The cafeteria sold 41 corn chips and 80 potato chips.
Step-by-step explanation:
Let,
Corn chips = x
Potato chips = y
Price of corn chips = $0.80
Price of potato chips = $0.60
According to given statement;
x+y= 121 Eqn 1
0.80x+0.60y=80.80 Eqn 2
Multiplying Eqn 1 by 0.80
![0.80(x+y= 121)\\0.80x+0.80y=96.80\ \ \ Eqn\ 3](https://tex.z-dn.net/?f=0.80%28x%2By%3D%20121%29%5C%5C0.80x%2B0.80y%3D96.80%5C%20%5C%20%5C%20Eqn%5C%203)
Subtracting Eqn 2 from Eqn 3
![(0.80x+0.80y)-(0.80x+0.60y)=96.80-80.80\\0.80x+0.80y-0.80x-0.60y=16\\0.20y=16](https://tex.z-dn.net/?f=%280.80x%2B0.80y%29-%280.80x%2B0.60y%29%3D96.80-80.80%5C%5C0.80x%2B0.80y-0.80x-0.60y%3D16%5C%5C0.20y%3D16)
Dividing both sides by 0.20
![\frac{0.20y}{0.20}=\frac{16}{0.20}\\y=80](https://tex.z-dn.net/?f=%5Cfrac%7B0.20y%7D%7B0.20%7D%3D%5Cfrac%7B16%7D%7B0.20%7D%5C%5Cy%3D80)
Putting y=80 in Eqn 1
![x+80=121\\x=121-80\\x=41](https://tex.z-dn.net/?f=x%2B80%3D121%5C%5Cx%3D121-80%5C%5Cx%3D41)
The cafeteria sold 41 corn chips and 80 potato chips.
Keywords: linear equation, subtraction
Learn more about linear equations at:
#LearnwithBrainly
Answer:
$37.00
Step-by-step explanation:
7x5=35
35+2= 37
now I want some tacos XD
Volume of the first dwarf planet (r₁ = 832 mi):
![V_1=\dfrac{4}{3}\cdot\pi\cdot r_1^3=\dfrac{4}{3}\cdot\pi\cdot 832^3=\dfrac{2303721472}{3}\pi\approx7.679\cdot10^8\pi\,\text{mi}^3](https://tex.z-dn.net/?f=V_1%3D%5Cdfrac%7B4%7D%7B3%7D%5Ccdot%5Cpi%5Ccdot%20r_1%5E3%3D%5Cdfrac%7B4%7D%7B3%7D%5Ccdot%5Cpi%5Ccdot%20832%5E3%3D%5Cdfrac%7B2303721472%7D%7B3%7D%5Cpi%5Capprox7.679%5Ccdot10%5E8%5Cpi%5C%2C%5Ctext%7Bmi%7D%5E3)
Volume of the second dwarf planet (r₂ = 829 mi):
![V_2=\dfrac{4}{3}\cdot\pi\cdot r_2^3=\dfrac{4}{3}\cdot\pi\cdot 829^3=\dfrac{2278891156}{3}\pi\approx7.5963\cdot10^8\pi\,\text{mi}^3](https://tex.z-dn.net/?f=V_2%3D%5Cdfrac%7B4%7D%7B3%7D%5Ccdot%5Cpi%5Ccdot%20r_2%5E3%3D%5Cdfrac%7B4%7D%7B3%7D%5Ccdot%5Cpi%5Ccdot%20829%5E3%3D%5Cdfrac%7B2278891156%7D%7B3%7D%5Cpi%5Capprox7.5963%5Ccdot10%5E8%5Cpi%5C%2C%5Ctext%7Bmi%7D%5E3)
So difference between the volumes is:
![V_1-V_2\approx7.679\cdot10^8\pi-7.5963\cdot10^8\pi=0.0827\cdot10^8\pi=\boxed{8270000\pi\,\text{mi}^3}](https://tex.z-dn.net/?f=V_1-V_2%5Capprox7.679%5Ccdot10%5E8%5Cpi-7.5963%5Ccdot10%5E8%5Cpi%3D0.0827%5Ccdot10%5E8%5Cpi%3D%5Cboxed%7B8270000%5Cpi%5C%2C%5Ctext%7Bmi%7D%5E3%7D)
or if we want exact value (we use (a³-b³) = (a-b)(a²+ab+b²) ):
In order to determine if the events are independent or not we need to find the conditional probabilities.
The conditional probability of event A, given event B is denoted as P(A|B)
![P(A|B)= \frac{P(A*B)}{P(B)}](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%20%5Cfrac%7BP%28A%2AB%29%7D%7BP%28B%29%7D%20)
P(A*B) indicates P(A and B)
Using the values, we get:
![P(A|B)= \frac{0.28}{0.8}=0.35](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%20%5Cfrac%7B0.28%7D%7B0.8%7D%3D0.35%20)
Since P(A|B) is not equal to P(A) this indicates that occurrence of event B has an impact on the occurrence of event A. This shows that the two events are dependent.
Therefore, the correct option is the second one.2. A and B are not independent events because P(A∣∣B)≠P(A)
Answer:
1
Step-by-step explanation:
3^0
Any number ( besides 0) raised to the zero power is 1