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16.04.2020 •
Mathematics
What is the square root of 7? Decimal form please. Person with the most decimal places gets brainliest.
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Ответ:
2.64575131106 2.6457513110645905905016157536392604257102591830824501803683344592010688232302
83627760392886474543610615064578338497463095743529888627214784427390555880107722
71715072972832389229968959486508726070097805420372382802371594110034193911600157
85255963059457410351523968027164073737990740415815199044034743194536713997305970
05051399692237545616097119027378154991633288287704000657570674651963497752083793
81811461309087647378659562433057994798128163230705483650107715617946361191553454
53647749482059309049484983403398900210478616673327950369392462257170537164925787
54832290732492671346980298949908037748251109227895568897919808814834090831685251
33535829539172211770714414974576907081989444441458972284741400303502353203719487
07382629318519364090832280596462783761021959794197089096354695861341181793067816
21360849101677835321255633463490021898146042255929503669562418692737327715022087
52309966469813203212818945478568020950635962446628550076190504139350447437123488
52233277362510045059621080672334698120004300514490251206257311759115423194459672
60497833404344683725636178255048160879406205511486397833055016369470076387773745
19511658095220474202064982102444056001996590904100285534069110102261166807200774
83070332613842826296809502470794656496344336830519708820348050486447262317930876
95722489377521119788376007845603903658809421599292501057753682356001720074065236
92473209967419778002535708540617794442886681589731184938101638162073015642647016
29841099690071341323798188477647769954391111945967670336972452475367740100245826
51593077528163005479339717508017899520565284447796194304512502890432970610508746
04492966897542257133380633247034508888234275409806214511439553803393190705392738
14520604335238180389333294731479058055670704161068722878104529957696633035133295
04704245502510500789645502552271857923370921821991843932537781386785650143790894
13002099040860186605228131329821735251716419633617853080179022873400337109527257
36428650922035916343820273976336550966714177816292894279884853951076819102168116
99677176780863793410667897509217050421558644370687652934899322442240273649792906
66842070305782257110537944215790013280304078494579431518120466309284152592404683
65282802722458530778415894238973955590959563491357495109757674781975590533726939
36521431268222909570986506137179452721677198255442288046052307455488310813325041
49932783468182066583447383366862454456169497251774270254688591746231942309355060
38899235355634465872922507362228284298215287903623847595555861643755472027361518
00826144981691174794610631845652307625691344410868551999982851633960745717970829
72776495645142655658205126240305961633868338746134237463526431296594527010213721
72174899143552932049575097114259427207988929665230498875939525378121455723193310
30690840194942118708515205734116214105775416917245804962369512932926647583857193
34312550616097509003957512063487575979549295499224726634074018815634940531052960
4465875564620943Step-by-step explanation:
Ответ:
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Miguel is a golfer, and he plays on the same course each week. The following table shows the probability distribution for his score on one particular hole, known as the Water Hole.
Score 3 4 5 6 7
Probability 0.15 0.40 0.25 0.15 0.05
Let the random variable X represent Miguel’s score on the Water Hole. In golf, lower scores are better.
(a) Suppose one of Miguel’s scores from the Water Hole is selected at random. What is the probability that Miguel’s score on the Water Hole is at most 5 ? Show your work.
(b) Calculate and interpret the expected value of X . Show your work.
A potential issue with the long hit is that the ball might land in the water, which is not a good outcome. Miguel thinks that if the long hit is successful, his expected value improves to 4.2. However, if the long hit fails and the ball lands in the water, his expected value would be worse and increases to 5.4.
c) Suppose the probability of a successful long hit is 0.4. Which approach, the short hit or long hit, is better in terms of improving the expected value of the score?
(d) Let p represent the probability of a successful long hit. What values of p will make the long hit better than the short hit in terms of improving the expected value of the score? Explain your reasoning.
a) 80%
b) 4.55
c) 4.92
d) P > 0.7083
Step-by-step explanation:
Score | Probability
3 | 0.15
4 | 0.40
5 | 0.25
6 | 0.15
7 | 0.05
Let the random variable X represents Miguel’s score on the Water Hole.
a) What is the probability that Miguel’s score on the Water Hole is at most 5 ?
At most 5 means scores which are equal or less than 5
P(at most 5) = P(X ≤ 5) = P(X = 3) + P(X = 4) + P(X = 5)
P(X ≤ 5) = 0.15 + 0.40 + 0.25
P(X ≤ 5) = 0.80
P(X ≤ 5) = 80%
Therefore, there is 80% chance that Miguel’s score on the Water Hole is at most 5.
(b) Calculate and interpret the expected value of X.
The expected value of random variable X is given by
E(X) = X₃P₃ + X₄P₄ + X₅P₅ + X₆P₆ + X₇P₇
E(X) = 3*0.15 + 4*0.40 + 5*0.25 + 6*0.15 + 7*0.05
E(X) = 0.45 + 1.6 + 1.25 + 0.9 + 0.35
E(X) = 4.55
Therefore, the expected value of 4.55 represents the average score of Miguel.
c) Suppose the probability of a successful long hit is 0.4. Which approach, the short hit or long hit, is better in terms of improving the expected value of the score?
The probability of a successful long hit is given by
P(Successful) = 0.40
The probability of a unsuccessful long hit is given by
P(Unsuccessful) = 1 - P(Successful)
P(Unsuccessful) = 1 - 0.40
P(Unsuccessful) = 0.60
The expected value of successful long hit is given by
E(Successful) = 4.2
The expected value of Unsuccessful long hit is given by
E(Unsuccessful) = 5.4
So, the expected value of long hit is,
E(long hit) = P(Successful)*E(Successful) + P(Unsuccessful)*E(Unsuccessful)
E(long hit) = 0.40*4.2 + 0.60*5.4
E(long hit) = 1.68 + 3.24
E(long hit) = 4.92
Since the expected value of long hit is 4.92 which is greater than the value of short hit obtained in part b that is 4.55, therefore, it is better to go for short hit rather than for long hit. (Note: lower expected score is better)
d) Let p represent the probability of a successful long hit. What values of p will make the long hit better than the short hit in terms of improving the expected value of the score?
The expected value of long hit is given by
E(long hit) = P(Successful)*E(Successful) + P(Unsuccessful)*E(Unsuccessful)
E(long hit) = P*4.2 + (1 - P)*5.4
We want to find the probability P that will make the long hit better than short hit
P*4.2 + (1 - P)*5.4 < 4.55
4.2P + 5.4 - 5.4P < 4.55
-1.2P + 5.4 < 4.55
-1.2P < -0.85
multiply both sides by -1
1.2P > 0.85
P > 0.85/1.2
P > 0.7083
Therefore, the probability of long hit must be greater than 0.7083 that will make the long hit better than the short hit in terms of improving the expected value of the score.