Melody

Here you go  ........   you can finish it.  

I have responded on the original.  :)

Henry sells H, Liam sells L  and  Jack sells J

L=0.3(J+H)     (1)

H=0.2(J+L)     (2)

J=L+87           (3)

Substitute (3) inot the other 2 and then solve them simulaneously.

Can you take it from there?

A club has 30 members: 15 boys and 15 girls. A 4-person committee is chosen at random. What is the probability that the committee has at least 1 boy and at least 1 girl?

1- P(all girls) - P(all boys)

=\(=1-2*\frac{15C4}{30C4}\\ =1-2*\frac{1365}{27405}\\ =1-\frac{26}{261}\\ =\frac{235}{261}\)

\(120^\circ=\frac{2\pi}{3}\;radians\)

hint:

(this example is a bit harder than your ones but the method is the same.)

\(A=2.5e^{\frac{2\pi}{3}i}\\ A=2.5[(cos\frac{2\pi}{3})+isin(\frac{2\pi}{3})]\\ A=2.5[-(cos\frac{\pi}{3})+isin(\frac{\pi}{3})]\\ A=2.5[-(\frac{\sqrt3}{2})+i(\frac{1}{2})]\\ A=1.25[-(\sqrt3)+i)]\\ A=-1.25\sqrt3+1.25i\\\)

Yes, they are the same BUT they have to be included.

I made a mistake in my original answer.

The point (5,4) is NOT a point on the graph  y=floor of x   because the floor of 5 is 5 (not 4)

So there are only 4 points of intersection

Here is the correct graph

Sorry asinus, I didn't see your question earlier.

[x] means nothing to me either.

I looked it up and it seems to be used sometimes in place of the floor function. \(\lfloor x\rfloor\)

I assume that this is because the floor function symbol is not on an ordinary keyboard and it is not a common symbol.

The floor function simply means 'round down' to the nearest integer.

so for example:

\(\lfloor 3 \rfloor =3\\ \lfloor 3.2 \rfloor =3\\ \lfloor 3.7 \rfloor =3\\ \lfloor 3.99999 \rfloor =3\\ \lfloor 4 \rfloor =4\\\)

Assuming that   [x] is a reference to the floor function,    which is normally written as  \(\lfloor x \rfloor\)

then there are 5

Thanks for that great interaction.

I think you have drawn the triangle correctly.

It does not work out to be isosceles.

I let the two unknown lengths be x and y

then I formed two equations using the cosint rule, one beginning with  26^2=    and the other with  7^2=

then I solved them simultateously (with subtraction) to get an expression for y in terms of x.

then i subed back into an original equation to get two numbers for x, 

[One is actually x and the other is y becasue the terms are interchangeable] 

See how much that helps.

* Note that my method may not be the best method.

The first thing you have to do is draw a pic.

You probably won't get it right the first time.

You have to tweak it, and redraw it, a few times until it is right.

Have you done that?

If so, upload a pic of  it, or just describe what you pic looks like.

after that you can use cosine rule twice and then solve them the best you can simultaneously

I won't say more until you have contributed something of your own.