Alan

Assuming the drawing is done without replacement:

1)  probability = 39/52*38/51*37/50*36/49*35/48*34/47*13/46 = 27417/605360 ≈ 0.045

2) We know with certainty that none of the first 5 cards is a spade (because we are told so!).  So probability = 34/47*13/46 = 221/1081 ≈ 0.204

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14% = 14/100

P + P*14/100 = 437.64

P*(1+14/100) = 437.64

1.14P = 437.64

P = 437.64/1.14

P = 383.89 kr

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You need to memorise the expressions for sin, cos and tan in a right-angled triangle:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent

and also memorise 

cot = 1/tan

csc = 1/sin

sec = 1/cos

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The quickest way is to use the calculator here:

If you have a head for numbers you might have spotted that the equation could be written as 

(x+1)(x+2)(x+9)=0

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6/√37 can also be written as 6√37/37

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$$x=\frac{-3\pm \sqrt{(3^2-4\times1\times25))}}{2\times1}$$

Because the discriminant (the part under the square root sign) is negative, the values of x will be complex numbers.

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You can write this as 

$$\frac{18}{t}+\frac{16}{t^2}\rightarrow \frac{2}{t}(9+\frac{8}{t})$$

or 

$$\frac{18}{t}+\frac{16}{t^2}\rightarrow \frac{2(9t+8)}{t^2}$$

but are these really any simpler?

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Simply divide 400 by 3.75

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This picture might help:

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