Answer:
I think that what you are trying to show is: If 
is irrational and 
is rational, then 
is rational. If so, a proof can be as follows:
Step-by-step explanation:
Suppose that is a rational number. Then and can be written as follows
Hence we have that
Then
This is a contradiction because we assumed that is an irrational number.
Then must be an irrational number.
Answer:
the probability is 0.311 (31.1%)
Step-by-step explanation:
defining the event L= being late to work :Then knowing that each mode of transportation is equally likely (since we do not know its travel habits) :
P(L)= probability of taking the bicycle * probability of being late if he takes the bicycle + probability of taking the car* probability of being late if he takes the car + probability of taking the bus* probability of being late if he takes the bus +probability of taking the train* probability of being late if he takes the train = 1/4 * 0.75 + 1/4 * 0.43 + 1/4 * 0.15 + 1/4 * 0.05 = 0.345
then we can use the theorem of Bayes for conditional probability. Thus defining the event C= Bob takes the car , we have
P(C/L)= P(C∩L)/P(L) = 1/4 * 0.43 /0.345 = 0.311 (31.1%)
where
P(C∩L)= probability of taking the car and being late
P(C/L)= probability that Bob had taken the car given that he is late
Answer:
4x²×(1+7x)
Step-by-step explanation:
Answer:
length=20.8
width=5.2
Step-by-step explanation:
Let the length be 4x and width be x
According to the question
perimeter=52ft
Now
perimeter of the rectangle=2(l+b)
52=2(4x+x)
52=10x
x=5.2ft
width=5.2ft
length=4x =4*5.2 =20.8ft
