What is the volume that can fit exactly 128 cubes with 1/2 inch sides?
1 answer:
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Answer:
Length of rectangular strip = 12
area of rectangular strip = 2*12 = 24
Area of square = x^2 = 12^2 = 144
Step-by-step explanation:
Area of square x^2
area of rectangle is given by length * width
Length of rectangular strip = x
width of rectangular strip = 2
area of rectangular strip = length * width = 2*x = 2x
Area of square piece of paper when rectangular strip is taken away from it
= Area of square - area of rectangular strip
=
It is given that Area of square piece of paper when rectangular strip is taken away from it is 120 square units.
Thus,
Thus,
either x+10 = 0 or x -12= 0
x = -10 or x = 12
but length cannot be negative hence neglecting x = -10
hence value of x is 12.
Hence,
Length of rectangular strip = 12
area of rectangular strip = 2*12 = 24
Area of square = x^2 = 12^2 = 144
We have given the table of number of male and female contestants who did and did not win prize
The probability that a randomly selected contestant won prize given that contestant was female is
P(contestant won prize / Contestant was female)
Here we will use conditional probability formula
P(A/B) =
Let Event A = selected contestant won prize and
event B = selected contestant is famale
Then numerator entity will
P(A and B) = P(Contestant won prize and Contestant is female)
= Number of female contestant who won prize / Total number of contestant
= 3 /(4+9+3+10)
= 3 / 26
P(A and B) = 0.1153
P(B) = P(contestant is female )
= Number of female contestant / Total number of contestants
= (3+10) / 26
P(B) = 0.5
Now P(A / B) =
= 0.1153 / 0.5
P(A / B) = 0.2306
The probability that randomly selected contestant won prize given that contestant is female is 0.2306
Converting probability into percentage 23.06%
The percentage that randomly selected contestant won prize given that contestant is female is 23%