By Stokes' theorem,
where
is the circular boundary of the hemisphere
in the
-
plane. We can parameterize the boundary via the "standard" choice of polar coordinates, setting
where
. Then the line integral is
We can check this result by evaluating the equivalent surface integral. We have
and we can parameterize
by
so that
where
and
. Then,
as expected.
Based on the table showing the percentage of households playing games over the net, the average rate of change from 1999 to 2003 is 3.9% per year.
<h3>What is average rate of change?</h3>
This can be found as:
= (27.9 - 12.3) / 4 years
= 3.9% per year
In 2000, the instantaneous rate of change would be:
= (Rate in 2001 - Rate in 1999) / difference in years
= (24.4 - 12.3) / (2001 - 1999)
= 6.05%
Find out more on the average rate of change at brainly.com/question/2263931.
#SPJ1
Let x represent the scores. With mean and standard deviation given,
The Empirical rule states that
1) About 68% of the x values lie between 1 standard deviation below and above the mean
2) About 95% of the x values lie between 2 standard deviation below and above the mean
3) About 99.7% of the x values lie between 3 standard deviation below and above the mean
If we consider this rule, then the percentage of scores that fall within 3 standard deviation (-3 to +3) is 99% because this is closer to 99.7%
A
D
F
That is the correct answer
Using it's concept, it is found that the probability that he winds up wearing the white shirt and tan pants is of 
.
<h3>What is a probability?</h3>
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.
In this problem:
- For the shirt, there is 4 outcomes, hence the probability of the white shirt is 1/4.
- For the pair of pants, there are 2 outcomes, blue or tan, hence the probability of tan pants is 1/2.
Since the shirt and the pants are independent, the probability is given by:
.
More can be learned about probabilities at brainly.com/question/14398287
#SPJ1
