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Out of 4 ways, there is only one way to set up the chords so that A_1 A_2 and A_3 A_4 intersect, so the probability is 1/4.

Let the cost of the game system be \(x\). Since the games cost three times as much as the game system, the cost of the games is \(3x\). 

Therefore, the total cost of the system and games, \($560\), is \(4x\). 

\(560 = 4x\)

\({560 \over 4} = {4x \over 4} \)

\(x = 140\)

The game system costs \($140\). The games cost \($420\).

52 cards in a deck  12 are face cards    so 40 are NOT face cards       40 out of 52   = 40/52 = 10/13

ahhh . . . sorry about the name! I suppose I can't change it now. Oops. 
First, @CalculatorUser thank you for recommending a video. I will try to work the problems. Also, Melody, I have not watched the video yet (I'm at school) but after I do, I will make sure to update you both. Thank you for helping me!
I'm sorry for the username (to be fair, I was argu-talking with my parents) and I will follow both your advice.

Again, thank you :)

First Melody, thank you for telling me what I did wrong. Like I said, I'm new to this site, and I thought I was following the rules properly but obviously I was not. I have now looked at the other answer and I will watch the youtube video. If I am still not able to figure it out, I will ask for further details. I'm sorry for posting both of the questions. I saw other people didn't post more than around 2 or 3 like a), b) in one question, so that's what I tried to do. However, I guess that was wrong. 

I understand that you are not here to do my homework for me, I was trying to find some advice, however, thank you for telling me the rules. I will leave this post up (how do you delete things anyway?) so maybe other people have a better grasp of the rules.

Anyway, I'm sorry, and thanks for telling me what I did wrong. Hope you have a good day! :D

As follows:

The last equation should read N_n+1 = N₁.3ⁿ   i.e.  we should have N₁ on the RHS, not N_n.

sin (- theta)  = - sin (x)        so sin x = 1/6

tan = sin / cos   =  1/6  /  cos  =  - sqrt35/35     solve for cos

                               cos =  1/6 * (-35/sqrt35)

                                     = -35 sqrt35 /210      ( does not match any of your answers....did you enter the Q correctly?? )

                                                                      OoOps ...as Alan has pointed out...it DOES match oe of the choices !

                                           1/6 * -35/sqrt35 = - sqrt35/6

Thanx, Alan !!!   

(22.20  - 11.70)  / 3 = pendant cost

Hi Melody, I understand. I was commenting on the problem and its "solution", not your comment!

As follows:

This graph should help:

total amount of platinum = 0.6*12 + 0.2*8 = 8.8 lb.

total alloy = 12 + 8 = 20 lb.

percentage platinum = 100*8.8/20 = 44%

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You are welcome. 

4x + 3 - (4x + 1) = 2  

So we must have 12x + 1 - (4x + 3) = 2

8x - 2 = 2

8x = 4

x = 1/2

See https://web2.0calc.com/questions/geometry-question_70#r4 

Solution as follows:

Note that O is the centre of the circle.

Also welcome back dimitris 

Determinant of the multiplication is always the multiplication of the determinants for any 2 square matrices

I'm with Zekken on this. 

Normally if you write a number as abc_p, for example, you mean that the number is already in base p, so that a, b and c are all less than p itself. 

For the question to make sense, we are presumably supposed to interpret each number as a base ten number, then convert it to various bases, p, and work out which values of p are possible.  So for 6_p, for example, we could have 110₂, or 20₃, or 11₅ etc.  However, without this sort of explanation accompanying the question I consider it to be poorly phrased.

As follows:

Your statement'

"I would like to state that 7 cannot be expressed in base 2 or 3,"

What on Earth are you on about?

\(7_{10}=111_{2}=21_{3}\)

Any positive integer, in any positive interger base, can be expressed in any other positive integer base.

Find the largest angle of quadrilateral ABCD in degrees, if (angle A)/2 = (angle B)/3 = (angle R)/4. ( R is C )

(Angle A)/2  => 48 / 2 = 24

(Angle B)/3  => 72 / 3 = 24

(Angle C)/4  => 96 / 4 = 24

The largest angle D = 360 - 48 - 72 - 96 = 144º