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Rama09 [41]
3 years ago
15

What is the sum of an infinite geometric series if the first term is 156 and the common ratio is 2⁄3?

Mathematics
1 answer:
Zanzabum3 years ago
4 0

Answer:

<h2>B. 468</h2>

Step-by-step explanation:

We have

a_1=156,\ r=\dfrac{2}{3}

If |r| < 1, then the formula of a sum of an infinite geometric sequence is:

S=\dfrac{a_1}{1-r}

Substitute:

S=\dfrac{156}{1-\frac{2}{3}}=\dfrac{156}{\frac{1}{3}}=156\cdot\dfrac{3}{1}=468

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Katarina [22]

First of all, you can simplify the 4 at the numerator and the 14 at the denominator (they're both multiple of 2):

\dfrac{4}{14\sqrt{2}} = \dfrac{2\cdot 2}{2\cdot 7\cdot\sqrt{2}} = \dfrac{2}{7\sqrt{2}}

Now, rationalize a denominator means that you have to get rid of the square root, in order to have an integer denominator.

To do so, remember that you can always multiply any number by 1 without changing its value, and you can always think of 1 as a fraction where numerator and denominator are equal:

\dfrac{2}{7\sqrt{2}} = \dfrac{2}{7\sqrt{2}}\cdot 1 = \dfrac{2}{7\sqrt{2}} \cdot \dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{2\sqrt{2}}{7\cdot 2} = \dfrac{\sqrt{2}}{7}

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3 years ago
You have $15 to spend in a candy store. If Kitkat cost $0.75 each and mini Snickers are $0.25 each.
zhuklara [117]

Answer:

1. 60 snickers

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Step-by-step explanation:

7 0
3 years ago
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Help I have a C in math. I don't understand this Alegbra. If you get it right then I will give you Brainlist!
I am Lyosha [343]

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1st Is rational

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2 years ago
If the product of two rational numbers is (-9/16) and one of them is (-4/15) find the other number.​
ololo11 [35]

Given:

  • The product of two numbers is (-9/16).
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To find: The other number.

Answer:

Let's assume the unknown number to be 'x'.

(-4/15) × x = (-9/16)

× = (-9/16) ÷ (-4/15)

When we divide a fraction by another fraction, the divisor will be taken in its reciprocal form.

x = (-9/16) × (-15/4)

x = 135/64

Therefore, the other number is 135/64.

Hope it helps. :)

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3 years ago
Write an equation for your trend line?
Soloha48 [4]
Find two points on the graph that the line crosses through almost perfectly. It looks like (1,10) and (9,1) will do.

Use them to compute the slope:
m = (1 - 10) / (9 - 1)
= -9/8

Then set up the "point-slope form":
y - y0 = m * (x - x0)

You choose some point (x0, y0) that the line crosses through. We already know the line passes through (1,10) pretty well, so let's use that.

x0 = 1
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Now finish plugging into the equation:
y - 10 = -9/8 * (x - 1)

The above equation will work fine for an answer, but let's go a step further and solve for y.

y - 10 = -9/8x + 9/8
y = -9/8x + 9/8 + 10
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y = -9/8x + (9 + 80)/8
y = -9/8x + 89/8
4 0
3 years ago
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