Analyzing Angle Relationships of Triangles
A triangle is shown with its exterior angles. Angles 2, 6, and 4 are the interior angles. Angle 1 is the exterior angle at angle 2. Angle 5 is the exterior angle at angle 6. Angle 3 is the exterior angle at angle 4.
Which statements are always true regarding the diagram? Check all that apply.
m∠3 + m∠4 = 180°
m∠2 + m∠4 + m∠6 = 180°
m∠2 + m∠4 = m∠5
m∠1 + m∠2 = 90°
m∠4 + m∠6 = m∠2
m∠2 + m∠6 = m∠5

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.1. (round your answers to four decimal places.) (a) if the distribution is normal, what is the probability that the sample mean hardness for a random sample of 8 pins is at least 51?

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.

A3-dimensional figure has a square base and 4 lateral faces that meet at a point. explain the difference between the cross sections when a slice is made perpendicular to the base through the vertex, and when a slice is made perpendicular to the base and not through the vertex