What value of b will cause the system to have an infinite number of solutions? A system of equations. y equals 6 x plus b. negat
2 answers:
Answer:
Step-by-step explanation:
we have
----> equation A
-----> equation B
we know that
If equation A is the same of equation B, then the system of equations will have infinite solutions
Convert equation B in slope intercept form
Isolate the variable y
Multiply by 2 both sides to remove the fractions
Adds 6x both sides
-----> equation C (slope intercept form)
Equate equation A and equation C and solve for b
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Answer:
Part 1: There are 4.7*10^21 ways to select 40 volunteers in subgroups of 10
Part 2: The research board can be chosen in 32760 ways
Step-by-step explanation:
Part 1:
The number of ways in which we can organized n elements into k groups with size n1, n2,...nk is calculate as:
So, in this case we can form 4 subgroups with 10 participants each one, replacing the values of:
- n by 40 participants
- k by 4 groups
- n1, n2, n3 and n4 by 10 participants of every subgroups
We get:
Part 2:
The number of ways in which we can choose k element for a group of n elements and the order in which they are chose matters is calculate with permutation as:
So in this case there are 4 offices in the research board, those are director, assistant director, quality control analyst and correspondent. Additionally this 4 offices are going to choose from a group of 5 doctors.
Therefore, replacing values of:
- n by 15 doctors
- k by 4 offices
We get: