X is greater than or equal to -5
Answer:
24.
Step-by-step explanation:
We can use the factorial function to find the number of unique arrangements in a word.
There are 4 unique characters in 'OPAL'. As such, 4! = 24.
In the case that there were repeating characters, such as 'OPALA', then we would divide by the factorial of the number of repeating letters. That looks something like this:

Hope this helped.
Answer:
(see image)
bottom right image
Explanation:
First try the origin (0,0) to rule out two of the graphs.
3y ≥ x - 9 3(0) ≥ (0) - 9
3 ≥ - 9
yes 3x + y > - 3 3(0) + (0) > - 3
3 > - 3
yes so the origin should be in the shaded area of the graph, which rules out the top right and bottom left graphs.
Now try a coordinate that is in the shaded area of one of the remaining graphs, but not in the other one. If it works, the graph is the one that has that point in the shaded region, and vice versa.
Try point (4, 2)
3y ≥ x - 9
3(2) ≥ (4) - 9
6 ≥ - 5
yes3x + y > - 3
3(4) + (2) > - 3
12 + 2 > - 3
14 > - 3
yesSo the graph is the bottom right one since (4, 2) is included in that shaded region.
Answer:
0.02651
Step-by-step explanation:
P(all 5 are boys) =

= 0.02651 ( wow low)