Ice cream usually comes in 1.5 quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some v
ariability in the amount of ice cream in a box as well as the amount of ice cream scooped out. We represent the amount of ice cream in the box as X and the amount scooped out as Y. Suppose these random variables have the following means, standard deviations, and variances. Mean SDVariance 48 0.25 0.0625 (a) An entire box of ice cream, plus 6 scoops from a second box is served at a party. How much ice cream do you expect to have been served at this party? fluid ounces 60 What is the standard deviation of the amount of ice cream served? (Round your answer to two decimal places.) 1.03 Xfluid ounces Enter a number (b) How much ice cream would you expect to be left in the box after scooping out one scoop of ice cream? That is, find the expected value of X - Y. fluid ounces What is the standard deviation of the amount left in the box? (Round your answer to two decimal places.) fluid ounces (c) Using the context of this exercise, explain why we add variances when we subtract one random variable from another Initially we do not know exactly how much ice cream is in the box, then we scoop out an unknown amount. Because we removed an unknown amount from a box where the amount of ice cream was unknown, we must add the variances to be confident of the difference when we subtract one unknown random variable from another unknown random variable Initially we do not know exactly how much ice cream is in the box, then we scoop out a known amount. Because we removed a known amount from a box where the amount of ice cream was unknown, we must add the variances to be confident of the difference when we subtract one known random variable from another unknown random variable. Initially we know exactly how much ice cream is in the box, then we scoop out an unknown amount. Because we removed an unknown amount, we must add the variances to be confident of the difference when we subtract one unknown random variable from another known random variable Initially we do know exactly how much ice cream is in the box, then we scoop out a known amount. Because we removed a known amount from a box where the amount of ice cream was known, we must add the variances to be confident of the difference when we subtract one known random variable from another known random variable
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Ok i apologise for the messy working but I'll try and explain my attempt at logic
Also note i ignore any air resistance for this.
First i wrote the two equations I'd most likely need for this situation, the kinetic energy equation and the potential energy equation.
Because the energy right at the top of the swing motion is equal to the energy right in the "bottom" of the swing's motion (due to conservation of energy), i made the kinetic energy equal to the potential energy as indicated by Ek = Ep.
I also noted the "initial" and "final" height of the swing with hi and hf respectively.
So initially looking at this i thought, what the heck, there's no mass. Then i figured that using the conservation of energy law i could take the mass value from the Ek equation and use it in the Ep equation. So what i did was take the Ek equation and rearranged it for m as you can hopefully see. Then i substituted the rearranged Ek equation into the Ep equation.
So then the equation reads something like Ep = (rearranged Ek equation for m) × g (which is -9.81) × change in height (hf - hi).
Then i simplify the equation a little. When i multiply both sides by v^2 i can clearly see that there is one E on each side (at that stage i don't need to clarify which type of energy it is because Ek = Ep so they're just the same anyway). So i just canceled them out and square rooted both sides.
The answer i got was that the max velocity would be 4.85m/s 3sf, assuming no losses (eg energy lost to friction).
I do hope I'm right and i suppose it's better than a blank piece of paper good luck my dude xx
