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:
We can use prime factorization to find the GCF:
The greatest value both 12 and 20 share is 4. By factoring this out of the equation, we get:
4(3 + 5) = 4(8) = 32
Answer:
Principal element is $475.43
Interest payment is $390
Step-by-step explanation:
The amount of interest paid in month one is 4%*$117,000*1/12=$390
The interest is calculated based on the annual interest rate of 4% apportioned to reflect one month interest by multiplying by 1/12
The principal element of monthly payment is the monthly payment minus interest.
principal paid in month one=$865.43-$390=$475.43
Ultimately,$475.43 goes toward reducing her loan balance while the $390 is interest on loan
Simplifying –8.3 + 9.2 – 4.4 + 3.7.
Identify and explain any errors in his work or in his reasoning
Original problem 1. −8.3 + 9.2 + 4.4 + 3.7
Additive inverse 2. −8.3 + 4.4 + 9.2 + 3.7 (error, not additive inverse; +3-3=0)
Commutative property 3. −8.3 + (4.4 + 9.2 + 3.7)
Associative property 4. −8.3 + 17.3
Simplify 5. 9
