An antique painting has a 40% chance of increasing in value by $10,000 and a 60% chance of decreasing in value by $5000. based on this information, would you recommend investing in the painting?

a. no, the expected value of the painting's worth is a decrease of $500.
b. no, the expected value of the painting's worth is a decrease of $1000.
c. yes, the expected value of the painting's worth is an increase of $500.
d. yes, the expected value of the painting's worth is an increase of $1000.

The probability that the antique painting's value will increase $10.000 is: 
P(increase)=0.4
The probability that the antique painting's value will decrease $5.000 is: 
P(decrease)=0.6
P(decrease)>P(increase) The probability is bigger the value of the painting to be decreased. But the amount is lower than the amount if the value increases.
We should calculate the expected value in order to decide if it is recommended to invest in the painting. Expected value is the return you can expect for buying the painting.
EV=(-10.000)*0.4+5000*0.6=-4000+3000=-1000
So, the correct answer is B.No I would not recommend investing in the painting, because the expected value of the painting's worth is a decrease of $1000. 

X^2 - 4x +(4/2^2) + y^2 + 8y + (8/2^2) = -4 + (4/2^2) + (8/2^2)(x + 2)^2 + (y + 4)^2 = -4 + 4 + 16your center is (-2, -4) and the radius is the sqrt of -4 + 4 + 16 which is 4