Suppose we have three data instances in a two-dimensional space: (1, 1), (2, 2), and (3, 4). we want to perform pca on these points, so we construct a 2 × 2 matrix whose eigenvectors are the directions that best represent these three points. construct and report this matrix.

Olive's solar powered scooter travels at a rate of 30 miles per hour. what equation can she use to calculate her distance with relation to the time she traveled? h=hours m=miles 1. h=m+30 2. m=30h 3. m=h+30 4. h=30m

The school track has eight lanes. each lane is 1.25 meters wide. the arc at each end of the track is 180. the distance of the home straight and the radii for the arcs in the 1st 4 lanes are given. s=85m r1=36.5m r2=37.75m r3=39m r4=40.25m part one: find the radii of lanes 5 through 8 of the track. show your work. part two: if max ran around lane one, how far did he run? show your work and explain your solution. part three: max wants to run a total of three laps around the track, choose two additional lanes (2-8) for him to run and find the distance around those two lanes. show your work and round to the hundredths. part 4: based on your lane choices in part three, what was the total distance max ran in the three laps around the track?

For the feasibility region shown below find the maximum value of the function p=3x+2y