Complete question :
The denarius was a unit of currency in ancient Rome. Suppose it costs the Roman government 10 denarius per day to support 3 legionaries and 3archers. It only costs 3 denarius per day to support one legionary and one archer. Use a system of linear equations in two variables. Can we solve for a unique cost for each soldier?
Answer:
No unique solution
Step-by-step explanation:
Given that:
Cost of supporting 3 legion aries and 3 archers = 10 denarius daily
Cost of supporting one legionary and one archer = 3 denarius
Let:
Legionaries = l ; archers = a
Equation for the first sentence :
3l + 3a = 10 - - - (1)
Second sentence :
l + a = 3 - - - - - (2)
From (2)
l = 3 - a
Substituting l = 3 - a into (1)
3(3 - a) + 3a = 10
9 - 3a + 3a = 10
9 - 0 = 10
The variable cancels out, Hence, ( there is no unique solution to find the cost of each soldier)
Answer:
13.5
Step-by-step explanation:
becoz,
18*9/12
=13.5
Answer:
![P(A) = \frac{30}{100}](https://tex.z-dn.net/?f=P%28A%29%20%3D%20%5Cfrac%7B30%7D%7B100%7D)
![P(B) = \frac{77}{100}](https://tex.z-dn.net/?f=P%28B%29%20%3D%20%5Cfrac%7B77%7D%7B100%7D)
![P(A\ n\ B) = \frac{22}{100}](https://tex.z-dn.net/?f=P%28A%5C%20n%5C%20B%29%20%3D%20%5Cfrac%7B22%7D%7B100%7D)
![P(A\ u\ B) = \frac{85}{100}](https://tex.z-dn.net/?f=P%28A%5C%20u%5C%20B%29%20%3D%20%5Cfrac%7B85%7D%7B100%7D)
Step-by-step explanation:
Given
See attachment for proper format of table
--- Sample
A = Supplier 1
B = Conforms to specification
Solving (a): P(A)
Here, we only consider data in sample 1 row.
In this row:
and ![No = 8](https://tex.z-dn.net/?f=No%20%3D%208)
So, we have:
![n(A) = Yes + No](https://tex.z-dn.net/?f=n%28A%29%20%3D%20Yes%20%2B%20No)
![n(A) = 22 + 8](https://tex.z-dn.net/?f=n%28A%29%20%3D%2022%20%2B%208)
![n(A) = 30](https://tex.z-dn.net/?f=n%28A%29%20%3D%2030)
P(A) is then calculated as:
![P(A) = \frac{n(A)}{Sample}](https://tex.z-dn.net/?f=P%28A%29%20%3D%20%5Cfrac%7Bn%28A%29%7D%7BSample%7D)
![P(A) = \frac{30}{100}](https://tex.z-dn.net/?f=P%28A%29%20%3D%20%5Cfrac%7B30%7D%7B100%7D)
Solving (b): P(B)
Here, we only consider data in the Yes column.
In this column:
and ![(3) = 30](https://tex.z-dn.net/?f=%283%29%20%3D%2030)
So, we have:
![n(B) = (1) + (2) + (3)](https://tex.z-dn.net/?f=n%28B%29%20%3D%20%281%29%20%2B%20%282%29%20%2B%20%283%29)
![n(B) = 22 + 25 + 30](https://tex.z-dn.net/?f=n%28B%29%20%3D%2022%20%2B%2025%20%2B%2030)
![n(B) = 77](https://tex.z-dn.net/?f=n%28B%29%20%3D%2077)
P(B) is then calculated as:
![P(B) = \frac{n(B)}{Sample}](https://tex.z-dn.net/?f=P%28B%29%20%3D%20%5Cfrac%7Bn%28B%29%7D%7BSample%7D)
![P(B) = \frac{77}{100}](https://tex.z-dn.net/?f=P%28B%29%20%3D%20%5Cfrac%7B77%7D%7B100%7D)
Solving (c): P(A n B)
Here, we only consider the similar cell in the yes column and sample 1 row.
This cell is: [Supplier 1][Yes]
And it is represented with; n(A n B)
So, we have:
![n(A\ n\ B) = 22](https://tex.z-dn.net/?f=n%28A%5C%20n%5C%20B%29%20%3D%2022)
The probability is then calculated as:
![P(A\ n\ B) = \frac{n(A\ n\ B)}{Sample}](https://tex.z-dn.net/?f=P%28A%5C%20n%5C%20B%29%20%3D%20%5Cfrac%7Bn%28A%5C%20n%5C%20B%29%7D%7BSample%7D)
![P(A\ n\ B) = \frac{22}{100}](https://tex.z-dn.net/?f=P%28A%5C%20n%5C%20B%29%20%3D%20%5Cfrac%7B22%7D%7B100%7D)
Solving (d): P(A u B)
This is calculated as:
![P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)](https://tex.z-dn.net/?f=P%28A%5C%20u%5C%20B%29%20%3D%20P%28A%29%20%2B%20P%28B%29%20-%20P%28A%5C%20n%5C%20B%29)
This gives:
![P(A\ u\ B) = \frac{30}{100} + \frac{77}{100} - \frac{22}{100}](https://tex.z-dn.net/?f=P%28A%5C%20u%5C%20B%29%20%3D%20%5Cfrac%7B30%7D%7B100%7D%20%2B%20%5Cfrac%7B77%7D%7B100%7D%20-%20%5Cfrac%7B22%7D%7B100%7D)
Take LCM
![P(A\ u\ B) = \frac{30+77-22}{100}](https://tex.z-dn.net/?f=P%28A%5C%20u%5C%20B%29%20%3D%20%5Cfrac%7B30%2B77-22%7D%7B100%7D)
![P(A\ u\ B) = \frac{85}{100}](https://tex.z-dn.net/?f=P%28A%5C%20u%5C%20B%29%20%3D%20%5Cfrac%7B85%7D%7B100%7D)
Answer:
Reflection across y=0
Step-by-step explanation:
The Y axis splits the octagon in half, so if it was reflected it would be mapped onto itself.
Answer:
What circle? Can you add a picture of it?
Step-by-step explanation: