Answer:
The probability that Joe's stock will go up and he will win in the lottery is 0.00005.
Step-by-step explanation:
Let the events be denoted as:
<em>X</em> = the stock goes up
<em>Y</em> = Joe wins the lottery
Given:
P (X) = 0.50
P (Y) = 0.0001
The events of the stock going up is not dependent on the the event of Joe winning the lottery.
So the events <em>X</em> and <em>Y</em> are independent of each other.
Independent events are those events that can occur together at the same time.
The joint probability of two independent events <em>A</em> and <em>B </em>is,
![P(A\cap B)=P(A)\times P(B)](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3DP%28A%29%5Ctimes%20P%28B%29)
Compute the value of P (<em>X ∩ Y</em>) as follows:
![P(X\cap Y)=P(X)\times P(Y)=0.50\times 0.0001=0.00005](https://tex.z-dn.net/?f=P%28X%5Ccap%20Y%29%3DP%28X%29%5Ctimes%20P%28Y%29%3D0.50%5Ctimes%200.0001%3D0.00005)
Thus, the probability that Joe's stock will go up and he will win in the lottery is 0.00005.
Answer:
The average rate of change from x = −2 to x = 0 is 3.
Step-by-step explanation:
The given function is,
![f(x)=2x^3+x^2-3x+1](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E3%2Bx%5E2-3x%2B1)
Put x=-2,
![f(-2)=2(-2)^3+(-2)^2-3(-2)+1=-5](https://tex.z-dn.net/?f=f%28-2%29%3D2%28-2%29%5E3%2B%28-2%29%5E2-3%28-2%29%2B1%3D-5)
Put x=0
![f(0)=2(0)^3+(0)^2-3(0)+1=-1](https://tex.z-dn.net/?f=f%280%29%3D2%280%29%5E3%2B%280%29%5E2-3%280%29%2B1%3D-1)
From the graph of f(x) it is noticed that the graph passing through (-2,-5) and (0,2).
Average rate of change is the change is function with respect to x.
![m=\frac{f(x_2)-f(x_1)}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bf%28x_2%29-f%28x_1%29%7D%7Bx_2-x_1%7D)
![m=\frac{f(0)-f(-2)}{0-(-2)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bf%280%29-f%28-2%29%7D%7B0-%28-2%29%7D)
![m=\frac{1-(-5)}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1-%28-5%29%7D%7B2%7D)
![m=\frac{1+5}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%2B5%7D%7B2%7D)
![m=\frac{6}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B6%7D%7B2%7D)
![m=3](https://tex.z-dn.net/?f=m%3D3)
Therefore the average rate of change from x = −2 to x = 0 is 3.
Answer:
a). Yes. Area will be less than 100 square in.
b). Area of octagon = 82 in²
Step-by-step explanation:
From the picture attached,
a). Octagon is inscribed in a square having one side = 10 inches.
Since, octagon is obtained by cutting off the four equal corners of the square,
Area of octagon will be less than the area of the square.
Area of square = (side)²
= 10²
= 100 in²
Therefore, area of octagon will be less than 100 in²
b). Since, corner cut off from the square are equal in shape and area,
Area of one corner (right angle triangle) = ![\frac{1}{2}(\text{Base})(\text{Height})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Ctext%7BBase%7D%29%28%5Ctext%7BHeight%7D%29)
=
= 4.5 in²
Area of 4 corners = 4.5 × 4 = 18 in²
Area of octagon = Area of square - Area of 4 corners removed
= 100 - 18
= 82 in²
<span>Ray BE bisects </span>∠ABD.
According to picture, this is the solution. In case the question is complete.
X^2 - 2x - 8
2 numbers that multiplied give -8
2 numbers that added give -2
2 x -4 = -8
2 + -4 = -2
(x + 2) (x -4 )
roots equal = -2, 4
x^2 - 2x -8
a. b. c because b is -2 in the equation you don't plug b as a negative
in the axis of symmetry
axis of symmetry = -b divide by 2a
2 divide by 2(1) =1
Vertex= (1, -9)