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sin cos -sin -cos (down is differentiate and up is integrate) so, y = sin5x  dy/dx = 5cos5x y=3cox      dy/dx = -3sinx y=3tan5x     dy/dx = 15sec²(5x) (remember sec(x) is the reciprocal of cos(...

Expand the brackets:

(3z + 18) - (8z + 2)

Simplify:

16 - 5z

Times both side by r to get ar+3r=2a+7 Subtract 2a and 3r from both side to bring a to one side, ar-2a=7-3r Factorise the left handside, a(r-2)=7-3r Divide both side by r-2, a=(7-3r)/(r-2)

The probability of picking a ball from a bag is the number of balls of that colour divided by the total number of balls.

Therefore in the first instance, the probability of a red ball is 3/9 or 1/3...

For the first ball the probability we pick a red ball is the same, it's the number of red balls divided by the total number of balls. Which in this case is 3/9. 

If we replace the balls the chance ...