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2 years ago

Mr. Starnes wondered what proportion of Katy Perry's Twitter followers are

Mathematics

1 answer:

Citrus2011 [14]2 years ago

5 0

Answer and Step-by-step explanation:

To calculate a confidence interval for a proportion:

1) Determine the proportion

$p=\frac{308}{500}$

p = 0.616

2) A 90% confidence interval has z-score that is 1.645.

3) Calculate margin of error

$ME=\sqrt{\frac{p(1-p)}{n} }$

where

n is the sample size

$ME=\sqrt{\frac{0.616(1-0.616)}{500} }$

$ME=\sqrt{\frac{0.616(0.384)}{500} }$

ME = 0.02175

Then the interval is given by

p ± z(ME)

0.62 ± 1.645(0.02175)

0.62 ± 0.035

The interval will be

0.585 < p < 0.655

What this means is that we are 90% confident that the true proportion of Katy Perry's Twitter female followers is between 0.585 and 0.655.

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Angelina_Jolie [31]

Answer:

V = 1/6 cubic units

Step-by-step explanation:

Applying the concept of integrals for volume calculation:

$V = \int\limits^b_a {S(x)} \, dx$ (1)

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S(x) = cross section area of the solid, perpendicular to the x axis

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Area of the triangle = $S(x)=\frac{y(x)*z(x)}{2}$ (2)

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We apply the equation of the point-slope line (plane xy):

Slope = $m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}$ (3)

Equation of the line = $y - y_{1} =m(x-x_{1} )$ (4)

Replacing the points (1,0) and (0,1) in (3):

$m=\frac{1-0}{0-1} =-1$

Replacing the point (1,0) and m = -1 in (4):

$y-0=(-1)(x-1)$

y(x) = -x + 1 (Line A-B) (5)

We apply the equation of the point-slope line (plane xz):

Slope = $m = \frac{z_{2} - z_{1} }{x_{2} - x_{1}}$ (6)

Equation of the line = $z - z_{1} =m(x-x_{1} )$ (7)

Replacing the points (1,0) and (0,1) in (6):

$m=\frac{1-0}{0-1} =-1$

Replacing the point (1,0) and m = -1 in (7):

$z-0=(-1)(x-1)$

z(x) = -x + 1 (Line A-C) (8)

Replacing (5) and (8) in (2)

$S(x) = \frac{(-x + 1) * (-x + 1)}{2} =\frac{(-x + 1)^{2} }{2}$ (9)

Replacing (9) in (1) and knowing that a = 0 and b = 1:

$V = \int\limits^1_0 {\frac{(-x + 1)^{2} }{2}} \, dx = \int\limits^1_0 {\frac{x^{2}-2x+1 }{2}} \, dx$

$V =\frac{1}{2} (\frac{x^{3} }{3} -2\frac{x^{2} }{2} +x)$ evaluated from x=0 to x=1

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3 years ago

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aev [14]

(1-52/2+5)=(1-26+5)=(-25+5)=-20

continuing:

-20*2*6*6= -40*6*6=-240*6=-1440

result: -1440

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2 years ago

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katrin [286]

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(I’m sorry if this wrong but hope it is not and you understand it)

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