Step-by-step explanation:
We are picking 6 numbers from the numbers 1,2,3,4,5,6,7,8,9,10. Since we care about numbers being next to each other, we might think of the 10 numbers as being distributed in 5 boxes (which you can think of as the holes):
| 1 2 | 3 4 | 5 6 | 7 8 | 9 10 |
So on the first box we have the numbers 1 and 2, on the second box we have the numbers 3 and 4, and so on. Since we are picking 6 numbers from those 10 numbers, that means we'll have to pick 6 boxes (and inside each box we pick a number), but we only have 5 available boxes, so by the pigeonhole principle, we'll have to pick 1 same box at least two times. Since on each picked box we'll need to pick a number, on this box which was picked two times, we will have to pick both of its numbers. And so those 2 numbers inside that box will be next to each other (meaning they're consecutive numbers).
Answer:
Rationalize the denominator by multiplying by the conjugate of (1 + √3), namely (1 - √3). this gives us
(1 - √3) / (1 - 3) or (1 - √3) / -2, which can be rewritten as
(-1 + √3)/2, the last answer choice.
It would be D. Very positive!!
Answer:
We calculate for the dimensions (the length of the sides) of both the poster and the cube. If the length of the side of the poster is shorter compared to that of the box then, the poster will lie flat in the cube. However, if the poster has a length that is longer than that of the cube then, it will not lie flat in the cube.
length of the poster = sqrt (9 ft^2) = 3 ft
length of the cube = cbrt (30 ft^3) = 3.11 ft
Since, the length of the cube is longer compared to the length of the poster then, the poster will lie flat on the cube
