One can also use the laplace transform to solve a system of differential equations. take the transform of both equation, then solve for both x(s) and y (s) algebraically. to finish, find the inverse laplace transform of both. use this idea to find the solution to the following system: x' = 5x − 3yy' = 3x − 5yx(0) = 1, y(0) = 1

Find the constant of variation for the relation and use it to write an equation for the statement. then solve the equation.

Find the equation of a line whose slope is 2/5 and y- intercept is 2.write your answer in the form 1) ax+by+c=02) x/a+y/b=1

(20 points) a bank has been receiving complaints from real estate agents that their customers have been waiting too long for mortgage confirmations. the bank prides itself on its mortgage application process and decides to investigate the claims. the bank manager takes a random sample of 20 customers whose mortgage applications have been processed in the last 6 months and finds the following wait times (in days): 5, 7, 22, 4, 12, 9, 9, 14, 3, 6, 5, 15, 10, 17, 12, 10, 9, 4, 10, 13 assume that the random variable x measures the number of days a customer waits for mortgage processing at this bank, and assume that x is normally distributed. 2a. find the sample mean of this data (x ě…). 2b. find the sample variance of x. find the variance of x ě…. for (c), (d), and (e), use the appropriate t-distribution 2c. find the 90% confidence interval for the population mean (îľ). 2d. test the hypothesis that îľ is equal to 7 at the 95% confidence level. (should you do a one-tailed or two-tailed test here? ) 2e. what is the approximate p-value of this hypothesis?