What is the price of each of the following bonds ($1,000 principal) if the current interest rate is 6 percent?

Firm A: coupon 6%, Maturity 6 years

Firm B: coupon 6%, Maturity 12 years

Firm C: coupon 13%, Maturity 6 years

Firm D: coupon 13%, Maturity 12 years

Firm E: coupon 0%, Maturity 6 years

Firm F: coupon 0%, Maturity 12 years

b) What is the duration of each bond?

c) Rank the bonds in terms of price fluctuations with the least volatile bond first and the most volatile bond last as judged by each bond’s duration

d) Confirm your volatility ranking by determining the percentage change in the price of each bond if interest rates rise up to 9%.

e) What generalizations can be made from the above exercise (2 Points)

What is the price of each of the following bonds ($1,000 principal) if the current interest rate is 6 percent?

Firm A: coupon 6%, Maturity 6 years

Firm B: coupon 6%, Maturity 12 years

Firm C: coupon 13%, Maturity 6 years

Firm D: coupon 13%, Maturity 12 years

Firm E: coupon 0%, Maturity 6 years

Firm F: coupon 0%, Maturity 12 years

b) What is the duration of each bond?

c) Rank the bonds in terms of price fluctuations with the least volatile bond first and the most volatile bond last as judged by each bond’s duration

d) Confirm your volatility ranking by determining the percentage change in the price of each bond if interest rates rise up to 9%.

e) What generalizations can be made from the above exercise (2 Points)

The table below describes the toy in the store

a)            Draw the supply and demand curves identified by the points on the table.

b)            What is the elasticity of demand for a reduction in price from $1.50 to $1?

c)            Draw the new supply line based on the following tax: $0.50 per unit for first 1.5M units and $1 per unit for all units 1.5M units and above.

d)            What is the new equilibrium price and quantity

e)            How much tax revenue was raised?

f)             Draw the dead weight loss triangle on the graph.

g)            Explain what dead weight loss is and why it happens when there is a tax.

h)            Estimate the area of dead weight loss.

Scenario

Media Wise sells a range of media products in package deals. The products sold within bundles are as follows.  

Package A consists of a TV and a stand and is sold for a discounted price of £420. Package B consists of a TV, a stand and two speakers and is sold for a discounted price of £480. Currently packages are sold in a ratio of 2 Package As for every 3 Package Bs and 600 packages are sold each month. Fixed costs are expected to be £82,000 for the month.  

Question 2

1. Calculate the break even point (in number of packages and sales revenue)
   1. If only Package As are sold                                                                
   2. If only Package Bs are sold                                                                
   3. If both packages are sold in the current sales mix, calculate the breakeven point per mix first, the unit for each product and the total units.   

.......Subject Java.....

main()

main() will ask the user for input and then call functions to do calculations. The calculations will be returned to main() where they will be printed out.

First function

Create a function named computeBill that receives on parameter. It receives the price of an item. It will then add 8.25% sales tax to this and return the total due back to main().

Second function

Create another function named computeBill that receives 2 parameters. It will receive the price of an item and the quantity ordered. It will calculated the total and then add 8.25% sales tax to that and return total due back to main().

Third function

Create a third function names computeBill that receives 3 parameters. It will receive the price of an item, the quantity ordered, and a coupon value. It will then calculate the total, then deduct the coupon amount, and add 8.25% sales tax. It will then return the total due to main().

Can you please use simple code  - Thank you

As part of Office Depot’s cost reducing strategy, research is being conducted on its line of printers. Currently Office Depot offers 5 types of printers, each having different features. Office Depot detected that when it comes to buying a printer, customers look first for a particular printing speed (pages per minute, or ppm) and only then they look to the price to make their decision. A regression analysis is performed to determine whether printer speed is a driver of (explains) the price. The following table displays the printers, their speeds and associated prices.

1. Calculate coefficient B1
2. Calculate coefficient Bo
3. The regression equation for this problem is......
4. Provide an interpretation for the intercept coefficient.
5. Provide an interpretation for the slope coefficient.

STRICT DOWNVOTE IF NOT DONE FULLY, WILL REPORT ALSO IF COPY PASTED OR MODIFIED ANSWER Develop a class, using templates, to provide functionality for a set of recursive functions. The functions specified as recursive must be written recursively (not iterativly). The UML class specifications are provided below. A main will be provided. Additionally, a make file will need to be developed and submitted. ● Recursion Set Class The recursion set template class will implement the template functions. recursionSet -length: int -*mySet: myType -MAX_VALUE = 500000 static const: int -LIMIT = 1000 static const: int +recursionSet() +recursionSet(const recursionSet&) +~recursionSet() +getSetLength() const: int +generateElements(int): void + getElement(int) const: myType +setElement(int, myType): void +readValue(const string) const: int +printSet() const: void +operator == (const recusrionSet&): bool +tak(myType, myType, myType) const: myType +printSeptenary(myType) const: void +squareRoot(myType, myType) const: myType -recSqRoot(myType, myType, myType) const: myType +recursiveSum() const: myType -rSum(int) const: myType +checkParentheses(string) const: bool -recChkPar(string, int, int) const: bool +recursiveInsertionSort(): void -recInsSort(int, int): void -insertInOrder(myType, int, int): voidYou may add additional private functions if needed (but, not for the recursive functions). Note, points will be deducted for especially poor style or inefficient coding. Function Descriptions • The recursionSet() constructor should set the length to 0 and mySet pointer to NULL. • The recusrsionSet(const recursionBucket&) copy constructor should create a new, deep copy from the passed object. • The ~recursionSet() destructor should delete the myType array, set the pointer to NULL, and set the size to 0. • The setElement(int, myValue) function should set an element in the class array at the given index location (over-writing any previous value). The function must include bounds checking. If an illegal index is provided, a error message should be displayed. • The getElement(int) should get and return an element from the passed index. This must include bounds checking. If an illegal index is provided, a error message should be displayed and a 0 returned. • The getSetLength() functions should return the current class array length. • The printSet(int) function should print the formatted class array with the passed number of values per line. Use the following output statement: cout << setw(5) << mySet[i] << " • "; Refer to the sample executions for formatting example. The readValue(string) function should prompt with the passed string and read a number from the user. The function should ensure that the value is 3 1 and £ MAX_VALUE. The function should handle invalid input (via a try/catch block). If an error occurs (out of range or invalid input) an appropriate message should be displayed and the user re- prompted. Example error messages include: cout << "readSetLenth: Sorry, too many " << "errors." << endl; cout << "readSetLenth: Error, value " << cnt << " not between 1 and " << numMax << "." << endl; • Note, three errors is acceptable, but a fourth error should end the function and return 0. The generateList(int) function should dynamically create the array and use the following casting for rand() to fill the array with random values. mySet[i] = static_cast(rand()%LIMIT); • • • The printSeptenary(myType) function should print the passed numeric argument in Septenary (base-7) format. Note, function must be written recursively. The recursiveSum() function will perform a recursive summation of the values in class data set and return the final sum. The function will call the private rSum(int) function (which is recursive). The rSum(int) function accepts the length of the data set and performs a recursive summation. The recursive summation is performed as follows: rSum ( position )= • { array[ 0] array[ position ] + rSum ( position−1) if position = 0 if position > 0 The tak(myType) function should recursively compute the Tak 1 function. The Tak function is defined as follows: tak ( x , y , z) = { z tak ( tak ( x−1, y , z) , tak ( y−1, z , x) , tak ( z −1, x , y ) ) 1 For more information, refer to: http://en.wikipedia.org/wiki/Tak_(function) if y≥ x if y < x• • The squareRoot(myType, myType) function will perform a recursive estimation of the square root of the passed value (first parameter) to the passed tolerance (second parameter). The function will call the private sqRoot(myType,myType,myType) function (which is recursive). The private recSqRoot(myType,myType,myType) function recursively determines an estimated square root. Assuming initially that a = x, the square root estimate can be determined as follows: recSqRoot ( x , a , epsilon) = • • • • • { 2 if ∣ a − x ∣ ≤ epsilon a 2 (a + x) sqRoot x , , epsilon 2 a ( ) if ∣ a 2 − x ∣ > epsilon The recursiveInsertionSort() function should sort the data set array using a recursive insertion sort. The recursiveInsertionSort() function should verify the length is valid and, if so, call the recInsSort() function to perform the recursive sorting (with the first element at 0 and the last element at length-1). The recInsSort(int, int) function should implement the recursive insertion sort. The arguments are the index of the first element and the index of the last element. If the first index is less than that last index, the recursive insertion sort algorithm is follows: ▪ Recursively sort all but the last element (i.e., last-1) ▪ Insert the last element in sorted order from first through last positions To support the insertion of the last element, the insertInOrder() function should be used. The insertInOrder(myType, int, int) function should recursively insert the passed element into the correction position. The arguments are the element, the starting index and the ending index (in that order). The function has 3 operations: ▪ If the element is greater than or equal to the last element in the sorted list (i.e., from first to last). If so, insert the element at the end of the sorted (i.e, mySet[last+1] = element). ▪ If the first is less than the last, insert the last element (i.e., mySet[last]) at the end of the sorted (i.e., mySet[last+1] = mySet[last]) and continue the insertion by recursively calling the insertInOrder() function with the element, first, and last-1 values. ▪ Otherwise, insert the last element (i.e., mySet[last]) at the end of the sorted (i.e., mySet[last+1] = mySet[last]) and set the last value (i.e., mySet[last]) to the passed element. The checkParentheses(string) function should determine if the parentheses in a passed string are correctly balanced. The function should call the private recChkPar(string, int, int) function (which is recursive) The recChkPar(string, int, int) function should determine if the parentheses in a string are correctly balanced. The arguments are the string, an index (initially 0), and a parenthesis level count (initially 0). The index is used to track the current character in the string. The general approach should be as follows: ◦ Identify base case or cases. ◦ Check the current character (i.e., index) for the following use cases: ▪ if str[index] == '(' → what to do then ▪ if str[index] == ')' → what to do then ▪ if str[index] == any other character → what to do then Note, for each case, increment the index and call function recursively.

STRICT DOWNVOTE IF NOT DONE FULLY, WILL REPORT ALSO IF COPY PASTED OR MODIFIED ANSWER Develop a class, using templates, to provide functionality for a set of recursive functions. The functions specified as recursive must be written recursively (not iterativly). The UML class specifications are provided below. A main will be provided. Additionally, a make file will need to be developed and submitted. ● Recursion Set Class The recursion set template class will implement the template functions. recursionSet -length: int -*mySet: myType -MAX_VALUE = 500000 static const: int -LIMIT = 1000 static const: int +recursionSet() +recursionSet(const recursionSet&) +~recursionSet() +getSetLength() const: int +generateElements(int): void + getElement(int) const: myType +setElement(int, myType): void +readValue(const string) const: int +printSet() const: void +operator == (const recusrionSet&): bool +tak(myType, myType, myType) const: myType +printSeptenary(myType) const: void +squareRoot(myType, myType) const: myType -recSqRoot(myType, myType, myType) const: myType +recursiveSum() const: myType -rSum(int) const: myType +checkParentheses(string) const: bool -recChkPar(string, int, int) const: bool +recursiveInsertionSort(): void -recInsSort(int, int): void -insertInOrder(myType, int, int): voidYou may add additional private functions if needed (but, not for the recursive functions). Note, points will be deducted for especially poor style or inefficient coding. Function Descriptions • The recursionSet() constructor should set the length to 0 and mySet pointer to NULL. • The recusrsionSet(const recursionBucket&) copy constructor should create a new, deep copy from the passed object. • The ~recursionSet() destructor should delete the myType array, set the pointer to NULL, and set the size to 0. • The setElement(int, myValue) function should set an element in the class array at the given index location (over-writing any previous value). The function must include bounds checking. If an illegal index is provided, a error message should be displayed. • The getElement(int) should get and return an element from the passed index. This must include bounds checking. If an illegal index is provided, a error message should be displayed and a 0 returned. • The getSetLength() functions should return the current class array length. • The printSet(int) function should print the formatted class array with the passed number of values per line. Use the following output statement: cout << setw(5) << mySet[i] << " • "; Refer to the sample executions for formatting example. The readValue(string) function should prompt with the passed string and read a number from the user. The function should ensure that the value is 3 1 and £ MAX_VALUE. The function should handle invalid input (via a try/catch block). If an error occurs (out of range or invalid input) an appropriate message should be displayed and the user re- prompted. Example error messages include: cout << "readSetLenth: Sorry, too many " << "errors." << endl; cout << "readSetLenth: Error, value " << cnt << " not between 1 and " << numMax << "." << endl; • Note, three errors is acceptable, but a fourth error should end the function and return 0. The generateList(int) function should dynamically create the array and use the following casting for rand() to fill the array with random values. mySet[i] = static_cast(rand()%LIMIT); • • • The printSeptenary(myType) function should print the passed numeric argument in Septenary (base-7) format. Note, function must be written recursively. The recursiveSum() function will perform a recursive summation of the values in class data set and return the final sum. The function will call the private rSum(int) function (which is recursive). The rSum(int) function accepts the length of the data set and performs a recursive summation. The recursive summation is performed as follows: rSum ( position )= • { array[ 0] array[ position ] + rSum ( position−1) if position = 0 if position > 0 The tak(myType) function should recursively compute the Tak 1 function. The Tak function is defined as follows: tak ( x , y , z) = { z tak ( tak ( x−1, y , z) , tak ( y−1, z , x) , tak ( z −1, x , y ) ) 1 For more information, refer to: http://en.wikipedia.org/wiki/Tak_(function) if y≥ x if y < x• • The squareRoot(myType, myType) function will perform a recursive estimation of the square root of the passed value (first parameter) to the passed tolerance (second parameter). The function will call the private sqRoot(myType,myType,myType) function (which is recursive). The private recSqRoot(myType,myType,myType) function recursively determines an estimated square root. Assuming initially that a = x, the square root estimate can be determined as follows: recSqRoot ( x , a , epsilon) = • • • • • { 2 if ∣ a − x ∣ ≤ epsilon a 2 (a + x) sqRoot x , , epsilon 2 a ( ) if ∣ a 2 − x ∣ > epsilon The recursiveInsertionSort() function should sort the data set array using a recursive insertion sort. The recursiveInsertionSort() function should verify the length is valid and, if so, call the recInsSort() function to perform the recursive sorting (with the first element at 0 and the last element at length-1). The recInsSort(int, int) function should implement the recursive insertion sort. The arguments are the index of the first element and the index of the last element. If the first index is less than that last index, the recursive insertion sort algorithm is follows: ▪ Recursively sort all but the last element (i.e., last-1) ▪ Insert the last element in sorted order from first through last positions To support the insertion of the last element, the insertInOrder() function should be used. The insertInOrder(myType, int, int) function should recursively insert the passed element into the correction position. The arguments are the element, the starting index and the ending index (in that order). The function has 3 operations: ▪ If the element is greater than or equal to the last element in the sorted list (i.e., from first to last). If so, insert the element at the end of the sorted (i.e, mySet[last+1] = element). ▪ If the first is less than the last, insert the last element (i.e., mySet[last]) at the end of the sorted (i.e., mySet[last+1] = mySet[last]) and continue the insertion by recursively calling the insertInOrder() function with the element, first, and last-1 values. ▪ Otherwise, insert the last element (i.e., mySet[last]) at the end of the sorted (i.e., mySet[last+1] = mySet[last]) and set the last value (i.e., mySet[last]) to the passed element. The checkParentheses(string) function should determine if the parentheses in a passed string are correctly balanced. The function should call the private recChkPar(string, int, int) function (which is recursive) The recChkPar(string, int, int) function should determine if the parentheses in a string are correctly balanced. The arguments are the string, an index (initially 0), and a parenthesis level count (initially 0). The index is used to track the current character in the string. The general approach should be as follows: ◦ Identify base case or cases. ◦ Check the current character (i.e., index) for the following use cases: ▪ if str[index] == '(' → what to do then ▪ if str[index] == ')' → what to do then ▪ if str[index] == any other character → what to do then Note, for each case, increment the index and call function recursively.

STRICT DOWNVOTE IF NOT DONE FULLY, WILL REPORT ALSO IF COPY PASTED OR MODIFIED ANSWER Develop a class, using templates, to provide functionality for a set of recursive functions. The functions specified as recursive must be written recursively (not iterativly). The UML class specifications are provided below. A main will be provided. Additionally, a make file will need to be developed and submitted. ● Recursion Set Class The recursion set template class will implement the template functions. recursionSet -length: int -*mySet: myType -MAX_VALUE = 500000 static const: int -LIMIT = 1000 static const: int +recursionSet() +recursionSet(const recursionSet&) +~recursionSet() +getSetLength() const: int +generateElements(int): void + getElement(int) const: myType +setElement(int, myType): void +readValue(const string) const: int +printSet() const: void +operator == (const recusrionSet&): bool +tak(myType, myType, myType) const: myType +printSeptenary(myType) const: void +squareRoot(myType, myType) const: myType -recSqRoot(myType, myType, myType) const: myType +recursiveSum() const: myType -rSum(int) const: myType +checkParentheses(string) const: bool -recChkPar(string, int, int) const: bool +recursiveInsertionSort(): void -recInsSort(int, int): void -insertInOrder(myType, int, int): voidYou may add additional private functions if needed (but, not for the recursive functions). Note, points will be deducted for especially poor style or inefficient coding. Function Descriptions • The recursionSet() constructor should set the length to 0 and mySet pointer to NULL. • The recusrsionSet(const recursionBucket&) copy constructor should create a new, deep copy from the passed object. • The ~recursionSet() destructor should delete the myType array, set the pointer to NULL, and set the size to 0. • The setElement(int, myValue) function should set an element in the class array at the given index location (over-writing any previous value). The function must include bounds checking. If an illegal index is provided, a error message should be displayed. • The getElement(int) should get and return an element from the passed index. This must include bounds checking. If an illegal index is provided, a error message should be displayed and a 0 returned. • The getSetLength() functions should return the current class array length. • The printSet(int) function should print the formatted class array with the passed number of values per line. Use the following output statement: cout << setw(5) << mySet[i] << " • "; Refer to the sample executions for formatting example. The readValue(string) function should prompt with the passed string and read a number from the user. The function should ensure that the value is 3 1 and £ MAX_VALUE. The function should handle invalid input (via a try/catch block). If an error occurs (out of range or invalid input) an appropriate message should be displayed and the user re- prompted. Example error messages include: cout << "readSetLenth: Sorry, too many " << "errors." << endl; cout << "readSetLenth: Error, value " << cnt << " not between 1 and " << numMax << "." << endl; • Note, three errors is acceptable, but a fourth error should end the function and return 0. The generateList(int) function should dynamically create the array and use the following casting for rand() to fill the array with random values. mySet[i] = static_cast(rand()%LIMIT); • • • The printSeptenary(myType) function should print the passed numeric argument in Septenary (base-7) format. Note, function must be written recursively. The recursiveSum() function will perform a recursive summation of the values in class data set and return the final sum. The function will call the private rSum(int) function (which is recursive). The rSum(int) function accepts the length of the data set and performs a recursive summation. The recursive summation is performed as follows: rSum ( position )= • { array[ 0] array[ position ] + rSum ( position−1) if position = 0 if position > 0 The tak(myType) function should recursively compute the Tak 1 function. The Tak function is defined as follows: tak ( x , y , z) = { z tak ( tak ( x−1, y , z) , tak ( y−1, z , x) , tak ( z −1, x , y ) ) 1 For more information, refer to: http://en.wikipedia.org/wiki/Tak_(function) if y≥ x if y < x• • The squareRoot(myType, myType) function will perform a recursive estimation of the square root of the passed value (first parameter) to the passed tolerance (second parameter). The function will call the private sqRoot(myType,myType,myType) function (which is recursive). The private recSqRoot(myType,myType,myType) function recursively determines an estimated square root. Assuming initially that a = x, the square root estimate can be determined as follows: recSqRoot ( x , a , epsilon) = • • • • • { 2 if ∣ a − x ∣ ≤ epsilon a 2 (a + x) sqRoot x , , epsilon 2 a ( ) if ∣ a 2 − x ∣ > epsilon The recursiveInsertionSort() function should sort the data set array using a recursive insertion sort. The recursiveInsertionSort() function should verify the length is valid and, if so, call the recInsSort() function to perform the recursive sorting (with the first element at 0 and the last element at length-1). The recInsSort(int, int) function should implement the recursive insertion sort. The arguments are the index of the first element and the index of the last element. If the first index is less than that last index, the recursive insertion sort algorithm is follows: ▪ Recursively sort all but the last element (i.e., last-1) ▪ Insert the last element in sorted order from first through last positions To support the insertion of the last element, the insertInOrder() function should be used. The insertInOrder(myType, int, int) function should recursively insert the passed element into the correction position. The arguments are the element, the starting index and the ending index (in that order). The function has 3 operations: ▪ If the element is greater than or equal to the last element in the sorted list (i.e., from first to last). If so, insert the element at the end of the sorted (i.e, mySet[last+1] = element). ▪ If the first is less than the last, insert the last element (i.e., mySet[last]) at the end of the sorted (i.e., mySet[last+1] = mySet[last]) and continue the insertion by recursively calling the insertInOrder() function with the element, first, and last-1 values. ▪ Otherwise, insert the last element (i.e., mySet[last]) at the end of the sorted (i.e., mySet[last+1] = mySet[last]) and set the last value (i.e., mySet[last]) to the passed element. The checkParentheses(string) function should determine if the parentheses in a passed string are correctly balanced. The function should call the private recChkPar(string, int, int) function (which is recursive) The recChkPar(string, int, int) function should determine if the parentheses in a string are correctly balanced. The arguments are the string, an index (initially 0), and a parenthesis level count (initially 0). The index is used to track the current character in the string. The general approach should be as follows: ◦ Identify base case or cases. ◦ Check the current character (i.e., index) for the following use cases: ▪ if str[index] == '(' → what to do then ▪ if str[index] == ')' → what to do then ▪ if str[index] == any other character → what to do then Note, for each case, increment the index and call function recursively.

STRICT DOWNVOTE IF NOT DONE FULLY, WILL REPORT ALSO IF COPY PASTED OR MODIFIED ANSWER Develop a class, using templates, to provide functionality for a set of recursive functions. The functions specified as recursive must be written recursively (not iterativly). The UML class specifications are provided below. A main will be provided. Additionally, a make file will need to be developed and submitted. ● Recursion Set Class The recursion set template class will implement the template functions. recursionSet -length: int -*mySet: myType -MAX_VALUE = 500000 static const: int -LIMIT = 1000 static const: int +recursionSet() +recursionSet(const recursionSet&) +~recursionSet() +getSetLength() const: int +generateElements(int): void + getElement(int) const: myType +setElement(int, myType): void +readValue(const string) const: int +printSet() const: void +operator == (const recusrionSet&): bool +tak(myType, myType, myType) const: myType +printSeptenary(myType) const: void +squareRoot(myType, myType) const: myType -recSqRoot(myType, myType, myType) const: myType +recursiveSum() const: myType -rSum(int) const: myType +checkParentheses(string) const: bool -recChkPar(string, int, int) const: bool +recursiveInsertionSort(): void -recInsSort(int, int): void -insertInOrder(myType, int, int): voidYou may add additional private functions if needed (but, not for the recursive functions). Note, points will be deducted for especially poor style or inefficient coding. Function Descriptions • The recursionSet() constructor should set the length to 0 and mySet pointer to NULL. • The recusrsionSet(const recursionBucket&) copy constructor should create a new, deep copy from the passed object. • The ~recursionSet() destructor should delete the myType array, set the pointer to NULL, and set the size to 0. • The setElement(int, myValue) function should set an element in the class array at the given index location (over-writing any previous value). The function must include bounds checking. If an illegal index is provided, a error message should be displayed. • The getElement(int) should get and return an element from the passed index. This must include bounds checking. If an illegal index is provided, a error message should be displayed and a 0 returned. • The getSetLength() functions should return the current class array length. • The printSet(int) function should print the formatted class array with the passed number of values per line. Use the following output statement: cout << setw(5) << mySet[i] << " • "; Refer to the sample executions for formatting example. The readValue(string) function should prompt with the passed string and read a number from the user. The function should ensure that the value is 3 1 and £ MAX_VALUE. The function should handle invalid input (via a try/catch block). If an error occurs (out of range or invalid input) an appropriate message should be displayed and the user re- prompted. Example error messages include: cout << "readSetLenth: Sorry, too many " << "errors." << endl; cout << "readSetLenth: Error, value " << cnt << " not between 1 and " << numMax << "." << endl; • Note, three errors is acceptable, but a fourth error should end the function and return 0. The generateList(int) function should dynamically create the array and use the following casting for rand() to fill the array with random values. mySet[i] = static_cast(rand()%LIMIT); • • • The printSeptenary(myType) function should print the passed numeric argument in Septenary (base-7) format. Note, function must be written recursively. The recursiveSum() function will perform a recursive summation of the values in class data set and return the final sum. The function will call the private rSum(int) function (which is recursive). The rSum(int) function accepts the length of the data set and performs a recursive summation. The recursive summation is performed as follows: rSum ( position )= • { array[ 0] array[ position ] + rSum ( position−1) if position = 0 if position > 0 The tak(myType) function should recursively compute the Tak 1 function. The Tak function is defined as follows: tak ( x , y , z) = { z tak ( tak ( x−1, y , z) , tak ( y−1, z , x) , tak ( z −1, x , y ) ) 1 For more information, refer to: http://en.wikipedia.org/wiki/Tak_(function) if y≥ x if y < x• • The squareRoot(myType, myType) function will perform a recursive estimation of the square root of the passed value (first parameter) to the passed tolerance (second parameter). The function will call the private sqRoot(myType,myType,myType) function (which is recursive). The private recSqRoot(myType,myType,myType) function recursively determines an estimated square root. Assuming initially that a = x, the square root estimate can be determined as follows: recSqRoot ( x , a , epsilon) = • • • • • { 2 if ∣ a − x ∣ ≤ epsilon a 2 (a + x) sqRoot x , , epsilon 2 a ( ) if ∣ a 2 − x ∣ > epsilon The recursiveInsertionSort() function should sort the data set array using a recursive insertion sort. The recursiveInsertionSort() function should verify the length is valid and, if so, call the recInsSort() function to perform the recursive sorting (with the first element at 0 and the last element at length-1). The recInsSort(int, int) function should implement the recursive insertion sort. The arguments are the index of the first element and the index of the last element. If the first index is less than that last index, the recursive insertion sort algorithm is follows: ▪ Recursively sort all but the last element (i.e., last-1) ▪ Insert the last element in sorted order from first through last positions To support the insertion of the last element, the insertInOrder() function should be used. The insertInOrder(myType, int, int) function should recursively insert the passed element into the correction position. The arguments are the element, the starting index and the ending index (in that order). The function has 3 operations: ▪ If the element is greater than or equal to the last element in the sorted list (i.e., from first to last). If so, insert the element at the end of the sorted (i.e, mySet[last+1] = element). ▪ If the first is less than the last, insert the last element (i.e., mySet[last]) at the end of the sorted (i.e., mySet[last+1] = mySet[last]) and continue the insertion by recursively calling the insertInOrder() function with the element, first, and last-1 values. ▪ Otherwise, insert the last element (i.e., mySet[last]) at the end of the sorted (i.e., mySet[last+1] = mySet[last]) and set the last value (i.e., mySet[last]) to the passed element. The checkParentheses(string) function should determine if the parentheses in a passed string are correctly balanced. The function should call the private recChkPar(string, int, int) function (which is recursive) The recChkPar(string, int, int) function should determine if the parentheses in a string are correctly balanced. The arguments are the string, an index (initially 0), and a parenthesis level count (initially 0). The index is used to track the current character in the string. The general approach should be as follows: ◦ Identify base case or cases. ◦ Check the current character (i.e., index) for the following use cases: ▪ if str[index] == '(' → what to do then ▪ if str[index] == ')' → what to do then ▪ if str[index] == any other character → what to do then Note, for each case, increment the index and call function recursively.