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We rearrange equation (1) to obtain an expression in terms of x. We then substitute this expression in place of x in equation (2), rearranging to find the numerical value of y. This value of y can then be...

As the derivative of e^x is e^x, so is the integral (plus some constant). As we wish to find the value of the integral from x = 1 to x = 2, we substitute x=2 into e^x, and from that we subtract e^x with x...

Comparing to this to ax^2 + bx + c = 0, you'll find that a=1, b=-1, c=90. You need to split b (in this case -1), into two numbers that add up to b (-1), and multiply to ac (90). -> These are -10 and 9....

x^2+5x+10 -> (x+p)^2+q (x+5/2)^2 - (5/2)^2 + 10 (x+5/2)^2 - (25/4) +40/4 (x+5/2)^2 +15/4

True probability of 2 consecutive balls picked being blue: (10/30)*(9/29)=3/29 which is 0.1034 (4 d.p.)

3/29-100% 0.2-x% so, x=0.2*100/(3/29)= 193.3 (1 d.p.) therefore Adam's result is 93.3 % (1 d....