If the given solutions y⃗ 1(t)=[2e3t+4e−t3e3t+10e−t], y⃗ 2(t)=[−4e3t+2e−t−6e3t+5e−t]. form a fundamental set (i. e., linearly independent set) of solutions for the initial value problem y⃗ ′=[915−4−7]y⃗ , y⃗ (0)=[−30−55], impose the given initial condition and find the unique solution to the initial value problem. if the given solutions do not form a fundamental set, enter none in all of the answer blanks.

Hardest math question of all time can you solve the equation. check for extraneous solutions.9∣9-8x∣ = 2x+3

Ur environment is very sensitive to the amount of ozone in the upper atmosphere. the level of ozone normally found is 4.04.0 parts/million (ppm). a researcher believes that the current ozone level is not at a normal level. the mean of 2525 samples is 4.44.4 ppm with a standard deviation of 0.80.8. assume the population is normally distributed. a level of significance of 0.020.02 will be used. make the decision to reject or fail to reject the null hypothesis. answer tables

You just purchased two coins at a price of $670 each. because one of the coins is more collectible, you believe that its value will increase at a rate of 7.1 percent per year, while you believe the second coin will only increase at 6.5 percent per year. if you are correct, how much more will the first coin be worth in 15 years?