Answer:
A sample of 997 is needed.
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 z-score that has a p-value of
.
The margin of error is of:

A previous study indicates that the proportion of left-handed golfers is 8%.
This means that 
98% confidence level
So
, z is the value of Z that has a p-value of
, so
.
How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?
This is n for which M = 0.02. So






Rounding up:
A sample of 997 is needed.
Answer:
31.25 percent increase
Step-by-step explanation:
To find the percent increase, we take
percent increase = (new - original)/new * 100 percent
= (420-320)/320 * 100 percent
100/320 * 100 percent
.3125 * 100 percent
31.25 percent increase
Answer:
18$
Step-by-step explanation:

Negative multiply negative = Positive
Negative multiply positive = negative

Thus the answer is -4a + 16b - 12c - 12d.