Answer:
Subtract 11 from both sides
Step-by-step explanation:
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:

Answer:
The domain of f(x) corresponds to the set of real numbers.
D f(x) ∈ ∀X; D f(x) ∈ R
Step-by-step explanation:
f(x)=X+18-3X-15
f(x)=-2X+3 (right line with negative slope)
This function exists for all values of X, so the domain corresponds to the set of real numbers.
D f(x) ∈ ∀X; D f(x) ∈ R
Answer:
follow me @peachllings
Step-by-step explanation:
and @wtfpeachess
Please consider the attached graph.
We have been given that a helicopter flies 8 km due north from A to B. It then flies 5 km from B to C and returns to A as shown in the figure. The measure of angle ABC is 150°. We are asked to find the area of triangle ABC.
We will use trigonometric area formula to solve our given problem.
, where angle b is angle between sides a and c.
For our given triangle
and measure of angle b is 150 degrees.



Therefore, the area of the triangle ABC is 10 square kilo-meters and option 'c' is the correct choice.