4. suppose the set {u, v} forms a basis for a subspace w, in r^n. let x = u+v and y u v. show [x. y is also a basis for w. (hint: use the basis theorem at the end of 2.9)

Describe in detail how you would construct a 95% confidence interval for a set of 30 data points whose mean is 20 and population standard deviation is 3. be sure to show that you know the formula and how to plug into it. also, clearly state the margin of error.

Which sentence describes why polygon mnop is congruent to polygon jklp? a. polygon jklp maps to polygon mnop through a translation. b. polygon jklp maps to polygon mnop through a rotation. c. polygon jklp maps to polygon mnop through a dilation. d. polygon jklp maps to polygon mnop through a stretch.

Aquantity with an initial value of 3900 decays exponentially at a rate of 35% every hour. what is the value of the quantity after 0.5 days, to the nearest hundredth?