(a) For f(x) = 1 4 x 4 − 6x 2 find the intervals where f(x) is concave up, and the intervals where f(x) is concave down, and the inflection points of f(x) by the following steps:

i. Compute f 0 (x) and f 00(x).

ii. Show that f 00(x) is equal to 0 only at x = −2 and x = 2.

iii. Observe that f 00(x) is a continuous since it is a polynomial. Conclude that f 00(x) is either always positive or always negative on each of the intervals (−∞, −2), (−2, 2), and (2, ∞).

iv. Evaluate f 00(c) at one point c in each of these three intervals to see if f 00(c) > 0 or f 00(c) < 0, and use this computation to indicate where f(x) is concave up and where f(x) is concave down.

v. Indicate the inflection points (c, f(c)) where f 00(x) changes sign at x = c.

(b) For g(x) = 5 6 x 3 − 1 12x 4 find the intervals where g(x) is concave up, and the intervals where g(x) is concave down, and all inflection points of g(x). HINT: Use same steps as previous problem

COMP 251: Data Structures and Algorithms – Lab 4 Page 1 of 2 Lab 4: Implementing a Stack Using Linked List Implementation Objectives: The aim of this lab session is to make you familiar with using the linked list implementation in week3 and implement a stack using it. In this lab you will complete the partially implemented StackUsingLinkedList. Specifically, you will implement the following methods. • The default constructor: public StackUsingLinkedList() • public void push(AnyType x) • public AnyType pop() • public AnyType peek() • public boolean isEmpty() • public void makeEmpty() You are expected to use Java programming language in Eclipse IDE with EGit tool for completion of this lab exercise. You should upload your completed code repository (the complete parent folder of your work) as a zip file to the assignment in the Blackboard. Task 1: Preliminary Work for Setting up the Git Repository and Project 1. If you have not done already, set your name and email address as instructed in the Eclipse EGit Tutorial: Task 1: Initial Setup section. 2. Create a local Git repository (if one is not available in your eclipse environment). 3. Create a new Java project named Lab4_ (for example Lab4_300321321). 4. Add the newly created project to your local Git repository. (Instructions available in Eclipse EGit Tutorial - Task 2: Creating a New Java Project and Adding it to a New Repository) 5. Make sure the editing history of all the project files are tacked by Git (Add to Index, Instructions available in Eclipse EGit Tutorial - Task 2: Creating a New Java Project and Adding it to a New Repository) 6. Add the Java classes ListNode and SimpleLinkedList classes provided with the code in the week 3 to the new project. 7. Add the StackUsingLinkedList class provided with the Lab 4 to new project. 8. Make sure the editing histories of all the newly created files are tracked by Git by adding it to the index (Add to Index, Instructions available in Eclipse EGit Tutorial - Task 2: Creating a New Java Project and Adding it to a New Repository). 9. For each Java class, update the comments section to indicate that you updated the code. For this add you as the second author of code and include your email address. 10. Commit all the changes done up to this point. COMPUTER INFORMATION SYSTEMS COMP 251: DATA STRUCTURES AND ALGORITHMS COMP 251: Data Structures and Algorithms – Lab 4 Page 2 of 2 Task 2: Implement the Methods Important Considerations: In this lab, you are using the SimpleLinkedList class as a library and you are not allowed to make any changes to the class. You should be only making changes to the StackUsingLinkedList class. Note: If you understand the ideas discussed in week 4, you should be able to complete the implementation of the five methods in 15 minutes. 1. Implement the default constructor public StackUsingLinkedList()method in the StackUsingLinkedList class. The constructor should initialize the stack to an empty stack. 2. Implement the push method in the StackUsingLinkedList class. 3. Implement the pop method in the StackUsingLinkedList class. 4. Implement the peek method in the StackUsingLinkedList class. 5. Implement the isEmpty method in the StackUsingLinkedList class. 6. Implement the makeEmpty method in the StackUsingLinkedList class. 7. Make sure your code is commented and properly indented. 8. Commit code changes. Task 3: Implement Code Testing 1. Add a new class named Lab4Tester class to test your implementation of the stack. Your test class should test all the methods implemented in the class. 2. Make sure your code compiles and executes without any errors. 3. Test the new implementation using Lab4Tester class. 4. Commit code changes. Submission: Upload your code repository to the assignment (named Lab4) in the blackboard. The file should be named as follows. Code Repository: Create a zip file of your final code repository (the complete parent folder of your work) and name it as _Lab4_Code.zip (for example 300321321_Lab4_Code.zip)

Qustion

1) List 4 mood disorders and 4 personality disorders.

2) Describe the principles of 12 step treatment approach to substance abuse.

3) List 3 effective treatments for clients with eating disorders

1. Consider the following data from two independent groups:

Liberals: 4, 1, 4, 2                                     Conservatives: 5, 1, 3, 3, 4

1. Calculate the t statistic

2. Calculate the 95% confidence interval.

3. Calculate Cohen’s d.

Firm ABC’s projected cash flows are as follows

We can choose one of the following two capital structure plans:

The cost of debt are as follows

The firm’s unlevered beta is 0.8, tax rate is 40%. Market return is 9%.

To calculate risk-free rate, we have the following information.

The 10-year Treasury bond with par value $100, annual coupon rate 3.125%, 10-year to maturity, is selling at $90.

What is the highest possible firm value?

1. For the following function ?(?) = (?^2−8?+16) / (?^2−4)

a. Find the critical values

b. Use the FIRST DERIVATIVE TEST to determine the intervals where the function is INCREASING and DECREASING.

c. Find the RELATIVE EXTREMA of the function and state where they occur.

d. Find the ABSOLUTE EXTREMA of the function on the interval [−1, 1.75]

· Ophelia purchased 1 bunch of grapes, 2 earrings, 4 rings, 2 jars of olives, and 3 plums, spending $135 total.

· Cyrus purchased 1 ring, 2 bunches of grapes, 2 earrings, 4 jars of olives, and 5 plums, spending $151 total.

· Tressa purchased 5 earrings, 3 bunches of grapes, 2 jars of olives, 4 plums, and 2 rings, spending $163 total.

· Olberic purchased 1 jar of olives, 1 earring, 2 plums, 6 rings, and 4 bunches of grapes, spending $146 total.

· Primrose purchased 1 plum, 4 rings, 5 bunches of grapes, 3 earrings, and 3 jars of olives, spending $187 total.

Find the prices of each item purchased.

2. Devos Inc. makes desks that are made up of 1 top, 2 sides, and 4 legs. We need to make at least 15,000 desks to fulfill the demand of our customers. The costs are as follow:

Make the top - $7, Buy the top - $10, Make the side - $3, Buy the side - $5, Make a leg - $2, Buy a leg - $3

1) One top requires 4 feet of wood, one side requires 2 feet of wood, and one leg requires 1 foot of wood and we have 180,000 feet of wood available.

2) Each top takes 8 minutes to make a top, each side takes 3 minutes to make, and each leg takes 2 minutes to make. We have 300,000 minutes available.

Each top takes up 2 units of space, each side takes up 2 units of space, and each leg takes up .1 units of space before it is assembled in our inventory. We have 80,000 units of space available.

Answer the following using solver:

1. How many tops should we make? How many tops should we buy? How many sides should we make? How many sides should we buy? How many legs should we make? How many legs should we buy?
2. Without re-running Solver, what happens to our cost if we require that we buy at least one leg?
3. Without re-running solver, what happens to our cost if we need to make 16,000 tops (instead of 15,000)?

1.) For the chemical reaction 2 Al + 3 H 2 SO 4 ⟶ 3 H 2 + Al 2 ( SO 4 ) 3 what mass of hydrogen is produced from 1.97 mol of aluminum?

2.) Convert 1.77×1024 atoms of carbon to moles of carbon.

1.77×1024 atoms=

3.) For the reaction

2KI+Pb(NO3)2⟶PbI2+2KNO3how many grams of lead(II) iodide, PbI₂, are produced from 89.7 g of potassium iodide, KI?

4.)For the reaction

2NaOH+H2SO4⟶Na2SO4+2H2O

how many grams of sulfuric acid, H₂SO₄, are needed to react completely with 33.1 g of sodium hydroxide, NaOH?

PLEASE HELP...I WOULD GREATLY APPRECIATE IT...