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b) A committee of 5 people is to be chosen from 6 men and 4 women. In how many ways can this be done (i) if there must be 3 men and 2 women on the committee (ii) if there must be more men than women on the committee (iii) if there must be 3 men and 2 women, and one particular woman refuses to be on the committee with one particular man? c) A shop sells old video tapes, of which 1 in 5 on average are known to be damaged. (i) A random sample of 15 tapes is taken. Find the probability that at most 2 are damaged (ii) Find the smallest value of n if there is a probability of at least 0.85 that a random sample of n tapes contains at least one damaged tape.

Given F(t) = (512 - 31 )i+61°-7 -70Kevaluate | F(t)dt. t=2

 

 

 

 

 

 

void Lab_Reflect(double a[][4], int n, double pt1[3], double pt2[3],
double b[][4])
/*
    function:     to generate a mirror image of a set of vertices 
                with respect to a mirroring line defined by its
                end points.

    input: a[][4] - a set of vertices
            a[i][0] - the x-coordinate of the (i+1)th vertex
            a[i][1] - the y-coordinate of the (i+1)th vertex
            a[i][2] - the z-coordinate of the (i+1)th vertex
            a[i][3] - the h-coordinate of the (i+1)th vertex

        n - no. of vertices specified in a[][]

        pt1[3] - the first end point of the mirroring line
                pt1[0] - x coordinate
                pt1[1] - y coordinate
                pt1[2] - z coordinate

        pt2[3] - the second end point of the mirroring line
                pt2[0] - x coordinate
                pt2[1] - y coordinate
                pt2[2] - z coordinate
        
    output: b[][4] - the set of transformed vertices
    b[i][0] - the x-coord of the (i+1)th mirrored vertex
    b[i][1] - the y-coord of the (i+1)th mirrored vertex
    b[i][2] - the z-coord of the (i+1)th mirrored vertex
    b[i][3] - the h-coord of the (i+1)th mirrored vertex
*/
{
    /* determine angle of rotation the brings the mirror line to
       become horizontal */
    double dx, dy;
    dx = pt2[0] - pt1[0];
    dy = pt2[1] - pt1[1];

    double ang;
    if (fabs(dx) < 0.0001) ang = 1.57079; // mirror line vertical
    else ang = atan2(dy, dx);
    ang = -1.0*ang; // inverse the sign

    /* store the sine and cosine of the angle, to be used in the
   rotation matrices */
    double cosine = cos(ang); 
    double sine = sin(ang);

    // setup the translation matrix
    double Mtrans1[4][4];
    matrix_identity(Mtrans1);
    for (int i=0; i<3; i++)
        Mtrans1[3][i] = -1.0*pt1[i];

    // setup the inverse translation matrix
    double Mtrans2[4][4];
    matrix_identity(Mtrans2);
    for (i=0; i<3; i++)
        Mtrans2[3][i] = pt1[i];

    // setup the rotation matrix
    double Mrot1[4][4];
    matrix_identity(Mrot1);
    Mrot1[0][0] = cosine;
    Mrot1[1][1] = cosine;
    Mrot1[0][1] = sine;
    Mrot1[1][0] = -1.0*sine;

    double Mrot2[4][4];
    matrix_identity(Mrot2);
    Mrot2[0][0] = cosine;
    Mrot2[1][1] = cosine;
    Mrot2[0][1] = -1.0*sine;
    Mrot2[1][0] = sine;

    // setup the reflection matrix
    double Mref[4][4];
    matrix_identity(Mref);
    Mref[1][1]=-1.0;

    // setup the concatenated matrix
    double Mcon[4][4], temp1[4][4], temp2[4][4], temp3[4][4];
    matrix_matrix(Mtrans1, Mrot1, temp1);
    matrix_matrix(temp1, Mref, temp2);
    matrix_matrix(temp2, Mrot2, temp3);
    matrix_matrix(temp3, Mtrans2, Mcon);

    // Apply multiplication to all vertices
    for (int k=0; k<n; k++) // loop for all vertices
            vector_matrix(a[k], Mcon, b[k]);
}

Question Modify the Lab_Reflect() function so that the function performs Scaling of a polygon with respect to the reference point pt1. The scale factor equals to 1/10 of the distance between pti and pt2. Note 1: The C function sqrt() can be used. The function sqrto provided in the C library computes the square root of a value. For example: double x, y; x= 4.0; y = sqrt(x); y will be given the value 2.0. Note 2: The Scaling transformation is similar to the operation of rotation about an arbitrary point. It consists of three steps: 1. Translate the polygon such that pti is moved to the origin. 2. Perform scaling using the following matrix. 3. Perform inverse translation. s 0 0 0 0 S 0 0 Matrix for scaling: o o 0 0 S 0 O 0 0 1 1 CS Scanned with CamScanner

Question Nine (9): The world has limited resources or limited factors of production (labor, capital, land, and entrepreneurship). These limited resources are met with the unlimited wants of all societies (we all want to consume these resources to the max but there is not enough to go around). This results in the economic problem of scarcity which leads the rational man (economic agent) to be forced to make a choice. Making a choice means that, you have to face an opportunity cost. So, *limited resources lead to the economic problem of scarcity. This, in turn, forces economic agents to make choices and thus incur opportunity costs.

* According to what you have studied about (scarcity, choice, opportunity cost, and factors of production. If you will put up your own business, how will you answer the three economic questions: (What to produce? How to produce? For whom to produce?).

in your own words, what do you understand with the concept of reinforcement and punishment?

QUESTION 14 Fill in the missing parts of the following code required to make the paragraph changes its content to "UTAS University" when clicked. 1/ add missing part

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