When the price of a certain commodity is p dollars per unit, the manufacturer is willing to supply x hundred units, where LaTeX: 3p^2-x^2=123 p 2 − x 2 = 12. How fast is the supply changing when the price is $4 per unit and is increasing at the rate of 87 cents per month?

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. increase the area of the base of the square pyramid by a factor of ten. increase the height of the cylinder by a factor of ten. increase the radius of the cone by a factor of ten. increase the radius of a sphere by a factor of ten. juan wants to build a greenhouse in his back yard. he needs to maximize the ratio of floor area to structure volume in order to provide the most room for plants while minimizing the area to be heated. find the description of the structure that best meets juan’s criteria. a cube with a side length of 12 feet a cone with a diameter of 12 feet and a height of 10 feet a square pyramid with a base side length of 12 feet and a height of 9 feet a hemisphere with a diameter of 12 feet marion has a bicycle that she is planning to take for a ride. the rim of the rear wheel lies 41 cm from the center of the wheel. the tire itself has a thickness of 3 cm.in order to marion to ride her bicycle 96,712 cm, approximately how many rotations will the rear wheel make? 350 15.9 376 5133 an isosceles trapezoid has perimeter of 42 inches. each of the congruent nonparallel sides is 5 inches long, and the trapezoid is 3 inches tall. how long are the two parallel sides? 10 inches and 16 inches 12 inches and 20 inches 16 inches and 16 inches 10 inches and 22 inches

Suppose y varies directly with x. write a direct variation equation that relates x and y. then find the value of y when x=12 y=7 when x=3

Question 1 of 10 2 points different groups of 50 graduates of an engineering school were asked the starting annual salary for their first engineering job after graduation, and the sampling variability was low. if the average salary of one of the groups was $65,000, which of these is least likely to be the average salary of another of the groups? o a. $64,000 o b. $65,000 o c. $67,000 o d. $54,000