If the ratio of purple bikes to red bikes is 8 to 12 and there are a total of 100 bikes, how many of them are red? *A company spent 32% of its annual budget developing a new machine. What fraction of the company's budget was spent developing the new machine?

1foot = 12 inches; 1 yard = 3 feet

Complex numbers multiply √-4 * √-25 and show all intermediate steps. alternative notation is sqrt(-4) * sqrt(-25).

Abag contains 4 red, 7 blue and 5 yellow marbles. event a is defined as drawing a yellow marble on the first draw and event b is defined as drawing a blue marble on the second draw. if two marbles are drawn from the bag, one after the other and not replaced, what is p(b|a) expressed in simplest form? a. 7/16 b. 7/15 c. 14/16 d. 14/15