The cost of renting a jumping castle includes a fixed charge of $325 for setup and delivery, and a variable charge of $175 for each hour the jumping castle is rented for. caitlin would like to rent a jumping castle for a party, and is willing to spend a minimum amount of $1200 and a maximum amount of $1725. solve for the range of hours “t” that she could hire the jumping castle for. give your answer as an inequality.

Nick and nora are married and have three children in college. they have an adjusted gross income of 47,400. if their standard deduction is 12,600 itemized deductions are 14,200 and they get an exemption of 4000 for each adult and each dependent what is their taxable income

Will mark 50 show all what is the solution to the system of equations? use the substitution method and show your work. -5x+y= -3 -15 x+3y=7 explain what your answer in part (a) tells you about the association of the lines in this system.

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)