Answer:
A and B are functions
Step-by-step explanation:
for A, none of the x's repeat which makes it a FUNCTION
for B, when it starts with x^2, it will always be a FUNCTION (its a quadratic)
for C, 10 repeats for the x so it is NOT A FUNCTION
Answer:
Multiplication
Step-by-step explanation:
x/5 = 3
Multiply by 5
x = 15
First off, let's take a look at what these numbers are:
Real numbers: It can be any numbers,both rational and irrational.
Natural numbers: The number has to be integer and positive.
Integers: A number without fraction or demical place.
Whole number: The number has to be natural and cannot be negative.
Therefore, as 12 is a positive number with no demical place or fraction, it is real numbers,integers, whole numbers, and natural numbers.
Hope it helps!
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)
Answer:
Step-by-step explanation:
(-3 + 1)/(2 + 2)= -2/4= -1/2 is the slope