Write the equation of the circle with center (0,0) and (-1,-3) a point on the circle

Equation of given circle :-  x² + y² = 4

Step-by-step explanation:

The equation of the circle with center (0, 0) and radius r is given by,

x² + y² = r²

It is given that, a  circle with center (0,0) and (-1,-3) a point on the circle

To find the radius of circle

radius r = √[(0 - - 1)² + (0 - -3)²] =√(1 + 3) =√4 = ±2

r = 2

To find the equation of circle

x² + y² = r²

x² + y² = 2²

x² + y² = 4

Step-by-step explanation:

Given that center of the circle is at (0,0) and it passes through a point (-1,-3).

Now we need to write the equation of the circle with given center and point on the circle.

So let's plug given values into standard formula of the circle

there (h,k) gives center of the circle then h=0, k=0

So we get equation :

...(i)

plug the given point (-1,-3) that is x=-1 and y=-3 into (i)

plug above value into (i)

Hence final answer is

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: