For this problem you can create a proportion.
Since 31,100 copies is 7.8% of the total copies spoke up to date you can make this proportion:
31,100. 7.8%
——— =. ———
x. 100%
Now you cross multiply and you will get
7.8x=3,110,000
After this you solve for x by isolating the variable.
7.8x/7.8. 3,110,000/7.8
x=398,717.949
Since the question asks you to round to the nearest whole number which is 7 then the final answer would be 398,718
Answer: There has been 398,718 copies sold to date.
Answer:
It will take 25.6 years for the mass of the sample to reach 400 grams.
Step-by-step explanation:
Element X is a radioactive isotope such that every 25 years, its mass decreases by half.
This means that the amount of the substance after t years can be modeled by a function in the following format:
![A(t) = A(0)(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
In which A(0) is the initial amount.
Initial mass of a sample of Element X is 910 grams.
This means that ![A(0) = 910](https://tex.z-dn.net/?f=A%280%29%20%3D%20910)
So
![A(t) = A(0)(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![A(t) = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
How long would it be until the mass of the sample reached 400 grams?
This is t for which ![A(t) = 400](https://tex.z-dn.net/?f=A%28t%29%20%3D%20400)
So
![A(t) = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![400 = 910(0.5)^{\frac{t}{25}}](https://tex.z-dn.net/?f=400%20%3D%20910%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D)
![(0.5)^{\frac{t}{25}} = \frac{400}{910}](https://tex.z-dn.net/?f=%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%20%3D%20%5Cfrac%7B400%7D%7B910%7D)
![(0.5)^{\frac{t}{25}} = 0.43956](https://tex.z-dn.net/?f=%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%20%3D%200.43956)
![\log{(0.5)^{\frac{t}{25}}} = \log{0.43956}](https://tex.z-dn.net/?f=%5Clog%7B%280.5%29%5E%7B%5Cfrac%7Bt%7D%7B25%7D%7D%7D%20%3D%20%5Clog%7B0.43956%7D)
![\frac{t}{25}\log{0.5} = \log{0.43956}](https://tex.z-dn.net/?f=%5Cfrac%7Bt%7D%7B25%7D%5Clog%7B0.5%7D%20%3D%20%5Clog%7B0.43956%7D)
![t = \frac{25\log{0.43956}}{\log{0.5}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B25%5Clog%7B0.43956%7D%7D%7B%5Clog%7B0.5%7D%7D)
![t = 25.6](https://tex.z-dn.net/?f=t%20%3D%2025.6)
It will take 25.6 years for the mass of the sample to reach 400 grams.
The picture in the attached figure
Part 1) <span>
What is the total area of the swimming pool?</span>
we know that
<span>area of the swimming pool=area rectangle-area semi circle
area rectangle=20*36-----> 720 ft</span>²
area semicircle=pi*r²/2
r=18/2----> 9 ft
area semicircle=pi*9²/2----> 127.17 ft²
area of the swimming pool=720 ft²-127.17 ft²----> 592.83 ft²
the answer Part 1) isThe area of the swimming pool is 592.83 ft²Part 2) <span>What is the perimeter of the swimming pool?
</span>
perimeter of the swimming pool=perimeter of rectangle-18 ft+perimeter semi circle
perimeter of rectangle=2*[20+36]---> 112 ft
perimeter semi circle=2*pi*r/2----> pi*r
r=9 ft
perimeter semi circle=pi*9----> 28.26 ft
so
perimeter of the swimming pool=112 ft-18 ft+28.26 ft----> 122.26 ft
the answer Part 2) is122.26 ft
Odd degree, negative leading coefficient.