Answer:
![Weighted\ Average = 73](https://tex.z-dn.net/?f=Weighted%5C%20Average%20%3D%20%2073)
Step-by-step explanation:
Given
![Lab = 21\%](https://tex.z-dn.net/?f=Lab%20%3D%2021%5C%25)
![Tests = 25\%](https://tex.z-dn.net/?f=Tests%20%3D%2025%5C%25)
![Exam = 29\%](https://tex.z-dn.net/?f=Exam%20%3D%2029%5C%25)
![Lab\ Score = 60](https://tex.z-dn.net/?f=Lab%5C%20Score%20%3D%2060)
![First\ Test = 81](https://tex.z-dn.net/?f=First%5C%20Test%20%3D%2081)
![Second\ Test = 69](https://tex.z-dn.net/?f=Second%5C%20Test%20%3D%2069)
![Exam = 79](https://tex.z-dn.net/?f=Exam%20%3D%2079)
Required
The weighted average
To do this, we simply multiply each score by the corresponding worth.
i.e.
![Weighted\ Average = Lab\ worth * Lab\ score + Tests\ worth * Tests\ score.....](https://tex.z-dn.net/?f=Weighted%5C%20Average%20%3D%20%20Lab%5C%20worth%20%2A%20Lab%5C%20score%20%2B%20Tests%5C%20worth%20%2A%20Tests%5C%20score.....)
So, we have:
![Weighted\ Average = 21\% * 60 + 25\% * 81 + 25\% * 69 + 29\% * 79](https://tex.z-dn.net/?f=Weighted%5C%20Average%20%3D%20%2021%5C%25%20%2A%2060%20%2B%2025%5C%25%20%2A%2081%20%2B%2025%5C%25%20%2A%2069%20%2B%2029%5C%25%20%2A%2079)
Using a calculator, we have:
![Weighted\ Average = 73.01](https://tex.z-dn.net/?f=Weighted%5C%20Average%20%3D%20%2073.01)
--- approximated
Hello!
Let's subtract the eight DVDs Joe received as gifts, because he didn't buy them on his own.
35 - 8 = 27
Now, divide the remaining CDs by the 3 years he collected his DVDs in.
27 ÷ 3 = 9
A N S W E R:
Joe bought 9 DVDs last year.
Good day!
I= sqrt (-1)
If the power is
- even then the value could be -1 or 1
-odd then the value could be -i or i
99 is odd so now is
-i if (99+1)/2 is even or is
i is (99+1)/2 is odd
Now check (99+1)/2= 100/2= 50,
50 is even so
i^99 = -i
Answer:
The conclusion "T" logically follows from the premises given and the argument is valid
Step-by-step explanation:
Let us use notations to represent the steps
P: I take a bus
Q: I take the subway
R: I will be late for my appointment
S: I take a taxi
T: I will be broke
The given statement in symbolic form can be written as,
(P V Q) → R
S → (¬R ∧ T)
(¬Q ∧ ¬P) → S
¬R
___________________
∴ T
PROOF:
1. (¬Q ∧ ¬P) → S Premise
2. S → (¬R ∧ T) Premise
3. (¬Q ∧ ¬P) → (¬R ∧ T) (1), (2), Chain Rule
4. ¬(P ∨ Q) → (¬R ∧ T) (3), DeMorgan's law
5. (P ∨ Q) → R Premise
6. ¬R Premise
7. ¬(P ∨ Q) (5), (6), Modus Tollen's rule
8. ¬R ∧ T (4), (7), Modus Ponen's rule
9. T (8), Rule of Conjunction
Therefore the conclusion "T" logically follows from the given premises and the argument is valid.
Answer:
![x=4\\\\y=-1](https://tex.z-dn.net/?f=x%3D4%5C%5C%5C%5Cy%3D-1)
Step-by-step explanation:
Given Equation:
Equation:1
Equation:2
Dividing Equation:2 by '3' both the sides:
or
Equation:3
Putting the vale of 'x' in Equation:1
![x-3y=7](https://tex.z-dn.net/?f=x-3y%3D7)
![(3-y)-3y=7\\\\3-y-3y=7\\\\3-4y=7\\\\](https://tex.z-dn.net/?f=%283-y%29-3y%3D7%5C%5C%5C%5C3-y-3y%3D7%5C%5C%5C%5C3-4y%3D7%5C%5C%5C%5C)
Subtracting '3' both sides
![-4y=7-3\\\\-4y=4](https://tex.z-dn.net/?f=-4y%3D7-3%5C%5C%5C%5C-4y%3D4)
![y=\frac{4}{-4}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B4%7D%7B-4%7D)
![y=-1](https://tex.z-dn.net/?f=y%3D-1)
Putting value of 'y' in Equation:3
![x=3-y](https://tex.z-dn.net/?f=x%3D3-y)
![x=3-(-1)\\\\x=3+1\\\\x=4](https://tex.z-dn.net/?f=x%3D3-%28-1%29%5C%5C%5C%5Cx%3D3%2B1%5C%5C%5C%5Cx%3D4)
The solution of the equations is :
![x=4\\\\y=-1](https://tex.z-dn.net/?f=x%3D4%5C%5C%5C%5Cy%3D-1)