Answer:
13800
Step-by-step explanation:
The order of the members is important (because each selected member will receive a different position), thus we then need to use the definition of permutation.
There are 25 members, of which 3 are selected.

Evaluate the definition of a combination:

Answer:
a) Y(x) = {900, x≤30; 900-40(x-30), x>30}
b) T(x) = {900x, x≤30; 2100x-40x², x>30}
c) dT/dx = {900, x≤30; 2100-80x, x>30}
Step-by-step explanation:
a) The problem statement gives the function for x ≤ 30, and gives an example of evaluating the function for x = 35. So, replacing 35 in the example with x gives the function definition for x > 30.

__
b) The yield per acre is the product of the number of trees and the yield per tree:
T(x) = x·Y(x)

__
c) The derivative is ...

_____
The attached graph shows the yield per acre (purple, overlaid by red for x<30), the total yield (black), and the derivative of the total yield (red). You will note the discontinuity in the derivative at x=30, where adding one more tree per acre suddenly makes the rate of change of yield be negative.
Answer:
67
Step-by-step explanation:
A linear pair is two angles which form a straight angle when combined (or 180 degrees). Thus do 180 - 113 to get 67 degrees for Angle 2
Refer to the attached image.
Given:
and measure of exterior angle at C =
.
We have to determine the measure of angle B and angle BCA.
By applying exterior angle property of the triangle which states:
"An exterior angle of a triangle is equal to the sum of the opposite interior angles".
So, exterior angle C = 


Now, applying angle sum property in triangle ABC which states:
"The sum of all the angles of a triangle is 180 degrees".





Therefore, the measure of
and
.
Answer:
a. 5i + 13j
b. 8i
c. 10i + 6j
Step-by-step explanation:
a. 2i + 6j + 3i + 7j = 5i + 13j
b. 3i + 7j + 5i - 7j = 8i
c. 2i + 6j + 3i + 7j + 5i - 7j = 10i + 6j