Let C[1; 1] be the vector space of all continuous functions over the interval 1 x 1. Let (f; g) be the inner product on C[1; 1] given by (f; g) = Z 1 1 f(x)g(x) dx: Find the cubic polynomial x3 + ax2 + bx + c that is orthogonal to 1; x and x2 1 3 in C[1; 1] under the inner product (f; g) dened above.

The weights of players in a basketball league are distributed normally. the distance (d) of each player's weight (w) from the mean of 86 kilograms was computed as follows: d = |w - 86| if d is greater than 7 for approximately 5% of the players, what is the approximate standard deviation of the players' weights? a. 1.75 kilograms b. 3.5 kilograms c. 4.3 kilograms d. 7 kilograms

Astore has clearance items that have been marked down by 60%. they are having a sale, advertising an additional 55% off clearance items. what percent of the original price do you end up paying?

Acertain volume of water contains 100000 hydrogen atoms and 50,000 oxygen atoms how many hydrogen atoms are in a volume of water containing 4 million oxygen atoms