Y-axis symmetry=(r, theta)=(-r,theta)
-5-5cos(theta)=r
-r=5+5cos(theta)
no y-axis symmetry
x-axis symmetry=(r,theta)=(r,-theta)
cosine is an even function, so yes it is symmetric around x-axis
origin symmetry=(r,theta)=(-r,theta) or (r, theta+pi)
no, as there is no y-axis symmetry
Answer: 11/2 x 15/4 = 165
/8 = 205
/8 = 20.625
Step-by-step explanation:
Multiple: 11
/2 * 15
/4 = 11 · 15 2 · 4 = 165
/8
Multiply both numerators and denominators.
Following the table and knowing that the total number of students interviewed were 158 ( we can see this by looking adding either the total number of upperclassment or adding the total number of people with jobs or no jobs, this value is at the bottom right of the table in the figure attached).
Recall that:

In the figure provided each of these terms is highlighted in a different color. To convert these values to their matching probabilities we have to divide each by the total number of students, this is due to the fact that the probability is the number of favorable cases (in this case a group matching the qualities we seek) divided by the total amount of cases ( that is the total number of people interviewed). In the figure the answer is provided. For the intersection of the two events we're looking for people that is both an undercalssman and also has a job.
Answer:
The minimum sample size needed is 125.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.

In which
z is the zscore that has a pvalue of
.
The margin of error is:

For this problem, we have that:

99% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?
This minimum sample size is n.
n is found when 
So






Rounding up
The minimum sample size needed is 125.