The sequence 2, 4, 1, 3, 5 has three inversions (2,1), (4,1), (4,3). Using C++ Code an O(nlog(n)) algorithm to count the number of inversions. Use the Merge sort Algorithm, and use the template below: (Use the file below that to test)

countInv.cpp -------------------------------------------------------------------------------------------------------------------------------

#include <vector>
#include <algorithm>

using namespace std;

int mergeInv(vector<int>& nums, vector<int>& left, vector<int>& right) {

// Your code here

}

int countInv(vector<int>&nums) {
// Your code here

}

CountInv_test.cpp -------------------------------------------------------------------------------------------------------------------------

#include <iostream>
#include <vector>

using namespace std;

int countInv(vector<int>& numvec);

int main()
{
int n;
vector<int> numvec{4, 5, 6, 1, 2, 3};
n = countInv(numvec);
cout << "Number of inversions " << n << endl; // Should be 9
  
numvec = {1, 2, 3, 4, 5, 6};
n = countInv(numvec);
cout << "Number of inversions " << n << endl; // Should be 0
  
numvec = {6, 5, 4, 3, 2, 1};
n = countInv(numvec);
cout << "Number of inversions " << n << endl; // Should be 15
  
numvec = {0, 0, 0, 0, 0, 0};
n = countInv(numvec);
cout << "Number of inversions " << n << endl;; // Should be 0
}

The sequence 2, 4, 1, 3, 5 has three inversions (2,1), (4,1), (4,3). Using C++ Code an O(nlog(n)) algorithm to count the number of inversions. Use the Merge sort Algorithm, and use the template below: (Use the file below that to test)

countInv.cpp -------------------------------------------------------------------------------------------------------------------------------

#include <vector>
#include <algorithm>

using namespace std;

int mergeInv(vector<int>& nums, vector<int>& left, vector<int>& right) {

// Your code here

}

int countInv(vector<int>&nums) {
// Your code here

}

CountInv_test.cpp -------------------------------------------------------------------------------------------------------------------------

#include <iostream>
#include <vector>

using namespace std;

int countInv(vector<int>& numvec);

int main()
{
int n;
vector<int> numvec{4, 5, 6, 1, 2, 3};
n = countInv(numvec);
cout << "Number of inversions " << n << endl; // Should be 9
  
numvec = {1, 2, 3, 4, 5, 6};
n = countInv(numvec);
cout << "Number of inversions " << n << endl; // Should be 0
  
numvec = {6, 5, 4, 3, 2, 1};
n = countInv(numvec);
cout << "Number of inversions " << n << endl; // Should be 15
  
numvec = {0, 0, 0, 0, 0, 0};
n = countInv(numvec);
cout << "Number of inversions " << n << endl;; // Should be 0
}

Investment A:
Year: 0 1 2 3 4 5
Cash flow: -$14,000 $6,000 $6,000 $6,000 $6,000 $6,000

Investment B:
Year: 0 1 2 3 4 5
Cash flow: -$15,000 $7,000 $7,000 $7,000 $7,000 $7,000

Investment C:
Year: 0 1 2 3 4 5
Cash flow: -$18,000 $12,000 $4,000 $4,000 $4,000 $4,000

The cash flows for three projects are shown above. The cost of capital is 7.5%. If an investor decided to take projects with a payback period two years or less, which of these projects would he take?

Select one:

A. Investment A

B. Investment B

C. Investment C

D. none of these investments

1. Supplementary motor cortex
2. Premotor cortex
3. Basal ganglia
4. Cerebellum
5. Parietal area of the cerebral cortex
6. Spinothalamic pathway
7. Corticospinal tract
8. Dorsal root ganglion
9. Dorsal Column pathway
Q1. Which structure or region is damaged in patients with Parkinson’s disease?
Answer 1Choose...1.2.3.4.5.6.7.8.9.
Q2. Which structure or region includes the cell bodies of sensory neurons?
Answer 2Choose...1.2.3.4.5.6.7.8.9.
Q3. Which structure or region conveys information from the brain to the spinal cord?
Answer 3Choose...1.2.3.4.5.6.7.8.9.
Q4. Which structure or region is damaged in patients with Huntington’s disease?
Answer 4Choose...1.2.3.4.5.6.7.8.9.
Q5. Which structure or region that is not part of the cerebral cortex is involved in initiating complex movements?
Answer 5Choose...1.2.3.4.5.6.7.8.9.
Q6. Which structure or region handles information from pain receptors?1.2.3.4.5.6.7.8.9.

Calculate Payback period, Net Present Value and Benefit Cost Ratio

(a) Find and interpret the expected value of X

(b)Find the variance of X

(c)Find the probability that a person has 1 sibling given that they have less than 3 siblings.

(d)Find the probability that a person has at least 1 sibling OR less than 2 siblings

A three-digit number is formed from nine numbers (1, 2, 3, 4, 5, 6, 7, 8 & 9). No number can be repeated. How many different three-digit numbers are possible if 1 and 2 will not be chosen together? a. 462 b. 210 c. 672 d. 336

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Consider the following time series data.

Round your answers to two decimal places.

a. Compute MSE using the most recent value as the forecast for the next period.

Mean squared error is ?

What is the forecast for month 8 ?

b. Compute MSE using the average of all data available as the forecast for the next period.

Mean squared error is ?

What is the forecast for month 8 ?

Consider the following time series.