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SVEN [57.7K]
3 years ago
11

How much would 200 invested at 4% interest compounded monthly be worth after 8 years round to the nearest cent

Mathematics
1 answer:
steposvetlana [31]3 years ago
5 0
A=200×(1+0.04÷12)^(12×8)
A=275.28
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Does the series converge or diverge? If it converges, what is the sum? Show your work. ∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
Mekhanik [1.2K]

Answer:

Step-by-step explanation:

Given the series,

∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)

So,

∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞

There are different types of test to show if a series converges or diverges

So, using Ratio test

Lim n → ∞ (a_n+1 / a_n)

Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))

Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))

Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)

Lim n→ ∞ (-1/2)^(n-n+1)

Lim n→ ∞ (-1/2)^1 = -1/2

Since the limit is less than 0, then, the series converge...

Sum to infinity

Using geometric progression formula

S∞ = a / 1 - r

Where

a is first term

r is common ratio

So, first term is

a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1

a_1 = -4

Common ratio r = a_2 / a_1

a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2

a_2 = 2

Then,

r = a_2 / a_1 = 2 / -4 = -½

S∞ = -4 / 1--½

S∞ = -4 / 1 + ½

S∞ = -4 / 3/2 = -4 × 2 / 3

S∞ = -8 / 3 = -2⅔

The sum to infinity is -2.67 or -2⅔

Check attachment for better understanding

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3 years ago
Use trianglePQR to write the trigonometric ratio as a decimal. round to four decimal places.
astraxan [27]
I hope this answer helps, it’s kinda messy, but it’s still understandable (I guess)

4 0
3 years ago
A shipping company uses an inclined conveyor belt to load or unload packages. The dock is 15 feet above ground. The base of the
alexgriva [62]
Hey there! :D

Think of this like a triangle. The dock is 15 feet above ground. It is the side of the triangle. The line connecting the bottom of the dock to the base of the conveyor belt is 40 feet. This is like the base. 

The conveyor belt itself is at a diagonal, and should be the hypotenuse. 

Use the Pythagorean theorem. 

a^2+b^2=c^2

15^2+40^2= c^2 

225+1,600= c^2

Add the values together. 

1,825= c^2

Find the square root of 1,825. 

c= 42.7 (rounded to the nearest tenth) 

The conveyor belt is 42.7 feet long.

I hope this helps!
~kaikers


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3 years ago
A specific amount or number that represent how much of something you have is _____
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A measurement or a unit
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What is the perimeter of this tile
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Provide a picture of the tile, thanks!
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