I need to know what 2 numbers go in here to equal 20

Four darts are thrown at this dartboard. If all four darts hit the board, how many different point totals are possible. (Dartboa

jonny [76]

Answer:

Different point total are possible = 497

Step-by-step explanation:

Given - Four darts are thrown at this dartboard. Dartboard regions are

1, 4, 7, 10 points

To find - If all four darts hit the board, how many different point totals are

possible.

Proof -

Are given there are 4 regions -

1st region - 1 point

2nd region - 4 points

3rd region - 7 points

4th region - 10 points

Case I :

If all the darts hit the different region -

Total points possible are - 1 + 4 + 7 + 10 = 22 points

Case II :

If all the darts hit the same region -

It means either they hit 1 region or 2nd region or 3rd region or 4th region

If they all 4 hit first region , points are - 1+1+1+1 = 4

If they all 4 hit second region , points are - 4+4+4+4= 16

If they all 4 hit third region , points are - 7+7+7+7 = 28

If they all 4 hit fourth region , points are - 10+10+10+10 = 40

So,

the Total points possible are - 4 + 16 + 28 + 40 = 88

Case III :

If 3 darts hit the same region -

Sub-case 1 :

If 1 dart hit 1st region, other 3 dart hit 2nd region

Points are - 1 + 4 + 4+ 4 = 13

Sub-case 2 :

If 1 dart hit 1st region , other 3 dart hit 3rd region

Points are - 1 + 7 + 7 + 7 = 22

Sub-case 3 :

If 1 dart hit 1st region , other 3 dart hit 4th region

Points are - 1 + 10 + 10 + 10 = 31

Sub-case 4 :

If 1 dart hit 2nd region , other 3 dart hit 1st region

Points are - 4 + 1 + 1 + 1 = 7

Sub-case 5 :

If 1 dart hit 2nd region , other 3 dart hit 3rd region

Points are - 4 + 7 + 7 + 7 = 25

Sub-case 6 :

If 1 dart hit 2nd region , other 3 dart hit 4th region

Points are - 4 + 10 + 10 + 10 = 34

Sub-case 7 :

If 1 dart hit 3rd region , other 3 dart hit 1st region

Points are - 7 + 1 + 1 + 1 = 10

Sub-case 8 :

If 1 dart hit 3rd region , other 3 dart hit 2nd region

Points are - 7 + 4 + 4 + 4 = 19

Sub-case 9 :

If 1 dart hit 3rd region , other 3 dart hit 4th region

Points are - 7 + 10 + 10 + 10 = 37

Sub-case 10 :

If 1 dart hit 4th region , other 3 dart hit 1st region

Points are - 10 + 1 + 1 + 1 = 13

Sub-case 11 :

If 1 dart hit 4th region , other 3 dart hit 2nd region

Points are - 10 + 4 + 4 + 4 = 22

Sub-case 12 :

If 1 dart hit 4th region , other 3 dart hit 3rd region

Points are - 10 + 7 + 7 + 7 = 31

So,

Total points possible are - 13+22+21+7+25+34+10+19+37+13+22+31 = 254

Case IV :

If 2 darts hit the same region -

Sub-case 1:

If 2 darts hits 1st region , other 2 darts hit 2nd region

Points are - 1 + 1 + 4 + 4 = 10

Sub-case 2:

If 2 darts hits 1st region , other 2 darts hit 3rd region

Points are - 1 + 1 + 7 + 7 = 16

Sub-case 3:

If 2 darts hits 1st region , other 2 darts hit 4th region

Points are - 1 + 1 + 10 + 10 = 23

Sub-case 4:

If 2 darts hits 2nd region , other 2 darts hit 3rd region

Points are - 4 + 4 + 7 + 7 = 22

Sub-case 5:

If 2 darts hits 2nd region , other 2 darts hit 4th region

Points are - 4 + 4 + 10 + 10 = 28

Sub-case 6:

If 2 darts hits 3rd region , other 2 darts hit 4th region

Points are - 7 + 7 + 10 + 10 = 34

So,

Total points possible are - 10 + 16 + 23 + 22 + 28 + 34 = 133

Case V :

If 1 darts hit the same region -

This case is include in the Case III.

∴ we get

Different point total are possible = Points in Case I + II + III + IV

= 22 + 88 + 254 + 133

= 497

⇒Different point total are possible = 497

4 0

2 years ago

Helpppppppppppppppppppppppppp

noname [10]

Answer:

F

Step-by-step explanation:

So lets use the process of elimantion to find the answer.

Firs off, we can tell that this is a greater/less than or equal to inequlaity, since there is a inclosed circle, not a open one. So this leaves the top left answer and bottem right answer.

Now, we can see that the graph is from 0-15. X is at 7.

This means its x+8, because the x would be smaller, or possibly even negatibe on this graph.

My theory that can better support my annwer is if we solve for x:

x+8=15

We can subtract 8 from both sides:

x=7

And as we can see on the inequality, x is at 7 in the graph.

Hope this makes sense and helps!

6 0

3 years ago

Which of the following statements is not true?

Lady bird [3.3K]

Statement: Your question is well elaborate and has all needed data.

6 0

3 years ago

Read 2 more answers

A parallelogram has coordinates A(1, 1), B(5, 4), C(7, 1), and D(3, -2). What are the coordinates of parallelogram A′B′C′D′ afte

saul85 [17]

Hey there! I'm happy to help!

First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).

Let's convert this below

A: (1,1)⇒(-1,-1)

B: (5,4)⇒(-5,-4)

C: (7,1)⇒(-7,-1)

D: (3,-2)⇒(-3,2)

Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.

A: (-1,-1)⇒(4,-2)

B: (-5,-4)⇒(0,-5)

C: (-7,-1)⇒(-2,-2)

D: (-3,2)⇒(2,1)

Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)

Now you know how to find the coordinates of translated figures! Have a wonderful day! :D

5 0

3 years ago

90 + 12 = 6(15 + 12) Yes or No

quester [9]

Answer:

This is false.

Step-by-step explanation:

90 + 12 = 102.

6(15+12) equals to 6(27) which is 162.

8 0

3 years ago

Read 2 more answers

I need to know what 2 numbers go in here to equal 20​

I need to know what 2 numbers go in here to equal 20