You have 10 pairs of socks, five black and five blue, but they are not paired up. Instead, they are all mixed up in a drawer. It’s early in the morning, and you don’t want to turn on the lights in your darkroom. How many socks must you pull out to guarantee that you have a pair of one colour? How many must you pull out to have two good pairs (each pair is the same colour)? How many must you pull out to be certain that you have a pair of black socks?

Mario has $14.35 left in his wallet. he spent $148.43 for tablecloths. then, he spent $92.05 for napkins. how much money did mario have in his wallet to start with?

How is the equation of this circle written in standard form? x2 + y2 - 6x + 14y = 142 a) (x - 3)2 + (y + 7)2 = 200 b) (x+ 3)2 + (y - 7)2 = 200 (x - 6)2 + (y + 14)2 = 142 d) (x+6)2 + (y- 14)2 = 142

The figure shows triangle def and line segment bc, which is parallel to ef: triangle def has a point b on side de and point c on side df. the line bc is parallel to the line ef. part a: is triangle def similar to triangle dbc? explain using what you know about triangle similarity. part b: which line segment on triangle dbc corresponds to line segment ef? explain your answer. part c: which angle on triangle dbc corresponds to angle f? explain your answer. asap