Answer:
Write each of the probabilities in part (a) as a percent. ... one marker at random. a. Make a tree diagram to find all the possible color ... the probability she doesn't choose blue paper?
Step-by-step explanation:
Answer:
Part 1) The radius is 6 in and the diameter is 12 in
Part 2) The area of the dinner plate is ![A=113.04\ in^2](https://tex.z-dn.net/?f=A%3D113.04%5C%20in%5E2)
Step-by-step explanation:
we know that
The circumference of a circle is equal to
![C=2\pi r](https://tex.z-dn.net/?f=C%3D2%5Cpi%20r)
Part 1) What are the
radius and diameter of the dinner plate?
we have
![C=37.68\ in](https://tex.z-dn.net/?f=C%3D37.68%5C%20in)
assume
![\pi =3.14](https://tex.z-dn.net/?f=%5Cpi%20%3D3.14)
substitute in the formula and solve for the radius r
![37.68=2(3.14)r](https://tex.z-dn.net/?f=37.68%3D2%283.14%29r)
![r=37.68/[2(3.14)]](https://tex.z-dn.net/?f=r%3D37.68%2F%5B2%283.14%29%5D)
![r=6\ in](https://tex.z-dn.net/?f=r%3D6%5C%20in)
Find the diameter
The diameter is two times the radius
so
![D=(2)6=12\ in](https://tex.z-dn.net/?f=D%3D%282%296%3D12%5C%20in)
Part 2) What is the area of the dinner plate
The area of a circle is equal to
![A=\pi r^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E%7B2%7D)
we have
![r=6\ in](https://tex.z-dn.net/?f=r%3D6%5C%20in)
assume
![\pi =3.14](https://tex.z-dn.net/?f=%5Cpi%20%3D3.14)
substitute
![A=(3.14)(6)^{2}](https://tex.z-dn.net/?f=A%3D%283.14%29%286%29%5E%7B2%7D)
![A=113.04\ in^2](https://tex.z-dn.net/?f=A%3D113.04%5C%20in%5E2)
<em>See</em><em> </em><em>above</em><em> </em><em>graph</em>
I am joyous to assist you anytime.
Answer:
16%
Step-by-step explanation:
To solve this we are using the standard growth equation:
![y=a(1+b)^x](https://tex.z-dn.net/?f=y%3Da%281%2Bb%29%5Ex)
Were
is the final value after
years
is the initial value
is the growth factor (yearly rate of appreciation in our case) in decimal form
is the time in years
We know from our problem that gold coin appreciated in value from $200.00 to $475.00 in 6 years, so
,
, and
.
Let's replace the values in our equation and solve for
:
![y=a(1+b)^x](https://tex.z-dn.net/?f=y%3Da%281%2Bb%29%5Ex)
![475=200(1+b)^6](https://tex.z-dn.net/?f=475%3D200%281%2Bb%29%5E6)
![\frac{475}{200} =(1+b)^6](https://tex.z-dn.net/?f=%5Cfrac%7B475%7D%7B200%7D%20%3D%281%2Bb%29%5E6)
![2.375=(1+b)^6](https://tex.z-dn.net/?f=2.375%3D%281%2Bb%29%5E6)
![\sqrt[6]{2.375} =\sqrt[6]{(1+b)^6}](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7B2.375%7D%20%3D%5Csqrt%5B6%5D%7B%281%2Bb%29%5E6%7D)
![1+b=\sqrt[6]{2.375}](https://tex.z-dn.net/?f=1%2Bb%3D%5Csqrt%5B6%5D%7B2.375%7D)
![b=\sqrt[6]{2.375}-1](https://tex.z-dn.net/?f=b%3D%5Csqrt%5B6%5D%7B2.375%7D-1)
![b=0.155](https://tex.z-dn.net/?f=b%3D0.155)
which rounds to
![b=0.16](https://tex.z-dn.net/?f=b%3D0.16)
Since our appreciation rate is in decimal form, we need to multiply it by 100% to express it as percentage:
0.16*100% = 16%
We can conclude that the yearly appreciation rate of our gold coin is approximately 16%