B. You are given nine stones which look and feel identical. One of them contains a valuable gem worth $250,000 and is actually slightly heavier than the other eight (but not enough to detect by lifting by hand). If you identify the gemstone it is yours to keep. You have a balance scale, (see diagram) which you can use exactly two times. Once you have used the scale twice you never get another opportunity. How can you be certain to find the stone contains the gem. (If you guess at any point you lose your chance to win the gem stone.)

Separate the stones into 3 groups of 3.

Let's call each the three groups A, B, and C.

1) Place group A and group B on the two plates of the scale. There are two possible outcomes i) and ii) below:

i) The groups have different weights. A is heavier than B or B is heavier than A. Take the heavier group. Place two stones from this group on the scale. If one is heavier than the other, this is it. If they are equal, the stone not on the scale is it.

ii) Groups A and B have equal weights. The heavier stone in in group C. Using group C, place two stones from this group on the scale. If one is heavier than the other, this is it. If they are equal, the stone not on the scale is it.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: