P(sum = 6) = 5/36 ; P(sum = 12) = 1/36
expected payoff = (5/36)(5) + (1/36)(9) = $0.94
There are 6 numbers in one die.
There are 2 numbers that are less than or equal to 2, they are 1 and 2
The probability of something happening is the number of chances / total number
The probability would be 2/6, which can be reduced to 1/3
Answer:
y=-3x-3
Step-by-step explanation:
9x+3y=-9
This is currently in standard form, or ax+by=c.
To get it to slope-intercept form, (y=mx+b) first subtract 9x to both sides.
3y=-9x-9
Divide both sides by 3.
y=-3x-3
C since that's the only triangle where A^2+B^2=C^2 (36+64=100).
Answer:
The percentage change is 140%
Step-by-step explanation:
Given
---- initial dimension
--- new width
--- new dimension
Required
The percentage increment
The length remains constant because only the width is extended.
The new area is:
![Area =Length * Width](https://tex.z-dn.net/?f=Area%20%3DLength%20%2A%20Width)
![A_2=L * W_2](https://tex.z-dn.net/?f=A_2%3DL%20%2A%20W_2)
Make L the subject
![L = \frac{A_2}{ W_2}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7BA_2%7D%7B%20W_2%7D)
Substitute values for A and W
![L = \frac{45m^2}{6m}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B45m%5E2%7D%7B6m%7D)
![L = \frac{45m}{6}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B45m%7D%7B6%7D)
--- this is the length of the garden
Calculate the initial width:
![L= 3W_1](https://tex.z-dn.net/?f=L%3D%203W_1)
Make W1 the subject
![W_1 = \frac{1}{3} * L](https://tex.z-dn.net/?f=W_1%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2A%20L)
![W_1 = \frac{1}{3} * 7.5](https://tex.z-dn.net/?f=W_1%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2A%207.5)
![W_1 = 2.5](https://tex.z-dn.net/?f=W_1%20%3D%202.5)
So, the initial area is:
![A_1 = L_1 * W_1](https://tex.z-dn.net/?f=A_1%20%3D%20L_1%20%2A%20W_1)
![A_1 = 2.5 * 7.5](https://tex.z-dn.net/?f=A_1%20%3D%202.5%20%2A%207.5)
![A_1 = 18.75](https://tex.z-dn.net/?f=A_1%20%3D%2018.75)
The percentage change in area is:
![\%A = \frac{A_2 - A_1}{A_1}](https://tex.z-dn.net/?f=%5C%25A%20%3D%20%5Cfrac%7BA_2%20-%20A_1%7D%7BA_1%7D)
![\%A = \frac{45 - 18.75}{18.75}](https://tex.z-dn.net/?f=%5C%25A%20%3D%20%5Cfrac%7B45%20-%2018.75%7D%7B18.75%7D)
![\%A = \frac{26.25}{18.75}](https://tex.z-dn.net/?f=%5C%25A%20%3D%20%5Cfrac%7B26.25%7D%7B18.75%7D)
![\%A = 1.4](https://tex.z-dn.net/?f=%5C%25A%20%3D%201.4)
Express as percentage
![\%A = 1.4*100\%](https://tex.z-dn.net/?f=%5C%25A%20%3D%201.4%2A100%5C%25)
![\%A = 140\%](https://tex.z-dn.net/?f=%5C%25A%20%3D%20140%5C%25)