Lesson 5 compare and order rational numbers
1 answer:
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Answer:
Mrs. Habib will have 22.25 feet of border left after she puts border around the board.
Step-by-step explanation:
You must find the perimeter of the board and subtract it from the amount of border she has to find how much she will have left after she uses it. The formula for perimeter is , where
the length of the board, and
the width of the board. You will add those together and multiply them by 2 because there are 4 sides to a rectangle. That means this equation will look like:
Now you can just solve for the perimeter.
The perimeter is 24 feet. That means it will take 24 feet of border to cover her board. In order to find out how much she'll have left over, just subtract 24 from the total amount of border she has.
Therefore Mrs. Habib will have 22.25 feet of border left over after she covers the bulletin board.
Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is less than 63 gallons per day at 1% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is less than 63, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one side lower test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is less than 63 gallons per day at 1% of signficance.