Answer:
Part a: The number of ways in which the candidates can be appointed on the executive posts are 11880.
Part b: The number of ways in which the candidates can be appointed as members of the planning committee are 495.
Step-by-step explanation:
As the complete question is not given a similar question is found online and is attached herewith.
Part a: Number of ways in which 12 candidates can be appointed for President, Chief Executive Officer, Chief Operating Officer and Chief Finance Officer.
Number of Candidates=12
Number of Posts=4
As the order is important the number of ways are identified using Permutations given as
So the number of ways in which the candidates can be appointed on the executive posts are 11880.
Part b: Number of ways in which 12 candidates can be appointed as members of the planning committee.
Number of Candidates=12
Number of Posts=4
As the order is not important the number of ways are identified using Combinations given as
So the number of ways in which the candidates can be appointed as members of the planning committee are 495.
Answer:
The student's mean score in the class is 80.6
Step-by-step explanation:
we know that
To find out the student's mean score in the class, multiply each score by its worth and adds the numbers
therefore
The student's mean score in the class is 80.6
Let speed of the boat in still water = x miles per hour
Let speed of the current = y miles per hour
When water and current both flow in same direction then effective speed will be sum of both speeds that is (x+y)
now plug the given values in formula speed=distance/time
we get equation:
(x+y)=160/8
or x+y=20...(i)
When water and current both flow in opposite direction then effective speed will be difference of both speeds that is (x-y)
now plug the given values in formula speed=distance/time
we get equation:
(x-y)=160/40
or x-y=4
or x=4+y...(ii)
plug value of x into (i)
4+y+y=20
4+2y=20
2y=16
y=8
plug value of y into (ii)
x=4+8=12
Hence final answer is given by:
Speed of the boat in still water = 12 miles per hour
Speed of the current = 8 miles per hour
The true speed and direction of the football thrown by the quarterback is 30.185 mph and 9⁰ respectively.
<h3>
Relative velocity of the football</h3>
The true speed and direction of the football is determined by applying the concept of relative velocity.
Vr/w = Vb - Vw
where;
- Vr/w is the velocity of the football with respect to the wind
- Vb is the velocity of the football
- Vw is the velocity of the wind
Vr/w = 41 mph - 11 mph = 30 mph
The direction speed can be determined by sketching a triangle
Direction of the speed, θ = (360 - 339) - (180 - 168)
θ = 21 - 12 = 9⁰
<h3>Resultant speed;</h3>
R² = 41² + 11² - 2(41 x 11 x cos9)
R² = 911.105
R = √911.105
R = 30.185 mph
Thus, the true speed and direction of the football thrown by the quarterback is 30.185 mph and 9⁰ respectively.
Learn more about relative velocity here: brainly.com/question/17228388
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A = (a+b)/2
2*A = 2*(a+b)/2 ... multiply both sides by 2
2A = a+b
2A-a = a+b-a ... subtract 'a' from both sides to isolate b
2A-a = b
b = 2A-a
Answer: b = 2A-a
