Answer:
So the annual percent of decay is: 7.77%
Step-by-step explanation:
If the value of a car was $18000 in 2006, and in 2016 it was worth $4000 it means, it lose 77.77% of its value in 10 years.
To calculate the percentage of decay we use the rule of three:
If the price of the car in 2006 ($18000) represents 100%, then, how much does $4000 represents?
4000*100/18000 = %22.22
Now, we know that $4000 represents 22.22% the original value, so it lose 100% - 22.22% = 77.77% of its value.
So the annual percent of decay is: 77.77% / 10 = 7.77%
<em>Just a little note you put 50 points and not 100 </em>
The y-axis doesn't start at zero.
The intervals on the y-axis are too large.
Different bar widths are used on the same graph.
The y-axis starts at zero but has different intervals.
Answer: The mean and variance of Y is $0.25 and $6.19 respectively.
Step-by-step explanation:
Given : You and a friend play a game where you each toss a balanced coin.
sample space for tossing two coins : {TT, HT, TH, HH}
Let Y denotes the winnings on a single play of the game.
You win $1; if the faces are both heads
then P(Y=1)=P(TT)=
You win $6; if the faces are both heads
then P(Y=6)=P(HH)=
You loose $3; if the faces do not match.
then P(Y=1)=P(TH, HT)=
The expected value to win : E(Y)=

Hence, the mean of Y : E(Y)= $0.25

Variance = ![E[Y^2]-E(Y)^2](https://tex.z-dn.net/?f=E%5BY%5E2%5D-E%28Y%29%5E2)

Hence, variance of Y = $ 6.19
Answer:
![\[3x+\frac{2}{3}\]](https://tex.z-dn.net/?f=%5C%5B3x%2B%5Cfrac%7B2%7D%7B3%7D%5C%5D)
Step-by-step explanation:
![\[f(x)=x-\frac{1}{3}\]](https://tex.z-dn.net/?f=%5C%5Bf%28x%29%3Dx-%5Cfrac%7B1%7D%7B3%7D%5C%5D)
![\[g(x)=3x+1\]](https://tex.z-dn.net/?f=%5C%5Bg%28x%29%3D3x%2B1%5C%5D)
Hence, ![\[(f o g)(x)=f(3x+1)\]](https://tex.z-dn.net/?f=%5C%5B%28f%20o%20g%29%28x%29%3Df%283x%2B1%29%5C%5D)
But, ![\[f(3x+1)=(3x+1)-\frac{1}{3}\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D%283x%2B1%29-%5Cfrac%7B1%7D%7B3%7D%5C%5D)
Simplifying,
![\[f(3x+1)=3x+(1-\frac{1}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%281-%5Cfrac%7B1%7D%7B3%7D%29%5C%5D)
= ![\[f(3x+1)=3x+(\frac{3-1}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%28%5Cfrac%7B3-1%7D%7B3%7D%29%5C%5D)
= ![\[f(3x+1)=3x+(\frac{2}{3})\]](https://tex.z-dn.net/?f=%5C%5Bf%283x%2B1%29%3D3x%2B%28%5Cfrac%7B2%7D%7B3%7D%29%5C%5D)
Hence, ![\[(f o g)(x)=3x+(\frac{2}{3})\]](https://tex.z-dn.net/?f=%5C%5B%28f%20o%20g%29%28x%29%3D3x%2B%28%5Cfrac%7B2%7D%7B3%7D%29%5C%5D)