Split the second term in 3a^2 - 8a + 4 into two terms
3a^2 - 2a - 6a + 4 = 0
Factor out common terms in the first two terms, then in the last two terms.
a(3a - 2) -2(3a - 2) = 0
Factor out the common term 3a - 2
(3a - 2)(a - 2) = 0
Solve for a;
a = 2/3,2
<u>Answer : B. (2/3,2)</u>
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
Answer:
A = 2.63
B = 2
Step-by-step explanation:
To find the population density, what we need to do simply is divide the population by the area of the UK
mathematically, that would be;
(6.41 * 10^7)/243,610 = 263.125
To the nearest whole person= 263 people/ square meter
So now we want to write 263 in standard form = 2.63 * 10^2
So this means A = 2.63 and B = 2
Plug in 83 for y and 3 for x
83 = 3^2 - 6 (3) + 92
83 = 9 - 18 + 92
83 = -9 + 92
83 = 83 so it works
The answer would be: -5
Heres how you solve it!
First, change the x into a 0 so it can be removed.
y+2= -3/4*4
Now with the GCF you can reduce the numbers with 4.
y+2= -3
Then move the 2 to the other side causing it to change its sign into a negative
y= -3-2
Since -3 and -2 are both negative it would be -5
y= -5
then you are left with your answer.
Hope this helps! :3
