Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = e^5x and z = e^2x. think of the corresponding vector solutions y1 and y2 and use the wronskian to show that the solutions are linearly independent wronskian = det [ ] = these solutions are linearly independent because the wronskian is [ ] choose for all x.

Students at a high school were asked about their favorite outdoor activity. the results are shown in the two-way frequency table below. fishing camping canoeing skiing total boys 36 44 13 25 118 girls 34 37 22 20 113 total 70 81 35 45 231 select all the statements that are true based on the given table. more girls chose camping as their favorite outdoor activity than boys. more girls chose canoeing as their favorite outdoor activity than those who chose skiing. more boys chose skiing as their favorite outdoor activity than girls. there were more boys surveyed than girls. twice as many students chose canoeing as their favorite outdoor activity than those who chose fishing. more students chose camping as their favorite outdoor activity than the combined number of students who chose canoeing or skiing.