The traditional Pythagorean developed by Bill James used an exponent of 2 for baseball and we’ll use this exponent. In the 2023 season, the Reds scored 783 runs and allowed 821 runs.  Let’s assume the lineup as constructed would repeat this output next year. Suppose the Reds had their choice of 2 players: 1) Cody Bellinger: accounted for 15 more runs than an average player due to his batting and baserunning and PREVENTED opponents from scoring 7 more run than an average fielder would have (i.e., he increases runs scored by 15 and DECREASES runs allowed by 7) 2) Blake Snell: allowed 20 fewer runs than an average pitcher and has no effect on the batting as the pitcher spot doesn’t hit.   What would the Pythagorean predict as the win% for the Reds if they replace an average player with Bellinger? Report your answer as a decimal to 4 places: i.e., 20.34% should be entered as .2034  

How would you write constraint 4?

The traditional Pythagorean developed by Bill James used an exponent of 2 for baseball and we’ll use this exponent. In the 2023 season, the Reds scored 783 runs and allowed 821 runs.  Let’s assume the lineup as constructed would repeat this output next year. Suppose the Reds had their choice of 2 players: 1) Cody Bellinger: accounted for 15 more runs than an average player due to his batting and baserunning and PREVENTED opponents from scoring 7 more run than an average fielder would have (i.e., he increases runs scored by 15 and DECREASES runs allowed by 7) 2) Blake Snell: allowed 20 fewer runs than an average pitcher and has no effect on the batting as the pitcher spot doesn’t hit.   What would the Pythagorean predict as the win% for the Reds if they replace an average player with Snell? Report your answer as a decimal to 4 places: i.e., 20.34% should be entered as .2034

The Ohio State Baseball team is looking at a few promotions to enhance attendance.  Unfortunately, weather can keep people away regardless of the pull of a bobblehead.  Below, you can find the expected profit from various promotion/weather combos (remember, promotions cost money that can’t be recouped if the tickets aren’t sold).   Weather   Very Hot yet Sunny Comfortable Rainy No Promotion $15,000 $20,000 $10,000 Bobblehead giveaway $25,000 $35,000 $0 Dime-a-dog $30,000 $30,000 $1,000 Kid’s free $20,000 $25,000 $2,000 The weatherman says there is a 25% chance of being very hot and sunny, a 35% chance of being comfortable, and a 40% chance of rain. The best strategy based on expected value of profit is with expected value of  

You have 1 ml of a drug and need to create a 1:20 dilution before administering this drug to your rat. How many mls of sterile saline should you use to create this dilution? 

The temperature in the room is 860 F. What is this temperature in 0C?

What is the term for the extent of cancer spread assessed during diagnosis?

Who is considered the father of nuclear medicine?

In the metric system, which of the following units is the base unit for distance?

What is a primary consideration when planning radiation therapy to minimize damage to normal tissues?