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Irina-Kira [14]
2 years ago
5

What is the smallest value of x, such that

Mathematics
1 answer:
gizmo_the_mogwai [7]2 years ago
8 0

Answer:

Dude, where's the picture?

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I'm in high school so you're screwed
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You decide to put $2,000 in a savings account to save for a $3,000 downpayment on a new car. If the account has an interest rate
DanielleElmas [232]

It takes 10.155 years until you have $3,000 ⇒ 3rd

Step-by-step explanation:

The formula for compound interest, including principal sum is:

A=P(1+\frac{r}{n})^{nt} , where

  • A is the future value of the investment/loan, including interest
  • P is the principal investment amount  
  • r is the annual interest rate (decimal)
  • n is the number of times that interest is compounded per unit t
  • t is the time the money is invested or borrowed for

∵ You decide to put $2,000 in a savings account

∴ P = 2000

∵ You want to save for $3,000

∴ A = 3000

∵ The account has an interest rate of 4% per year and is

   compounded monthly

∴ r = 4% = 4 ÷ 100 = 0.04

∴ n = 12 ⇒ compounded monthly

- Substitute all of these values in the formula above to find t

∵ 3000=2000(1+\frac{0.04}{12})^{12t}

- Divide both sides by 2000

∴ 1.5=(1+\frac{1}{300})^{12t}

∴ 1.5=(1\frac{1}{300})^{12t}

- Change the mixed number to an improper fraction

∴ (1.5)=(\frac{301}{300})^{12t}

- Insert ㏒ for both sides

∴ log(1.5)=log(\frac{301}{300})^{12t}

- Remember log(a)^{n}=nlog(a)

∴ log(1.5)=(12t)log(\frac{301}{300})

- Divide both sides by log(\frac{301}{300})

∴ 121.84 = 12 t

- Divide both sides by 12

∴ 10.155 = t

It takes 10.155 years until you have $3,000

Learn more:

You can learn more about the compound interest in brainly.com/question/4361464

#LearnwithBrainly

5 0
3 years ago
What are the solutions to the equation -5x2 + 3x = -9
Aleks04 [339]

Answer: Move terms to the left side−52+3=−9−5x2+3x=−9−52+3−(−9)=0−


Common factor−52+3+9=0−5x2+3x+9=0−(52−3−9)=0


Divide both sides by the same factor−(52−3−9)=0−(5x2−3x−9)=052−3−9=0


Solution=3±321 over 10

Step-by-step explanation:

7 0
2 years ago
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Stephanie has a total of 27 nickels and dimes. The total value of the coins is $1.95. Which system of equations can be used to f
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The correct equation to use is A. n+d=27 0.05n+0.10d=1.95
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You invest an initial $1,000 in an account that has an annual interest rate of 2%, compounded quarterly. How much money will you
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1,400 it will be 20 qrtly making 80 a year time 5 years
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