Problem A stone is thrown from the top of a building with an initial velocity of 24.3 m/s straight upward, at an initial height of 53.1 m above the ground. The stone just misses the edge of the roof on its way down, as shown in Figure 2.20.

(a) Determine the time needed for the stone to reach its maximum height.
(b) Determine the maximum height.
(c) Determine the time needed for the stone to return to the height from which it was thrown, and the velocity of the stone at that instant.
(d) Determine the time needed for the stone to reach the ground.
(e) Determine the velocity and position of the stone at t = 5.68 s.

from typing import List

def longest_chain(submatrix: List[int]) -> int:
"""
Given a list of integers, return the length of the longest chain of 1's
that start from the beginning.

You MUST use a while loop for this! We will check.

>>> longest_chain([1, 1, 0])
2
>>> longest_chain([0, 1, 1])
0
>>> longest_chain([1, 0, 1])
1
"""
i = 0
a = []
while i < len(submatrix) and submatrix[i] != 0:
a.append(submatrix[i])
i += 1
return sum(a)

def largest_rectangle_at_position(matrix: List[List[int]], x: int, y: int
) -> int:
"""
Returns the area of the largest rectangle whose top left corner is at
position , in .

You MUST make use of here as you loop through each row
of the matrix. Do not modify the input matrix.

>>> case1 = [[1, 0, 1, 0, 0],
... [1, 0, 1, 1, 1],
... [1, 1, 1, 1, 1],
... [1, 0, 0, 1, 0]]
>>> largest_rectangle_at_position(case1, 0, 0)
4
>>> largest_rectangle_at_position(case1, 2, 0)
5
>>> largest_rectangle_at_position(case1, 1, 2)
6
"""

pass

replace the word pass with a function body by implementing the 1st function. make sure nested loops can be a max of 3. try to keep it as short as possible and fulfill the docstring requirements

CIA Review, Inc., provides review courses twice each year for students studying to take the CIA exam. The cost of textbooks is included in the registration fee. Text material requires constant updating and is useful for only one course. To minimize printing costs and ensure availability of books on the first day of class, CIA Review has books printed and delivered to its offices two weeks in advance of the first class. To ensure that enough books are available, CIA Review normally orders 10 percent more than expected enrollment. Usually there is an oversupply and books are thrown away. However, demand occasionally exceeds expectations by more than 10 percent and there are too few books available for student use. CIA Review has been forced to turn away students because of a lack of textbooks. CIA Review expects to enroll approximately 200 students per course. The tuition fee is $900 per student. The cost of teachers is $18,000 per course, textbooks cost $55 each, and other operating expenses are estimated to be $32,000 per course. Assume all financial statements data are prepared in accordance with GAAP.

Required

1. a. Prepare an income statement, assuming that 200 students enroll in a course. Determine the cost of waste associated with unused books.

2. b-1. Prepare an income statement, assuming that 242 students attempt to enroll in the course, but 22 students are turned away because of too few textbooks.

3. b-2. Prepare an income statement, assuming that 242 students attempt to enroll in the course, with all being accepted.

4. b-3. Determine the amount of lost profit resulting from the inability to serve the 22 additional students.

5. c. Suppose that textbooks can be produced through a high-speed copying process that permits delivery just in time for class to start. The cost of books made using this process, however, is $60 each. Assume that all books must be made using the same production process. In other words, CIA Review cannot order some of the books using the regular copy process and the rest using the high-speed process. Prepare an income statement under the JIT system assuming that 200 students enroll in a course.

6. d-1. Assume the same facts as in requirement c with respect to a JIT system that enables immediate delivery of books at a cost of $60 each. Prepare an income statement under the JIT system, assuming that 242 students enroll in a course.

7. d-2. Which system results in higher income?

Mr. Hooper is a fifth-grade teacher at Mt. General Elementary School. He believes very strongly in Gardner's theory of intelligence and that students have various areas of relative strength and weakness. He has attended numerous workshops regarding the application of multiple intelligence theory in the classroom. Over the years, he has developed a classroom that he believes fosters development in all of Gardner's eight Frames of Mind. Mr. Hooper's classroom is bright and cheerful. On the walls hang motivational posters that he believes help children to think about who they are and what they want out of life. In addition, the walls are covered with student-produced art. The room has a conversation area, a naturalist area, and a reading area, as well as the main area where each table accommodates four students. The conversation and reading areas have beanbag chairs so students can be comfortable and are set apart by rolling bookcases. The naturalist area consists of a table filled with rocks, bird nests, shells, and other objects that Mr. Hooper's students have found. Mr. Hooper is also fortunate enough to have three computers in his room. Mr. Hooper believes that allowing students to work in each academic area within their areas of strength will enhance learning. Therefore, when studying the American Revolution, students whose strength is in linguistic intelligence engage in research and write about what they have found. Those whose strength is spatial intelligence create maps of the colonies and battles. Those whose strength is logical-mathematical reasoning compute distances between points and estimate the amount of time required for soldiers to travel. Students with high naturalistic intelligence discuss the various plants and animals likely to be found in different regions of the colonies and discuss whether colonial soldiers could have eaten them to ward off starvation. To ensure that bodily-kinesthetic needs are met, Mr. Hooper regularly has his students stand and either run in place or jump up and down. Interpersonal intelligence needs are met for all students through the use of cooperative learning groups. Intrapersonal intelligence needs are met through journaling. Mr. Hooper always has music playing while the students are working to help meet student's musical intelligence needs.

To what extent do you believe Mr. Hooper has appropriately implemented Gardner's theory of multiple intelligences? Why? What do you think the student's reactions to this classroom would be? Why? How do you think parents would respond? Why? How could you improve on Mr. Hooper's ideas? Explain.

Erin Examinator is an educational researcher that has created an exam to measure the football knowledge of students across the nation.  She has decided to focus her research on students at the University of Alabama, as she believes that have a high level of football knowledge.  In her previous work, she has determined that the nationwide average for her exam is 65 (µ = 65) with a standard deviation equal to 12 (σ = 12).  Assume the data are normally distributed. Use this information to answer parts a-i.

1. (6 points) Freddy Footballer is not an average college student, he is over the top when it comes to his football knowledge.  Erin is very interested in seeing how Freddy compared to the national average.  Freddy scored a 99 (X = 99) on the exam.  Find the probability that she can find a student that scored higher than him. That is: P(X > 99).

2. b) (2 points) What is the probability that Erin will find a student that scored exactly 91? (X = 91)

3. (5 points) What is the percentile score of Freddy’s cousin, Frank Footballer? (His X = 92)

4. (7 points) Erin is interested in determining if any of the students that attended last week’s football game were below the 80^thpercentile of scores on the exam.  In order to do that, she needs to find the exam score, X, that falls in the 80^thpercentile.  Find that score for her.  

Note: (µ = 65) and (σ = 12).  

5. e. (8 points) Erin then samples 35 students (n = 35) that attended the game on Saturday that were seated in the student section.  She wants to determine if the students in this section are more knowledgeable than other students attending the games.  She finds the sample mean of this sample of students to be 72 .  Find the percentile score for mean of the students from the student section.   Note: (µ = 65) and (σ = 12).  

6. f. (6 points)  Now help Erin find the mean score,  , that falls in the 75^thpercentile of exam scores for the same sample size.  Note:  (µ = 65), (σ = 12) and (n = 35).     

7. (10 points) Help Erin to better estimate the true mean knowledge score of students from the University of Alabama.  Find a 99% Confidence Interval for true mean based on the 35 students (n = 35). Interpret the confidence interval.  Note:  and (σ = 12).  

8. (5 points) Erin is a perfectionist and wants to estimate the true mean within 1 point (E = 1).  Find the sample size she would need to collect in order to reduce the error to 1 in her 99% confidence interval.  Note: (σ = 12).  

1.   (10 points) Erin’s assistant, Abbie Assister, decides she would like to learn how to estimate the sample mean.  For practice, she collects data from 12 students (n = 12) and the sample mean was  and a sample standard deviation equal to (s = 9.87).  Find the 95% confidence interval for this sample mean and interpret the interval.  

The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514.† SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree.

(a)

Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. (Let μ₁ = population mean verbal score of students whose parents are college graduates with a bachelor's degree and μ₂ = population mean verbal score of students whose parents are high school graduates but do not have a college degree.) For purposes of this study, assume the population variances are unequal when conducting the t-test.

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

(b)

What is the point estimate of the difference between the means for the two populations?

(c)

Find the value of the test statistic. (Round your answer to three decimal places.)

Compute the p-value for the hypothesis test. (Round your answer to four decimal places.)

p-value =

(d)

At

α = 0.05,

what is your conclusion?

Reject H₀. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.Do not Reject H₀. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.      Do not reject H₀. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.Reject H₀. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.

The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514.† SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree.

College Grads 485            503

550        517

666        542

554        394

534        531

572        562

497        448

576        469

High School Grads 442 492

580        478

479        425

486        485

528        390

524        535

(a)

Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. (Let μ1 = population mean verbal score of students whose parents are college graduates with a bachelor's degree and μ2 = population mean verbal score of students whose parents are high school graduates but do not have a college degree.) For purposes of this study, assume the population variances are unequal when conducting the t-test.

H0: μ1 − μ2 = 0

Ha: μ1 − μ2 ≠ 0

H0: μ1 − μ2 < 0

Ha: μ1 − μ2 = 0

H0: μ1 − μ2 ≥ 0

Ha: μ1 − μ2 < 0

H0: μ1 − μ2 = 0

Ha: μ1 − μ2 > 0

H0: μ1 − μ2 ≠ 0

Ha: μ1 − μ2 = 0

(b)

What is the point estimate of the difference between the means for the two populations?

(c)

Find the value of the test statistic. (Round your answer to three decimal places.)

Compute the p-value for the hypothesis test. (Round your answer to four decimal places.)

p-value =

(d)

At

α = 0.05,

what is your conclusion?

Reject H0. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. Do not reject H0. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.     Reject H0. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates. Do not Reject H0. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.

IN JAVA ECLIPSE PLEASE

The xxx_Student class

A Student has a:

– Name - the name consists of the First and Last name separated by a space.

– Student Id – a whole number automatically assigned in the student class

– Student id numbers start at 100. The numbers are assigned using a static variable

in the Student class

• Include all instance variables

• Getters and setters for instance variables

• A static variable used to assign the student id starting at 100

• A toString method which returns a String containing the student name and id in the

format below:

Student: John Jones ID: 101

The xxx_Course class

A Course has the following information (modify your Course class):

– A name

– An Array of Students which contains an entry for each Student enrolled in the course

(allow for up to 10 students)

– An integer variable which indicates the number of students currently enrolled in the

course.

Write the constructor below which does the following:

Course (String name)

Sets courseName to name

Creates the students array of size 10

Sets number of Students to 0

Write the 3 getters

+getCourseName() : String

+getStudents() : Student []

+getNumberOfStudents() : int

Write the 2 setters

public void addStudent (Student student)

public void addStudent (String studentName)

Write toString

Return a String that contains the following information concatenated so that the

information prints on separate lines as shown in the sample output:

Course: xxxxx Number of Students: xx

The students in the class are:

Each of the Student objects in the students array followed by a \n so they print on

separate lines

Write a class xxx_TestCourse which will

Prompt the user for the name of a Course and create a Course object

In a loop, until the user enters a q or a Q,

Prompt the user to enter student names or Q to end

For each student entered,

create a Student object and add it to the Course using the addStudent method of

the Course class

At the end of the loop, print the Course object. Its toString method will format the

output as shown on the next slide

Sample Output

Enter the course name

CPS2231-04

Enter the name of a student or Q to quit

Jon

Enter the name of a student or Q to quit

Mary

Enter the name of a student or Q to quit

Tom

Enter the name of a student or Q to quit

q

Course: CPS2231-04 Number of Students: 3

The students in the class are:

Student: Jon ID: 100

Student: Mary ID: 101

Student: Tom ID: 102

Enhancement 1 (5 extra points)

Change the Course class so that a Course can have an unlimited number of students.

Start out with an Array of 10 Student objects

Once the Array is full,

Create a new Array of Student of twice the size as the original

Copy the elements from the full array to the new array

Re-assign the references

You may need to use the appropriate technology to answer this question.

The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514.† SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree.

(a)

Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education. (Let μ₁ = population mean verbal score of students whose parents are college graduates with a bachelor's degree and μ₂ = population mean verbal score of students whose parents are high school graduates but do not have a college degree.) For purposes of this study, assume the population variances are unequal when conducting the t-test.

H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ > 0

(b)

What is the point estimate of the difference between the means for the two populations?

(c)

Find the value of the test statistic. (Round your answer to three decimal places.)

Compute the p-value for the hypothesis test. (Round your answer to four decimal places.)

p-value =

(d)

At

α = 0.05,

what is your conclusion?

Do not reject H₀. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.Do not Reject H₀. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.      Reject H₀. There is insufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.Reject H₀. There is sufficient evidence to conclude that higher population mean verbal scores are associated with students whose parents are college graduates.