Each marble bag sold by lucy's marble company contains 7 purple marbles for every 5 orange marbles. if a bag has 49 purple marbles, how many orange marbles does it contain?

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.

Question 3 (essay worth 10 points) (03.06 mc) part a: max rented a motorbike at $465 for 5 days. if he rents the same motorbike for a week, he has to pay a total rent of $625. write an equation in the standard form to represent the total rent (y) that max has to pay for renting the motorbike for x days. (4 points) part b: write the equation obtained in part a using function notation. (2 points) part c: describe the steps to graph the equation obtained above on the coordinate axes. mention the labels on the axes and the intervals. (4 points)

Acircle has a radius of 12.6cm what is the exact length of an arc formed by a central angle measuring 120