CPhill

A (sector)  = (1/2) r^2 θ

21  =  (1/2) r^2  ( 9/14)pi

42 = (9/14) pi r^2

42 / [ (9/14 * pi)]  = r^2

196 / (3pi) = r^2

14 / sqrt (3pi)  = r ≈ 4.6 m

B

Here's a more simple way

Amount spent on each nephew = N

Amount spent on  each  sister= N + 10

So

2N  + 3(N + 10) = 180     simplify

2N + 3N + 30   =180       subtract  30 from both sides and simplify the left side

5N  = 150    divide both sides by  5

N = $30   = amt spent on each nephew

N + 10 = $ 40  = amt spent on each sister

(75/2.25) * ( 1.79)  ≈  $59.66

40x   and  be  written as  4*10^2  + 0*10 + x  =  400 + x

1x  can be written as    1*10  + x  =  10 + x

So we  have

[ 400 + x ] / ;[ 10 + x ] =  31     multiply both sides by 10 + x

400 + x  +  31 [ 10 + x ]    simplify

400 + x  = 310 + 31x

400 - 310  =  31x - x

90  = 30x  diivide  both sides  by 30

x = 3

Check   403 / 13 =  31

Sorry, jugoslav.....we are not  given any info as to what  the length of  legs RT and ST might be....we cannot assume that  this is a 3-4-5 right  triangle

6!  ways to list the presidential candidates  = 720

4! ways to list the vice-presidential candidates  = 24

5! ways to list the secreterial candidates = 120

So    720 * 24 * 120  = 2,073,600 ways

Possibilities

ABA  = Choose any one of three positions for  B  = 3

ABB  = Choose any  one of three positions for A  = 3

ABC  =   3!  ways to arrange this =  6

ABD =    3! ways to arrange this = 6 

18 possible "words"

Since SR = 5   then so is  QP

And since the perimeter of  PQRS  is 26, then QR =  (26 - 10) / 2 = 16/2   = 8 

And the  area  of PQRS  =   QR * ST

So

28 = 8 * ST

28/8 = ST

7/2  = ST  = 3.5

And using the Pythagorean Theorem

RT^2 + ST^2  = RS^2

RT^2  + (3.5)^2 =  5^2

RT^2  = 5^2 - 3.5^2

RT^2  = 25 - 12.25

RT^2 = 12.75

RT = sqrt (12.75)

Perimeter of QOST =   2 ( QR + RT + ST)  =  2 ( 8  + sqrt (12.75)  + 3.75)  = 

23 + 2sqrt (12.75)

It was a repeat question, T4H.....I'd already answered it elsewhere.....