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Alex_Xolod [135]
3 years ago
15

Sam colors each tile in a 4 by 4 grid white or black. A coloring is called rotationally

Mathematics
1 answer:
DiKsa [7]3 years ago
8 0

Answer:

  65,280

Step-by-step explanation:

Consider the 4×4 grid ...

  \left[\begin{array}{cc}a&b\\d&c\end{array}\right]

where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.

The same will be true of 270° rotational symmetry, for the same reason.

__

For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)

__

The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...

  65,536 -256 = 65,280 . . . . colorings not rotationally symmetric

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Money adding how to do it
Vilka [71]
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FOR EXAMPLE:
$1 and $2.75
You would ignore dollar sign and add together like normal to get
3.75
But remember to add dollar sign back at the end.
If the value only have 2 values with cents it should be something like
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7 0
3 years ago
Read 2 more answers
After painting the fence steve and janet realize that their house also needs painting. But steve will have to do the painting hi
gladu [14]

Answer:

Therefore, Steve will paint house for 20.6 days.

Step-by-step explanation:

We know that Steve determines that it would take them 9 days to paint the house together (if they were both healthy) and that it would take Janet (when healthy) 16 days to paint the house alone.

We conclude that in 1 day Janet painted 1/16 of the house. In nine days, Janet painted 9/16 of house.

So, 7/16 of house paint Steve in nine days.

We have the following proportion:

\frac{7}{16}:9=1:x\\\\\frac{7}{16}x=9\\\\x=9\cdot \frac{16}{7}\\\\x=20.6

Therefore, Steve will paint house for 20.6 days.

4 0
3 years ago
I need help please!!!!!
charle [14.2K]
Obtuse angle. If wrong I’m sorry lol
5 0
3 years ago
Please help! I need answers for both questions it’s very confusing!
Lilit [14]

Answer:

for number 5 its:

-15 -8 8/9 -3.3

and for number 6 its:

-3.3 -8 8/9 and -15

also sorry if its wrong

5 0
2 years ago
Read 2 more answers
Suppose P(E) = 0.3. Find P(not E). Suppose P(not E) = 65%. Find P(E).
larisa [96]
Try this option:
1. rule: P(E)+P(not E)=1.
2. according to the rule above
P(not E)=1-P(E)=1-0.3=0.7;
P(E)=1-P(not E)=(100-65)%=35%.
6 0
3 years ago
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