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2 years ago

A change purse contains a total of 35 nickels and dimes. The total value of the coins is $2.25

Mathematics

1 answer:

Montano1993 [528]2 years ago

6 0

Answer: 25 nickels

10 dimes

Step-by-step explanation:

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Find the product (-3) • (1.2) A. 4.5 B. -3.6 C. -4.6 D. 5.3

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find the value of an investment of $3500 for 3 years at an interest rate of 5.6% if the money is compounded weekly

sergeinik [125]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$3500\\
r=rate\to 5.6\%\to \frac{5.6}{100}\to &0.056\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
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\end{array}\to &52\\
t=years\to &3
\end{cases}$

$\bf A=3500\left(1+\frac{0.056}{52}\right)^{52\cdot 3}\implies A=3500\left( \frac{6507}{6500} \right)^{156}
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3 years ago

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2 years ago

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The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

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3 years ago