Positive Slope
<em>TIP for finding what slope it is:</em>
<em>Positive </em>- the line is pointing right
<em>Negative</em> - the line is pointing left
<em>Undefined </em>- the line is pointing up and down
<em>Zero</em> - the line is point from left to right
So, one trillion is 1 and twelve zeros, thus 2.4 trillion is 2 trillions and 400 billions or 24 followed by eleven zeros, because the "4" is using up a space.
now, 1 million is 1 and six zeros, thus 100 millions is 100 and six zeros or 1 and 8 zeros.
now, is 2.4 trillions in four months, thus 2.4trillion/4 will give us how many gallons in 1 month.
to find how many households, simply let's divide it by 100 millions
If
is a random variable representing your winnings from playing the game, then it has support
![W=\begin{cases}43&\text{if you draw something with value at most 3}\\-11&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=W%3D%5Cbegin%7Bcases%7D43%26%5Ctext%7Bif%20you%20draw%20something%20with%20value%20at%20most%203%7D%5C%5C-11%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
There are 52 cards in the deck. Only the 1s, 2s, and 3s fulfill the first condition, so there are 12 ways in which you can win $43. So
has PMF
![P(W=w)=\begin{cases}\frac{12}{52}=\frac3{13}&\text{for }w=43\\1-\frac{12}{52}=\frac{10}{13}&\text{for }w=-11\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=P%28W%3Dw%29%3D%5Cbegin%7Bcases%7D%5Cfrac%7B12%7D%7B52%7D%3D%5Cfrac3%7B13%7D%26%5Ctext%7Bfor%20%7Dw%3D43%5C%5C1-%5Cfrac%7B12%7D%7B52%7D%3D%5Cfrac%7B10%7D%7B13%7D%26%5Ctext%7Bfor%20%7Dw%3D-11%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
You can expect to win
![E[W]=\displaystyle\sum_ww\,P(W=w)=\frac{43\cdot3}{13}-\frac{11\cdot10}{13}=\boxed{\frac{19}{13}}](https://tex.z-dn.net/?f=E%5BW%5D%3D%5Cdisplaystyle%5Csum_ww%5C%2CP%28W%3Dw%29%3D%5Cfrac%7B43%5Ccdot3%7D%7B13%7D-%5Cfrac%7B11%5Ccdot10%7D%7B13%7D%3D%5Cboxed%7B%5Cfrac%7B19%7D%7B13%7D%7D)
or about $1.46 per game.
One example is when n is 11. 11^2 + 4 = 125. 11 is odd but the 11th term of the sequence, 125, is not prime because 125 is divisible by 5 and 25.
The slope intercept form using the two points would be : y= 2x-13