A hiker leaves camp and walks 6 miles east. Then he walks 18 miles south. How far from camp is the hiker? Distance in miles: Usi
ng quadratic applications
1 answer:
Answer: 19 miles
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case the distance between the hiker and the camp) and a and b are the other sides.
Replacing with the values given:
x^2 = 6^2 + 18^2
x^2 = 36+324
x^2 = 360
x = √360
x = 18.97miles = 19 miles
Feel free to ask for more if needed or if you did not understand something.
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Answer:
At a .05 level of significance, it can be concluded that the mean of the population is significantly more than 3 minutes.
Step-by-step explanation:
We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
At the null hypothesis, we test if the mean is of at most 3 minutes, that is:
At the alternative hypothesis, we test if the mean is of more than 3 minutes, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
3 is tested at the null hypothesis:
This means that
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute.
This means that
Value of the test statistic:
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 3.1, which is 1 subtracted by the p-value of z = 2.
Looking at the z-table, z = 2 has a p-value of 0.9772.
1 - 0.9772 = 0.0228
The p-value of the test is of 0.0228 < 0.05, meaning that the is significant evidence to conclude that the mean of the population is significantly more than 3 minutes.
