Question and Answers Forum

Journey inside a regular hexagon The operation is to connect three dots of a regular hexagon′s heads. 1• How many types of geometric shapes will we get? 2• How many each type?

$J o u r n e y i n s i d e a r e g u l a r h e x a g o n$ $T h e o p e r a t i o n i s t o c o n n e c t t h r e e d o t s o f$ $a r e g u l a r {h e x a g o n}^{'} s h e a d s .$ $1 ∙ H o w m a n y t y p e s o f g e o m e t r i c s h a p e s w i l l w e g e t ?$ $2 ∙ H o w m a n y e a c h t y p e ?$

Question Number 178134 Answers: 0 Comments: 8

Am not a friend with this isssue: 6 red, 1 black and 3 white balls We draw 3 balls in a raw, returning the drawn ball each time. How many different results which include at least one black ball. Way_1 : 1000−9^3 = 271 results That′s very ok Way_2 : 1×9×9_(very ok) ×3_(Omg, Why?) + 1×1×9×3_(the same confused above) + 1×1×1_(very ok and i like it.... but why not ×3) = 271 result Explanation_(about the story of ×3) ?

$A m n o t a f r i e n d w i t h t h i s i s s s u e :$ $6 r e d, 1 b l a c k a n d 3 w h i t e b a l l s$ $W e d r a w 3 b a l l s i n a r a w, r e t u r n i n g t h e$ $d r a w n b a l l e a c h t i m e .$ $H o w m a n y d i f f e r e n t r e s u l t s w h i c h i n c l u d e$ $a t l e a s t o n e b l a c k b a l l .$ ${W a y}_{1} : 1000 - 9^{3} = 271 r e s u l t s {T h a t}^{'} s v e r y o k$ ${W a y}_{2} : 1 \times 9 \times 9_{v e r y o k} \times 3_{O m g, W h y ?}$ $+ 1 \times 1 \times 9 \times 3_{t h e s a m e c o n f u s e d a b o v e}$ $+ 1 \times 1 \times 1_{v e r y o k a n d i l i k e i t . . . . b u t w h y n o t \times 3}$ $= 271 r e s u l t$ ${E x p l a n a t i o n}_{a b o u t t h e s t o r y o f \times 3} ?$

Question Number 181541 Answers: 4 Comments: 2

solve for f(x) such that f′(x)=f^(−1) (x)

$s o l v e f o r f (x) s u c h t h a t$ $f^{'} (x) = f^{- 1} (x)$

Question Number 178113 Answers: 1 Comments: 0

8 yellow, 8 red, 8 green and 8 blue cards, each grouo is numbered from 1 to 8 . We want to know how many pulls contain at least one card with number 1 through pull processes 5 cards each time

$8 y e l l o w, 8 r e d, 8 g r e e n a n d 8 b l u e c a r d s,$ $e a c h g r o u o i s n u m b e r e d f r o m 1 t o 8 .$ $W e w a n t t o k n o w h o w m a n y p u l l s c o n t a i n$ $a t l e a s t o n e c a r d w i t h n u m b e r 1 t h r o u g h$ $p u l l p r o c e s s e s 5 c a r d s e a c h t i m e$

Question Number 178073 Answers: 1 Comments: 4

Question Number 178054 Answers: 2 Comments: 3

Mr. w wants to distribute n+1 different prizes to n friends so that each one gets at least one prize, how many results of this process. I hope to be that one gets 2

$M r . w w a n t s t o d i s t r i b u t e n + 1 d i f f e r e n t$ $p r i z e s t o n f r i e n d s s o t h a t e a c h o n e g e t s$ $a t l e a s t o n e p r i z e, h o w m a n y r e s u l t s$ $o f t h i s p r o c e s s . I h o p e t o b e t h a t o n e g e t s 2$

Question Number 178021 Answers: 1 Comments: 0

Let S={1, 2, 3, 4, 5} , we want to make a group H of numbers have the following properties: 1. Each number has different digits and taken from S 2. Each number is greater than 20 000 3. None of them is multiple of five How many items of H?

$L e t S = {1, 2, 3, 4, 5}, w e w a n t t o m a k e a$ $g r o u p H o f n u m b e r s h a v e t h e f o l l o w i n g$ $p r o p e r t i e s :$ $1 . E a c h n u m b e r h a s d i f f e r e n t d i g i t s a n d$ $t a k e n f r o m S$ $2 . E a c h n u m b e r i s g r e a t e r t h a n 20 000$ $3 . N o n e o f t h e m i s m u l t i p l e o f f i v e$ $H o w m a n y i t e m s o f H ?$