A circular circuit of radius 30 cm is built to rotate about a

pair of insulating posts. The circuit consists of a 100 volt

battery, two 25 kW resistors in parallel and one 75 kW

resistor in series. The circuit is exposed to an external uniform magnetic field

of magnitude 0.75 Tesla and directed 20 degrees from the

normal vector of the circuit and the axis of rotation.

Calculate the total torque (magnitude and direction) on the

circuit

Calculate the component of the torque on the circuit

(magnitude and direction) at point A (exactly ¼ of the way

around the loop)

Calculate the component of the torque on the circuit

(magnitude and direction) at point B (exactly 7/8 of the way

around the loop)

1. A fund is built with annual deposits increasing by 1 from 1 to 10 and then decreasing by 1 to $0 at an annual effective interest rate of 5%. At the end of 19 years, the fund is used to purchase a 8-year annuity with level payment $X at an annual effective interest rate of 3% with the first payment 20 years from today.

Calculate X

2. Annie wants to accumulate $60500 in a fund at the end of 20 years. She plans to deposit $800+tX at the end of year t (t = 1,2,...,10) and $1500 at the end of last 10 years. The fund earns an annual effective interest rate of 6%.

Calculate X

Please show all work and do not use excel, thanks!

1. The built-in data “trees” provide the measurements of diameter (Girth), height and volume of trees. These are in inches for Girth, feet for Height and cubic feet for Volume. We will focus on Girth and Height. Write a function convert() that converts the values into the metric system (meters). Your function should take as arguments the value to convert and the unit it was expressed in (inches or feet) (use the following: x inches = x*0.0254 meters, x feet = x*0.3048 meters). If the first argument is not numeric or if the second argument is not “inch” or “feet”, use stop() function with an error message. Here is how it should work:

> convert(8.3,"inches")

[1] 0.21082

> convert(8.3,"feet")

[1] 2.52984

> convert(8.3,"foot")

Error in convert(8.3, "foot") : the unit was not "inches" or "feet"

Use your function to convert the values of Girth and Height to meters. Using cor.test() function, calculate the correlation (and the corresponding p-value) between Girth and Height in meters.

1. The Coase theorem is built on certain assumptions that, if violated, implies that private bargaining may not always achieve an efficient outcome. Give two cases where we cannot expect private bargaining to deliver an efficient outcome, where each case represents a violation of a different underlying assumption. Briefly explain your answers.

Mark Burnett and Kamran Pourgol were the only shareholders in a corporation that built and sold a house. When the buyers discovered that the house exceeded the amount of square footage allowed by the building permit, Pourgol agreed to renovate the house to conform to the permit. No work was done, however, and Burnett filed a suit against Pourgol. Burnett claimed that, without his knowledge, Pourgol had submitted incorrect plans to obtain the building permit, misrepresented the extent of the renovation, and failed to fix the house. Was Pourgol guilty of misconduct? If so, how might it have been avoided? Discuss.

1) Burnett is a (memeber, partner, or shareholder) in the corporation.

2) Pourgol held a (majority, minority, unclear) amount of shares in the close corporation.

3) Assume that Pourgol and Burnett agreed to the plans submitted to the town and Burnett and was made aware beforehand of the promise to fix the buyer's home. Would Pourgol most likely be held liable in this instance? (yes, no)

4) Would the buyers still be able to recover the costs of renovation to conform the house allowed by the building permit? (yes, no)

A (time-homogeneous) Markov chain built on states A and B is depicted in the diagram below. What is the probability that a process beginning on A will be on B after 2 moves?

consider the Markov chain shown in Figure 11.14.

Figure 11.14- A state transition diagram.

1. Is this chain irreducible?
2. Is this chain aperiodic?
3. Find the stationary distribution for this chain.
4. Is the stationary distribution a limiting distribution for the chain?

Firm XYZ is considering a project to built a new facility to install a new production line. The firm requires a minimum return of 10% in this project, due to the risks involved. The firm is a 34% tax bracket. Sales, revenues and costs details are given in the table below:

Tasks:

Estimate the CCFA for the next 5 years of operation

Using the NPV and IRR decision methods, decide if the firm should take the project.

A developer wants to know if the houses in two different neighborhoods were built at roughly the same time. She takes a random sample of six houses from each neighborhood and finds their ages from local records. The accompanying table shows the data for each sample​ (in years). Assume that the data come from a distribution that is Normally distributed.

Neighborhood 1: 50, 68, 65, 52, 53, 54

Neighborhood 2: 33, 32, 44, 38, 54, 51

​a) Find a 95​% confidence interval for the mean​ difference μ1- μ2​, in ages of houses in the two neighborhoods. (Round to two decimal places as needed)

​b) Is 0 within the confidence​ interval?

(Yes or No)

​c) What does the confidence interval suggest about the null hypothesis that the mean difference is​ 0?

A.Reject H0 since 0 is a plausible value for the true mean difference.

B. Fail to reject H0 since 0 is a plausible value for the true mean difference.

C.Reject H0 since 0 is not a plausible value for the true mean difference.

D.Fail to reject H0 since 0 is not a plausible value for the true mean difference.

A binary search tree can be built with a traditional insertion method given a list of integers. Binary search trees (BSTs) are binary trees where the data is ordered such that nodes in the subtree to the left of a given node are smaller than or equal to the node, and the right subtree will contain nodes with values greater than the given node. With a built binary search tree, one can traverse the tree to print each node’s data in each order of traversal or perform some other operations. Further, one can tell by comparing nodes between two given trees whether they relate to each other, by having a reflected symmetric structure (i.e. being mirror images of each other), having identical structure, or not being related at all. In this assignment, you are asked to implement the following features.
Hard-code some paired lists of integers.
Build binary search trees from each list
Print the binary search trees in the three orders discussed in class.
Determine if the two binary search trees are identical, mirrors of each other, or neither
Remove a number in each tree at random and compare the tree pair again

Further, since the methods of the binary search tree class have been presented with recursive function calls, it is now up to you to implement these recursive functions with iterative loops.

You must write a Class Node, a class TreeChecker and a class BinarySearchTree. For Java users, they must implement the following interfaces respectively:

public interface INode {

   //Getter of node data
   T getData();

   //Setter of node data
   void setData(T data);

    INode getLeftChild() ;

   void setLeftChild(INode leftChild) ;

   INode getRightChild() ;

   void setRightChild(INode rightChild);
  
}
public interface ITree {
   void setRoot(INode root);
INode getRoot();
void preorder();   // print tree in a preorder traversal
void inorder();   // print tree in an inorder traversal
void postorder();   // print tree in a postorder traversal
INode insert(INode root, T data); // insert data into tree
   INode remove(INode root, T data); //search/remove node with data
   T search(INode root, T data); //search and return data if it exists
   INode getMax(INode root); //return node with maximum value of subtree
   INode getMin(INode root); //return node with minimum value of subtree
}  
public interface ITreeChecker {
  
boolean isMirror(ITree root1, ITree root2); // check if two trees are mirror
// images
   boolean isSame(ITree root1, ITree root2); // check if two trees are identical
}

In C++

Write a program that dynamically allocates a built-in array large enough to hold a user-defined number of test scores. (Ask the user how many grades will be entered and use a dynamic array to store the numbers.) Once all the scores are entered, the array should be passed to a function that calculates the average score. The program should display the scores and average. Use pointer notation rather than array notation whenever possible. (Input Validation: Do not accept negative numbers for test scores.) Make it a class, call it something like gradeholder. You will need a destructor because you are using dynamic arrays.

I need your help. Thank you