Using geometric sequence concepts, it is found that:
a) The rule is: 
.
b) An exponential relationship exists between the two variables.
<h3>What is a geometric sequence?</h3>
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
In which 
is the first term.
A geometric sequence represents an exponential relationship between the variables.
In this problem, considering that the first-place finisher wins half of $1.500.000 in total prize money, and each finisher earns half of the one who finished above, the first term and the common ratio are given by:
.
Hence the nth term of the sequence is given by:
More can be learned about geometric sequence concepts at brainly.com/question/11847927
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cos4x = cos2x
We know that:
cos2x = 1-2cos^2 x
==> cos4x = 1-2cos^2 (2x)
Now substitute:
==> 1-2cos^2 (2x) = cos2x
==> 2cos^2 (2x) + cos2x - 1 = 0
Now factor:
==> (2cos2x -1)(cos2x + 1) = 0
==> 2cos2x -1 = 0 ==> cos2x =1/2 ==> 2x= pi/3
==> x1= pi/6 , 7pi/6
==> x1= pi/6 + 2npi
==> x2= 7pi/6 + 2npi
==> cos2x = -1 ==> 2x= pi ==> x3 = pi/2 + 2npi.
<span>==> x= { pi/6+2npi, 7pi/6+2npi, pi/2+2npi}</span>
Sample space is (3FD , 3MD, 4MN, 6FN)
where F=female M= male N=Nurse D=doctor)
so P(doctor or female ) = (3+3+6) / 16 = 12/16 answer
Its C
7) • A straight line is 180 deg
• So B = 180-138 = 42 degrees
• Isosceles triangles have equal angles on the equal sides
• So G = 42 degrees
• We know a triangle has 180 degrees
• So 180 - 42 - 42 = 96 degrees for A
8) • Use similar logic to above
• TCB = 180 - 87 = 2x
• TCB = 46.5 degrees
• ACB = 180 - 65 = 2x
• ACB = 57.5 degrees
• TCB + ACB = ACT = 104 degrees
