The amount that should be put into account is $6171.88
The formula for the compounded continuously is
(1)
where , A = future amount or the final amount
P = principal amount to be invested
r = annual interest rate
t = time
n = number of compounding in a year
According to the question we have been given that
A = $8000
r = 0.052
t = 5
n = 12
putting the required values in equation (1) we get
8000 = P(1 + 0.052/12)^(5*12)
8000 = P (1.004)^60
8000 = P*1.27
P = 8000/1.27
P = $6171.88
Thus the amount that should be put into account is $6171.88
Learn more about principal amount here : brainly.com/question/25545513
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The answer is (6, 8).
EXPLANATION
If you are given two numbers, you can find the number exactly between them by averaging them, by adding them together and dividing by two. The Midpoint Formula works exactly the same way. If you need to find the point that is exactly halfway between two given points, just average the x-values and the y-values.
That is:
![( \frac{x1 + x2}{2}. \frac{y1 + y2}{2} )](https://tex.z-dn.net/?f=%28%20%5Cfrac%7Bx1%20%2B%20x2%7D%7B2%7D.%20%5Cfrac%7By1%20%2B%20y2%7D%7B2%7D%20%29)
But since the midpoint is given, we'll work this out in a different way.
To find the x of the other endpoint or x2, we'll have first to plug-in the given x values in the midpoint and x1.
So,
![m = \frac{x1 + x2}{2} \\ 5= \frac{4 + x2}{2}\\ 10= 4 + x2 \\ x2 = 6](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7Bx1%20%2B%20x2%7D%7B2%7D%20%5C%5C%205%3D%20%5Cfrac%7B4%20%2B%20x2%7D%7B2%7D%5C%5C%2010%3D%204%20%2B%20x2%20%5C%5C%20x2%20%3D%206)
Now, let's proceed to y2.
![m = \frac{y1 + y2}{2} \\ 9= \frac{10 + y2}{2}\\ 18= 10 + y2 \\ y2 = 8](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By1%20%2B%20y2%7D%7B2%7D%20%5C%5C%209%3D%20%5Cfrac%7B10%20%2B%20y2%7D%7B2%7D%5C%5C%2018%3D%2010%20%2B%20y2%20%5C%5C%20y2%20%3D%208)
So now you have the x and y values of the other endpoint: (6,8).
<h3>
Answer is Choice B. 1:1</h3>
Explanation:
We have three numbers that aren't even, and they are {1,3,5}
There are three numbers that are even, and they are {2,4,6}
The odds in favor of not getting an even number is 3:3 = 1:1
To list the odds in favor, you write the number of ways to get what you want, followed by a colon, then the number of ways to get what you don't want. In this case, both counts are 3. The ratio 3:3 reduces to 1:1 after dividing both parts by 3.
Answer:
Please find attached pdf
Step-by-step explanation: