4. determine the center and radius of each circle.
a. 3x2^+3y^2=75
b. 2(x+1)^2+2(y+2)^2=10
c. 4(x−2)^2+4(y−9)^2−64=0

Step-by-step explanation:

Equation of circle with (h,k) as center and radius r is given by,

          (x-h)²+(y-k)² = r²

a) 3x²+3y²=75

   Dividing by 3

                    x²+y²=25

                    (x-0)²+(y-0)² = 5²  

          Center (0,0) and radius 5

b) 2(x+1)²+2(y+2)²=10

 Dividing by 2

        (x+1)²+(y+2)²=5

        (x-(-1))²+(y-(-2))²= 2.236²

          Center (-1,-2) and radius 2.236

c)  4(x−2)²+4(y−9)²−64=0  

           4(x−2)²+4(y−9)²= 64

 Dividing by 4

          (x−2)²+(y−9)²= 16

          (x−2)²+(y−9)²= 4²

          Center (2,9) and radius 4                                  

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

happy to

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step-by-step explanation: