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Svetradugi [14.3K]
4 years ago
10

Marlin Davies buys a truck for $28,000 in three years the truck depreciates 48% in value how much is the truck worth in 3 years

Mathematics
2 answers:
marysya [2.9K]4 years ago
6 0

Answer:  $ 14560

Step-by-step explanation:

Here, The initial price of truck = $ 28,000

According to the question,

In three years the truck depreciates 48% in value.

Thus, the truck worth in three year = (100-48)% of 28,000

= 52% of 28,000

= \frac{28000\times 52}{100}

= \frac{1456000}{100}

=  14560

⇒ the truck worth in three year = $ 14560

serious [3.7K]4 years ago
3 0
28,000 × 0.48 = 13,440
and
28,000
- 13,440
---------------
$14,560 is the current value of the truck
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ratelena [41]

By the definition of the hyperbolic function tanh x, we have proven that \frac{1-tanh \ x}{1 + tanh \ x}=e^{-2x}

<h3>Hyperbolic functions & Proof of identities </h3>

By definition

tanh \ x=\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}}

Then,

\frac{1-tanh \ x}{1 + tanh \ x}=\frac{1-\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} }{1+ \frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} }

=1-\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} \div (1+ \frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} })

=\frac{e^{x} +e^{-x}-(e^{x} -e^{-x})}{e^{x} +e^{-x}} \div (\frac{e^{x} +e^{-x}+e^{x} -e^{-x}}{e^{x} +e^{-x}} })

=\frac{e^{x} +e^{-x}-e^{x} +e^{-x}}{e^{x} +e^{-x}} \div \frac{e^{x} +e^{-x}+e^{x} -e^{-x}}{e^{x} +e^{-x}} }

=\frac{e^{-x}+e^{-x}}{e^{x} +e^{-x}} \div \frac{e^{x} +e^{x} }{e^{x} +e^{-x}} }

=\frac{2e^{-x}}{e^{x} +e^{-x}} \div \frac{2e^{x} }{e^{x} +e^{-x}} }

=\frac{2e^{-x}}{e^{x} +e^{-x}} \times \frac{e^{x} +e^{-x}}{2e^{x}}

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=e^{-x} \times \frac{1}{e^{x}}

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= e^{-x+-x}

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= e^{-2x}

Hence, we have proven that \frac{1-tanh \ x}{1 + tanh \ x}=e^{-2x}

Learn more on Proof of Identities here: brainly.com/question/2561079

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6 0
2 years ago
A random sample of 384 people in a mid-sized city (city one) revealed 112 individuals who worked at more than one job. A second
Svetlanka [38]

Answer:

99% confidence interval is:

(0.00278 < P1 - P2< 0.15921)

Step-by-step explanation:

For calculating a confidence intervale for the difference between the proportions of workers in the two cities, we calculate the following:

[(p_{1} - p_{2}) \pm z_{\alpha/2} \sqrt{\frac{p_{1}(1-p_{1})}{n_{1}} + \frac{p_{2}(1-p_{2})}{n_{2}} }

             Where  p_{1} : proportion sample of individuals who worked      

                                                     at more than one job in the city one

                           n_{1}: Number of respondents in the city one

                           p_{1} : proportion sample of individuals who worked      

                                                     at more than one job in the city two

                           n_{1}: Number of respondents in the city two

Then

α = 0.01 and α/2 = 0.005

and z_{\alpha/2} = 2.575

p_{1} = \frac{112}{384} = 0.2916

p_{2} = \frac{91}{432} = 0.2106

n_{1}= 384  and n_{2}= 432

The confidence interval is:

[(0.2916 - 0.2106) \pm 2.575 \sqrt{\frac{0.2916(1-0.2916)}{384} + \frac{0.2106(1-0.2106)}{432} }

(0.00278 < P1 - P2< 0.15921)

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