1 answer:
You might be interested in
Answer:
x = 6, 9
Step 1:
To solve this equation, we need to subtract 3 from both sides like this:
Step 2:
We square both sides (multiply using FOIL) to get rid of the radical.
If you did not understand how these were done, here is an example:
(x + 1)(x + 2)
First terms: x * x = <u><em>x^2</em></u>
Outer terms: x * 2 = 2x
Inner terms: 1 * x = x
2x - x = <u><em>x</em></u>
Last terms: 1 * 2 =<em> </em><u><em>2</em></u>
x^2 + x + 2
Step 3:
Solve for x:
9x - 45 = x^2 - 6x + 9
x^2 - 6x + 9 (+45) = 9x - 45 (+45)
x^2 - 6x + 54 (-9x) = 9x (-9x)
x^2 - 15x + 54 = 0
Factor:
(x^2 - 6x) + (- 9x + 54)
x(x - 6) - 9(x - 6)
Factor out (x - 6):
(x - 6)(x - 9) = 0
x - 6 = 0; 6 - 6 = 0
x - 9 = 0; 9 - 9 = 0
Our anwer: x = 6, 9
Answer:
There is a 1.39% probability that "B is between A and C in the queue".
Step-by-step explanation:
The first step to solve this problem is find the total number of possible orderings:
The first person of the queue can be any of the six. The second, can be any but the first, so five.
So
There are 6*5*4*3*2*1 = 720 total queue orderings.
Now we find the number of queues that B is between A and C. So:
We have:
B as the second, A as the first and C as the third
B as the second, C as the first and A as the third
B as the third, A as the second and C as the fourth
B as the third, C as the second and A as the fourth
B as the fourth, A as the third and C as the fifth.
B as the fourth, C as the third and A as the fifth.
B as the fifth, A as the fourth and C as the sixth.
B as the fifth, C as the fourth and A as the sixth.
So 8 total outcomes in which B is between A and C.
What is its probability?
There is a 1.11% probability that "B is between A and C in the queue".