A satellite system consists of n components and functions on any given day if at least k of the n components function on that day. On a rainy day, each of the components independently functions with probability p 1 , whereas on a dry day, each independently functions with probability p 2 . If the probability of rain tomorrow is α , what is the probability that the satellite system will function?

Choose the linear inequality that describes the graph. the gray area represents the shaded region. a: y ≤ –4x – 2 b: y > –4x – 2 c: y ≥ –4x – 2 d: y < 4x – 2

Maria found the least common multiple of 6 and 15. her work is shown below. multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . multiples of 15: 15, 30, 45, 60, . . the least common multiple is 60. what is maria's error?

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?