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3 years ago

Which of the following fractions is equivalent to 2:11?

Mathematics

1 answer:

Lostsunrise [7]3 years ago

8 0

Answer:

Step-by-step explanation:

Step 1:

2 : 11 Ratio

Having a ratio is the same thing as dividing so if you divide 2 by 11 you get 2/11.

Step 3

2 ÷ 11

Answer:

C. 2/11

Hope This Helps :)

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riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

2 years ago

What is the surface area of each triangular prism?

SOVA2 [1]

the surface area of the above triangular prism is 156 square inches.

Step-by-step explanation:

multiply the sum of the triangle sides by the height of the prism and add the values together for the answer, remembering to include the correct unit of measurement.

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%7B2%7D%5E%7Bn%7D%20%20%3D%20226%20%20" id="TexFormula1" title=" {2}^{n} = 226 " alt=" {2

Rudik [331]

N equals to 7.82 (to 2 decimal places)

5 0

3 years ago

Read 2 more answers

Expand (x-3)(x-8) to form a quadratic expression

AlladinOne [14]

Answer:

x^2 - 11x + 24

Step-by-step explanation:

Foil the equation

x^2 - 3x - 8x + 24

x^2 - 11x + 24

8 0

3 years ago

Shannon bought 518 pounds of apples. Bill bought 278pounds of apples. Which most closely estimates how many more pounds of apple

Aleksandr-060686 [28]

Answer:

240 pounds.

Step-by-step explanation:

Given that,

Shannon bought 518 pounds of apples.

Bill bought 278 pounds of apples.

We need to find how many more pounds of apples Shannon bought than Bill.

More Apples = Shannon Apples - Bill Apples

= 518 - 278

= 240

Hence, 240 pounds of apples Shannon bought than Bill.

3 0

2 years ago