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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?

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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