What are you finding or solving?
Answer:
The required sample size for the new study is 801.
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:

25% of all adults had used the Internet for such a purpose
This means that 
95% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
What is the required sample size for the new study?
This is n for which M = 0.03. So






Rounding up:
The required sample size for the new study is 801.
USING PYTHAGORAS THEORAM,
x²+3²= 5²
x²+9= 25
x²= 25-9 = 16
x= √16
x= 4
OPTION D
Let

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

So, the base case is ok. Now, we need to assume
and prove
.
states that

Since we're assuming
, we can substitute the sum of the first n terms with their expression:

Which terminates the proof, since we showed that

as required
Answer:
15000(1.003425)^12t ;
4.11%
4.188%
Step-by-step explanation:
Given that:
Loan amount = principal = $15000
Interest rate, r = 4.11% = 0.0411
n = number of times compounded per period, monthly = 12 (number of months in a year)
Total amount, F owed, after t years in college ;
F(t) = P(1 + r/n)^nt
F(t) = 15000(1 + 0.0411/12)^12t
F(t) = 15000(1.003425)^12t
2.) The annual percentage rate is the interest rate without compounding = 4.11%
3.)
The APY
APY = (1 + APR/n)^n - 1
APY = (1 + 0.0411/12)^12 - 1
APY = (1.003425)^12 - 1
APY = 1.04188 - 1
APY = 0.04188
APY = 0.04188 * 100% = 4.188%