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Medium pizza radius   = (S + 3) / 2  .....so....

A  = pi  [ (S + 3) / 2 ] ^2

Large pizza  radius =  ( S + 3 + 3) / 2 =  (S + 6) / 2.....so....

A  =   pi  [ ( S + 6) / 2 ] ^2

8y  - 1  =   7                         2x  - 3  =  9

8y  =  7 + 1                           2x   =  9  + 3 

8y  =  8                                 2x   =  12

y =  8 / 8 = 1                           x =  12 / / 2  =  6

x + y  =  

6 + 1  =

7

Probability   = 1  -  minus  the probability  that  none  of the  top three geography students are  chosen  =

1  -  ( 25/28) (24/27) (23 / 26) (22/25)  =   

313 / 819

2/5*2/5 = 4/ 25 = 0.16 

Maybe not very sure

-wolfie

Welcome....!!!

Thank you!

Sum of 1st   120  integers   =   (120) (121)  /  2    =   60 * 121

(60 * 121)  mod 5  = 0       since 60 is evenly divisiblle  by  5

121 + 122 + 123  =

366

366 mod 5  =  1

Remainder =  1

Ah...I see now  that  they  refer to  the   angles  rather  than  the radii  !!!

THX, civomanzuk  for the correction !!!

5x - 2 + 2x + 8 = 90

7x = 84

x = 12

JB   =  KB   since  these are radii   .....so

5x - 2  =  2x +  8

5x - 2x  =  8  +  2

3x  =   10

x  =   10  / 3

"26"   is  the  number of  terms  in  ( 101  + 97 + 93  +  ....  + 1)

To  see this, note. that

(101  - 1)  / 4    +  1   =

100/ 4   +  1  =

25  +  1   =

26

a)  height =  50 (.52)^(n - 1)    cm     

b)  At  top of  3rd path  we  have   

50 (.52)^ ( 4 - 1)   =

50 (.52)^3*    ≈   7 cm.

Thank you! Quick question, where did the 26 come from?

pi/4

LOL....I try to get to them as quickly  as possible.....!!!

Rearrange  as

x^2   +  2sqrt (2)x   =   -1

Take 1/2 of 2sqrt 2   = sqrt 2.......square  this  =  2      ....add  to  both sides

x^2  + 2sqrt (2) x   +  2  =  -  1  + 2

( x + sqrt (2) ) ^2   =   1

s  = 1

thank you so much, and im suprised my question got answered so fast

We  can use  the Law  of Cosines

c^2  =   10^2  +  17^2  -  2(10 * 17) cos (98.8)

c^2  =   441.015

c =  sqrt  (441.015)   ≈    21

H  =  -16t^2  +  45t   +  5

Find  the  zeroes

16t^2  -  45t  -  5   =  0

Using  the  quadratic formula

         45  ±  sqrt  ( 45^2  - ( 4)(-5) (16)  )

t =   _____________________________         2.92   sec   or   -.11  sec      

                       2 * 16

Take  the positive answer  =   2.92  sec

13  inch diameter =   6.5 in radius

Area  of two of these pizzas  =   2 * 3.14 * 6.5^2   =   265.33 in ^2

So.....we  need  to solve  for    in this

265.33  =  3.14 r^2             divide both sides  by 3.14

265.33  / 3.14  = r^2

84.5   =  r^2               take  the positive root

r ≈  9.2

So....we  need   a  2 ( 9.2)   =    18.4 in pizza  to have  the same area as two 13 in pzzas

If I understand  the question correctly.....

Let        a  =  7     b  =  2    c   =  9

When  x  =  0

702090  / 9    =  7801

When x  =  3

732393  /  9   =  81377

When x  =  6

762696 / 9   =  84744

a +  b  +  c    =   18

I like this one. Let the sides be $x,y,1-(x+y)$. By the triangle inequality, all of the following must be true:

$$x<1-x$$

$$y<1-y$$

$$1<2x+2y$$

Graph each of these on the coordinate plane and use the principle of geometric probability. It's $\frac14$. 

Thanks! Have a nice day!

Yep, believe so. Nice job :)

Let's say there are $r$ reds and $y$ yellows. Then:
$\frac{r}{r+y}\cdot \frac{r-1}{r+y-1}=\frac{2}{15}$

Now solve the diophantine for $r$.