Suppose that you were going to using the Permutation approach to see if there was a difference in the amount of money spent on c

First way. Start with 10 objects—imagine 10 triangles:

Answer:

a) 11,880

b) 495

c) 0.00202

Step-by-step explanation:

Given:

Here is the full question:

"A corporation needs to select a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It also needs to form a planning committee comprising four distinct members. There are 12

qualified candidates, and the officers can also serve on the committee.

Find:

a. Determine the number of ways to appoint the officers.

Solution:

- Total qualified candidates = 12

 - Number of officers to appoint = 4 (President, Chief Executive Officer, Chief Operating Officer, Chief Financial Officer)

- Since the order matters, we use permutations:

- The number of different arrangements to appoint officers = 12P4 = 11,880

b. Determine the number of ways to select the committee members.

   Total qualified candidates = 12

  The number of planning committee members = 4  

  Here, order doesn't matter, so we use combinations:

  The number of different ways to form a committee = 12C4 = 495

c. What is the likelihood of randomly choosing the committee members being the four youngest qualified candidates?

  P ( 4 youngest officers ) =  Chances of selecting 4 youngest / Total number of committees

                                           = 1 / 495

                                           = 0.00202

Answer:

1) E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)   reflects across the x-axis

2) E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)     translates 5 units downward

3) E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)    reflects across the y-axis

4) E(4, 4), F(8, 3), G(10, 6), and H(8, 6)    translates 7 units to the right

Step-by-step explanation:

The vertices of quadrilateral ABCD are A(-3, 4), B(1, 3), C(3, 6), and D(1, 6).

1) E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this instance, the vertices share the same x-coordinates while their y-coordinates are opposites, indicating a reflection across the x-axis.

2) E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this case, the x-coordinates of the vertices remain constant, while the y-coordinates of EFGH are reduced by 5 units, indicative of a downward translation of 5 units.

3) E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

Here, the vertices share the same y-coordinates while the x-coordinates are opposites, representing a reflection across the y-axis.

4) E(4, 4), F(8, 3), G(10, 6), and H(8, 6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

For this case, the y-coordinates for EFGH remain the same while the x-coordinates have increased by 7 units, showing a rightward translation of 7 units.