The ratio of the lengths of strings that play the notes f and g is 9 to 8. if a string 88 centimeters long plays a g, what is the lenght of the string thst plausan f?

9/8 = 1.125 is called a "just" major second.  Just tuning means each interval in a fixed key is tuned as consonant as possible, to small whole number ratios.

In modern music we change keys all the time, and equal temperament is used.  That means each frequency or length is related to the previous semitone by a factor of , the 12th root of 2.  So a tempered major second is , about four cents flat compared to a just second.

That doesn't matter to the problem, but I have to do something to keep these straightforward ones interesting.

f/g = 9/8

f = (9/8) g = (9/8) 88 cm = 99 cm

99 cm

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw