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nevsk [136]
3 years ago
15

Rebecca deposited $5,338.18 into a savings account with an interest rate of 5.9% compounded twice a year. About how long will it

take for the account to be worth $10,000?
15 years, 11 months
32 years, 5 months
10 years, 10 months
11 years, 0 months
Mathematics
1 answer:
MariettaO [177]3 years ago
8 0
Given:
P = $5338.18, principal
r = 5.9% = 0.059, interest rate
n = 2, nuber of compoundings per year
t =  duraton, years
A = $10,000, target value.

Use the formula
P(1 +  \frac{r}{n})^{nt} = A

That is,
5338.18(1 +  \frac{0.59}{2})^{2t} =10000\\1.0295^{2t}=1.8773
t =  \frac{1}{2} ( \frac{ln(1.8773)}{ln(1.0295)} )=10.832\, yrs\,=10yrs,\,10\,mo

Answer: 10years, 10 months


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A sample size must be determined for estimating a population mean given that the confidence level is ​% and the desired margin o
Sauron [17]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

 n =290

b

 n =129

c

 The correct option is  D

Step-by-step explanation:

From the question we are told that

    The margin of error is   E  =  0.23

     The largest value is  k =  15

     The smallest value is  u = 7

From the question we are told the confidence level is  95% , hence the level of significance is    

      \alpha = (100 - 95 ) \%

=>   \alpha = 0.05

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.96

Generally population  standard deviation estimate is mathematically represented as

      \sigma  =  \frac{Range }{4}

Here the Range is mathematically represented as

       Range  =  k - u

=>    Range  = 15 - 7

=>    Range  = 8

=>   \sigma  =  \frac{8 }{4}

=>   \sigma  =  2

Generally the sample size is mathematically represented as

n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2

=>   n = [1.96  *  2 }{0.23} ] ^2

=>   n =290

Generally to obtain a  conservatively small sample size the population standard deviation estimate becomes

=>   \sigma  =  \frac{Range }{6}

=>   \sigma  =  \frac{8 }{6}

=>   \sigma  =1.333

Generally the conservatively small sample size is mathematically evaluated as

n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2

=>   n = [1.96  *  1.333 }{0.23} ] ^2

=>   n =129  

 

6 0
2 years ago
PLZZZZZZ HELP 10 POINTS!!!!!
Anuta_ua [19.1K]
The answer is 1 to 3
3 0
3 years ago
Read 2 more answers
20 points!! Pls help
Studentka2010 [4]

Answer:

<h3>(-4, 1)</h3>

Step-by-step explanation:

-x-3=y, therefore x = -y-3

-3x - 8y = 4

Find the value of y

Substitute the x in -3x - 8y = 4 with -y-3

We get

-3·(-y-3) - 8y = 4

3y + 9 - 8y = 4

-5y = 4-9

-5y = -5

<h3>y = 1</h3>

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x = -y-3

x = -1-3

<h3>x = -4</h3>

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Answer (x, y) =

<h3>(-4, 1)</h3>

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5 0
3 years ago
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You have a credit card with a balance of 1187.92 and the interest is 12.25% apr. a late fee of 30.00 is charged for payments aft
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We start with
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With the interest and the late fee charge
$1,187.92 (1 + 0.1225/12) + 30 = $1,230.05
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$1,230.05 (1 + 0.1225/12) - $125 = $1,117.60

The new principal after the latest payment is $1,117.60.
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2 years ago
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For the equation ae^ct=d, solve for the variable t in terms of a,c, and d. Express your answer in terms of the natural logarithm
saveliy_v [14]

We have been given an equation ae^{ct}=d. We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

\frac{ae^{ct}}{a}=\frac{d}{a}

e^{ct}=\frac{d}{a}

Now we will take natural log on both sides.

\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})

Using natural log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})

We know that \text{ln}(e)=1, so we will get:

ct\cdot 1=\text{ln}(\frac{d}{a})

ct=\text{ln}(\frac{d}{a})

Now we will divide both sides by c as:

\frac{ct}{c}=\frac{\text{ln}(\frac{d}{a})}{c}

t=\frac{\text{ln}(\frac{d}{a})}{c}

Therefore, our solution would be t=\frac{\text{ln}(\frac{d}{a})}{c}.

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3 years ago
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