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You draw a card from a standard deck of cards, shuffle it back into the deck, draw a card again, shuffle it back into the deck, then draw a third card.  Find the probability of drawing at least one ace, rounded to three decimal places. The test will take an answer within 0.001

What is Washington’s Huntington-Hill number?  The test will take an answer within 1.

Given the apportionment as in Question 29-31, if a 16th teacher is to be assigned to a school, what school should receive the teacher using the Huntington-Hill method?

Find the probability the sum is 9 or larger, given that at least one die shows a 6, rounded to three decimal places. The test will take an answer within 0.001

Suppose the 15 teachers have been apportioned as follows: Washington: 8 Lincoln: 3 Roosevelt: 4 Calculate each school’s Huntington-Hill number, rounded to the nearest whole number.

You will roll a fair six-sided die.  You will win $4 is the roll is 5 or higher, and lose $3 if the roll is 4 or lower.  Find the expected value of the die roll to the nearest penny. [positiveornegative]$[15ones].[15tenths][15hundredths]

Study Design (Modified) Initiation of either metformin use or sulfonylurea use was defined as not having a history of use of either medication before entering the study and refilling at least 1 prescription within 60 days after the end of the supply of the first prescription (30). The date of the first refill was denoted as the index date. We did not exclude the patients with type 2 diabetes who used other types of antidiabetic medication before the first prescription of either metformin or a sulfonylurea. Because metformin is contraindicated for patients with severe chronic kidney disease (31), we excluded persons with severe chronic kidney disease (30), defined as an estimated glomerular filtration rate less than 30 mL/minute/1.73 m2 on at least 2 occasions more than 90 days apart or at least 1 Read code for advanced chronic kidney disease (32). In addition, we also excluded persons who had a history of VTE before the index date or who had no general practitioner visit or specialist referral within 1 year before the index date. Assessment of outcomes (Modified) The primary outcome of interest was a diagnosis of incident VTE (the combined endpoint of PE and DVT), with secondary outcomes of PE and DVT separately. An individual was considered to have developed the outcome of interest if he or she had a recorded Read code of PE or DVT and received anticoagulant treatment (36). Since VTE is potentially fatal and some individuals might have died before receiving an anticoagulant, we also considered participants to have developed VTE if they died within 1 month after a recorded code of PE or DVT but without a prescription for an anticoagulant or autopsy results (37). Note: Read codes are a thesaurus of terms, synonyms, and abbreviations used in medical practice in the UK and can be mapped on to ICD-10 codes. Results (Modified) Table 1 Metformin Sulfonylurea Total VTE 555 75 630 No VTE 116,917 13,760 130,677 Total 117,472 13,835 131,307 Question 1c: Using data from Table 1, calculate the appropriate crude relative measure of association comparing VTE among those using metformin and those using sulfonylurea. Show your formula in the free-text space provided. Round your final answer to two decimal places (0.00). 

Question 1g: Based on your calculations in Question 1f and the DAG below, what role does biological sex play in the relationship between metformin and VTE? Briefly justify your answer in the context of the question and provide a general conclusion based on your findings (2-4 sentences). Assume anything greater than a 1% change from the crude measure of association is a notable difference between measures. 

EC Question 2: 

Wu, K., Feskanich, D., Fuchs, C.S., Willett, W.C., Hollis, B.W. and Giovannucci, E.L., 2007. A nested case–control study of plasma 25-hydroxyvitamin D concentrations and risk of colorectal cancer. Journal of the National Cancer Institute, 99(14), pp.1120-1129. Study Purpose and Design (Modified): Wu et al conducted a study to investigate the relationship between low vitamin D status (25-hydroxyvitamin D level 90%) were confirmed through medical records; the remaining cases were confirmed by corroborating information on cancer diagnosis from participants (i.e., through consent forms sent by participants). Participants without cancer were identified by the year (same year) and month (within 1 month) of blood donation. Results (Modified) Vitamin D Status Colorectal Cancer No Colorectal Cancer Total Deficient 103 167 270 Not Deficient 76 189 265 Total 179 356 535 Question 2a. Calculate the appropriate relative measure of association for this study comparing those who are not vitamin D deficient (exposed) to those who are vitamin D deficient (unexposed). Show your calculations in the free-text space provided. Round your final answer to two decimal places (i.e., 0.00).