Answer:
a.
b.
Step-by-step explanation:
First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:
Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:
The rate is negative as it represents the amount of caffeine leaving the body at certain time.
Answer:
Remainder is 691.
Step-by-step explanation:
Given function is .
Now we need to find remainder if we divide given function by (x-3)
(x-3) means plug x=3 into to find remainder.
Hence remainder is 691.
Answer:
The 96% confidence interval for the population proportion of customers satisfied with their new computer is (0.77, 0.83).
Step-by-step explanation:
We have to calculate a 96% confidence interval for the proportion.
We consider the sample size to be the customers that responded the survey (n=800), as we can not assume the answer for the ones that did not answer.
The sample proportion is p=0.8.
The standard error of the proportion is:
The critical z-value for a 96% confidence interval is z=2.054.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 96% confidence interval for the population proportion is (0.77, 0.83).
If she was to volunteer 32 hours and it is worth 20%, then that means 32 hours is 1/5 of her yearly hours. If you were to multiply her volunteer hours by five, then you are getting the year number of hours she has volunteered.
32 x 5 = 160
So, she volunteers 160 hours this year.