Find a solution to the linear equation y=8x−32 by filling in the boxes with a valid value of x and y.

Response:

The fence's width is 6 feet.

Detailed explanation:

To start, let’s define some variables.

Let the width of the fence be denoted as w, and the length as l.

Next, determine the length: the width is 2 feet less than half of the length.

w = l/2 - 2

Alternatively, l/2 can be expressed as w + 2, leading to l = 2(w + 2).

The total perimeter of the fence is 44 feet. The perimeter for a rectangle can be calculated using the formula:

P = 2(l + w)

Inserting what we know:

P = 44 and l = 2(w + 2)

44 = 2(2(w+2) + w)

44 = 2(2w + 4 + w)

44 = 2(3w + 4)

44 = 6w + 8

6w = 36

w = 36/6

w = 6 feet

Imagine having a pile of pennies and you want to determine if the count is odd or even without tallying them one by one. You can separate them into pairs by placing one coin in the left pile and one in the right.

If no coin is left unmatched, then the total number is even; if there is one coin remaining unpaired, the number is odd.

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