In how many ways can you spell the word ROOM in the grid below? You can start on any letter R, then on each step you can step on
e letter in any direction (up, down, left, right, or diagonal).
2 answers:
Answer:
96
Step-by-step explanation:
In a straight line, the word can only be spelled on the diagonals, and there are only two diagonals in each direction that have 2 O's.
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If 90° and reflex turns are allowed, then the number substantially increases.
Corner R: can only go to the adjacent diagonal O, and from there to one other O, then to any of the 3 M's, for a total of 3 paths.
2nd R from the left: can go to either of two O's, one of which is the same corner O as above. So it has the same 3 paths. The center O can go to any of 4 Os that are adjacent to an M, for a total of 10 more paths. That's 13 paths from the 2nd R.
Middle R can go the three O's on the adjacent row, so can access the three paths available from each corner O along with the 10 paths available from the center O, for a total of 16 paths.
Then paths accessible from the top row of R's are 3 +13 +16 +13 +3 = 48 paths. There are two such rows of R's so a total of 96 paths.
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Answer:
Null hypothesis:
Alternative hypothesis:
The statistic to check the hypothesis is given by:
And is distributed with n-2 degrees of freedom
And the statistic to check the significance of a coeffcient in a regression is given by:
For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:
Always
Step-by-step explanation:
In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:
Null hypothesis:
Alternative hypothesis:
The statistic to check the hypothesis is given by:
And is distributed with n-2 degrees of freedom
And the statistic to check the significance of a coeffcient in a regression is given by:
For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:
Always
To calculate minimum value, do -b/2a to get the x-value, and plug it in to get the y-value:
-6/8 = -3/4
So the minimum value of g(x) is -81/4
This shows that g(x) has a lesser minimum value than f(x)
-6/8 = -3/4
So the minimum value of g(x) is -81/4
This shows that g(x) has a lesser minimum value than f(x)