we have
This is the equation of a vertical parabola with vertex at point 
The parabola open upward------> the vertex is a minimum
This is the equation of a vertical parabola with vertex at point 
The parabola open upward------> the vertex is a minimum
so
the rule of the translation is
that means
the translation is 
units to the right and 
units up
the graph of the function g(x) is the translated graphic of the function f(x) units to the right and units up
therefore
<u>the answer is</u>
g(x) is shifted units right and units up
Answer:
117
Step-by-step explanation:
yehheherhehejehheeh
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:
(w + 11)(w + 7)
Step-by-step explanation:
Consider the factors of the constant term ( + 77) which sum to give the coefficient of the w- term ( + 18)
The factors are + 11 and + 7, since
11 × 7 = 77 and + 11 + 7 = + 18
w² + 18w + 77 = (w + 11)(w + 7)
Answer:
a > −
18 or (
−
18
,
∞
)
Step-by-step explanation:
