Nt) consider the two dimensional subspace u of r3 spanned by the set {u1,u2} where u1=⎡⎣⎢3−2−2⎤⎦⎥,u2=⎡⎣⎢690⎤⎦⎥. the orthogonal complement v=u⊥ of uϵr3 is the one dimensional subspace of r3 such that every vector vϵv is orthogonal to every vector uϵu. in other words, u⋅v=0 for all uϵu and vϵv. find the first two components v1 and v2 of the vector vϵv for which
a. v3=1.
b. v1=
c. v2 =
d. v3=1.

Write the sine and cosine values of a, b, respectively, in the figure for (1) and (2) + explanation.

One of every 20 customers reports poor customer service on your company’s customer satisfaction survey. you have just created a new process that should cut the number of poor customer service complaints in half. what percentage of customers would you expect to report poor service after this process is implemented? 1.) 5% 2.) 10% 3.) 2% 4.) 2.5%

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )