Answer:
B
Step-by-step explanation:
For a relationship to be a function
Each value of x in the domain can only have 1 unique value of y in the range. That is, one-to-one correspondence.
The only relation which meets this criteria is B
I think it’s the first option
The answer is v=5x^2-100x+500. First, since we are finding the volume of a square you already know that the equation for a square is volume= length*width*height. Because 5 inches was cut off from each side, that means that each side is now 10 inches shorter than it originally was. So, then you substitute the values into the formula. So the length is x-10 and the width is also x-10 and the height is 5in. Then you write the formula like this (x-10)(x-10)5. Second, you substitute the values into the formula. Since there are 2 x's that would make x^2 and add that to 5 that would make 5x^2. Then you multiply -10*10=-100. Finally, you multiply -10*-10-5=500. Then you add them all together to get 5x^2-100x+500
Answer:Given:
P(A)=1/400
P(B|A)=9/10
P(B|~A)=1/10
By the law of complements,
P(~A)=1-P(A)=399/400
By the law of total probability,
P(B)=P(B|A)*P(A)+P(B|A)*P(~A)
=(9/10)*(1/400)+(1/10)*(399/400)
=51/500
Note: get used to working in fraction when doing probability.
(a) Find P(A|B):
By Baye's Theorem,
P(A|B)
=P(B|A)*P(A)/P(B)
=(9/10)*(1/400)/(51/500)
=3/136
(b) Find P(~A|~B)
We know that
P(~A)=1-P(A)=399/400
P(~B)=1-P(B)=133/136
P(A∩B)
=P(B|A)*P(A) [def. of cond. prob.]
=9/10*(1/400)
=9/4000
P(A∪B)
=P(A)+P(B)-P(A∩B)
=1/400+51/500-9/4000
=409/4000
P(~A|~B)
=P(~A∩~B)/P(~B)
=P(~A∪B)/P(~B)
=(1-P(A∪B)/(1-P(B)) [ law of complements ]
=(3591/4000) ÷ (449/500)
=3591/3592
The results can be easily verified using a contingency table for a random sample of 4000 persons (assuming outcomes correspond exactly to probability):
===....B...~B...TOT
..A . 9 . . 1 . . 10
.~A .399 .3591 . 3990
Tot .408 .3592 . 4000
So P(A|B)=9/408=3/136
P(~A|~B)=3591/3592
As before.
Step-by-step explanation: its were the answer is
