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There are 11 pens in a box. 8 are black and 3 are red. Two pens are taken out at random without replacement. Work out the probability that the two pens are the same colour.

There are two solutions here which must be found. Both 2 red pens and 2 black pens being selected. First the red pensIf the total number of pens is 11 and number of red pens is 3, the probability of selectin...
JR
Answered by Jack R. • Maths tutor
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The equation of the line L1 is y=3x–2. The equation of the line L2 is 3y–9x+5=0. Show that these two lines are parallel.

We should recall that two lines are parallel when they have the same gradient. We can see the gradient of a line by writing it in the form y=mx+c, which will make the gradient equal to the coefficient of x (...
DG
Answered by Dylan G. • Maths tutor
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Solve the equations x^2+y^2=13 and x-2y=1 simultaneously.

Rearranging the second equation gives x=2y+1. Substituting this into equation 1 gives (2y+1) 2 +y 2 =13.Rearrangingthis and factorising the quadratic equation gives (5y-6)(y+2)=0, givingsolutions of y=6/5 an...
PS
Answered by Phoebe S. • Maths tutor
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Find the integral of 3x-x^(3/2)

3/2x 2 -2/5x 5/2 +C
HN
Answered by Henry N. • Maths tutor
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Integrate tan(x)^2 with respect to x

sin(x)2 + cos(x)2 = 1 divide by cos(x)2 tan(x)2 + 1 = sec(x)2 therefore tan(x)2 = sec(x)2 - 1 integral of sec(x)2 - 1 rwt x = tan(x) - x + C therefore the integral of tan(x)2 rwt x = tan(x) - x + C
OO
Answered by Osman O. • Maths tutor
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