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3 years ago

Help me thank you ! appreciate it

Mathematics

1 answer:

Leviafan [203]3 years ago

6 0

Answer:

what does it mean by equation

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The game of clue involves 6 suspects, 6 weapons, and 9 rooms. one of each is randomly chosen and the object of the game is to gu

mina [271]

Part A:

Given that the game of clue involves 6 suspects, 6 weapons, and 9 rooms.

The number of ways that one of each is randomly chosen is given by:

$^6C_1\times{ ^6C_1}\times{ ^9C_1}=6\times6\times9=324$

Therefore, the number of solutions possible is 324.

Part B:

Given that a players is randomly given three of the remaining cards, let s, w, and r be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player.

The number of suspects, weapons, and rooms remaining respectively after the player observes his or her three cards are: 6 - s, 6 - w, and 9 - r.

Let x denote the number of solutions that are possible after that player observes his or her three cards, then:

$x={ ^{6-s}C_1}\times{ ^{6-w}C_1}\times{ ^{9-r}C_1}=(6-s)(6-w)(9-r)$

Therefore, x in terms of s, w, and r is given by x = (6 - s)(6 - w)(9 - r).

Part C:

The expected value E(x) of a data set $x_i$ with probabilities $p(x_i)$ is given by $E(x)=\Sigma xp(x)$

There are $^{3+3-1}C_{3-1}={ ^5C_2}=10$ possible combinations s, w and r. They are (3, 0, 0), (0, 3, 0), (0, 0, 3), (2, 1, 0), (0, 2, 1), (1, 0, 2), (2, 0, 1), (1, 2, 0), (0, 1, 2), (1, 1, 1)

Thus the expected value is given by

$E(x)=3\cdot6\cdot9p(3, 0, 0)+6\cdot3\cdot9p(0, 3, 0)+6\cdot6\cdot6p(0, 0, 3) \\ 4\cdot5\cdot9p(2, 1, 0)+6\cdot4\cdot8p(0, 2, 1)+5\cdot6\cdot7p(1, 0, 2)+4\cdot6\cdot8p(2, 0, 1) \\ +5\cdot4\cdot9p(1, 2, 0)+6\cdot5\cdot7p(0, 1, 2)+5\cdot5\cdot8(1, 1, 1) \\ \\ = \frac{1}{ ^{21}C_3} (162\cdot{ ^6C_3}\cdot{ ^6C_0}\cdot{ ^9C_0}+162\cdot{ ^6C_0}\cdot{ ^6C_3}\cdot{ ^9C_0}+216\cdot{ ^6C_0}\cdot{ ^6C_0}\cdot{ ^9C_3} \\ \\ +180\cdot{ ^6C_2}\cdot{ ^6C_1}\cdot{ ^9C_0}+192\cdot{ ^6C_0}\cdot{ ^6C_2}\cdot{ ^9C_1}$

$+210\cdot{ ^6C_1}\cdot{ ^6C_0}\cdot{ ^9C_2}+192\cdot{ ^6C_2}\cdot{ ^6C_0}\cdot{ ^9C_1}+180\cdot{ ^6C_1}\cdot{ ^6C_2}\cdot{ ^9C_0} \\ \\ +210\cdot{ ^6C_0}\cdot{ ^6C_1}\cdot{ ^9C_2}+200\cdot{ ^6C_1}\cdot{ ^6C_1}\cdot{ ^9C_1} \\ \\ =\frac{1}{1,330}(324\cdot20+216\cdot84+360\cdot90+384\cdot135+420\cdot216+200\cdot324) \\ \\ =\frac{1}{1,330}(6,480+18,144+32,400+51,840+90,720+64,800) \\ \\ =\frac{1}{1,330}(264,384) \\ \\ =\bold{198.78}$

6 0

3 years ago

Help with this please ..

abruzzese [7]

Answer:

the answer is 2.59x10^7

7 0

3 years ago

PLEASE HELPPPPPP. I NEED IT DONEEEEE.

agasfer [191]

Answer:

1. Couples tickets: $8

Individual tickets: $4

2. Song download cost: $2

Movie download cost: $15

Step-by-step explanation:

You can solve both of these questions by doing system of equations.

Let's start with question 1.

There are 2 variables in this equation:

- Couples tickets price: let's represent these with the letter C

- Individual tickets price: let's represent these with the letter K

Writing the two equations would look this these:

5c + 2k = 48

3c + 2k = 32

Next, isolate a variable. I am going to isolate K in the first equation.

$2k = -5c + 48 \\k = -\frac{5}{2}c + 24$

Now that we isolated a variable we can plug that back in to the second equation:

$3c + 2(-\frac{5}{2}c + 24) = 32\\3c - \frac{10}{2}c + 48 = 32\\3c -5c + 48 = 32\\-2c + 48 = 32\\-2c = -16\\c = 8$

We found that c is equal to 8 so we can put that back in to an equation to solve for k.

5(8) + 2k = 48

40 + 2k = 48

2k = 8

k = 4

Therefore, the price for couples tickets is $8 and the price for individual tickets is $4.

Check #1:

5(8) + 2(4) = 48

40 + 8 = 48

48 = 48

3(8) + 2(4) = 32

24 + 8 = 32

32 + 32

Now, let's go on to question 2.

There are 2 variables in this equation:

- Price of songs downloaded: let's represent these with S

- Price of movies downloaded: let's represent these with M

Writing the two equations would look like this:

15s + 11m = 195

15s + 8m = 150

There is a simple way to answer this system, however.

If you change the bottom equations signs to negative you can minus the second equation from the first equation like this:

15s + 11m = 195

-(15s +8m = 150)

Minus them to get this equation:

3m = 45

Solve

m = 15

We have found that each movie download costs $15, now let's plug this back into an equation:

15s + 11(15) = 195

15s + 165 = 195

15s = 30

s = 2

Each song costs $2 to download.

Check #2:

15(2) + 11(15) = 195

30 + 165 = 195

195 = 195

15(2) + 8(15) = 150

30 + 120 = 150

150 = 150

I hope this helps!!

- Kay :)

6 0

3 years ago

What is the area of the semicircle?

Bumek [7]

A = pi r^2 / 2
if 22mm = radius
then
A = (3.14 * 22^2) / 2
A = 759.88

if 22mm is the diameter
then
A = (3.14 * 11^2) /2
A = 189.97

5 0

3 years ago

Read 2 more answers

Is 2 x+6-x=1/3(3x+18) a one solution ,no solution ,or an infinite numbers of solutions

nalin [4]

To determine this, the first thing we should do is simplify the expression. As usual, bring like terms to either side of the "=" and then simplify.
2x + 6 - x = 1/3 (3x + 18)
x + 6 = 1/3 (3x + 18)
x + 6 = 1/3 (3x) + 1/3(18)
x + 6 = x + 6

We can already see that both sides have the same expression "x+6". Now, if you try to simplify any further, you will get 0=0. That means that for any value of x, the expression will simplify to 0=0. Because 0=0 is a true statement, for every value of x, the expression will be true. Therefore, there are an infinite number of solutions.

Hope this helped!! :D
Note: If you are still confused, let me know. I realize that I might have been a bit confusing in my explanation

5 0

4 years ago