the chorus has 35 members. which expression represents the number of ways a group of 6 members can be chosen to do a special per
2 answers:
Answer:
Step-by-step explanation:
Given : The chorus has 35 members.
To Find: which expression represents the number of ways a group of 6 members can be chosen to do a special performance?
Solution:
We will use combination to find the number of ways a group of 6 members can be chosen to do a special performance .
So, Formula :
Since we are given that total members are 35
So, n =35
No. of members in a group = 6
So, r =6
So,
Thus expression represents the number of ways a group of 6 members can be chosen to do a special performance is
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The summation indicates the sum from n = 1 to n = 3 of the expression 2(n+5).
2 (n+5) = 2n + 10
2n + 10 denotes an Arithmetic Series, with a common difference of two and first term as 12.
For n =1, it equals 12
For n = 2, it equals 14
For n = 3, it equals 16
So the sum from n=1 to n=3 will be 12 + 14 + 16 = 42
Sum of an Arithmetic Series can also be written as:
Using the value of a₁ and d, we can simplify the expression as:
This expression is equivalent to the given expression and will yield the same result.
For n=3, we get the sum as:
S₃ = 3(11+3) = 42
2 (n+5) = 2n + 10
2n + 10 denotes an Arithmetic Series, with a common difference of two and first term as 12.
For n =1, it equals 12
For n = 2, it equals 14
For n = 3, it equals 16
So the sum from n=1 to n=3 will be 12 + 14 + 16 = 42
Sum of an Arithmetic Series can also be written as:
Using the value of a₁ and d, we can simplify the expression as:
This expression is equivalent to the given expression and will yield the same result.
For n=3, we get the sum as:
S₃ = 3(11+3) = 42
Answer:
A - 90 units
B = 0 units
Step-by-step explanation:
Here we have two models A and B with the following particulars
Model A B (in minutes)
Assembly 20 15
Packing 10 12
Objective function to maxmize is the total profit
where A and B denote the number of units produced by corresponding models.
Constraints are
These equations would have solutions as positive only
Intersection of these would be at the point
i) (A,B) = (60,40)
Or if one model is made 0 then the points would be
ii) (A,B) = (90,0) oriii) (0, 90)
Let us calculate Z for these three points
A B Profit
60 40 1040
90 0 1080
0 90 720
So we find that optimum solution is
A -90 units and B = 0 units.