Based on the information provided, it follows that there are 1,728 possible seating arrangements.
<h3>How can we find the number of possible arrangements?</h3>
To find the number of arrangements in this problem situation we must take into account the following key factors:
- Chris only has 1 possible seat.
- Jo has 2 possible seats.
- Dave, Alex, and Barb have 3 possible seats.
- Gareth, Fred, and Eddie have 3 possible seats.
- There are 4 other adults who do not have a preference in seats but have the possibility of using 4 seats.
According to the above, we must use the factorization of these numbers to find out the number of possibilities we have to seat them.
<h3>What is factoring?</h3>
A factorial function is a mathematical tool that is characterized by using the exclamation mark “!” behind a number. The factorial function is used to express that the number accompanied by the symbol must be multiplied by all positive integers between that number and 1.
In accordance with the above, in the problem situation that we must solve, we must use the factorial function with the possibilities of:
- Dave, Alex and Barb: 3! = 3 × 2 × 1 = 6
- Gareth, Fred and Eddie: 3! = 3 × 2 × 1 = 6
- Other 4 adults: 4! = 4 × 3 × 2 × 1 = 24
Subsequently, to calculate the number of total possibilities of the entire group we must multiply the possibilities of each group and individual as shown below:
- Number of possibilities = 1 × 2 × 6 × 6 × 24
- Number of possibilities = 1728
Learn more about the factorial function in: brainly.com/question/16674303
The total number of seats in the theater is 600 seats, if the students filled up 570 seats, which was 95% of the total number of seats in the theater.
Step-by-step explanation:
The given is,
Seats filled by students are 570 seats
Which is 95% of the total number of seats in the theater
Step: 1
Let, x - Total number of seats available in theater
Percentage of seats filled, y= 95%
Seats filled by students = 570
Formula to calculate total number of seats in theater,
95% of seats
570 = 
x = 
= 600
x = 600 seats
Step: 2
Check for solution,
5% of seats 
= (0.05 × 600)
= 30 seats
Total no. of seats = 5% of seats + 95% of seats
= 30 + 570
600 = 600
Result:
The total number of seats in the theater is 600 seats.
Firstly, we will select three corner points
A=(2,3)
B=(6,8)
C=(7,4)
we are given
the transformation with the rule (x, y)→(x, −y)
y--->-y
so, it is reflected about x-axis
so, we will multiply y-value by -1
we get new points as
A=(2,-3)
B=(6,-8)
C=(7,-4)
now, we can locate these points and draw graph
we get
X < -16 is the solution
Hope this helped