Abag contains 57 coins which are only quarters and dimes the total value of coins is $9.45 how many dimes are in the bag

There are 32 dimes and 25 quarters.

Step-by-step explanation:

q + d = 57 or q = 57 - d  

25q + 10d = 945  

substitute first equation into second equation:  

25(57 - d) + 10d = 945  

1425 - 25d + 10d = 945  

-15d = -480  

d = -480/-15 = 32  

using first equation:  

q = 57 - 32 = 25  

check using second equation:  

25(25) + 10(32) = 945 checks

a)    

The degrees of freedom are given by:

b) The conclusion depends on the significance level selected, if the p value is lower than a significance level given we have enough evidence to conclude that the true mean is different from 57.61, otherwise we FAIl to reject the null hypothesis and thare is no evidence to conclude that the true mean is different from 57.61

Step-by-step explanation:

Data provided

represent the mean for the retail price

represent the sample standard deviation

sample size selected  

represent the value that we want to verify

represent the significance level

t would represent the statistic

represent the p value for the test

Part a

System of hypothesis

We want to check if the true mean for the reatil price is 57.61 or not, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

 (1)  

The statistic is given by:

P value

The degrees of freedom are given by:

The p value would be:

Part b: Conclusion  

The conclusion depends on the significance level selected, if the p value is lower than a significance level given we have enough evidence to conclude that the true mean is different from 57.61, otherwise we FAIl to reject the null hypothesis and thare is no evidence to conclude that the true mean is different from 57.61