To determine which relation is a function, we can perform something called the vertical line test. We cover the graph in repeating vertical lines and if one vertical line connects with more than one point of the relation, the relation is not a function.
The relation in the bottom right corner is the only relation that passes the vertical line test.
Answer:
Step-by-step explanation:
Answer: 1: x^2 + 25 = 0 x=5
2: x^2 - 11x + 28 = 0 x=7 i think
3: x^2 + 8x + 16 = 0 x=-4
Step-by-step explanation:
X=_________
or
y=_________
Most likely it will be x=s.
Answer:
![P(35-2 < X 35+2) = P(33< X< 37)= P(X](https://tex.z-dn.net/?f=%20P%2835-2%20%3C%20X%2035%2B2%29%20%3D%20P%2833%3C%20X%3C%2037%29%3D%20P%28X%3C37%29%20-P%28X%3C32%29)
And using the cumulative distribution function we got:
![P(35-2 < X 35+2) = P(33< X< 37)= P(X](https://tex.z-dn.net/?f=%20P%2835-2%20%3C%20X%2035%2B2%29%20%3D%20P%2833%3C%20X%3C%2037%29%3D%20P%28X%3C37%29%20-P%28X%3C32%29%20%3D%20%5Cfrac%7B37-20%7D%7B50-20%7D%20-%5Cfrac%7B33-20%7D%7B50-20%7D%20%3D0.567-0.433%3D0.134%20)
The probability that preparation is within 2 minutes of the mean time is 0.134
Step-by-step explanation:
For this case we define the following random variable X= (minutes) for a lab assistant to prepare the equipment for a certain experiment , and the distribution for X is given by:
![X \sim Unif (a= 20, b =50)](https://tex.z-dn.net/?f=%20X%20%5Csim%20Unif%20%28a%3D%2020%2C%20b%20%3D50%29)
The cumulative distribution function is given by:
![F(x) = \frac{x-a}{b-a} , a \leq X \leq b](https://tex.z-dn.net/?f=%20F%28x%29%20%3D%20%5Cfrac%7Bx-a%7D%7Bb-a%7D%20%2C%20a%20%5Cleq%20X%20%5Cleq%20b)
The expected value is given by:
![E(X) = \frac{a+b}{2} = \frac{20+50}{2}=35](https://tex.z-dn.net/?f=%20E%28X%29%20%3D%20%5Cfrac%7Ba%2Bb%7D%7B2%7D%20%3D%20%5Cfrac%7B20%2B50%7D%7B2%7D%3D35)
And we want to find the following probability:
![P(35-2 < X 35+2) = P(33< X< 37)](https://tex.z-dn.net/?f=%20P%2835-2%20%3C%20X%2035%2B2%29%20%3D%20P%2833%3C%20X%3C%2037%29)
And we can find this probability on this way:
![P(35-2 < X 35+2) = P(33< X< 37)= P(X](https://tex.z-dn.net/?f=%20P%2835-2%20%3C%20X%2035%2B2%29%20%3D%20P%2833%3C%20X%3C%2037%29%3D%20P%28X%3C37%29%20-P%28X%3C32%29)
And using the cumulative distribution function we got:
![P(35-2 < X 35+2) = P(33< X< 37)= P(X](https://tex.z-dn.net/?f=%20P%2835-2%20%3C%20X%2035%2B2%29%20%3D%20P%2833%3C%20X%3C%2037%29%3D%20P%28X%3C37%29%20-P%28X%3C32%29%20%3D%20%5Cfrac%7B37-20%7D%7B50-20%7D%20-%5Cfrac%7B33-20%7D%7B50-20%7D%20%3D0.567-0.433%3D0.134%20)
The probability that preparation is within 2 minutes of the mean time is 0.134