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2 years ago

Sam invests $800 at 6%/a compounded annually for 5 years. What is the total interest earned?

Mathematics

1 answer:

s2008m [1.1K]2 years ago

4 0

<h3>Answer: 270.58 dollars</h3>

======================================================

Work Shown:

A = account value after t years
P = principal or amount deposited = 800
r = interest rate in decimal form = 0.06
n = number of times we compound per year = 1
t = number of years = 5

So,

A = P*(1+r/n)^(n*t)

A = 800*(1+0.06/1)^(1*5)

A = 1070.58046208

A = 1070.58

After five years, the account will have $1,070.58 in it.

The amount of interest earned is A-P = 1070.58 - 800 = 270.58 dollars.

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You are considering two cars that you plan on keeping for 5 years. One has an EPA combined city and highway rating of 33 mpg. Th

amid [387]

Answer:

a) $86.11

b) $467.33

Step-by-step explanation:

no. of gallons saved 'n' per year

n = (10000/33) - (10000/36)

n = 2500/99

Amount saved = 3.41×n = 3.41×2500/99

= $86.11

b) over 5 years:

86.11( 1 + (1.041) + (1.041)² + (1.041)³ + (1.041)⁴ )

= 86.11(5.427157431)

= $467.33

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3 years ago

The amount y (in cups) of flour is proportional to the number x of eggs in a recipe. The recipe calls for 6 cups of flour for ev

AlladinOne [14]

A. y=3/2x
B. y=3/2x
C. 18

My Dad helped me with this.

5 0

3 years ago

In 2002, the mean age of an inmate on death row was 40.7 years with a standard deviation of 9.6 years according to the U.S. Depa

marissa [1.9K]

Answer:

The 95% confidence interval for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

Step-by-step explanation:

The confidence interval of the mean is given by the next formula:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$ [1]

We already know (according to the U.S. Department of Justice):

The (population) standard deviation for this case (mean age of an inmate on death row) has a standard deviation of 9.6 years ( $\\ \sigma = 9.6$ years).
The number of observations for the sample taken is $\\ n = 32$ .
The sample mean, $\\ \overline{x} = 38.9$ years.

For $\\ z_{1-\frac{\alpha}{2}}$ , we have that $\\ \alpha = 0.05$ . That is, the level of significance $\\ \alpha$ is 1 - 0.95 = 0.05. In this case, then, we have that the z-score corresponding to this case is:

$\\ z_{1-\frac{\alpha}{2}} = z_{1-\frac{0.05}{2}} = z_{1-0.025} = z_{0.975}$

Consulting a cumulative standard normal table, available on the Internet or in Statistics books, to find the z-score associated to the probability of, $\\ P(z$ , we have that $\\ z = 1.96$ .

Notice that we supposed that the sample is from a population that follows a normal distribution. However, we also have a value for n > 30, and we already know that for this result the sampling distribution for the sample means follows, approximately, a normal distribution with mean, $\\ \mu$ , and standard deviation, $\\ \sigma_{\overline{x}} = \frac{\sigma}{\sqrt{n}}$ .

Having all this information, we can proceed to answer the question.

Constructing the 95% confidence interval for the current mean age of death-row inmates

To construct the 95% confidence interval, we already know that this interval is given by [1]:

$\\ \overline{x} \pm z_{1-\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

That is, we have:

$\\ \overline{x} = 38.9$ years.

$\\ z_{1-\frac{\alpha}{2}} = 1.96$

$\\ \sigma = 9.6$ years.

$\\ n = 32$

Then

$\\ 38.9 \pm 1.96*\frac{9.6}{\sqrt{32}}$

$\\ 38.9 \pm 1.96*\frac{9.6}{5.656854}$

$\\ 38.9 \pm 1.96*1.697056$

$\\ 38.9 \pm 3.326229$

Therefore, the Upper and Lower limits of the interval are:

Upper limit:

$\\ 38.9 + 3.326229$

$\\ 42.226229 \approx 42.23$ years.

Lower limit:

$\\ 38.9 - 3.326229$

$\\ 35.573771 \approx 35.57$ years.

In sum, the 95% confidence interval for the current mean age of death-row inmates is between 42.23 years and 35.57 years.

Notice that the "mean age of an inmate on death row was 40.7 years in 2002", and this value is between the limits of the 95% confidence interval obtained. So, according to the random sample under study, it seems that this mean age has not changed.

7 0

4 years ago

in wereda election where four candidates appeared for election, the winning candidate received 36,000 votes which represented 45

Dmitry [639]

Let's see

Total votes be x

45% of x=3600
0.45x=3600
x=3600/0.45
x=8000

Now total percentage of vote

45+20+25+6=96%

Not voted=4%

Find not voted

0.04(8000)
320

Total voted

8000-320
7680

7 0

2 years ago

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A 42" diameter table needs a tablecloth that hangs off the edge 8". What is the radius of the tablecloth? 29" 21" 25" 50"

Blababa [14]

I think the answer is 50" because if the table is 42" and it needs to hang over 8" then it would have to be 50"

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3 years ago

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