Calculating Spiciness for 400 People: Jalapeno vs. Habanero

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To prepare dinners for 400 people using habanero peppers instead of jalapenos, the total required spiciness must be calculated. Each serving calls for 2 jalapenos, totaling 800 jalapenos, which equates to 3,200,000 SHU (800 jalapenos x 4000 SHU). Since one habanero has 300,000 SHU, the equivalent number of habaneros needed is approximately 11 (3,200,000 SHU ÷ 300,000 SHU). Therefore, to achieve the same spiciness level, about 11 habanero peppers should be used for the 400 dinners. This substitution ensures the desired heat level is maintained in the dish.
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Homework Statement


You are to fix dinners for 400 people at a convention of Mexican food fans. Your recipe calls for 2 jalapeno peppers per serving (one serving per person). However, you have only habanero peppers on hand. the spiciness of peppers is measured in terms of the scoville heat unit (SHU). On average, one jalapeno pepper has a spiciness of 4000 SHU and one habanero pepper has a spiciness of 300000 SHU. To get the desired spiciness, how many habanero peppers should you substitute for the jalapeno peppers in the recipe for the 400 dinners?


Homework Equations


Show me. I really don't know.


The Attempt at a Solution

 
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Look up some methods in dimensional analysis and see if that helps.
 
^^ U don't need to check up dimensional analysis, this is a common sense question.
 
Think of the relative spiciness of the pepper's to each other.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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