Total no. of ways = 8!
= 40320
No. of dwarves = 4
No. of elves = 4
Hence, let all dwarves be considered as one object
No. of ways accordingly = 5!
= 120
No. of ways to arrange among themselves = 4!
Thus, required no. of ways = 2880
For 1st month = 80
For 2nd month = 80 + 30
=110
For 3rd month = 110 + 30
= 140
For 4th month = 140 +30
= 170
So, for 4th month is $170
Total no. of marbles = 6 + 3 + 4 + 1
= 14
a) P(3 red) = \({6 \over 14} * {5 \over 13} * {4 \over 12}\)
= 0.06
b) P(2 green) = 0
c) P(blue then yellow) = \({6 \over 14}*{4 \over 13}\)
= 0.13
d) P(1 red, 1 blue) = \(({6 \over 14}*{3 \over 13}) + ({3 \over 14}*{6 \over 13})\)
= \({36 \over 182}\)
= 0.2
Since the centroid divides the median of a triangle in 2:1 ratio,
\({3x+5 \over 2x-1} = {2\over 1}\)
⇒3x + 5 = 4x - 2
⇒x = 7
In first row, no. of color permutations = 3!
= 6
similarly for the next 2 rows = 2 * 6
= 12
Thus, total no. of ways are 12.
Here you go :-
2y = 8x - 6
⇒y = 4x - 3
⇒\({dy \over dx} = 4\)
Slope of perpendicular line = -1/4
Hence, equation of line
\(y - 3 = ({-1\over 4})({x - (-3)})\)
\(4y - 12 = -x - 3\)
⇒\(x + 4y = 9 \)
a) Coordinate points are (2015,4023) and (2018,3711).
b) Difference = 4023 - 3711
= 312
Rate of change = \({312 \over 4023}* 100\)
= 7.76%
Its wrong
Solution -
\(tan A + sec A = 3 \)
\({sin A\over cos A} + {1\over cos A} = 3 \)
\(sin A + 1 = 3cos A\)
\(sin A = 3cos A - 1\)
sin2A = 9cos2A - 6cos A + 1
1 - cos2A = 9cos2A - 6cos A +1
10cos2A - 6cos A = 0
5cos A - 3 = 0
cos A = 3/5
