3(x-7)+8=-20
Multiply the bracket by 3
(3)(x)(3(-7)+8= -20
3x-21+8= -20
3x-13= -20
Move -13 to the other side. Sign changes from -13 to +13.
3x-13+13= -20+13
3x= -7
Divide by 3
3x/3= -7/3
x= -7/3 or in mixed number : -2 1/3
Answer : x= -7/3 or in mixed number : -2 1/3
<span>B. {-5,-4,-3…. }
............</span>
Answer:
We need to remember that we have independent events when a given event is not affected by previous events, and we can verify if two events are independnet with the following equation:
![P(A \cap B) = P(A) *P(B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20P%28A%29%20%2AP%28B%29)
For this case we have that:
![P(A) *P(B) = 0.01*0.02= 0.0002](https://tex.z-dn.net/?f=%20P%28A%29%20%2AP%28B%29%20%3D%200.01%2A0.02%3D%200.0002)
And we see that ![0.0002 \neq P(A \cap B)](https://tex.z-dn.net/?f=%200.0002%20%5Cneq%20P%28A%20%5Ccap%20B%29)
So then we can conclude that the two events given are not independent and have a relationship or dependence.
Step-by-step explanation:
For this case we can define the following events:
A= In a certain computer a memory failure
B= In a certain computer a hard disk failure
We have the probability for the two events given on this case:
![P(A) = 0.01 , P(B) = 0.02](https://tex.z-dn.net/?f=%20P%28A%29%20%3D%200.01%20%2C%20P%28B%29%20%3D%200.02)
We also know the probability that the memory and the hard drive fail simultaneously given by:
![P(A \cap B) = 0.0014](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%200.0014)
And we want to check if the two events are independent.
We need to remember that we have independent events when a given event is not affected by previous events, and we can verify if two events are independnet with the following equation:
![P(A \cap B) = P(A) *P(B)](https://tex.z-dn.net/?f=%20P%28A%20%5Ccap%20B%29%20%3D%20P%28A%29%20%2AP%28B%29)
For this case we have that:
![P(A) *P(B) = 0.01*0.02= 0.0002](https://tex.z-dn.net/?f=%20P%28A%29%20%2AP%28B%29%20%3D%200.01%2A0.02%3D%200.0002)
And we see that ![0.0002 \neq P(A \cap B)](https://tex.z-dn.net/?f=%200.0002%20%5Cneq%20P%28A%20%5Ccap%20B%29)
So then we can conclude that the two events given are not independent and have a relationship or dependence.
Answer:
LCM = 4590
Step-by-step explanation:
1. Find the prime factorization of 306
306 = 2 × 3 × 3 × 17
2. Find the prime factorization of 270
270 = 2 × 3 × 3 × 3 × 5
3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2 × 3 × 3 × 3 × 5 × 17