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Regular singular point for differential equationx(x-2)²d²y/dx²+2(x-2)dy/dx+(x+3)y=0
Researchers studying people’s sense of smell devised a measure of smelling ability. A higher score on this scale means the subject can smell better. A random sample of 36 people (18 male and 18 female) were involved in the study. The average score for the males was 10 with a standard deviation of 3.4 and the average score for the females was 11 with a standard deviation of 2.7. Which of the following is the correct standard error for the test evaluating whether the males and females have differing smelling abilities, on average? Choose the closest answer.
this year (10 years after i took out my first loan) i check my loan balance. Only part of my payments have been going to pay down the loan; the rest has been going towards interest. I see that i still have $88,536 left to pay on my loan. My house is now valued at $160,000. How much of the original loan have i paid off?

Pull 5 cards from a standard deck, replacing and shuffling each time, and count the number of face cards.  Create probability distributions 

Set up one example question(also provide solutions) which falls ubder the following:
Level 1 : mathematical knowledge
Level 2 : Routin procedure( in a real life context)
Level 3 : complex procedure ( in real life context)
Level 4 : problem solving ( in real life context)
Time value—Annuities Marian Kirk wishes to select the better of two 5-year annuities, C and D. Annuity Cis an ordinary annuity of $2,500 per year for 5 years. Annuity D Is an annuity due of $2,200 per year for 5 years.
a. Find the future value of both annuities at the end of year 5, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest.
b. Use your findings in part a to indicate which annuity has the greater future value at the end of year 5 for both the (1) 10% and (2) 20% Interest rates.
c. shows the future value of ordinary and due through time line on the above solutions.

Out of 25 employees of a company, 5 are engineers. Three employees are selected at random for granting leave. What is the probability that (i) all the three are engineers?(ii) none of them is an engineer? (iii) at least one of them is an engineer? 

It is desired to filter a cell broth at a rate of 1700 liters/h on a rotary vacuum filter at a vacuum pressure of 70kPa. The cycle time for the drum will be 60 s, and the cake formation time (filtering time) will be 15 s. The broth to be filtered has a viscosity of 0.08 P and a cake solids (dry basis) per volume of filtrate of 10 g/l. From laboratory tests, the specific cake resistance has been determined to be 9 x 1010 cm/g. Determine the area of the filter that is required. The resistance of the filter can be neglected. 

 It is then desired to wash the product (antibiotic) out of the cake so that only 5% of the antibiotic in the cake is left after washing. The washing efficiency is 50%. Estimate the washing time per cycle that would be required. Assume that the filtered cake contains 70% water

A Family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 26 houses that sold in their neighborhood took an average time of 218 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 72 days.

a. What assumption regarding the population is necessary for making an interval estimate for the population mean?

b. Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood.

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