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Ksenya-84 [330]
3 years ago
15

Anna bought 8 goldfish and 2 rainbow fish for her aquarium. The rainbow fish cost 6 dollars more than the goldfish. She paid a t

otal of 37 dollars for the fish. Write an equation to find the cost of each of the goldfish.
Mathematics
1 answer:
Anton [14]3 years ago
5 0
Let the price of the goldfish be x
Let the price of the rainbow fish be y

Anna bought 8 fish, therefore, Anna paid 8x for the gold fish
Anna bought 2 rainbow fish, therefore, Anna paid 2y for the rainbow fish

We know that the total amount that Anna paid is 37$.
Therefore:
8x + 2y = 37 ..................> equation I

Now, we know that the rainbow fish cost 6$ more than the goldfish (since the verb "cost" is plural, therefore the total payment of rainbow fish is 6$ more than the total payment of gold fish).
Based on this,
2y + 6 = 8x 
2y = 8x - 6 ...................> equation II

Substitute by equation II in equation I, we can get the following equation:
8x + 8x - 6 = 37 
16x = 43 ................> The desired equation (equation III)

Solving equation III, we can calculate the price of one gold fish as follows:
16x = 43
x = 2.6875$

If we substitute by the value of x in equation I, we can calculate the price of one rainbow fish as follows:
8(2.6875) + 2y = 37
y = 7.75$
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Step-by-step explanation:

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Crash Hospital Costs. A study was conducts to estimate hospital costs for accident victims who wore seat belts. Twenty randomly
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Answer:

a) The 99% confidence interval would be given by (5004.168;12603.832)

b) For this case we can use the lower bound for the confidence interval as estimation, on this case 5004.168. But we need to take in count that this value it's with 99% of confidence and 1% of significance and 1% of probability to commit type Error I

Step-by-step explanation:

1) 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 =9004 represent the sample mean for the sample  

\mu population mean (variable of interest)

s=5629 represent the sample standard deviation

n=20 represent the sample size  

2) Part a

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

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

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=20-1=19

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,19)".And we see that t_{\alpha/2}=2.86

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

9004-2.86\frac{5629}{\sqrt{20}}=5004.168    

9004+2.86\frac{5629}{\sqrt{20}}=12603.832

So on this case the 99% confidence interval would be given by (5004.168;12603.832)    

3) Part b

For this case we can use the lower bound for the confidence interval as estimation, on this case 5004.168. But we need to take in count that this value it's with 99% of confidence and 1% of significance and 1% of probability to commit type Error I

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3 years ago
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