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Svetlanka [38]
3 years ago
13

A storekeeper increased the price of hats by 8% A hat was originally priced at $12.00. What is the new cost of the hat?

Mathematics
1 answer:
german3 years ago
6 0

Answer:

$12.96

Step-by-step explanation:

determine what the decimal form of 8% is

⇒ 8% = 0.08

multiply $12 by 0.08

⇒ $12 x 0.08

⇒ $0.96

add $0.96 to $12

⇒ $12 + $0.96

⇒ $12.96

new price

⇒ $12.96

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The number of Internet users in Latin America grew from 25.8 million in 2009 to 70.6 million in 2016. Use the geometric mean to
ipn [44]

Answer:

the annual growth rate is 15.47 %

Step-by-step explanation:

Given the data in the question;

Internet users grew from 25.8 million to 70.6 million,

from the year 2009 to the year 2016.

Using geometric mean, Annual growth rate = ?

To determine the average growth rate of a time series using geometric mean, we use the following formula;

r_{geo = [ ( Xₙ / X₀ )^{\frac{1}{n} ] - 1

where Xₙ is the data value of the last year { 70.6 million }

X₀ is the data value for the first year { 25.8 million }

n is the sample size or the time difference, ( 2016 - 2009 = 7 )

so we substitute;

r_{geo =  [ ( 70.6 / 25.8  )^{\frac{1}{7} ] - 1

r_{geo = [ ( 2.736434  )^{\frac{1}{7} ] - 1

r_{geo = [ 1.15466 ] - 1

r_{geo = 0.15466

r_{geo = ( 0.15466 × 100 )%

r_{geo = 15.47 %

Therefore, the annual growth rate is 15.47 %

5 0
3 years ago
Answer this volume based Question. I will make uh brainliest + 50 points​
Harlamova29_29 [7]

Answer:

\huge{\purple {r= 2\times\sqrt[3]3}}

\huge 2\times \sqrt [3]3 = 2.88

Step-by-step explanation:

  • For solid iron sphere:
  • radius (r) = 2 cm (Given)

  • Formula for V_{sphere} is given as:

  • V_{sphere} =\frac{4}{3}\pi r^3

  • \implies V_{sphere} =\frac{4}{3}\pi (2)^3

  • \implies V_{sphere} =\frac{32}{3}\pi \:cm^3

  • For cone:
  • r : h = 3 : 4 (Given)
  • Let r = 3x & h = 4x

  • Formula for V_{cone} is given as:

  • V_{cone} =\frac{1}{3}\pi r^2h

  • \implies V_{cone} =\frac{1}{3}\pi (3x)^2(4x)

  • \implies V_{cone} =\frac{1}{3}\pi (36x^3)

  • \implies V_{cone} =12\pi x^3\: cm^3

  • It is given that: iron sphere is melted and recasted in a solid right circular cone of same volume
  • \implies V_{cone} = V_{sphere}

  • \implies 12\cancel{\pi} x^3= \frac{32}{3}\cancel{\pi}

  • \implies 12x^3= \frac{32}{3}

  • \implies x^3= \frac{32}{36}

  • \implies x^3= \frac{8}{9}

  • \implies x= \sqrt[3]{\frac{8}{3^2}}

  • \implies x={\frac{2}{ \sqrt[3]{3^2}}}

  • \because r = 3x

  • \implies r=3\times {\frac{2}{ \sqrt[3]{3^2}}}

  • \implies r=3\times 2(3)^{-\frac{2}{3}}

  • \implies r= 2\times (3)^{1-\frac{2}{3}}

  • \implies r= 2\times (3)^{\frac{1}{3}}

  • \implies \huge{\purple {r= 2\times\sqrt[3]3}}
  • Assuming log on both sides, we find:

  • log r = log (2\times \sqrt [3]3)

  • log r = log (2\times 3^{\frac{1}{3}})

  • log r = log 2+ log 3^{\frac{1}{3}}

  • log r = log 2+ \frac{1}{3}log 3

  • log r = 0.4600704139

  • Taking antilog on both sides, we find:

  • antilog(log r )= antilog(0.4600704139)

  • \implies r = 2.8844991406

  • \implies \huge \red{r = 2.88\: cm}

  • \implies 2\times \sqrt [3]3 = 2.88
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