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Quote from Google

"If a number is being divided by 9, add each of the digits to each other until you are left with one number (e.g., 1164 becomes 12 which in turn becomes 3), which is the remainder."

n (mod9) = S(n) (mod 9) = S(S(n)) (mod 9)     for all integer n

so

n = S(n) + S(S(n)) (mod  9)

becomes

n (mod9) = n (mod9) +n (mod9) 

2n=n (mod9)

2n=n+9k 

n=9k

n must be a muliple of 9

How many multiples of 9 are there between 100 and 999?

111-10  =  101  

If anyone thinks I have made a logic error please let me know, with your reasons of course.

...given what?

26 letters, 5 vowels

5 choices for the second letter, then 25 choices for the 3rd letter, then 26 choices for the first letter.

Now what?  

Have you graphed this with desmos?

I suggest you do so and attach a link to the graph.  It is always a good starting point.

One question per post, thank you.

14/30

The probability is 5/144.

c = -3.

The probability is 1/360300

I think one leg is the radius       One leg is the radius + 1.5     and the hypotenuse = 4.5 m

Use Pythagoras' theorem. 

One leg of the right-angled triangle is r(the radius); the other leg is 4.5; the hypotenuse is (r+1.5).

Convert 62910 to base 7 and base 8 and compare:

351261_7
172676_8

This is not really a trig question. It is an understanding question.

dH/dt will be 0 when the tangent to the circle is horizontal.  That is at the top and bottom.   (say 12oclock and 6oclock)

If is starts horizontal to the axis that is at  3oclock or 9 oclock.

So it must travel a quarter of a rotation to get to the top or the bottom,

45/4 = 11.25 seconds  then again at  11.25+22.5k  seconds      (where k is a positive integer)

3.5/4.3 = sin40º/sin(ADB)

sin(ADB) = (4.3 * sin40º) / 3.5

Angle ADB = 52.15846474º

Enough from me

x² - 16 = 6x

x² - 6x - 16 = 0

x = 8,  x = -2

AC = 96

The sample space for 2 dice is as follows:

(2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 12)>>Total = 36

There are 15 ways of making up a prime number on a roll of 2 dice, but only one way of making up a 2, and that is: 1 +1 ==2, 

Therefore the probabikity is: 1 / 15 ==6.67%

AP / CP = 2 / 5

Yes, it does look like it. 

The possible outcomes are 2,3,5,7,&11

There is only 1 way to get a 2, since 1 and 1 is the same as 1 and 1

So the probability is 1/5

Gave my best shot, hope it helped!

We start off with g(5) which is 8

Then we do f(8) which is 200

So the value of f(g(5)) is 200

Now we do f(5) which is 5^2+10+5 which simplifies to 40

Now we do g(40) which is 48

So the value of g(f(5)) is 48

In conclusiong f(g(5)) - g(f(5)) is 200-48 which is 152.

Gave it my best shot, hope it helped!

x=$5

It's been answered a few days ago; google it...

R - r ≈ 7.052 - 2.657

We had this one the other day. 

XY² = XB * XA

DE = EF / tan(∠D)