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3 years ago

8

Use the formula to evaluate the series 1/4 + 1/9 + 1/27 + 1/81.

1 answer:

Dmitriy789 [7]3 years ago

8 0

Is the first term supposed to be 1/4, or did you actually mean 1/3?

I'll assume the latter. Write

$S=\dfrac13+\dfrac19+\dfrac1{27}+\dfrac1{81}$
$S=\dfrac13+\dfrac1{3^2}+\dfrac1{3^3}+\dfrac1{3^4}$
$\dfrac13S=\dfrac1{3^2}+\dfrac1{3^3}+\dfrac1{3^4}+\dfrac1{3^5}$
$\implies S-\dfrac13S=\dfrac13-\dfrac1{3^5}$
$\dfrac23S=\dfrac13\left(1-\dfrac1{3^4}\right)$
$S=\dfrac12\left(1-\dfrac1{81}\right)$
$S=\dfrac{40}{81}$

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A theatre has the capacity to seat people across two levels, the Circle and

andriy [413]

Answer: $76.19\%$

Step-by-step explanation:

<h3> The complete exercise is: " A theatre has the capacity to seat people across two levels, the Circle, and the stalls. The ratio of the number of seats in the circle to a number of seats in the stalls is 2:5. Last Friday, the audience occupied all the 528 seats in the circle and $\frac{2}{3}$ of the seats in the stalls. What is the percentage of occupancy of the theatre last Friday?"</h3>

Let be "s" the total number of seats in the Stalls.

The problem says that the ratio of the number of seats in the Circle to the number of seats in the Stalls is $2:5$ .

Since the number of seats that were occupied last Friday was 528 seats, we can set up the following proportion:

$\frac{2}{5}=\frac{528}{s}$

Solving for "s", we get:

$s*\frac{2}{5}=528\\\\s=528*\frac{5}{2}\\\\s=1,320$

So the sum of the number of seats in the Circle and the number of seats in the Stalls, is:

$Total=1,320\ seats+528\ seats=1,848\ seats$

We know that $\frac{2}{3}$ of the seats in the Stalls were occupied. Then, the number of seat in the Stalls that were occupied is:

$(1,320)(\frac{2}{3})=880$

Therefore, the total number of seats that were occupied las Friday is:

$Total\ occupied=880\ seats+528\ seats=1,408\ seats$

Knowing this, we can set up the following proportion, where "p" is the the percentage of occupancy of the theatre last Friday:

$\frac{100}{1,848}=\frac{p}{1,408}$

Solving for "p", we get:

$(1,408)(\frac{100}{1,848})=p\\\\p=76.19\%$

8 0

2 years ago

What is the quotient of 43,482 ÷ 12?

Bad White [126]

Answer:

(C) 3,623 R6

Step-by-step explanation:

43,482 ÷ 12 = 3623 and 6 remainder

So answer is 3623 R6

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3 years ago

2 • a • b • a • b=<br> simplify the expression in the exponential notation

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3 years ago

Solve x+2/x-4<0<br><br> A)–4 < x < –2<br> B)–2 < x < 4<br> C)–2 < x < –4

Gelneren [198K]

$Domain:\ x\neq-2\\\\\dfrac{x+2}{x-4}$

Other method:

$\dfrac{x+2}{x-4}$

zeros of numerator and denominator are x = -2 and x = 4.

Look at the second picture.

for x < -2 → x + 2 < 0 and x - 4 < 0

therefore $\dfrac{x + 2}{x - 4}=\dfrac{(-)}{(-)}>0$

for -2 < x < 4 → x + 2 > 0 and x - 4 < 0

therefore $\dfrac{x+2}{x-4}=\dfrac{(+)}{(-)} < 0$

for x > 4 → x + 2 > 0 and x - 4 > 0

therefore $\dfrac{x+2}{x-4}=\dfrac{(+)}{(+)} > 0$

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2 years ago

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BlackZzzverrR [31]

Answer:

c

Step-by-step explanation:

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3 years ago

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