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Anika [276]
3 years ago
10

Add Linear Expressions

Mathematics
1 answer:
lawyer [7]3 years ago
5 0

Answer:

10x-3

Step-by-step explanation:

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The bottom one is 90
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Is 8.47 greater than or less than 8.63
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Answer:

8.47 is less than 8.63

Step-by-step explanation:

Although they both contain the number 8, if you look at the decimals, 63 is more than 47. Hence, 8.47 is less than 8.63.

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Marty has saved $72. He spent $8 on a video rental. Write a ratio as a fraction in simplest form to represent what portion of hi
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The solution to the problem is as follows:

The savings left is just $72 - $8 = $64.
Therefore, the ratio is $64 : $72 = 8 : 9.

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Karen wants to invest $750 per quarter for a period of 25 years in order to accumulate a value of $120,000. What minimum annual
Anika [276]

Answer:

Step-by-step explanation:

For Compound Interest with continuous deposit,

We have that:

\frac{dS}{dt}=rS+k

\frac{dS}{dt}-rS=k

Using Integrating factor: e^{\int\ {-r} \, dt }=e^{-rt}

\frac{dS}{dt}e^{-rt}=ke^{-rt}

Taking Integrals from 0 to t

Se^{-rt}=\frac{k}{-r}e^{-rt}+C\\S=\frac{k}{-r}+Ce^{rt}\\When t=0\\C=S_{0}+\frac{k}{r}

Now substituting back C

We have:

Se^{-rt}=\frac{k}{-r}e^{-rt}+S_{0}+\frac{k}{r}\\S(t)=S_{0}e^{rt}+\frac{k}{r}-\frac{k}{r}e^{rt}\\S(t)=S_{0}e^{rt}+\frac{k}{r}(1-e^{rt})

Se^{-rt}=\frac{k}{-r}e^{-rt}+S_{0}+\frac{k}{r}\\S(t)=S_{0}e^{rt}+\frac{k}{r}-\frac{k}{r}e^{rt}\\S(t)=S_{0}e^{rt}+\frac{k}{r}(1-e^{rt})

If initial deposit =$750, Continuous Deposit = 750, t= 4X 25 years=100

S(t)=S_{0}e^{rt}+\frac{k}{r}(1-e^{rt})\\120000=750e^{100r}+\frac{750}{r}(1-e^{100r})\\160=e^{100r}+\frac{750}{r}-\frac{750}{r}e^{100r}\\

5 0
3 years ago
A tree measured 18 feet tall. Over the next 3 1/2 years, it grew to final height of 35 1/2 feet. During those 3 1/2 years, what
NeTakaya
35.5 minus 18 is 17.5

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the average growth during the last 3 1/2 years was 5 feet, each year
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