David charges $17 plus $7.00 per hour to mow lawns. Ari charges $11 plus $7.75 per hour to mow lawns. In what situations is Ari'
1 answer:
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Answer:
First part: 2 miles.
Second part: 45 minutes
Third part: 8 mph.
Step-by-step explanation:
We can divide this question into 3 parts.
Begin by solving for the distance traveled after 15 minutes by creating a ratio:
Cross multiply:
20 · 15 = 150 · x
300 = 150x
300/150 = 150x/150
x = 2 miles.
2nd part: How long it took her to ride 6 miles.
Set up another ratio similar to the one used before:
Cross multiply:
20 · x = 6 · 150
20x = 900
20x/20 = 900/20
x = 45 minutes.
3rd part:
For this part, we will need to convert from minutes to hours.
Therefore, her speed is 8 mph.
Answer:
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is less than 140 pounds at 5% 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 mean is less than 140, 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 left tailed test the p value would be:
Conclusion
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is less than 140 pounds at 5% of signficance.