What is the relationship between gross pay and net pay? Gross pay is less than net pay. Gross pay is more than net pay. Gross pa
2 answers:
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Answer with Step-by-step explanation:
We are given that are in
and
is linearly dependent then {v_1,v_2,v_3,v_4}[/tex] is also linearly dependent.
We have to find that given statement is true or false.
Dependent vectors:Dependent vectors are those vectors in which atleast one vector is a linear combination of other given vectors.
Or If we have vectors
Then their linear combination
There exist at least one scalar which is not zero.
If are dependent vectors then
for scalars
Then , by definition of dependent vectors
There exist a vector which is not equal to zero
If vector is a linear combination of
, So at least one of vectors in the set is a linear combination of others and the set is linearly dependent.
Hence, by definition of dependent vectors
{} is linearly dependent.
Option B is true.
Answer:
a) Probability that vehicle is Light Truck is 0.69
b) Probability that vehicle is imported car is 0.08 or 8%.
Step-by-step explanation:
Part a)
Event that vehicle is a car is given by A. Since, the vehicles can only be classified as cars or light trucks, the event that a vehicle will be light truck will be compliment of A.
i.e. Event that vehicle is a Light Truck =
It is given that in recent year 69% of vehicles sold were light trucks, 78% were domestic, and 55% were domestic light trucks.
So, from here we can say that, if a vehicle is randomly selected from all the vehicles the probability that it would be a light truck will be:
P(Vehicle will be Light Truck) = P() = 69% = 0.69
Part b)
Event that vehicle is imported is given by B. We need to find the probability the a randomly chosen vehicle is an imported car i.e. we have to find probability of occurrence of events A and B together, which will be denoted as: P(A and B)
Since, P() = 69% = 0.69
P(A) = 1 - P() = 1 - 0.69 = 0.31
It is also given that 78% of vehicles were domestic. This means, the percentage/probability of imported vehicles is:
P(B) = 1 - 0.78 = 0.22
55% of vehicles were domestic light trucks. This can be expressed as:
, the compliment of this event will give us P(A or B).
i.e.
P(A or B) = 1 - = 1 - 0.55 = 0.45
According to the addition rule of probabilities:
P(A or B) = P(A) + P(B) - P(A and B)
Substituting the calculated values gives us:
0.45 = 0.31 + 0.22 - P(A and B)
P(A and B) = 0.08
This means, the probability that vehicle is imported car is 0.08 or 8%.