A pentomino is made up of five squares where two squares are joined along an entire side. Two pen- tominos are the same if they
can be matched by turning or flipping. How many different pentomino shapes are possible?
1 answer:
There are 12 such shapes. One can start with two squares, adding squares around the edge and rejecting shapes that have been previously seen. Repeating until you have 5 squares results in 12 distinct shapes.
_____
2 shapes are possible with 3 squares: L, I
5 shapes are possible with 4 squares: L, I, N, T, O
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Answer:
(x +6)^2 +(y +2)^2 = 72
Step-by-step explanation:
The given points are vertices of a right triangle. The circle circumscribing that triangle (through all 3 vertices) will have its center at the midpoint of the hypotenuse:
((0, 4) +(-12, -8))/2 = (-6, -2)
The equation of a circle with center (h, k) through point (a, b) is ...
(x -h)^2 +(y -k)^2 = (a -h)^2 +(b -k)^2
For center (-6, -2) and point (0, 4), the equation is ...
(x +6)^2 +(y +2)^2 = (0+6)^2 +(4 +2)^2
(x +6)^2 +(y +2)^2 = 72
Answer:
The probability that at least one of the children get the disease from their mother is P=0.7125.
Step-by-step explanation:
This can be modeled as a binomial random variable.
The parameter p=0.34 is the probability of a child being infected, and is constant and independent of the other events.
The parameter n=3 is the number of children (sample size).
Then, we have to calculate the probabilty that at least one of the children get the disease from their mother. That is:
The probability of exactly k children being infected can be calculated as:
Then, the easiest way to calculate this probability is using the complement: the value of the probability is 1 (or 100%) less the probability that no children gets infected.