The <span>given the piecewise function is :
</span>
![f(x) = \[ \begin{cases} 2x & x \ \textless \ 1 \\ 5 & x=1 \\ x^2 & x\ \textgreater \ 1 \end{cases} \]](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5C%5B%20%5Cbegin%7Bcases%7D%20%0A%20%20%20%20%20%202x%20%26%20x%20%5C%20%5Ctextless%20%5C%20%201%20%5C%5C%0A%20%20%20%20%20%205%20%26%20x%3D1%20%5C%5C%0A%20%20%20%20%20%20x%5E2%20%26%20x%5C%20%5Ctextgreater%20%5C%201%20%0A%20%20%20%5Cend%7Bcases%7D%0A%5C%5D)
To find f(5) ⇒ substitute with x = 5 in the function → x²
∴ f(5) = 5² = 25
To find f(2) ⇒ substitute with x = 5 in the function → x²
∴ f(2) = 2² = 4
To find f(-2) ⇒ substitute with x = 5 in the function → 2x
∴ f(-2) = 2 * (-2) = -4
To find f(1) ⇒ substitute with x = 1 in the function → 5
∴ f(1) = 5
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So, the statements which are true:<span>
</span><span>
</span>
Answer:
(5/12)d - (23/36)g
Step-by-step explanation:
First you can eliminate g and -g to get (1/6)d - (3/4)g + (1/9)g + (1/4)d. Then you need to get common denominators to add like terms together.
1/6 = 4/24 and 1/4 = 6/24. Add them together to get (10/24)d or (5/12)d.
-3/4 = -27/36 and 1/9 = 4/36. Add them together to get (-23/36)g.
So in standard form, (5/12)d - (23/36)g
Answer:
its true or 0
Step-by-step explanation:
Step-by-step explanation:
here's the answer to your question
Answer:
a) 
b) 
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
And 0 for other case. Let X the random variable that represent "life lengths of automobile tires of a certain brand" and we know that the distribution is given by:
The cumulative distribution function is given by:
Part a
We want to find this probability:
and for this case we can use the cumulative distribution function to find it like this:
Part b
For this case w want to find this probability
We have an important property on the exponential distribution called "Memoryless" property and says this:
On this case if we use this property we have this:
We can use the definition of the density function and find this probability:
