They both equal 78 degrees because they are the same angle which means that they have the same degrees for f and e.
Answer:
Please check the explanation.
Step-by-step explanation:
<u>Calculating the area of the outer rectangle:</u>
Given
- The length outer rectangle = l = 3x - 1
- The width of outer rectangle = w = 5x + 2
Thus,
The area of the outer rectangle:
![A = wl](https://tex.z-dn.net/?f=A%20%3D%20wl)
![= (5x + 2) (3x - 1)](https://tex.z-dn.net/?f=%3D%20%285x%20%2B%202%29%20%283x%20-%201%29)
![=5x\cdot \:3x+5x\left(-1\right)+2\cdot \:3x+2\left(-1\right)](https://tex.z-dn.net/?f=%3D5x%5Ccdot%20%5C%3A3x%2B5x%5Cleft%28-1%5Cright%29%2B2%5Ccdot%20%5C%3A3x%2B2%5Cleft%28-1%5Cright%29)
![=5\cdot \:3xx-5\cdot \:1\cdot \:x+2\cdot \:3x-2\cdot \:1](https://tex.z-dn.net/?f=%3D5%5Ccdot%20%5C%3A3xx-5%5Ccdot%20%5C%3A1%5Ccdot%20%5C%3Ax%2B2%5Ccdot%20%5C%3A3x-2%5Ccdot%20%5C%3A1)
![=15x^2+x-2](https://tex.z-dn.net/?f=%3D15x%5E2%2Bx-2)
<u>Calculating the area of the inner rectangle:</u>
Given
- The length inner rectangle = l = x + 7
- The width of inner rectangle = w = x
Thus,
The area of the outer rectangle:
A = wl
= x(x+7)
= x² + 7
<u>Calculating the area of the shaded region:</u>
As
The area of the outer rectangle = 15x² + x - 2
The area of the inner rectangle = x² + 7
- The area of the shaded region can be determined by subtracting the area of the inner rectangle from the area of the outer rectangle.
Thus,
shaded region Area = Outer Rectangle Area - Inner Rectangle Area
= 15x² + x - 2 - (x² + 7)
= 15x² + x - 2 - x² - 7
= 14x² + x - 9
Therefore, the Area of the shaded region is: 14x² + x - 9
Answer:
Aloha,
Hope you are having a wonderful day, y=1.5x-1 is your answer. Hope this helps.
noʻu ka hauʻoli
Answer:
The expected value of the game to the player is -$0.2105 and the expected loss if played the game 1000 times is -$210.5.
Step-by-step explanation:
Consider the provided information.
It is given that if ball lands on 29 players will get $140 otherwise casino will takes $4.
The probability of winning is 1/38. So, the probability of loss is 37/38.
Now, find the expected value of the game to the player as shown:
![E(x)=(140)\times \frac{1}{38}+(-4)\times \frac{37}{38}](https://tex.z-dn.net/?f=E%28x%29%3D%28140%29%5Ctimes%20%5Cfrac%7B1%7D%7B38%7D%2B%28-4%29%5Ctimes%20%5Cfrac%7B37%7D%7B38%7D)
![E(x)=\frac{140-148}{38}](https://tex.z-dn.net/?f=E%28x%29%3D%5Cfrac%7B140-148%7D%7B38%7D)
![E(x)=\frac{-8}{38}=-$0.2105](https://tex.z-dn.net/?f=E%28x%29%3D%5Cfrac%7B-8%7D%7B38%7D%3D-%240.2105)
Hence, the expected value of the game to the player is -$0.2105.
Now find the expect to loss if played the game 1000 times.
1000×(-$0.2105)=-$210.5
Therefore, the expected loss if played the game 1000 times is -$210.5.