A ladybug is walking at random on a hexagon. She starts at vertex $A$. Every minute, she moves to one of the two vertices (chosen at random) adjacent to the one she's currently on. What is the probability that, after $10$ minutes, she is back at $A$

On monday, the water was shut off 3 times for 1/4 hours, 2/3 hours, and 1-3/4 hours, respectively. what was the tireless number of hours the water was off?

Alayna wonders how much water it would take to fill her cup she drops her pencil in her cup and notices that it just fits diagonal the pencil is 17 cm long and the cup is 15 cm tall how much water can the cup hold

Two trains leave a station on different tracks. the tracks make an angle of 130°, with the station as a vertex. the first train travels 100 km and makes its first stop at point a, while the second train travels 200 km and makes it first stop at point b. how far apart are the trains when both are at their first stop? round the answer to the nearest integer. a) 65 km b) 139 km c) 224 km d) 275 km