Find two positive numbers satisfying the given requirements. The product is 768 and the sum of the first plus three times the second is a minimum.
(first number)
(second number)

1. there are 25 students who started computer programming in elementary school and 25 students who started computer programming in middle school. the first group had a mean final project grade of 95% and the second group had a mean final project grade of 92%. the line plot shows the differences after 10 rerandomizations. determine whether the difference in the means of the two groups is significant based on the line plot. explain your answer.

Lindsay used two points, (x,y; ) and (+2.82), to find the equation of the line, y = mx + b, that passes through the points. y2-y, first, she used the definition of slope and determined that the value of mis x, - . given this information, which expression must represent the value of b?

The price of an item has been reduced by 30%. the original price was $30. what is the price of the item now ?