Abug is moving along the parabola y=x^2 at a rate such that its distance from the origin is increasing at a rate of 1 cm/min. at what rates are the x and y coordinates of the bug increasing when it is at the point (2,4)?

In triangle △abc, ∠abc=90°, bh is an altitude. find the missing lengths. ah=4 and hc=1, find bh.

If you are dealt 4 cards from a shuffled deck of 52? cards, find the probability that all 4 cards are diamondsdiamonds.

Aroulette wheel has 38 slots in which the ball can land. two of the slots are green, 18 are red, and 18 are black. the ball is equally likely to land in any slot. the roulette wheel is going to be spun twice, and the outcomes of the two spins are independent. the probability that it lands one time on red and another time on black in any order is(a) 0.5 (b) 0.25 (c) 0.4488 (d) 0.2244