7. (a) (5 points) Use the properties of determinant to prove that a b c b c a c a b = (a + b + c)(ab + bc + ca − a 2 − b 2 − c 2 ). (b) (4 points) Use the result in part (a) to calculate the volume of parallelepiped with adjacent edges represented by the vectors u = (2, 3, 5), v = (3, 5, 2), and w = (5, 2, 3). (Your solution should clearly reflect the use of part (a), to receive any credit.)

Which statement is always true? a negative exponent cannot be part of an expression's numerator. a negative base raised to the power of 2 has a negative value. a negative base raised to the power of 2 has a positive value. any number to the first power is zero.

The factorization of 8x3 -125 is (2x-5)(jx2 +kx+25)

The table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation. best actor best supporting actor muequals42.0 muequals49.0 sigmaequals7.3 sigmaequals15 in a particular year, the best actor was 59 years old and the best supporting actor was 45 years old. determine the z-scores for each. best actor: z equals best supporting actor: z equals (round to two decimal places as needed.) interpret the z-scores. the best actor was (more than 2 standard deviations above more than 1 standard deviation above less than 1 standard deviation above less than 2 standard deviations below) the mean, which (is not, is) unusual. the best supporting actor was (less than 1 standard deviation below more than 1 standard deviation above more than 2 standard deviations below more than 1 standard deviation below) the mean, which (is is not) unusual.