Which fraction is in the simplest form of 224/360?
1 answer:
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Answer:
Step-by-step explanation:
We are given that a and b are rational numbers where and x is irrational number .
We have to prove a+bx is irrational number by contradiction.
Supposition:let a+bx is a rational number then it can be written in form
where
where p and q are integers.
Proof:
After dividing p and q by common factor except 1 then we get
r and s are coprime therefore, there is no common factor of r and s except 1.
where r and s are integers.
When we subtract one rational from other rational number then we get again a rational number and we divide one rational by other rational number then we get quotient number which is also rational.
Therefore, the number on the right hand of equal to is rational number but x is a irrational number .A rational number is not equal to an irrational number .Therefore, it is contradict by taking a+bx is a rational number .Hence, a+bx is an irrational number.
Conclusion: a+bx is an irrational number.
Answer:
And the p value since we have a right tailed test is given by:
And for this case the p value is higher than the significance level of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and the best conclusion for this case is:
t = 2, p-value > 5%, fail to reject the null hypothesis. There is not enough evidence to conclude that the mean drying time is greater than 15 minutes.
Step-by-step explanation:
For this problem we have the following info given:
represent the sample size
represent the sample mean for the drying time
represent the sample deviation
We want to test the claim that the mean drying time of their product is, at most, 15 minutes, so then the system of hypothesis are:
Null hypothesis:
Alternative hypothesis:
The statistic is given by this formula since we don't know the population deviation:
And replacing we have:
Now we can find the degrees of freedom given by:
And the p value since we have a right tailed test is given by:
And for this case the p value is higher than the significance level of 0.05 so then we have enough evidence to FAIL to reject the null hypothesis and the best conclusion for this case is:
t = 2, p-value > 5%, fail to reject the null hypothesis. There is not enough evidence to conclude that the mean drying time is greater than 15 minutes.