GingerAle

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Solution:

$V = \pi * r^2 * h \pm \text {(error)}\\ \small \text {For this equation, the easiest method is to calculate each error as a decimal and }\\ \small \text {then use the sum of the decimals to calculate the error range.}\\ \large \text { }\\ \text {Gauss Error Function } \small \text { (uncertainties in decimal).}\\ r= 10 cm \pm 0.03\\ r_{error} = (2)\frac{0.03}{10} = 0.006\\ h= 20 cm \pm 0.05\\ h_{error} = \frac{0.05}{20} = 0.003\\ \small \text{sum of errors } = 0.006+0.003 = 0.009\\ V_{error} = 0.009 (6283.18) = \pm 56.54cm^3 \\ \large \text { }\\ V= \pi * 10^2 * 20 = 6283cm^3 \pm 56.54cm^3 \, | \,\small \text{68% confidence interval}\\ 6226.6cm^3 \leq V \leq 6339.7cm^3 \, | \,\small \text{68% confidence interval}\\ $

For more information see:

Rom, the RHS your equation was correct; it’s the LHS (formula) that has the error.

$E[X] = \underbrace {\sum \limits_{k=0}^3 k \cdot P[k]}_{LHS}=   \frac{57}{203} + 2 \cdot \frac{95}{203} + 3 \cdot \frac{45}{203} + 4 \cdot \frac{6}{203} = 2\\ $

The general formula for expectation:

${E} [X]=\sum \limits _{i=1}^{k}x_{i} \cdot p_{i} ,|, \small \text{Where (k) is the total number of events, and (i) is its index, multiplied by its probability.}$

You (intuitively) corrected for this on the RHS. I assume the different use of the (k) variable derailed your intent. In the moment, we intellectually know that while every kiss begins with (k), not every kiss is the same. But... it’s easier to analyze that after the fact, though. 

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For this question, it’s easy to verify that two (2) is the expected number of juniors in the committee: The 20 juniors represent (2/3) of the total sample space of 30.  (2/3) of (a random sample of) three (3) = 2; the expected number of juniors.

GA

To be fair, the number of persons in the set must be a divisor of 28.

The divisors of 28 are {1, 2, 4, 7, 14, 28}

One of these divisors is a match on the multiple choice list.

GA

History may have been very different for you, if you were named Melody.

In the many universes (theory), where you were named Melody, you are, instead of an engineer, an opera singer –probably a baritone in most universes, but a tenor in some of the others.   In the universes where you cannot sing, then you may be a bouncer for the MMA, ejecting aggressive troublemakers who breach ringside security perimeters.  This, adapted as a theory from the Shel Silverstine song, "A Boy Named Sue," made famous by Johnny Cash.

The song and this theory aside, the real boy named Sue -- Sue Hicks, whose name inspired the song, was a famed jurist; most notably as a prosecutor in the Scope’s Monkey Trial.  So in a universe not too far removed from this one, there is the Honorable Melody Rom who presides over murder cases and solves physics problems in his spare time. 

GA

A few years ago, I met at a male student at university named Ginger Shay Tang.  His family immigrated to America from China when he was a young child, and they adopted Americanized, English names based on the Chinese meaning of their Asian names.  He was born (Tang) Jiāng Jíwén, which translates to Ginger Shay, both of which are typically female names. His family, at the time, was unaware of the gender connotation, but neither they nor he ever considered changing his name. 

BTW, his wife’s name is Mary Ann. (No kidding.)  So, he actually had an answer for the ever importunate question, directed to all persons named Ginger: “Where’s Mary Ann? ...”  His answer compelled a follow-up question, asking if Gilligan might be the name for their firstborn, proving there is never an escape from fifty-year-old pop culture. 

GA

Sorry EP. I just did the calculation and I can see that you have the same result as I do.

$GS = \sqrt{TAS^2 - {V_C}^2 + {V_W}^2 + 2 \cdot \sqrt{TAS^2 - {V_C}^2}\cdot V_W \cdot cos(\Phi)}\\ \\ \text{ }\\ \sqrt{470^2 - 120^2 +  120^2 + 2 \cdot \sqrt{470^2 - 120^2}\cdot 120 \cdot cos(315)}  \approx 566.3\\$

Site calculator input:

a=475; v=120; w=120; t=315; sqrt(a^2 – (v)^2 + (w)^2 + 2 *\sqrt(a^2 - v^2)*w * cos(t))

I only glanced at your work and when I saw this:

 ...the ascending speed has nothing to do with the ground speed (This is true, but it does affect airspeed, and airspeed is used to calculate ground speed.)

and I just assumed you’d not corrected for the vertical component.

I’ll be drop-kicking my cat into next week for this screw-up. I need to figure out the proper temporal launching vector, else a week later he’ll return to normal time, landing on my head with claws fully extended for braking. My dog thinks it’s quite funny!

Do you have any ideas for a temporal launching vector? There may not be one ... this just might be temporal karma. 

GA

EmeraldWonder, only one of the questions is correctly answered.

Where did you learned to bullshit so affirmatively?

Yes you are in fact correct. When something is normally distributed, it means that the amount is a very common continuous probability distribution. The first three cannot be determined and it is not naturally distributed.

While the last one is something that is measured to be distributed correctly.

Did you learn this naturally or were you mentored by a professional bullshitter?  Whatever the case, you are good at it. That’s for sure!

Note to Admin: Please bring the atomic-powered sewage treatment plants online. It’s getting deep, here! 

In the mean time, I need a heavy-duty pair of hip boots...and a new shovel ...an assortment of flowering plants ...

GA

My dog just pointed out to my cat that the wind direction is presented (unconventionally) as a bearing, and not as a source, making it a partial tail wind.  EP’s solution would be correct if the plane was not ascending.   

GA