Answer:
9.11*10^-4 %
Step-by-step explanation:
To find the probability, you simply need to find the possible outcomes that allows no rooks to be in danger, and the possible amount of ways to place the rooks.
For the first outcome, you start by putting 1 rook in the first columns, you have 8 possible rows to do this. The next rook in the next column will only have 7 possible rows, as you have to exclude the one where the previous rook is located. The next rook, 6 possibilities, the next 5, and so on. So we conclude that the total amount of ways so that none of the rooks can capture any of the other rooks is 8*7*6*5*4*3*2*1 = 8! = 40320
In order to find the total amount of ways to place the rooks, you can just use a combinatoric:
![\left[\begin{array}{ccc}64\\8\end{array}\right]= \frac{64!}{8!(64-8)!} = 4.43*10^9](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D64%5C%5C8%5Cend%7Barray%7D%5Cright%5D%3D%20%5Cfrac%7B64%21%7D%7B8%21%2864-8%29%21%7D%20%3D%204.43%2A10%5E9)
Then:
P = 
I don’t know about the slope but the Y-Intercept is just the Y.
Answer:
h = -t+20
After 8 hours the candle will be 12 inches
Step-by-step explanation:
We have 2 points (time, inches)
(3,17) and (5,15)
We can find the slope
m = (y2-y1)/(x2-x1)
= (15-17)/(5-3)
= -2/2
= -1
We can use point slope form
y-y1 = m(x-x1)
Replace y with h and x with t
h-17 = -1 (t-3)
Distribute
h-17 = -t+3
Add 17 to each side
h-17+17 = -t+3+17
h = -t+20
we know that
the volume of a solid oblique pyramid is equal to
where
B is the area of the base
h is the height of the pyramid
in this problem we have that
B is a square
where
<u>
</u>
so
substitute in the formula of volume
![V=\frac{1}{3}*x^{2}*(x+2)\\ \\V=\frac{1}{3}*[x^{3} +2x^{2}]\ cm^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%2Ax%5E%7B2%7D%2A%28x%2B2%29%5C%5C%20%5C%5CV%3D%5Cfrac%7B1%7D%7B3%7D%2A%5Bx%5E%7B3%7D%20%2B2x%5E%7B2%7D%5D%5C%20cm%5E%7B3%7D)
therefore
<u>the answer is</u>
![V=\frac{1}{3}*[x^{3} +2x^{2}]\ cm^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%2A%5Bx%5E%7B3%7D%20%2B2x%5E%7B2%7D%5D%5C%20cm%5E%7B3%7D)
Answer:
Step-by-step explanation:
(4+1)/(8-2)= 5/6
y + 1 = 5/6(x - 2)
y + 1 = 5/6x - 5/3
y + 3/3 = 5/6x - 5/3
y = 5/6x - 8/3
6(y = 5/6x - 8/3)
6y = 5x - 16
-5x + 6y = -16
