Answer:
B: (x, y) --> (x + 4, y - 3)
Step-by-step explanation:
the shape DEF went to the right along the x axis wich <em>increased</em> x and then went down the y axis or <em>decreased </em>y to make D'E'F'
some good way to remember these translations and orders are...
- x is first when plotting points, then y (x, y)
- x increases going right, and decreases going left, as well as y increasing going up, then decreasing going down
BONUS FACT:
the symbol ( ' ) is called a prime when refering to transformations and geometry ((as in D' is pronounced D prime))
It really depends on what month or year. but typically a month is 4-5 weeks so it's either 16 or 20 miles
Answer:
x = 8
Step-by-step explanation:
→ Add 16 to both sides
x = 8
Answer:
a) 0.1353
b) 0.3679
Step-by-step explanation:
Let's start by defining the random variable T.
T : ''The time (in hours) required to repair a machine''
T ~ exp (λ)
T ~ exp (1)
The probability density function for the exponential distribution is
(In the equation I replaced λ = L)
![f(x)=Le^{-Lx}](https://tex.z-dn.net/?f=f%28x%29%3DLe%5E%7B-Lx%7D)
With L > 0 and x ≥ 0
In this exercise λ = 1 ⇒
![f(x)=e^{-x}](https://tex.z-dn.net/?f=f%28x%29%3De%5E%7B-x%7D)
For a)
![P(T>2)](https://tex.z-dn.net/?f=P%28T%3E2%29)
![P(T>2)=1-P(T\leq 2)](https://tex.z-dn.net/?f=P%28T%3E2%29%3D1-P%28T%5Cleq%202%29)
![P(T>2)=1-\int\limits^2_0 {e^{-x} } \, dx](https://tex.z-dn.net/?f=P%28T%3E2%29%3D1-%5Cint%5Climits%5E2_0%20%7Be%5E%7B-x%7D%20%7D%20%5C%2C%20dx)
![P(T>2)=1-(-e^{-2}+1)](https://tex.z-dn.net/?f=P%28T%3E2%29%3D1-%28-e%5E%7B-2%7D%2B1%29)
![P(T>2)=e^{-2}=0.1353](https://tex.z-dn.net/?f=P%28T%3E2%29%3De%5E%7B-2%7D%3D0.1353)
For b)
![P(T\geq 10/T>9)](https://tex.z-dn.net/?f=P%28T%5Cgeq%2010%2FT%3E9%29)
The event (T ≥ 10 / T > 9) is equivalent to the event T ≥ 1 so they have the same probability of occur
![P(T\geq 10/T>9)=P(T\geq 1)](https://tex.z-dn.net/?f=P%28T%5Cgeq%2010%2FT%3E9%29%3DP%28T%5Cgeq%201%29)
![P(T\geq 1)=1-P(T](https://tex.z-dn.net/?f=P%28T%5Cgeq%201%29%3D1-P%28T%3C1%29%3D1-%5Cint%5Climits%5E1_0%20%7Be%5E%7B-x%7D%20%7D%20%5C%2C%20dx)
![P(T\geq 1)=1-(-e^{-1}+1)=e^{-1}=0.3679](https://tex.z-dn.net/?f=P%28T%5Cgeq%201%29%3D1-%28-e%5E%7B-1%7D%2B1%29%3De%5E%7B-1%7D%3D0.3679)