Let v be a vector space and let w be a. nonempty subset of v. then w is a subspace of v if and only if the following conditions hold (a) if u and v are in w, then uv is in w. (b) if u is in w and c is a scalar, then cu is in w. use the theorem above to determine whether w is a subspace of v. v f, w (fin f : f(-x) = -f(x)} w is a subspace of v w is not a subspace of v.

Find the area and perimeter of each composite figure. use 3.14 for π. round your answer to the nearest tenth. a square and a right triangle share a common side. image long description a 3-meter by 0.5-meter rectangle has triangles attached like wings to the 3-meter sides. the other two sides of both triangles measure 2.5 meters. the height of each triangle is 2 meters. a 6-inch by 4-inch rectangle has 2 half-circles attached like wings to the 6-inch sides. the radius of each half-circle is 3 inches. find the surface area and volume of each figure. use 3.14 for π. round your answer to the nearest tenth. a right circular cylinder has a base radius of 6 yards and a height of 20 yards. a rectangular prism has a base that is 9 centimeters long and 7 centimeters wide. the height is 2 centimeters. a rectangular prism has a base that measures 11 millimeters by 11 millimeters. the height is 11 millimeters.

Ajar of gumballs contains 4 reds, 2 greens, and 6 blues. what is the probability of getting two blues in a row without replacement?

Suppose that one doll house uses the 1 inch scale, meaning that 1 inch on the doll house corresponds to 1/2 foot for life-sized objects. if the doll house is 108 inches wide, what is the width of the full-sized house that it's modeled after? in inches and feet.