Answer:
0.000298 = 0.0298% probability that the system will collapse
Step-by-step explanation:
Number of possible ways the system can fail:
2 lines from a set of 3 fail, or all three fail.
Two from a set of 3:
Can be A and B, A and C, or B and C. Three possible outcomes then.
The probability of each is:
0.01*0.01*0.99
Two failling, each with 0.01 probability, and 1 working, with 0.99 probability.
All three:
Each with 0.01 probability.
a) What is the probability that the system will collapse
Both cases, so
0.000298 = 0.0298% probability that the system will collapse
Answer: b.14
Step-by-step explanation:
We have two shelves, the top shelf 
and the bottom shelf 
.
Now, firstly we are told the top shelf has 10 more than 1/3 the number of books on the bottom shelf. This can be expressed as:
(1)
Then, we are told there are 12 books on the bottom shelf:
(2)
Substituting (2) in (1):
(3)
(4)
(5) This is the number of books on the top shelf
Hence, the correct option is b.
Answer:
The plane's distance from the radar station will increase about 8 miles per minute when it is 5 miles away from it.
Step-by-step explanation:
When the plane passes over the radar station, the current distance is the altitude h = 2. Then it moves b horizontally so that the distance to the station is 5. We can form a rectangle triangle using b, h and the hypotenuse 5. Therefore, b should satisfy
h²+b² = 5², since h = 2, h² = 4, as a result
b² = 25-4 = 21, thus
b = √21.
Since it moved √21 mi, then the time passed is √21/540 = 0.008466 hours, which is 0.51 minutes. Note that in 1 minute, the plane makes 540/60 = 9 miles.
The distance between the plane and the radar station after x minutes from the moment that the plane passes over it is given by the function
We have to compute the derivate of f in x = 0.51. The derivate of f is given by
also,
The plane's distance from the station will increase about 8 miles per minute.
Answer:
Probability Distributions
A listing of all the values the random variable can assume with their corresponding probabilities make a probability distribution.
A note about random variables. A random variable does not mean that the values can be anything (a random number). Random variables have a well defined set of outcomes and well defined probabilities for the occurrence of each outcome. The random refers to the fact that the outcomes happen by chance -- that is, you don't know which outcome will occur next.
X+x+1+x+2=51
3x+3=51
Use inverse operations to solve
subtract 3 from both sides
3x=48
Divide by 3 on both sides
x=16
16, 17, 18
