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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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Ella and jade both ran a marathone ella finished 4 hours 6 mins and 13 seconds jade finished in 4 hours and 3 mins and 18 second
spin [16.1K]

Answer:

Jade is faster than Ella by 2 minutes and 55 seconds.

Step-by-step explanation:

We are told that Ella and Jade both ran a marathon. Ella finished marathon in 4 hours 6 mins and 13 seconds. Jade finished marathon in 4 hours and 3 mins and 18 seconds.

We can write 4 hour 6 minutes 13 seconds as 4 hour 5 minutes 73 seconds. 1 minute has been borrowed to the seconds side, and seconds become 13+60 = 73 seconds.

We can see that Ella took more time than Jade. Let us find how much more time Ella took than Jade by subtracting time taken by Jade from time taken by Ella.  

4\text{ hr }5\text{ min }73\text{ sec }-4\text{ hr }3\text{ min }18{ sec }= 2\text{ min }55\text{ sec }  

We can see that Jade took 2 minute and 55 seconds less than Ella , therefore, Jade was faster than Ella by 2 minutes 55 seconds.

4 0
3 years ago
Si el velocimetro de un auto marca un 25% mas que la verdadera velocidad y en este momento marca 100km/h entonces la velocidad v
GenaCL600 [577]

Answer:

True speed of the car is 87 km/h.

Step-by-step explanation:

Speed = 100 km/h

hike in speed = 25 %

Let the true speed is v.

v + 15% of v = 100 \\\\v + 0.15 v = 100 \\\\1.5 v = 100\\\\ v = 87  km/h

6 0
3 years ago
Pls pls help me I need it and the other one pls guys
snow_lady [41]

do u need all the answers?


3 0
3 years ago
Find the perimeter of the pentagon MNPQR with vertices ​M(2​, 4​), ​N(5​, 8​), ​P(​8, 4​), ​Q(8​, 1​), and ​R(2​, 1​)
Gekata [30.6K]

Answer:

The pentagon MNPQR has a perimeter of 22 units.

Step-by-step explanation:

Geometrically speaking, the perimeter of the pentagon is the sum of the lengths of each side, that is:

p = MN + NP + PQ + QR + RM (1)

p = \sqrt{\overrightarrow{MN}\,\bullet \, \overrightarrow{MN}} + \sqrt{\overrightarrow{NP}\,\bullet \, \overrightarrow{NP}} + \sqrt{\overrightarrow{PQ}\,\bullet \, \overrightarrow{PQ}} + \sqrt{\overrightarrow{QR}\,\bullet \, \overrightarrow{QR}} + \sqrt{\overrightarrow{RM}\,\bullet \, \overrightarrow{RM}} (1b)

If we know that M(x,y) = (2,4), N(x,y) = (5,8), P(x,y) = (8,4), Q(x,y) = (8,1) and R(x,y) = (2,1), then the perimeter of the pentagon MNPQR is:

p =\sqrt{(5-2)^{2}+(8-4)^{2}} + \sqrt{(8-5)^{2}+(4-8)^{2}}+\sqrt{(8-8)^{2}+(1-4)^{2}}+\sqrt{(2-8)^{2}+(1-1)^{2}}+\sqrt{(2-2)^{2}+(4-1)^{2}}p = \sqrt{3^{2}+4^{2}} + \sqrt{3^{2}+(-4)^{2}}+\sqrt{0^{2}+(-3)^{2}}+\sqrt{(-6)^{2}+0^{2}}+\sqrt{0^{2}+3^{2}}

p = 22

The pentagon MNPQR has a perimeter of 22 units.

4 0
3 years ago
PLS NEED HELP DON'T UNDERSTAND ONE PART
velikii [3]

Answer:

Step-by-step explanation:

Work = (12 - 2) x 180 = 10 x 180 = 1800 degrees

Answer = 1800 degrees

Hope that helps!

7 0
3 years ago
Read 2 more answers
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