Answer:

Step-by-step explanation:
a) 
b) 
c) 
d) 
e) 
f) 
To determine the probability that one or the other circumstances will occur, you will count the number of possible outcomes and divide it by all the possible outcomes.
#of female teaching assistants + # of male teaching assistants + # of female professors
6 + 16 + 11 = 33
Total = 41
33/41 = 80
There is a approximate 80% probability that one or the other will occur.
Answer:
The coordinates of the circumcenter of this triangle are (3,2)
Step-by-step explanation:
we know that
The circumcenter is the point where the perpendicular bisectors of a triangle intersect
we have the coordinates

step 1
Find the midpoint AB
The formula to calculate the midpoint between two points is equal to

substitute the values


step 2
Find the equation of the line perpendicular to the segment AB that passes through the point (-2,2)
Is a horizontal line (parallel to the x-axis)
-----> equation A
step 3
Find the midpoint BC
The formula to calculate the midpoint between two points is equal to

substitute the values


step 4
Find the equation of the line perpendicular to the segment BC that passes through the point (3,-1)
Is a vertical line (parallel to the y-axis)
-----> equation B
step 5
Find the circumcenter
The circumcenter is the intersection point between the equation A and equation B
-----> equation A
-----> equation B
The intersection point is (3,2)
therefore
The coordinates of the circumcenter of this triangle are (3,2)
Answer:
39/20 = 1.95
That's my simplified answer
39/20 = 1 19/20
Will this help?
Step-by-step explanation:
Answer:
Step-by-step explanation:
Required to prove that:
Sin θ(Sec θ + Cosec θ)= tan θ+1
Steps:
Recall sec θ= 1/cos θ and cosec θ=1/sin θ
Substitution into the Left Hand Side gives:
Sin θ(Sec θ + Cosec θ)
= Sin θ(1/cos θ + 1/sinθ )
Expanding the Brackets
=sinθ/cos θ + sinθ/sinθ
=tanθ+1 which is the Right Hand Side as required.
Note that from trigonometry sinθ/cosθ = tan θ