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3 years ago

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4) A safe contains 120 coins, the value of which is $10. If the coins consist of nickels and dimes, how many of each kind are in

it?
5) A sum of $14 is made of 92 coins, consisting of dimes and quarters.How many are there of each kind of coin?
6) A boy's coins, consisting of nickels and dimes, amount to 42.15. If the number of dimes exceeds 3 times the number of nickels by 4, find the number of each kind of coin?

1 answer:

Sergio [31]3 years ago

3 0

120=x+y and 10=.05x+.10y
120-x=y then subsitute 10=.05x+.10(120-x) distruibte and solve you can do it feel free to go off of my math.
x(nickels) y(dimes)

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Step-by-step explanation:

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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".

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Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=\pm 1.64$

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The distribution for the sample mean is given by:

$\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})$

And the standard error is given by:

$SE = \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{9}}=1$

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

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

And the margin of error is:

$ME= z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = 1.64$

And then the confidence interval is be given by:

$200-1.64 = 198.36$

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