Which sequence of transformations takes figure b to its image b'?
a. a reflection in the y-axis, followed by a translation 6 units up
b. a reflection in the x-axis, followed by a translation 2 units left
c. a reflection in the x-axis, followed by a counterclockwise rotation of 180 about the origin
d. a reflection in the y-axis, followed by a counterclockwise rotation of 270 about the origin

D. a reflection in the y-axis, followed by a counterclockwise rotation of 270 about the origin

Step-by-step explanation:

Well, the first obvious step is to reflect it across the y-axis. Now, for the next step, since we do not have a 90°-clockwise rotation option, we have to go with something similar to that, which would be a 270°-counterclockwise rotation. If you think about it, since 3 × 90 is 270, and rotating this figure 90° clockwise [one rotation] would go from Quadrant III to Quadrant II, going the other way around [270°counterclockwise (three rotations)] will also go from Quadrant III to Quadrant II [to Quadrant to Quadrant I to Quadrant II].

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answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.