Question

Tiles number from 1 to 6 is placed in a bag are drawn out to determine which of six tasks will be assigned to six people. What is probability that the tiles numbered 5 and 6 are drawn consecutively?

Answer 1

1/30

Answer 2

you have a 1/6 chance of drawing a 5 and a 1/5 chance of drawing the 6 aftwards, thus 1/6*1/5 = 1/30

Answer 3

There is one '5' tile, and 6 tiles total when you want to grab the 5, so the probability is:
\[\frac{1}{6}\]
Then there is one '6' tile, and 5 tiles left in the bag because you took out the 5 tile, so now you have:
\[\frac{1}{5}\]
Multiply the individual probabilities:
\[(\frac{1}{6})(\frac{1}{5}) = \frac{1}{30}\]

Answer 4

the key is
F) 2/3
G) 2/5
H) 1/2
J) 1/3

Answer 5

1/30

Answer 6

@Nancy, as in those are your only choices? because none of them are correct

Answer 7

they are all drawn, and the 5 and 6 could be consecutive in any position, so you are all wrong so far.

Answer 8

yes I copy exactly in text book

Answer 9

let me send you

Answer 10

touche

Answer 11

look number 52

Answer 12

i understand now, its 1/3

Answer 13

first you count how many different ways are there to pull the tiles out (how many ways are there to order the numbers 1-6), that would be 6! which is 720.

Answer 14

Then you want to know how many of those cases have the 5 and 6 next to each other (that would mean they are drawn consecutively) to figure that out, treat the 5 and 6 tile as one piece, so now there are only 5 pieces, and you want to figure out how many different ways you can pull them out. that is 5! = 120. But it could be 5 then 6, or 6 then 5, so multiply by 2. thats 240. so the final answer is 240/720 = 1/3

Answer 15

thank joemath314159, can you help me number 60, and 62

Answer 16

well done

Answer 17

for 60: you are looking for all the possible fractions that can be made using {1,2} for the numerator, and (1,2,7,14} for the denominator. The most efficient way to do this is to pick a number from the first set, and go through all the numbers in the second set. For example lets start with 1from the first set:
\[\frac{1}{1},\frac{1}{2},\frac{1}{7},\frac{1}{14}\]
Then we switch a to '2' and do the same thing. Oh and downt forget the plus/minus

Answer 18

+-1/1,
+-1/2
+-1/7
+-1/14

+-2/1
+-2/2=+-1
+-2/7+-2/14
?

Answer 19

thats correct :) you might have to reduce some fractions, but thats the general idea

Answer 20

ty

Answer 21

can you help me one more

Answer 22

51)
state negative and positive real root ,count sign change, I still don't know how many roots

Answer 23

I attach file
after count the sign change how I know how many number negative or positive real roots

Answer 24

Well, there are 5 roots in general (because the degree of the polynomial is 5). let me think about this for a bit, one sec.

Answer 25

Ah, there is actually a nice trick for this, what you do is start on the left side of the polynomial. then you count how many times the sign changes (from positive to neg, or neg to positive). that will tell you how many roots are positive

Answer 26

So for your problem, there are 4 sign changes, so that means there are 4 positive roots, which leaves one negative root.

Answer 27

51)
positive x: the sign change is
y n y y y ( I don't know how many roots)

negative roots : sign change is
n y n n n (have one real roots )