A church has 8 bells in its bell tower. Before each church service 5 bells are rung in sequence. No bell is rung more than once.

The illustration is omitted. Please see the attachment below.

Answer:

The area of the shaded sector is 144π square units.

Step-by-step breakdown:

Given:

The central angle for the sector is,

The circle's radius is,

The area of a sector with radius 'R' and angle can be determined with:

Substituting gives

Thus, the area of the shaded sector calculates to 144π square units.

b

Given:

A quadratic function has a line of symmetry positioned at x = –3.5 with one root located at –9.

To find:

The second root.

Solution:

It is understood that the line of symmetry splits the quadratic function's graph into two identical halves. Hence, both roots are equidistant from this line.

This implies that the line of symmetry passes through the midpoint of the two roots.

Let the other root be denoted as x.

Multiply both sides by 2.

Add 9 to both sides.

Consequently, the other zero of the quadratic function is concluded to be 2.

Approximately 111.97

The total number of juices equals 27, with the probabilities for each type being as follows: apple juice = 12/27, grape juice = 15/27, sugar-free = 14/27, and not sugar-free = 13/27. Since it has already been established that the chosen juice is not sugar-free, we do not need to factor that probability into our calculations. Of the apple juices, 9 are sugar-free, leaving 3 that are not, and for the grape juices, 5 are sugar-free, resulting in 10 that are not. Consequently, among 13 juices that are not sugar-free, 10 are grape juice, so the likelihood of selecting a non-sugar-free grape juice is 10/13. Therefore, the answer is A). Sorry if my explanation was lengthy; I tend to elaborate.