Consider dy dx = yx2, y(0) = 1. a) use runge-kutta (see above) with step sizes h = 1 and h = 1=2 to approximate y(1). b) use euler’s method with h = 1 and h = 1=2. c) solve exactly, find the exact value of y(1), and compare.

20+ ! come and answer quick! triangle mno is reflected over the x-axis and then translated up 4 and right 3. how can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position? a translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis. b translate the pre-image up 3 and right 4 and then reflect the figure over the x-axis. c translate the pre-image up 4 and left 3 and then reflect the figure over the y-axis. d translate the pre-image down 3 and right 4 and then reflect the figure over the x-axis.

(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?

Find the measurement of angle b in the following triangle