Write the pair of fractions as a pair of fractions with a common denominator

Mathematics

1 answer:

andrew-mc [135]2 years ago

5 0

We would need the fractions given

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Camden is going to invest $600 and leave it in an account for 12 years. Assuming the

UkoKoshka [18]

$~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$920\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &12 \end{cases}$

$920=600e^{\frac{r}{100}\cdot 12}\implies \cfrac{920}{600}=e^{\frac{3r}{25}}\implies \cfrac{23}{15}=e^{\frac{3r}{25}}\implies \log_e\left( \cfrac{23}{15} \right)=\log_e\left( e^{\frac{3r}{25}} \right) \\\\\\ \ln\left( \cfrac{23}{15} \right)=\cfrac{3r}{25}\implies 25\cdot \ln\left( \cfrac{23}{15} \right)=3r\implies \cfrac{25\cdot \ln\left( \frac{23}{15} \right)}{3}=r \\\\\\ 3.5620\approx r\implies \stackrel{\%}{3.56}\approx r$

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2 years ago

Sid goes to the store and buys a shirt for $65. The store has sales tax rate of 5.4%. How much tax will Sid have to pay?

mojhsa [17]

Answer:

$3.51

Step-by-step explanation:

We change 5.4% into a decimal which is .054, we then multiply 65 by .054

$65 x .054 = $3.51

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2 years ago

A vat with 700 gallons of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 7 gal/m

dolphi86 [110]

Answer:

5.2%.

Step-by-step explanation:

After 1 hour (60 / 100) * 700 = 420 gallons of beer have been exchanged.

So we have 420 gallons of 6% and 280 gallons of 4% after 1 hour.

So the strength at that time = (420* 6) + 280*4) / 700

= 5.2%.

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3 years ago

Please answer this question

Gelneren [198K]

A=2(LW+LH+WH)

A=2((7/8)(1/3)+(7/8)(2/5)+(1/3)(2/5))

A=2(7/24+14/40+2/15)

A=14/24+28/40+4/15

A=7/14+7/10+4/15 210

A=(105+147+56)/210

A=308/210

A=(210+98)/210

A=1 98/210

A=1 7/15

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2 years ago

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Prove that if a quadrilateral has four equal sides and one right angle, then the quadrilateral is a square

mars1129 [50]

So lets ABCD are the sides of the square and AB=CD, AC=BD and the Angle ABC = 90 so therefore by making a diagonal we can use the SAS or SSS congruency for two triangles, so we can prove two triangles are equal and that is why the shape is square.

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2 years ago