The number of batches of salsa that can be made = x = 6 batches
The number of bat tomato sauce that can be made = y = 3 batches
Step-by-step explanation:
We are given the system of equations:
![x+5y=21\\x+y=9](https://tex.z-dn.net/?f=x%2B5y%3D21%5C%5Cx%2By%3D9)
where variable x represents the number of batches of salsa that can be made and y represents the number of bat tomato sauce that can be made.
We need to solve the systems to find the values of x and y.
Let:
![x+5y=21\,\,\,eq(1)\\x+y=9\,\,\,eq(2)](https://tex.z-dn.net/?f=x%2B5y%3D21%5C%2C%5C%2C%5C%2Ceq%281%29%5C%5Cx%2By%3D9%5C%2C%5C%2C%5C%2Ceq%282%29)
Subtract both equations:
![x+5y=21\\x+y=9\\-\,\,\,-\,\,\,\,\,\,-\\------\\4y=12\\y=\frac{12}{4}\\y=3](https://tex.z-dn.net/?f=x%2B5y%3D21%5C%5Cx%2By%3D9%5C%5C-%5C%2C%5C%2C%5C%2C-%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C-%5C%5C------%5C%5C4y%3D12%5C%5Cy%3D%5Cfrac%7B12%7D%7B4%7D%5C%5Cy%3D3)
So, value of y=3
Putting value of y in eq(2) and finding value of x:
![x+y=9\\x+3=9\\x=9-3\\x=6](https://tex.z-dn.net/?f=x%2By%3D9%5C%5Cx%2B3%3D9%5C%5Cx%3D9-3%5C%5Cx%3D6)
So, value of x=6
The number of batches of salsa that can be made = x = 6 batches
The number of bat tomato sauce that can be made = y = 3 batches
Keywords: System of equations
Learn more about system of equations at:
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The rolls of the dice are independent, i.e. the outcome of the second die doesn't depend in any way on the outcome of the first die.
In cases like this, the probability of two events happening one after the other is the multiplication of the probabilities of the two events.
So, the probability of rolling two 6s is the multiplication of the probabilities of rolling a six with the first die, and another six with the second:
![P(\text{rolling two 6s}) = P(\text{rolling a 6}) \cdot P(\text{rolling a 6}) = \dfrac{1}{6} \cdot \dfrac{1}{6} = \dfrac{1}{36}](https://tex.z-dn.net/?f=%20P%28%5Ctext%7Brolling%20two%206s%7D%29%20%3D%20P%28%5Ctext%7Brolling%20a%206%7D%29%20%5Ccdot%20P%28%5Ctext%7Brolling%20a%206%7D%29%20%3D%20%5Cdfrac%7B1%7D%7B6%7D%20%5Ccdot%20%5Cdfrac%7B1%7D%7B6%7D%20%20%3D%20%5Cdfrac%7B1%7D%7B36%7D%20)
Similarly,
![P(\text{rolling two 3s}) = P(\text{rolling a 3}) \cdot P(\text{rolling a 3}) = \dfrac{1}{6} \cdot \dfrac{1}{6} = \dfrac{1}{36}](https://tex.z-dn.net/?f=%20P%28%5Ctext%7Brolling%20two%203s%7D%29%20%3D%20P%28%5Ctext%7Brolling%20a%203%7D%29%20%5Ccdot%20P%28%5Ctext%7Brolling%20a%203%7D%29%20%3D%20%5Cdfrac%7B1%7D%7B6%7D%20%5Ccdot%20%5Cdfrac%7B1%7D%7B6%7D%20%20%3D%20%5Cdfrac%7B1%7D%7B36%7D%20)
Actually, you can see that the probability of rolling any ordered couple is always 1/36, since the probability of rolling any number on both dice is 1/6:
![P(\text{rolling any ordered couple}) = P(\text{rolling the first number}) \cdot P(\text{rolling the second number}) = \dfrac{1}{6} \cdot \dfrac{1}{6} = \dfrac{1}{36}](https://tex.z-dn.net/?f=%20P%28%5Ctext%7Brolling%20any%20ordered%20couple%7D%29%20%3D%20P%28%5Ctext%7Brolling%20the%20first%20number%7D%29%20%5Ccdot%20P%28%5Ctext%7Brolling%20the%20second%20number%7D%29%20%3D%20%5Cdfrac%7B1%7D%7B6%7D%20%5Ccdot%20%5Cdfrac%7B1%7D%7B6%7D%20%20%3D%20%5Cdfrac%7B1%7D%7B36%7D%20)
19 is the answer for this question
- Please find the picture for your triangle.
- We know, area of a ∆ = <u>1/2 × base × height</u>
- Here, base = ( 1 + 7 ) units = <u>8 units</u>
- Height = ( 7 - 1 ) units = <u>6 units</u>
- Therefore, area of the ∆
- = <u>(1/2 × 8 × 6) square units</u>
- = <u>24 square units.</u>
<u>Answer</u><u>:</u>
<em><u>2</u><u>4</u><u> </u><u>square </u></em><em><u>units</u></em>
Hope you can get an idea from it.
Carry on learning.
Doubt clarification - use comment section.