Given:
A figure in which a transversal line intersect two parallel lines.
and 
.
To find:
The value of x and y.
Solution:
We know that, if a transversal line intersect two parallel lines, then
(1) Alternate exterior angles are equal.
(2) Same sided interior angles are supplementary. So their sum is 180 degrees.
In the given figure j and k are parallel lines and l is a transversal line.
From the given figure, it is clear that,
(Alternate exterior angles are equal)
Therefore, the value of x is 20.
Now,
(Same sided interior angles are supplementary)
Therefore, the value of y is 38.
Answer:
student a because the line has a negative slope not a positive slope
Step-by-step explanation:
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.
Answer: Option b.
Step-by-step explanation:
1. You have the following parent function given in the problem above:
f(x)=x³ (This is the simplest form. We need to translate it 3 units left and 2 units down)
2. If you take the parent function and make y=f(x+3), then you have:
(The function is shifted 3 units left on the x-axis).
3. Then you if you make y=f(x+3)-2, as following, you obtain:
(The function is shifted 2 units down on the y-axis).
4. Therefore, that is how you obtain the final function.
The answer is the graph shown in the option b.
Answer:
what I'm am supposed to be answering
