Melody

This should work I think

the side length of the dark little triangle is half that of the large triange.

All the points inside the little triangle will be closer to the centre (which in my pic is J) than they will to any side ot the big triangle.

The sides of the little to big are in the ratio 1:2

So the are of the little to big will be 1:4

The area of the little to the area in the big, not including the little wil be  1:4-1   =    1:3

So probability that the distance to the centre is less than the distance to the edge is 1:3   i.e.    \(33.\dot3\;\%\)

Hi Lina,

If you comment on my answers you will be more likely to get help from me into the future.

\(\boxed{\color{red}{R}}\qquad \boxed{\color{white}{A}}\qquad \boxed{\color{red}{R}}\qquad \boxed{\color{white}{A}}\qquad \boxed{\color{red}{R}}\qquad \)

Here is a start, now work out how many combinations there are for the other 2 boxes.

\(0=-15t^2+28t+144\\ t=\frac{-28\pm\sqrt{784+8640}}{-30}\\ t=\frac{-28\pm\sqrt{9424}}{-30}\\ t=\frac{+28+4\sqrt{589}}{30}\\ t\approx 4.17 sec\)

Hi Lizzie

Jessica bought 1.2 * 5 yards

and 

Derek bought  1.25* 3  yards

You can simplify those (with a calc if necessary)  and see which is bigger  

Hi Lina,

Welcome to Web2.0calc forum  

This is called partial fractions, it comes in useful when doing calculus.

\(\frac{3x+2}{x^2-x-12}=\frac{A}{(x-4)}+\frac{B}{(x+3)}\\ So\\ Ax+3A+Bx-4B=3x+2\\ (A+B)x+(3A-4B)=3x+2\\ A+B=3\qquad and \qquad 3A-4B=2\\ A=3-B\\ \text{sub to get B}\\ 3(3-B)-4B=2\\ -7B+9=2\\ B=1\\ A=3-1=2\\ \frac{3x+2}{x^2-x-12}=\frac{2}{(x-4)}+\frac{1}{(x+3)}\\ \)

You can finish :)

First I went online to find all the formulas that I need

You can make h=0  and k =0  so it is centred at the origin,  I'll use the blue one

a=94 and b=52

Plug those numbers in and you will have your formula.

Plug them into the c formula and you will have c

You should be able to finish it but you can ask questions if you want.

I am not too sure about the reflections part of it. 

First place a shell  down anywhere, call it A, now there are 9 shells left  so

9! takes into consideration of the rotation part

Maybe for the reflection you just divide by 2 becasue there is only one axis of symmetry through A

So maybe the answer is 9!/2

If you have access to the answers can you check and comment on whether this is the same.?

FIRSTLY Delphinia,  do not down vote answers just becasue you think it is wrong.

If a person makes a serious attempt at answering then you should thank them and not punish them in ANY way.

I answered you before I realiszed you had done this, otherwise I probably would not have answered you.

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Suppose 5 different integers are randomly chosen from between 20 and 69, inclusive. What is the probability that they each have a different tens digit?

there are  69-20+1= 50 numbers altogether

There are 5 different 10 digits,   2,3,4,5,6

Choose a number any number  prob = 1

now there are  49 numbers left and 40 of them have a tens unit not yet chose, 

P of the next one being a good choice is  40/49

and so on:

\(Prob = 1 * \frac{40}{49}*\frac{30}{48}*\frac{20}{47}*\frac{10}{46}\)

You can finish it. 

You are always welcome OldTimer  :))