and 2 you may not use ''' '''

Question 1 Print the messages below without using variables.

Output must be 2 lines identical to below:

What is the snake's favorite language?

"I love Python", said the snake.

Question 2 Write a python statements to match the 5 lines of output below.

Use a single print statement to produce the list of 4 languages

The 3 most popular programming languages of 2020 are:

1.         Python

2.         Javascript

3.         Java

4.         C#

-Source: https://www.northeastern.edu/graduate/blog/most-popular-programming-languages/

Question 3 (Multiple Choice)

lstrip and rstrip are examples of Python

(a)complex data types

(b)methods

(c)structures

(d)string variables

Question 4 (Multiple Choice)

What is true about Python variables?

(a)They are labels that can be assigned to values

(b)They reference a certain value

(c)A variable name cannot start with a number

(d)All of the above

Refer to a duopoly market in which the inverse demand function is given by P = 96 − Q. Firm 1's cost function is c(q₁) = 6q₁ + 300, and firm 2's cost function is c(q₂) = 6q₂ + 600 (such that each firm has MC = 6).

Q1: The outputs of the two firms in Cournot-Nash equilibrium will be:

1) q₁ = 45 and q₂ = 0.

2) q₁ = 30 and q₂ = 30.

3) q₁ = 45 and q₂ = 22.5.

4) q₁ = 28 and q₂ = 28.

5) None of the other answers is correct.

Q2: The profits of the two firms in Cournot-Nash equilibrium will be:

1) π₁ = 600 and π₂ = 300.

2) None of the other answers is correct.

3) π₁ = 300 and π₂ = 600.

4) π₁ = 900 and π₂ = 900.

5) π₁ = 2,025 and π₂ = 0.

Q3: The outputs of the two firms in Stackelberg equilibrium, with firm 2 as the leader, will be:

1) q₁ = 45 and q₂ = 22.5.

2) q₁ = 0 and q₂ = 45.

3) q₁ = 22.5 and q₂ = 45.

4) q₁ = 45 and q₂ = 0.

5) None of the other answers is correct.