Jess and Brian are playing the following game: Jess thinks of a fraction, and Brian flips a coin. If the coin turns up heads, Jess multiplies the number she's thinking of by 5/6. If the coin turns up tails, she multiplies the number she's thinking of by 6/5 Brian flips the coin ten times, and after each flip Jess multiplies the number in her head by either 5/6 or6/5, depending on the coin flip. The ten coin flips turn out to be:\[ \text{THTTHTHTTT},
\]where H means 'heads' and T means 'tails.' What number is Jess thinking of at the end of the game if she starts out with the fraction 5/9?

2: 10

step-by-step explanation:

part a: triangles gcb and epb

part b. sides cg and rp are parallel by definition of parallelogram.

angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.

part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.

calculation of be:

gb/be = cb/bp

(400 ft)/be = 300/200

(400 ft)/be = 3/2

3be = 2 * 400 ft

3be = 800 ft

be = 800/3 ft

calculation of pe:

gc/pe = cb/bp

(350 ft)/pe = 300/200

(350 ft)/pe = 3/2

3pe = 2 * 350 ft

3pe = 700 ft

pe = 700/3 ft