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7 ≤ p

8 ≤ p

8 < p

9 < p

which inequality best shows how many more pages (p) Devin needs?     <======= DO YOU HAVE SOME CHOICES?

Simultaneous equations      x =   3 egg + 2 flour recipe     (CHOCOLATE)

                                             y =  5 egg  + 3 flour recipe     (RED VELVET)

For the eggs     3x   + 5y   = 111

for the flour       2x  +  3y  = 69     multiply by - 1.5  to get :

                         -3x  - 4.5y = -103.5           add the red equations to get  y = 15     then   x = 12   CHOCOLATE CAKES

1500/5 = 300 scale factor

1:300  

My mistake corrected here

Sum of the first 99 integers   =====    99/2 ( 1 + 99) = 4950

Thank you!

Here yA  go:

4+5+3=12 ways. 

Case 1: You pick no red marbles... to get that you would have to pick either green or blue marbles only. So there would be 6x5x4=120 ways. 

Case 2: You pick only 1 red marble. There are 3 ways to pick a red marble and then 6x5 more ways to choose a green or blue marble, so 6x5x3=90 ways. 

So you add up both cases and get 120+90=210 ways. 

18  +  3x  =  35

3x  =  35  - 18

3x =  17

x = 17/3   =   5  2/3

They  can only  buy  5  side dishes

Sum of first   n positive integers =  n (n + 1)   /2

So...sum  of 1st 100 positive integers =  100  ( 101) /  2   =   50 * 101 =  5050

Another way to see this

100 + 1  =101

99 + 2  =   101

98 + 3  =  101

.......

We will heve 50  paired sums of 101 each  ....so   ...50 * 101  =  5050

Dividing the  shaded  area  in half  from  the bottom left  vertex of the figure  to  the point of intersection  we  have  this  area :

Area of a quarter  circle  with  a radius  of 12  - area of a  right triangle with legs of 12  = 

pi (12)^2 / 4   =  (1/2) (12)^2   =   (12)^2  ( pi/4  - 1/2)    

And  by symmetry  the total shaded area  =

2 (12^2) ( pi/4  - 1/2)  =   288  ( pi/4 - 1/2) units^2  ≈  82.19  units^2

**EDITED**

Never mind I was wrong :/

100/2 ( 1 + 99)  = 5000

Leaves new york to atlanta   and takes 10 hours

the trains leaving atlanta for new york every 30 minutes....it takes 10 hours   so there is 20 trains on the track when YOUR

NY to ATL train leaves......during the 10 hour trip ANOTHER 20 trains will launch from ATL going to NY

   so you will pass 40 trains that are going from ATL to NY    while you are travelling to ATL   

This assumes that the trains go every 30 minutes around the clock ...... is this implied?

       I think this is correct ......

If they do not go around the clock , you will only pass trains that launch for the 10 hours after your departure from NY

   that would be 20 trains

THX, BF !!!!

Here's another  way to see this

Let  the circumference of the Earth  =  C

So  every  hour    Superman  covers   C / 2.5   = C /( 5/2) =    (2/5)C

And  every hour Fals covers   C /(1/5)   = C / (3/2)  = (2/3)C

So...every  hour  they cover   (2/5 + 2/3)  C =   (16/15)C

Which  means  that  it  takes them  (15/16)  hrs  to  meet   every time

So...the  number of times  they  meet in 24 hrs  =  24 / (15/16) ≈ 25.6  times  ≈  25 times  

The maximum distance the ant could walk is 10 edges.

Ok thx!

(1/2.5h)x+(1/1.5h)x=1
x=0.9375

24/0.9375= 25.6

They will pass each other 25 times

one side will be √37 which about 6.0827625303. Round that to the nearest tenth, that is 6.1 

Be forewarned....putting multiple questions in a single post will often get your post ignored.....

Note  that  we  could move A  to  B  and have concentric circles

The radius  of  the larger circle =  8

We  are looking for this

Area of  circle B  -  area  of  circle A   =  shaded area

And

Shaded  area  =  8 * area  of circle A....so

Area of  circle B  -  area of circle A  =  8 *  area ofcircle A

Area of  circle B  =  9 *  area of circle A

pi * 8^2  = 9 *pi * r^2          where  r  is  the radius  of circle A

64  = 9 r^2

64/9  = r^2                 take  the positive root of both sides

8 / 3   cm   = r  =  radius  of smaller circle A

So....the diameter of  circle A = 2 (8/3)   =  16 / 3   cm

see if that works. :0

For this question, we cannot see it as a normal finding problem because this have 2 adjacent side, so here is how you really should do it:

3x2x2x2 :) because A is effected by D so 3 choices only,

B is effected by A and C so 2

C is effected by B and D so 2

, and same for D.

correct