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safereturndoubtful · 2 years

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Day 78 - at Storvatnet Lake, Dovrefjell-Sunndalsfjell National Park

Late last night, after I the 11.30 edition of The Papers on BBC World and while I was reading a suitably ghostly tale (it is October..) the dog indicated he wanted to go outside. He occasionally does this with no problem. On return last night though, no sooner was he inside than he was afflicted with a sneezing fit. This continued for several hours, and not surprisingly, led to him losing some blood as well. I guess, rare for this time of year, he had sniffed (hence his surname) pollen or something from the lichen that had caught inside his nose. Gradually it lessened, but still every hour or so it woke him, and me, with another series of 50 or more violent sneezes.

It had not abated by morning, and I had my plan, conceived while restless, to take him to the vet for some sort of sedative, in Oppdal. I dreaded to think of the cost.

However, after breakfast, it cleared a bit further, but still not completely.

10 am and decision time. The vet in Oppdal closed at midday, so it was necessary to leave now, or not. I gambled on the latter, and we headed to the hill.

After a few stream and lake dips it cleared further. And by the time we returned, it was the occasional, more like normal, sneeze.

The snow level had shifted up a few metres today which gave me the confidence to head up onto the plateau to the west side, at about 1100 metres, of the lakes from which peaks protrude, like Rastu at 1673 metres, and Seterfjellet at 1812 metres. The wet snow is not appealing at present.

It was a fine morning, about 5C with a gusty wind making it feel a few degrees lower. The ascent alongside the Svou river waterfall was fine, lots of it on bare rock, but at the top we caught a heavy shower. The descent was not going to be east anyway, but the rain made it as if liquid soap had been dowsed on it. So it was steady going, but there were wonderful views, and the chance for some good photos.

It had been a slow 8 kilometre in almost 4 hours. Though it’s frustrating with my neurological condition, there’s really no hurry. I would however, like a full day out, but I’m not up to that just yet. One reason for the slowness is my concern over slipping on descent, which is, I tell myself, more sensible, alone on the hill with little or no cell phone coverage.

We were back at the van for a late lunch, and a restful afternoon catching up on my review blogs. Two very interesting books today, The Saint Perpetuus Club of Buenos Aires by Eric Stener Carlson and A Hair Divides by Claude Houghton from 1930. Both reviews over at GR.

Film wise, I review very briefly only, the Javanese folk-horror I mentioned yesterday, and Sunset Boulevard, which I enjoyed (again) at the weekend…

Striking for me this time round, was it’s cynical treatment of Hollywood as a whole, in how it manages people like Norma, makes them stars then spits them into the garbage when they are no longer needed.

There’s lots of good performances, William Holden, his change of expression as he realises Norma is falling in love with him. But Swanson is incredible. There may have been a temptation to ham it up, but the madness just rears it’s head occasionally, and saves it all for the end when the last seen is terrifying.

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shophrvats · 2 years

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Sergio Ramos vodi svlačionicu Paris Saint-Germaina

Sergio Ramos ima sposobnost upravljanja svlačionicom momčadi, dokazao se u bivšoj momčadi. Bilo da se radi o odnosima u igri ili među igračima, potrebno je da igrač zadrži olakšanje. Sergio Ramos prošlog se ljeta oprostio od Real Madrid nogometni dres s brojem 4, a uprava Paris Saint-Germaina ove je godine cijenila njegove liderske kvalitete.

Igra Paris Saint-Germaina bila je vrlo uzbudljiva ove sezone, a momčad je pobjeđivala u posljednjim kolima. Mnogi obožavatelji primijetili su da Neymar i Lionel Messi rastu u samopouzdanju, a kombinacija između njih kao da se vratila u dane FC Barcelone. S povratkom Kyliana Mbappéa u momčad za treće kolo, pobjeda Paris Saint-Germaina bila je puna dvojbi. Nakon utakmice najozbiljnija rasprava među navijačima bio je Kylian Mbappé, ključno je što je odustao od napada tijekom utakmice. Uprava Paris Saint-Germaina i glavni trener Christophe Galtier bili su bijesni, a Kylian Mbappé nije bio sretan tijekom cijele utakmice. Glavni trener Paris Saint-Germaina Christophe Galtier, kako bi smirio odnos među igračima, i on i uprava počeli su cijeniti sposobnosti Sergija Ramosa. Sergio Ramos nije imao neprijateljski odnos s ostalim igračima u momčadi, a postao je najbolji igrač za upravljanje svlačionicom.

Mnogi navijači La Lige ne mogu zamisliti koliko se često Sergio Ramos i Lionel Messi sada grle i slave. Svi su se oprostili od kapetana i postali su dobri suigrači. Ove sezone, druga sezona Sergia Ramosa i Lionela Messija u Paris Saint-Germain nogometni dres, nastoje napraviti iskorak u Ligue 1. Sergio Ramos također potiče pozitivnu formu svojih suigrača, koji također trebaju osvojiti UEFA Ligu prvaka.

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ukopcavanje · 5 years

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Binomna verovatnoća IV

Koliki je najverovatniji broj dobijenih šestica u 20 bacanja kocke za igru? Kolika je verovatnoća tog najverovatnijeg događaja?

Neka je P šansa da padne šestica u jednom eksperimentu, P = \( \frac{1}{6} \).

Q je šansa da ne padne šestica u jednom eksperimentu, Q = 1 - P = \( \frac{5}{6} \).

\[P\left(k\right)=\binom{n}{k}\times P^{k} \times Q^{n-k}=\binom{20}{k}\times \left(\frac{1}{6}\right)^{k} \times \left(\frac{5}{6}\right)^{20-k}, k=\left\{1,2,...20\right\}\]

Pokušaćemo da odredimo do koje vrednosti k verovatnoće rastu, odnosno za koje sve k važi da je P(k) manje ili jednako od P(k+1)?

\[\binom{20}{k}\times \left(\frac{1}{6}\right)^{k} \times \left(\frac{5}{6}\right)^{20-k}\leq\binom{20}{k+1}\times \left(\frac{1}{6}\right)^{k+1} \times \left(\frac{5}{6}\right)^{20-\left(k+1\right)}\] \[\frac{20!}{k!\times\left(20-k\right)!}\times\left(\frac{1}{6}\right)^{k} \times \left(\frac{5}{6}\right)^{20-k}\leq\frac{20!}{\left(k+1\right)!\times\left(20-k-1\right)!}\times\left(\frac{1}{6}\right)^{k+1} \times \left(\frac{5}{6}\right)^{20-\left(k+1\right)}\] \[\frac{1}{20-k}\times\frac{5}{6}\leq\frac{1}{k+1}\times\frac{1}{6}\] \[5\times(k+1)\leq20-k\] \[5\times k+5\leq20-k\] \[6\times k\leq15\] \[k\leq\frac{5}{2}\]

Dobijamo da je k=2, pa treba da važi P(k) manje od P(k+1), odnosno P(2) manje od P(3). Proverimo.

\[P\left(2\right)=\binom{20}{2}\times \left(\frac{1}{6}\right)^{2} \times \left(\frac{5}{6}\right)^{18}\approx0.19824\] \[P\left(3\right)=\binom{20}{3}\times \left(\frac{1}{6}\right)^{3} \times \left(\frac{5}{6}\right)^{17}\approx0.23789\]

Nakon vrednosti k=3, verovatnoće dobijanja k šestica u 20 bacanja kocke opadaju. Najverovatnije je, dakle, dobiti 3 šestice.

Rešenje predložila učenica: Teodora Đukić. Škola: Matematička gimnazija Kraljevo. Odeljenje: IV-7. Koordinator Ukop(č)avanja: Jovan Pavlović. ✓ pAyPAL.ME DoNiRAJ BLoG → ✓ REDBuBBLE sHop / izLoG → ✓ pHoTocRowD FoToGRAF → ✓ FAcEBook sTRANicA → ✓ piNTEREsT TABLA → Ilustracija: Vera Molnar [France] (b 1924) - 'Sainte-Victoire Border Line', 2018. Pigment printing on Canson paper 310g (150 x 50 cm).

#matematika #verovatnoća #binomna verovatnoća #vera molnar

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