Solve y"-2y+26y= 0, y(0) = 2, y'(0) = -13 y(t) =

Solve y"+6y+10y= 0, y(0) = 4, y'(0) = 16 y(t) =

Solve y"-6y+9y= 0, y(0) = -5, y(0) = -10 y(t) =

Question 2 The data below provides the battery life of thirty eight (38) motorcycle batteries. 100 83 83 105 110 81 114 99 101 105 78 115 74 96 106 89 94 81 106 91 93 86 79 103 94 108 113 100 117 120 77 93 93 85 76 89 78 88 680 a. Test the hypothesis that mean battery life is greater than 90. Use the 1% level of significance. b. Determine if the mean battery life is different from 80. Use the 10% level of significance. Show all steps for the hypothesis test c. Would your conlcusion in part (b) change at the 5% level of significance? | d. Confirm test results in part (b) using JASP. Note: All JASP input files and output tables should be provided

Suppose that 80% of athletes at a certain college graduate. You randomly select eight athletes. What’s the chance that at most 7 of them graduate?

Suppose that you flip a fair coin four times. What’s the chance of getting at least one head?

Suppose that the chance that an elementary student eats hot lunch is 30 percent. What’s the chance that, among 20 randomly selected students, between 6 and 8 students eat hot lunch (inclusive)?

Bob’s commuting times to work are varied. He makes it to work on time 80 percent of the time. On 12 randomly selected trips to work, what’s the chance that Bob makes it on time at least 10 times?

Your chance of winning a small prize in a scratch-off ticket is 10 percent. You buy five tickets. What’s the chance you will win at least one prize?