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elixir [45]
3 years ago
10

Given the formula, Sn=a 1-r^n/1-r, what is the sum of the first nine terms of the geometric series: 324, -108, 36, -12...

Mathematics
1 answer:
vlada-n [284]3 years ago
3 0

Answer:

243.01.

Step-by-step explanation:

The first term (a) = 324.

The common ratio (r) = -108/324 = -1/3.

So sum of 9 terms is:

S(9) = 324 * (1 - (-1/3)^9) / ( 1 - (-1/3)

= 324 ( 1 - (-0.00005076)) / 4/3

= 324 * 1.00005076 / 1.33333

= 243.012.

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8 9 10 11 12 13 14 15 16 17 18 19 20You and two friends (Adam and Alana) wonly play a game if it is fair for all three of you. T
pav-90 [236]
Well I don't know ! 
Let's take a look and see:

The idea is that there could be more than one way
for a roll of the dice to land with the same number.  

-- If the sum is from 1-4, you get the point.
There are  6  different ways for a roll of the dice to come up 1-4.

-- If the sum is from 5-8, Adam gets the point.
There are  20  different ways for a roll of the dice to come up 5-8.

-- If the sum is 9-12, Lana gets the point.
There are  10  different ways for a roll of the dice to come up 9-12.

-- The game is not fair to all three of you.
-- Lana has a distinct advantage over you.
-- Adam has a big advantage over Lana.
-- Adam has an even bigger advantage over you.
-- You are at a big disadvantage.  (Notice that one of your
numbers ... 1 ... can never come up unless one of the dice
falls off of the table.)
_______________________________

Here's how to figure it:

Ways to roll a 2:
1 ... 1

Ways to roll a 3:
1 ... 2
2 ... 1

Ways to roll a 4:
1 ... 3
2 ... 2
3 ... 1

Ways to roll a 5:
1 ... 4
2 ... 3
3 ... 2
4 ... 1

Ways to roll a 6:
1 ... 5
2 ... 4
3 ... 3
4 ... 2
5 ... 1

Ways to roll a 7:
1 ... 6
2 ... 5
3 ... 4
4 ... 3
5 ... 2
6 ... 1

Ways to roll an 8:
2 ... 6
3 ... 5
4 ... 4
5 ... 3
6 ... 2

Ways to roll a 9:
3 ... 6
4 ... 5
5 ... 4
6 ... 3

Ways to roll a 10:
4 ... 6
5 ... 5
6 ... 4

Ways to roll 11:
5 ... 6
6 ... 5

Ways to roll 12:
6 ... 6

5 0
3 years ago
The bases of a right prism are isosceles trapezoids with bases of 10 ft and 18 ft
likoan [24]

Answer:

540 ft^2.

Step-by-step explanation:

The area of the trapezoid = h/2 (10 + 18) = 14h.

By Pythagoras the height h = √(5^2 - 4^2) = 3.

So the area of the 2 trapezoidal bases = 2 * 14*3

= 84 ft^2.

Now we calculate the area of the four lateral rectangular sides:

= 10*12 + 18*12 + 2*5*12

= 456 ft^2.

Total area =  456 + 54

= 540 ft^2.

4 0
3 years ago
I need this for today
stiks02 [169]

Answer: The Last option is the only option equivalent to that equation.

7 0
3 years ago
In the adjoining figure, ABCD is a square of side 28 cm find the area of shaded region​
vodka [1.7K]

Step-by-step explanation:

Area of square

A = s²

A = 28²

A = 28 × 28

A = 784 cm²

7 0
2 years ago
Peter has 30 pens and Tony has 14 pens .How many pens must Tony give Peter so that Peter shall have 3 times as many as Tony?​
Svetradugi [14.3K]

Answer:

Let p be the number of pencils.

3(14-p)=30+p

42-3p=30+p

4p=12, p=3.

So Peter ends up with 33 and Tony with 11. 3*11=33, so that confirms that Tony gave Peter 3 pencils.

3 0
3 years ago
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