amygdaleon305

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