Answer:
h(7) = 29
h'(7) = 44
Step-by-step explanation:
If , to find h(7) we can substitute the values of f(7) and g(7) and we get:
To find the derivative, we know that the derivative of a sum of functions equals the sum of the derivatives of those functions.
This would mean that , we can substitute the values for f'(7) and g'(7)
Answer:
Since the pvalue of the test is 0.09 > 0.01, we do not reject the null hypothesis that the average size of new homes is of 2400 square feet.
Step-by-step explanation:
Toll Brothers is a luxury home builder that would like to test the hypothesis that the average size of new homes exceeds 2,400 square feet. Test to see if the average size of new homes exceeds 2,400 square feet.
At the null hypothesis, we test if the average is of 2400 square feet, that is:
At the alternate hypothesis, we test if the average is greater than 2400 square feet, that is:
The test statistic is:
Since we have the standard deviation for the sample, we use the t-distribution.
In which X is the sample mean, is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
2400 is tested at the null hypothesis:
This means that
A random sample of 36 newly constructed homes had an average of 2,510 square feet with a sample standard deviation of 480 square feet.
This means that
Test statistic:
Pvalue of the test and decision:
The pvalue of the test is the probability of finding a sample mean of at least 2510, which is the pvalue of t = 1.375 with 36 - 1 = 35 degrees of freedom, using a one-tailed test.
With the help of a calculator, this pvalue is of 0.09
Since the pvalue of the test is 0.09 > 0.01, we do not reject the null hypothesis that the average size of new homes is of 2400 square feet.
Answer:
3u-2v =
5u-v =
2u-3v =
u+4v =
Step-by-step explanation:
I just started by doing the results for each of the operations given.
<u>3u-2v:</u>
3u = (-9, 24) 2v = (-28, 12)
Do the operation of 3u-2v and you get a resultant vector of (19, 12).
You calculate this by doing the square root of 19^2 + 12^2, which is the square root of 505.
<u>5u-v:</u>
5u = (-15, 40) v = (-14, 6)
Do the operation of 5u-v and you get a resultant vector of (-1, 34).
You calculate this by doing the square root of (-1)^2 + 34^2, which is the square root of 1,157.
<u>2u-3v:</u>
2u = (-6, 16) 3v = (-42, 18)
Do the operation of 2u-3v and you get a resultant vector of (36, -2).
You calculate this by doing the square root of 36^2 + (-2)^2, which is the square root of 1,300.
<u>3u+2v:</u>
3u = (-9, 24) 2v = (-28, 12)
Do the operation of 3u+2v and you get a resultant vector of (-37, 36).
You calculate this by doing the square root of (-37)^2 + 36^2, which is the square root of 2,665. This is not a given tile, so we can just ignore this one.
<u>u+4v:</u>
u = (-3, 8) 4v = (-56, 24)
Do the operation of u+4v and you get a resultant vector of (-59, 32).
You calculate this by doing the square root of (-59)^2 + 32^2, which is the square root of 4,505.
Since this is a given tile, I didn't do 7u-2v, but you would use the same methodology.