Suppose the police operate a sobriety checkpoint after 9 p. m. on a Saturday night when national traffic experts suspect about 12% of drivers have been drinking. Trained officers can correctly decide if a person has been drinking 80% of the time. What's the probability that

a) any given driver will be detained for drunk driving?

b) a driver who was detained has actually been drinking?

c) a driver who was released had actually been drinking?

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

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?

Factor the following expression completely 6x^11-24x^7