Answer:
11.1 years
Step-by-step explanation:
The formula for interest compounding continuously is:
Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years. Filling in what we have looks like this:
We will simplify this first a bit by dividing 2000 by 1150 to get
To get that t out the exponential position it is currently in we have to take the natural log of both sides. Since a natural log has a base of e, taking the natual log of e cancels both of them out. They "undo" each other, for lack of a better way to explain it. That leaves us with
ln(1.739130435)=.05t
Taking the natural log of that decimal on our calculator gives us
.5533852383=.05t
Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.
Answer: C
g(x) = 1/2 f (x)
Step-by-step explanation:
Answer:
He must survey 123 adults.
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:
Assume that a recent survey suggests that about 87% of adults have heard of the brand.
This means that 
90% confidence level
So 
, z is the value of Z that has a p-value of 
, so 
.
How many adults must he survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage?
This is n for which M = 0.05. So
Rounding up:
He must survey 123 adults.
The answer would be A.132 because when you add the corner length to 90 it equals 132
Answer:
Here we will use algebra to find three consecutive integers whose sum is 300. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 300. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 300
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 300
3X + 3 = 300
3X + 3 - 3 = 300 - 3
3X = 297
3X/3 = 297/3
X = 99
Which means that the first number is 99, the second number is 99 + 1 and the third number is 99 + 2. Therefore, three consecutive integers that add up to 300 are 99, 100, and 101.
99 + 100 + 101 = 300
We know our answer is correct because 99 + 100 + 101 equals 300 as displayed above.
Step-by-step explanation:
