-3,-7.5,2 2/3 are the opposites of those numbers
        
             
        
        
        
Answer:
The correct answer B) The volumes are equal.
Step-by-step explanation:
The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,

which when evaluated gives 4pi/3.
Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,

If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.
 
        
             
        
        
        
Answer:1.01
Step-by-step explanation:
 
        
             
        
        
        
Answer: a) 0.2222, b) 0.3292, c) 0.1111
Step-by-step explanation:
Since we have given that 
Let the probability of getting head be p.
Since,  its head is twice as likely to occur as its tail.

a)If the coin is flipped 3 times, what is the probability of getting exactly 1 head?
So, here, n  = 3


Now, 

b)If the coin is flipped 5 times, what is the probability of getting exactly 2 tails?
2 tails means 3 heads.
So, it becomes,

c)If the coin is flipped 4 times, what is the probability of getting at least 3 tails?

Hence, a) 0.2222, b) 0.3292, c) 0.1111