5) engineers want to design an auxiliary pipeline from a new natural gas source; 3 km from the main pipeline, to a power plant located 10 km down the main pipeline, in the least amount of time (see figure 1). if the oil can flow 10 km/hr along the auxiliary pipeline (ob) and 15 km/hr along the main pipeline (ap), where should the engineers join the auxiliary pipeline to the main pipeline to get the gas to p as soon as possible? figure 1 natural gas source power plant 10-x 10 5) (a) 0 (b) 0.89 (c) 0.97 (d) 6/n5 (e) none of the above

What is the reflection image of (5,-3) across the line y = -x?

Apsychology student wishes to investigate differences in political opinions between business majors and political science majors at her college. she randomly selects 100 students from the 260 business majors and 100 students from the 180 political science majors. does this sampling plan result in a simple random sample? why or why not? no, because each group of 200 students in the sample does not have the same chance of being selected. yes, because each group of 200 students in the sample has the same chance of being selected. no, because each individual student does not have an equal chance of being selected. yes, because each individual student has the same chance of being selected.

Complex numbers multiply √-4 * √-25 and show all intermediate steps. alternative notation is sqrt(-4) * sqrt(-25).