Assume the input graph is directed but may or may not have cycle in it, that is, may or may not be a directed acyclic graph. Consider the recursive topological sorting algorithm shown below. TopologicalSort(G) { If G has only one node v then return v. Find a node v with no incoming edge and remove v from G. Return v followed by the order returned by TopologicalSort(G). }

(a) Extend the recursive algorithm shown below so it can detect and output a cycle if the input graph G is not a directed acyclic graph. Clearly mark the extended part of the algorithm and state your reasoning behind the extension made.

A professor is studying to see if there is a relationship between the grades and gender of his students. He picks a random sample of his students and notes their grades (A, B, or C) and their gender (male or female). He finds that:

1. 28% are A students.
2. 58% are B students.
3. 62% of his students are female.
4. Of those who are female, one-third are A students.
5. Of those who are B students, three-fifths are female students.

What percentage of the students are male and have a C grade?

A professor is studying to see if there is a relationship between the grades and gender of his students. He picks a random sample of his students and notes their grades (A, B, or C) and their gender (male or female). He finds that:

1. 28% are A students.
2. 58% are B students.
3. 62% of his students are female.
4. Of those who are female, one-third are A students.
5. Of those who are B students, three-fifths are female students.

What percentage of the students are male and have a C grade?

Outline the Constitutional rights of public employees. What restrictions can be placed upon public employees? Refer to Supreme Court cases where appropriate.

            Pickering v Board of Education (1968)

            Norton v Macy (1969)

            Kelly v Johnson (1976)

In the figure below, the switch is left in position a for a long time interval and is then quickly thrown to position b. Rank the magnitudes of the voltages across the four circuit elements a short time thereafter from the largest to the smallest.
a.ΔV1200 Ω > ΔVL > 12.0 V > ΔV12.0 Ω
b.ΔVL > ΔV1200 Ω > 12.0 V > ΔV12.0 Ω
c.ΔV1200 Ω > ΔVL = 12.0 V > ΔV12.0 Ω
d.ΔV1200 Ω = ΔVL > 12.0 V > ΔV12.0 Ω

1.let {v=(1,2,3,5,9),v2=(3,1,2,8,9),v3=(2,-5,5,9,4)} and {u1=(0,1,1,1,2),u2=(0,2,-2,-2,0)} be basis of subspaces V and U of R5 respectively.find a basis and the dimension of V+U and V intersection U.

2.does a matrix have a right inverse ?if so find one A=[2,-3,-7,11;3,-1,-7,13;1,2,0,2]

3.find the interpolating polynomial that passes through the point (1,2),)(-1,-8) and (2,1)

Calculate E o , E, and ΔG for the following cell reactions

(a) Mg(s) + Sn2+(aq) ⇌ Mg2+(aq) + Sn(s)

where [Mg2+] = 0.035 M and [Sn2+] = 0.040 M

E o = V

E = V

ΔG = kJ

(b) 3Zn(s) + 2Cr3+(aq) ⇌ 3Zn2+(aq) + 2Cr(s)

where [Cr3+] = 0.090 M and [Zn2+] = 0.0085 M

E o = V

E =    V

ΔG = kJ

(From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Review Exercises for Chapter 2, # 7)

Use the chain rule to find D ( f ∘ g ) ( − 1 , 2 ) for f ( u , v , w ) = ( v 2 + w 2 , u 3 − v w , u 2 v + w ) and g ( x , y ) = ( 3 x + 2 y , x 3 y , y 2 − x 2 ).

There is a Java program that is missing one recursive function:

public class BinarySearch {

  /*                          / -1                    when min > max
   *                          | mid                   when A[mid] = v
   * search(A, v, min, max) = | search(A,v,mid+1,max) when A[mid] < v
   *                          \ search(A,v,min,mid-1) otherwise
   * where mid = (min+max)/2
   */
  public static int search_rec(int[] A, int v, int min, int max) {
    return 0;
  }

  public static int search(int[] A, int v) {
    return search_rec(A, v, 0, A.length-1);
  }

  /* Binary Search Test Framework
   *
   */
  public static void main(String[] args) {
    int[] inputA  = { 0, 1,    3, 4, 5, 6, 7, 8, 9, 10};
    int[] inputV  = { 3, 8,  2};
    int[] expect  = { 2, 7, -1};

    boolean error = false;

    for(int i = 0 ; i < inputV.length; i++) {
      int answer = search(inputA, inputV[i]);
      if(answer != expect[i]) {
        System.out.printf("ERROR: search(A,%d) returned %d not %d.\n",
                           inputV[i], answer, expect[i]);
        error = true;
      }
    }

    if(error)
      System.exit(1);
    else
      System.out.println("Good Job!");
  }
}

MAJOR VESSELS OF THE BODY

Unless otherwise indicated, the veins have the same naming of the arteries and are paired with the artery. Most of the exceptions are found with superficial veins in the limbs, or veins in the thorax.

Vessels of the Thorax & Neck:

• Aorta

• Common Carotid A.

• Brachiocephalic V.

• Arch of Aorta
• Subclavian A & V
• Superior Vena Cava

• Brachiocephalic Trunk • External Jugular V.
• Inferior Vena Cava

1. Focus on the difference between the Brachiocephalic TRUNK and the Brachiocephalic VEIN

2. What side of the body does the brachiocephalic trunk supply?

Vessels of the Upper Limb:

• Axillary • Brachial

• Ulnar • Cephalic V.

• Median Cubital V.

• Radial
• Basilic V.

1. What are the 2 superficial veins of the upper limb that drain the skin and do not have paired arteries?

2. Is the Cephalic Vein found on the medial or lateral side of the arm?

Vessels of the Lower Limb:

• Common Iliac •

• Femoral •

• Great Saphenous V. •

Internal Iliac • External Iliac Popliteal • Dorsal Venous Arch Small Saphenous V.

1. What are the 2 superficial veins of the lower limb that drain the skin and do not have paired arteries?

2. Is the Great Saphenous Vein found on the medial or lateral side of the leg?

PLEASE ANSWR ALL OF THE ABOVE.