B.) 3.250*106 days
I figured it out!! Yay!
You take 7.8 and divide it by 24 which will get you 0.325
In order to get it match one of the options, multiply it by 10 (which will add 1 to 105!) Leaving you 3.25*106
In your calculator, input arcsin(7/12). Make sure that your calculator is in degree mode. The answer is 35.69 degrees.
So on the top, you split it up using the difference of squares rule.
You get (x - 6)(x + 6) on the top.
On the bottom, you can undistribute (pull out) -7x.
This gives you -7x(x-6) on the bottom.
Now you can cancel like terms in the numerator and denominator.
You can cancel the (x-6).
You can also move the negative sign from the 7x to the (x + 6)
This leaves you with -(x + 6) over 7x, or (6 - x) over 7x.
To find excluded values, all you need to know is that you can't divide by zero under any circumstances, and you can't have a zero on the top in a rational expression.
The only values for x that would make either of these statements true are if x = 0 (7 × 0 = 0 on the bottom), or if x = 6 (6 - 6 +0 on the top)
So the answer is (6 - x) over 7x, x ≠ 0, 6
<span>Vector Ā * Vector B = -10. This is the scalar dot product and can calculated by taking the magnitude in the x, y, and z of the two vectors and the operation is done.
The angle </span> Ɵ AB between vector Ā and vector B is 133.635°.
<span>2 Vector B * 3 Vector C = -1. A similar approach is done for this one.</span>
Answer:
The expected number of minutes the rat will be trapped in the maze is 21 minutes.
Step-by-step explanation:
The rat has two directions to leave the maze.
The probability of selecting any of the two directions is, 
.
If the rat selects the right direction, the rat will return to the starting point after 3 minutes.
If the rat selects the left direction then the rat will leave the maze with probability 
after 2 minutes. And with probability 
the rat will return to the starting point after 5 minutes of wandering.
Let <em>X</em> = number of minutes the rat will be trapped in the maze.
Compute the expected value of <em>X</em> as follows:
![E(X)=[(3+E(X)\times\frac{1}{2} ]+[2\times\frac{1}{6} ]+[(5+E(X)\times\frac{2}{6} ]\\E(X)=\frac{3}{2} +\frac{E(X)}{2}+\frac{1}{3}+\frac{5}{3} +\frac{E(X)}{3} \\E(X)-\frac{E(X)}{2}-\frac{E(X)}{3}=\frac{3}{2} +\frac{1}{3}+\frac{5}{3} \\\frac{6E(X)-3E(X)-2E(X)}{6}=\frac{9+2+10}{6}\\\frac{E(X)}{6}=\frac{21}{6}\\E(X)=21](https://tex.z-dn.net/?f=E%28X%29%3D%5B%283%2BE%28X%29%5Ctimes%5Cfrac%7B1%7D%7B2%7D%20%5D%2B%5B2%5Ctimes%5Cfrac%7B1%7D%7B6%7D%20%5D%2B%5B%285%2BE%28X%29%5Ctimes%5Cfrac%7B2%7D%7B6%7D%20%5D%5C%5CE%28X%29%3D%5Cfrac%7B3%7D%7B2%7D%20%2B%5Cfrac%7BE%28X%29%7D%7B2%7D%2B%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B5%7D%7B3%7D%20%2B%5Cfrac%7BE%28X%29%7D%7B3%7D%20%5C%5CE%28X%29-%5Cfrac%7BE%28X%29%7D%7B2%7D-%5Cfrac%7BE%28X%29%7D%7B3%7D%3D%5Cfrac%7B3%7D%7B2%7D%20%2B%5Cfrac%7B1%7D%7B3%7D%2B%5Cfrac%7B5%7D%7B3%7D%20%5C%5C%5Cfrac%7B6E%28X%29-3E%28X%29-2E%28X%29%7D%7B6%7D%3D%5Cfrac%7B9%2B2%2B10%7D%7B6%7D%5C%5C%5Cfrac%7BE%28X%29%7D%7B6%7D%3D%5Cfrac%7B21%7D%7B6%7D%5C%5CE%28X%29%3D21)
Thus, the expected number of minutes the rat will be trapped in the maze is 21 minutes.
