Country a inadvertently launches ten guided missiles—six armed with nuclear warheads—at country b. in response, country b fires seven antiballistic missiles, each of which will destroy exactly one of the incoming rockets. the antiballistic missiles have no way of detecting, though, which of the ten rockets are carrying nuclear warheads. what are the chances that country b will be hit by at least one nuclear missile? larsen, richard j.. an introduction to mathematical statistics and its applications (p. 115). pearson education. kindle edition.\

Beryl states that insulation with the smallest possible thermal conductivity is best to keep a house warm in winter, but worst for keeping a house cool in summer. sapphire insists the reverse is true: low thermal conductivity is good in the summer, but bad in the winter. which one, if either is correct? a. beryl, because low thermal conductivity results in low heat transfer. b. beryl, because low thermal conductivity results in high heat transfer. d. sapphire, because low thermal conductivity results in high heat transfer. e. neither, because low heat transfer is desirable both in summer and in winter.

The inside surface of a cylindrical-shaped cave of inner diameter 1.0 m is continuously covered with a very thin layer of water. the cave is very long and it is open on both ends. the water on the cave surface is at a constant temperature of 15.5 °c. the cave is constantly exposed to wind such that 15.5 °c air flows through the cave at 4.5 m/s. the kinematic viscosity of the air is 14.66 x 10-6 m2/s and the molecular diffusion coefficient of water vapor in the air is 0.239 x 10-4 m2/s. because the cave diameter is so large, the flow of wind down the length of the cave, in the x direction, can be treated like it is external flow and the cave surface can be approximated as flat where appropriate. calculate the x value, in a) the transition to turbulent flow occurs at rex meters, where the air flow transitions from laminar to turbulent along the inside surface of the cave b) calculate the x value, in meters, where the bulk steady state concentration of water vapor in the air flowing in the cave is 10% of the saturation concentration. assume the air at the surface of the water layer is 100% saturated with water vapor. assume the wind entering the cave contained no moisture before it entered the cave. take into account the transition from laminar to turbulent flow when solving part b

1. explain how you calculate the net force in any direction on the box. 2. suppose an upward force of 15n is added to the box. what will be the net vertical force on the box? 3. what force could be applied to the box to make the net force in the horizontal direction zero? explain. 4. suppose a force of 25n to the right is added to the box. what will be the net force to the right?