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Recent problems solved by 'stanbon'
stanbon answered: 57239 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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41130..41159 , 41160..41189 , 41190..41219 , 41220..41249 , 41250..41279 , 41280..41309 , 41310..41339 , 41340..41369 , 41370..41399 , 41400..41429 , 41430..41459 , 41460..41489 , 41490..41519 , 41520..41549 , 41550..41579 , 41580..41609 , 41610..41639 , 41640..41669 , 41670..41699 , 41700..41729 , 41730..41759 , 41760..41789 , 41790..41819 , 41820..41849 , 41850..41879 , 41880..41909 , 41910..41939 , 41940..41969 , 41970..41999 , 42000..42029 , 42030..42059 , 42060..42089 , 42090..42119 , 42120..42149 , 42150..42179 , 42180..42209 , 42210..42239 , 42240..42269 , 42270..42299 , 42300..42329 , 42330..42359 , 42360..42389 , 42390..42419 , 42420..42449 , 42450..42479 , 42480..42509 , 42510..42539 , 42540..42569 , 42570..42599 , 42600..42629 , 42630..42659 , 42660..42689 , 42690..42719 , 42720..42749 , 42750..42779 , 42780..42809 , 42810..42839 , 42840..42869 , 42870..42899 , 42900..42929 , 42930..42959 , 42960..42989 , 42990..43019 , 43020..43049 , 43050..43079 , 43080..43109 , 43110..43139 , 43140..43169 , 43170..43199 , 43200..43229 , 43230..43259 , 43260..43289 , 43290..43319 , 43320..43349 , 43350..43379 , 43380..43409 , 43410..43439 , 43440..43469 , 43470..43499 , 43500..43529 , 43530..43559 , 43560..43589 , 43590..43619 , 43620..43649 , 43650..43679 , 43680..43709 , 43710..43739 , 43740..43769 , 43770..43799 , 43800..43829 , 43830..43859 , 43860..43889 , 43890..43919 , 43920..43949 , 43950..43979 , 43980..44009 , 44010..44039 , 44040..44069 , 44070..44099 , 44100..44129 , 44130..44159 , 44160..44189 , 44190..44219 , 44220..44249 , 44250..44279 , 44280..44309 , 44310..44339 , 44340..44369 , 44370..44399 , 44400..44429 , 44430..44459 , 44460..44489 , 44490..44519 , 44520..44549 , 44550..44579 , 44580..44609 , 44610..44639 , 44640..44669 , 44670..44699 , 44700..44729 , 44730..44759 , 44760..44789 , 44790..44819 , 44820..44849 , 44850..44879 , 44880..44909 , 44910..44939 , 44940..44969 , 44970..44999 , 45000..45029 , 45030..45059 , 45060..45089 , 45090..45119 , 45120..45149 , 45150..45179 , 45180..45209 , 45210..45239 , 45240..45269 , 45270..45299 , 45300..45329 , 45330..45359 , 45360..45389 , 45390..45419 , 45420..45449 , 45450..45479 , 45480..45509 , 45510..45539 , 45540..45569 , 45570..45599 , 45600..45629 , 45630..45659 , 45660..45689 , 45690..45719 , 45720..45749 , 45750..45779 , 45780..45809 , 45810..45839 , 45840..45869 , 45870..45899 , 45900..45929 , 45930..45959 , 45960..45989 , 45990..46019 , 46020..46049 , 46050..46079 , 46080..46109 , 46110..46139 , 46140..46169 , 46170..46199 , 46200..46229 , 46230..46259 , 46260..46289 , 46290..46319 , 46320..46349 , 46350..46379 , 46380..46409 , 46410..46439 , 46440..46469 , 46470..46499 , 46500..46529 , 46530..46559 , 46560..46589 , 46590..46619 , 46620..46649 , 46650..46679 , 46680..46709 , 46710..46739 , 46740..46769 , 46770..46799 , 46800..46829 , 46830..46859 , 46860..46889 , 46890..46919 , 46920..46949 , 46950..46979 , 46980..47009 , 47010..47039 , 47040..47069 , 47070..47099 , 47100..47129 , 47130..47159 , 47160..47189 , 47190..47219 , 47220..47249 , 47250..47279 , 47280..47309 , 47310..47339 , 47340..47369 , 47370..47399 , 47400..47429 , 47430..47459 , 47460..47489 , 47490..47519 , 47520..47549 , 47550..47579 , 47580..47609 , 47610..47639 , 47640..47669 , 47670..47699 , 47700..47729 , 47730..47759 , 47760..47789 , 47790..47819 , 47820..47849 , 47850..47879 , 47880..47909 , 47910..47939 , 47940..47969 , 47970..47999 , 48000..48029 , 48030..48059 , 48060..48089 , 48090..48119 , 48120..48149 , 48150..48179 , 48180..48209 , 48210..48239 , 48240..48269 , 48270..48299 , 48300..48329 , 48330..48359 , 48360..48389 , 48390..48419 , 48420..48449 , 48450..48479 , 48480..48509 , 48510..48539 , 48540..48569 , 48570..48599 , 48600..48629 , 48630..48659 , 48660..48689 , 48690..48719 , 48720..48749 , 48750..48779 , 48780..48809 , 48810..48839 , 48840..48869 , 48870..48899 , 48900..48929 , 48930..48959 , 48960..48989 , 48990..49019 , 49020..49049 , 49050..49079 , 49080..49109 , 49110..49139 , 49140..49169 , 49170..49199 , 49200..49229 , 49230..49259 , 49260..49289 , 49290..49319 , 49320..49349 , 49350..49379 , 49380..49409 , 49410..49439 , 49440..49469 , 49470..49499 , 49500..49529 , 49530..49559 , 49560..49589 , 49590..49619 , 49620..49649 , 49650..49679 , 49680..49709 , 49710..49739 , 49740..49769 , 49770..49799 , 49800..49829 , 49830..49859 , 49860..49889 , 49890..49919 , 49920..49949 , 49950..49979 , 49980..50009 , 50010..50039 , 50040..50069 , 50070..50099 , 50100..50129 , 50130..50159 , 50160..50189 , 50190..50219 , 50220..50249 , 50250..50279 , 50280..50309 , 50310..50339 , 50340..50369 , 50370..50399 , 50400..50429 , 50430..50459 , 50460..50489 , 50490..50519 , 50520..50549 , 50550..50579 , 50580..50609 , 50610..50639 , 50640..50669 , 50670..50699 , 50700..50729 , 50730..50759 , 50760..50789 , 50790..50819 , 50820..50849 , 50850..50879 , 50880..50909 , 50910..50939 , 50940..50969 , 50970..50999 , 51000..51029 , 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53010..53039 , 53040..53069 , 53070..53099 , 53100..53129 , 53130..53159 , 53160..53189 , 53190..53219 , 53220..53249 , 53250..53279 , 53280..53309 , 53310..53339 , 53340..53369 , 53370..53399 , 53400..53429 , 53430..53459 , 53460..53489 , 53490..53519 , 53520..53549 , 53550..53579 , 53580..53609 , 53610..53639 , 53640..53669 , 53670..53699 , 53700..53729 , 53730..53759 , 53760..53789 , 53790..53819 , 53820..53849 , 53850..53879 , 53880..53909 , 53910..53939 , 53940..53969 , 53970..53999 , 54000..54029 , 54030..54059 , 54060..54089 , 54090..54119 , 54120..54149 , 54150..54179 , 54180..54209 , 54210..54239 , 54240..54269 , 54270..54299 , 54300..54329 , 54330..54359 , 54360..54389 , 54390..54419 , 54420..54449 , 54450..54479 , 54480..54509 , 54510..54539 , 54540..54569 , 54570..54599 , 54600..54629 , 54630..54659 , 54660..54689 , 54690..54719 , 54720..54749 , 54750..54779 , 54780..54809 , 54810..54839 , 54840..54869 , 54870..54899 , 54900..54929 , 54930..54959 , 54960..54989 , 54990..55019 , 55020..55049 , 55050..55079 , 55080..55109 , 55110..55139 , 55140..55169 , 55170..55199 , 55200..55229 , 55230..55259 , 55260..55289 , 55290..55319 , 55320..55349 , 55350..55379 , 55380..55409 , 55410..55439 , 55440..55469 , 55470..55499 , 55500..55529 , 55530..55559 , 55560..55589 , 55590..55619 , 55620..55649 , 55650..55679 , 55680..55709 , 55710..55739 , 55740..55769 , 55770..55799 , 55800..55829 , 55830..55859 , 55860..55889 , 55890..55919 , 55920..55949 , 55950..55979 , 55980..56009 , 56010..56039 , 56040..56069 , 56070..56099 , 56100..56129 , 56130..56159 , 56160..56189 , 56190..56219 , 56220..56249 , 56250..56279 , 56280..56309 , 56310..56339 , 56340..56369 , 56370..56399 , 56400..56429 , 56430..56459 , 56460..56489 , 56490..56519 , 56520..56549 , 56550..56579 , 56580..56609 , 56610..56639 , 56640..56669 , 56670..56699 , 56700..56729 , 56730..56759 , 56760..56789 , 56790..56819 , 56820..56849 , 56850..56879 , 56880..56909 , 56910..56939 , 56940..56969 , 56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Nexttest/263931: Please help. I am so lost I have to pass this final. I have a few questions.
1. Graph on a number line where x is a real number. -5
I think the graph should look like, a hollow circle on -5 with a solid line going to 5 and the circle on 5 is filled in, is this correct?
2. Solve by elimination method.
4x + 5y= 5
8x + 10y= 10
a. The solution is _____
b. There are infinitely many solutions.
c. There is no solution.
3. Solve Using the multiplication principle.
-6x > 1/3
The solution set is {x|x_____ ______}
4. The equation y= -1777x + 27,153 can be used to predict the number y of gun deaths in the United Steates x years after 2000, that is, x=0 corresponds to 2000, x=2 corresponds to 2002, x=6 corresponds to 2006, and so on. Predict the number of gun deaths in 2006 and 2008. In what year will the number of gun deaths be 9383?
The predicted gun deaths in 2006 will be ________?
The predicted gun deaths in 2008 will be ________?
The predicted number of gun deaths will be 9383 in the year _____?
7. Solve using the multiplication principle. Don't forget to perform a checkl
-1/6x = -9/10
This is all for now I thank you all in advance.
Deborah
1 solutions
Answer 194427 by stanbon(57307)   on 2010-02-01 13:19:24 (Show Source):
You can put this solution on YOUR website!1. Graph on a number line where x is a real number. -5
I think the graph should look like, a hollow circle on -5 with a solid line going to 5 and the circle on 5 is filled in, is this correct?
Ans: Correct
----------------------------
2. Solve by elimination method.
4x + 5y= 5
8x + 10y= 10
-----
Multiply thru the 1st equation by 2 so the system becomes:
8x + 10y = 10
8x + 10y = 10
--
Subtract and you get 0 = 0
-----------
That means the two eqations are the same.
Every point on the line 4x+5y=5 is a solution.
a. The solution is (x,(-4/5)x+1)_____
b. There are infinitely many solutions.
c. There is no solution.
Ans: b
----------------------
3. Solve Using the multiplication principle.
-6x > 1/3
Multiply both sides by (-1/6) and remember to reverse the inequality sign.
(-1/6)(-6x) > (-1/6)(1/3)
x < (-1/18)
The solution set is {x|x< (-1/18})
==========================================
4. The equation y= -1777x + 27,153 can be used to predict the number y of gun deaths in the United Steates x years after 2000, that is, x=0 corresponds to 2000, x=2 corresponds to 2002, x=6 corresponds to 2006, and so on.
Predict the number of gun deaths in 2006 and 2008. In what year will the number of gun deaths be 9383?
d(6) = -1777(6) + 27,153 = 16,491
d(8) = -1777(8) + 27,153 = 12,937
---
9383 = -1777x + 27153
-1777x = -17770
x = 10
Year = 2010
------------------------------------------------
The predicted gun deaths in 2006 will be ________?
The predicted gun deaths in 2008 will be ________?
The predicted number of gun deaths will be 9383 in the year _____?
7. Solve using the multiplication principle. Don't forget to perform a checkl
-1/6x = -9/10
(-6)(-1/6)x = (-6)(-9/10)
x = 54/10
x = 27/5
Checking:
(-1/6)(27/5) = (-9/10)
(-27/30) = (-9/10)
(-9/10) = (-9/10)
=========================
Cheers,
Stan H.
|
Probability-and-statistics/263874: In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for the three vehicles?
Goliath Varmint Weasel
1,600 1,290 1,090
760 1,400 2,100
880 1,390 1,830
1,950 1,850 1,250
1,220 950 1,920
1 solutions
Answer 194424 by stanbon(57307) on 2010-02-01 12:58:02 (Show Source):
You can put this solution on YOUR website!In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for the three vehicles?
Goliath Varmint Weasel
1,600 1,290 1,090
760 1,400 2,100
880 1,390 1,830
1,950 1,850 1,250
1,220 950 1,920
--------------
Ho: u1=u2=u3
Ha: At least one of the means is different
---------------
I ran an ANOVA program on my TI calculator to get:
ts: F = 0.93665..
p-value: 0.4188
df=2
------------------
Conclusion:
Since the p-value is 41%, fail to reject Ho
Statistically, the means are the same for the three cars.
=====================================
Cheers,
Stan H.
|
Probability-and-statistics/263875: 7) In a test of the equality of two means, the variable of interest is the difference between the values of the observations, rather than the observations.
A.
True
B.
False
1 solutions
Answer 194423 by stanbon(57307) on 2010-02-01 12:50:30 (Show Source):
You can put this solution on YOUR website!In a test of the equality of two means, the variable of interest is the difference between the values of the observations, rather than the observations.
True
Cheers,
Stan H.
|
Probability-and-statistics/263705: the orange county department of public health tests water for contamination due to the presence of E.coli bacteria. To reduce laboratory costs, water samples from six public swimming areas are combined for one test, and further testing is done only if the combined sample fails. Based on past results, there is a 2% chance of finding E.coli bacteria in a public swimming area. Find tthe probbality that a combined sample from six public swimming area will reveal the presence of E.coli bacteria.
I have tried it so far.
Sample space=6
(2/100)*6= .12
I am not sure if its right, please any help?
1 solutions
Answer 194375 by stanbon(57307) on 2010-02-01 08:29:53 (Show Source):
You can put this solution on YOUR website!the orange county department of public health tests water for contamination due to the presence of E.coli bacteria.
To reduce laboratory costs, water samples from six public swimming areas are combined for one test, and further testing is done only if the combined sample fails.
Based on past results, there is a 2% chance of finding E.coli bacteria in a public swimming area.
Find the probality that a combined sample from six public swimming area will reveal the presence of E.coli bacteria.
-----------
If the six samples are combined and only one of them has
E.coli the combined sample will have show E.coli.
------------
P(show E. coli ) = 1 - P(none of the 6 samples has E.coli)
= 1 - (0.98)^6
= 1- 0.8858
= 0.1142
==========================================
Cheers,
Stan H.
============================
I have tried it so far.
Sample space=6
(2/100)*6= .12
I am not sure if its right, please any help?
|
Probability-and-statistics/263800: A box contains some green marbles and exactly four red marbles. The probability of selecting a red marble is x%. If the number of green marbles is doubled, the probability of selecting one of the four red marbles from the box is (x – 15)%. How many green marbles are in the box before the number of green marbles is doubled?
1 solutions
Answer 194371 by stanbon(57307) on 2010-02-01 07:57:26 (Show Source):
You can put this solution on YOUR website!A box contains some green marbles and exactly four red marbles. The probability of selecting a red marble is x%. If the number of green marbles is doubled, the probability of selecting one of the four red marbles from the box is (x – 15)%. How many green marbles are in the box before the number of green marbles is doubled?
----
Original setup
P(1 red) = 4/(g+4) = x/100
Then g + 4 = 4/x/100
g = (4/(x/100))-4
g = (400/x) -4
----------------------
New setup
P(1 red) = 4/(2g+4) = (x-15)/100
(2g+4) = 400/(x-15)
g+2 = 200/(x-15)
g = 200/(x-15) -2
----------------------------
Solve for "g":
(400/x) -4 = (200/(x-15) -2
Divide thru by 200 to get:
(2/x) - 2/100 = (1/(x-15) - 1/100
(2/x) - (1/(x-15) = 1/100
200(x-15) - 100x = x(x-15)
200x - 3000 - 100x = x^2-15x
x^2 -115x +3000 = 0
(x-75)(x-40) = 0
----------------------------
x is 75 or x = 40
Need to solve for "g"
g = 200/(x-15) -2
================================
If x = 75,
g = 200/(50) -2 = 2
If x = 40,
g = 200/25 - 2 = 6
---------------------------
Looks like original # of green is 2 or 6.
Hummmm!!!
---------------------------
Cheers,
Stan H.
----------------------------------
|
Probability-and-statistics/263759: Art works in a small retail store that sells widgets. Market research shows that red is, by far, the most popular color of widget, and that 38% of customers purchase red widgets. If Art selects 5 random customers and records the color of widget purchased, what is the probability that at least one of those customers purchased a red widget?
What I did was take .38 x .38= .1444 and then add .1444 to .38. I got .5244, then multiplied that by .38. I then added this new number to .38 and got .579272, I kept doing this until I got 0.6080468. I don't know if this is right so I need help.
1 solutions
Answer 194367 by stanbon(57307) on 2010-02-01 07:37:17 (Show Source):
You can put this solution on YOUR website!Art works in a small retail store that sells widgets. Market research shows that red is, by far, the most popular color of widget, and that 38% of customers purchase red widgets. If Art selects 5 random customers and records the color of widget purchased, what is the probability that at least one of those customers purchased a red widget?
-----
P(at least one of anything) = 1 - P(none of anything)
------------------------------
Your Problem:
P(none of the 5 purchased a red widget) = (0.62)^5 = 0.0916
---
So, P(at least one pruchased a red widget + 1 - 0.0916 = 0.9084
=========================================
Cheers,
Stan H.
What I did was take .38 x .38= .1444 and then add .1444 to .38. I got .5244, then multiplied that by .38. I then added this new number to .38 and got .579272, I kept doing this until I got 0.6080468. I don't know if this is right so I need help.
|
Polynomials-and-rational-expressions/263682: find all numbers for which the rational expression is undefined
(9)/(5v+4)
1 solutions
Answer 194304 by stanbon(57307) on 2010-01-31 21:04:35 (Show Source):
You can put this solution on YOUR website!find all numbers for which the rational expression is undefined
(9)/(5v+4)
----
The expression is undefined if the denominator is zero.
---
5v+4 = 0
v = -4/5
---------------
The expression is undefined if v = -4/5
===========================================
Cheers,
Stan H.
|
Exponential-and-logarithmic-functions/263685: what is the answer to (243) with an exponent of 2/5
1 solutions
Answer 194303 by stanbon(57307) on 2010-01-31 21:02:35 (Show Source):
You can put this solution on YOUR website!what is the answer to (243) with an exponent of 2/5
-----------------
(243)^(2/5) = ?
---
The 5 in the denominator means "take the 5th root".
The 2 in the numerator means "square".
------
Taking the 5th root first you get:
(243)^(2/5) = 3^2
Now squaring gives you
3^2 = 9
=========
Cheers,
Stan H.
|
Expressions-with-variables/263683: Solve using subtitution method
5x+3y = 80
2x+y = 30
1 solutions
Answer 194299 by stanbon(57307) on 2010-01-31 20:59:03 (Show Source):
You can put this solution on YOUR website!Solve using subtitution method
5x+3y = 80
2x+y = 30
----------------
Solve the 2nd equation equation for "y":
y = -2x+30
----
Substitute into the 1st equation and solve for "x":
5x + 3(-2x+30) = 80
-x + 90 = 80
x = 10
---
Since y = -2x+30, y = 10
================================
Cheers,
Stan H.
|
Graphs/263651: y < x+5
Which is not a point?
4 -4
-1 4
4 6
1 4
-3 1
And please explain how to do it (:
1 solutions
Answer 194298 by stanbon(57307) on 2010-01-31 20:54:25 (Show Source):
You can put this solution on YOUR website!y
---
You are asked to check the x/y values and
determine if they satisfy the inequality.
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Which is not a point of the inequality ?
Test 4 -4 : -4 < 4+5 ; true
Test -1 4 : 4 < -1+5 ; false
Test 4 6 ; 6 < 4 + 5; true
1 4 etc.
-3 1 etc.
And please explain how to do it (:
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Cheers,
Stan H.
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Probability-and-statistics/263636: The University of Metropolis requires its students to pass an examination in college-level mathematics before they can graduate. The students are given three chances to pass the exam; 61% pass it on their first attempt, 63% of those that take it a second time pass it then, and 42% of those that take it a third time pass it then.
What percent of the students are not allowed to graduate because of their performance on the exam? (Round the answer to the nearest whole number.)
1 solutions
Answer 194278 by stanbon(57307) on 2010-01-31 20:12:31 (Show Source):
You can put this solution on YOUR website!The students are given three chances to pass the exam;
Assume there are 1000 applicants.
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61% pass it on their first attempt,
That leaves 1000-610 = 390
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63% of those that take it a second time pass it then,
0.63*390 = 245.7
That leaves 390-245.7 = 144.3
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42% of those that take it a third time pass it then.
0.42*144.3 = 60.06
That leaaves 144.3-60.06 = 83.69 students who have not passed the test
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What percent of the students are not allowed to graduate because of their performance on the exam?
% = 83.69/1000 = 0.08360 = 8%
=============================================
If you start with "x" students
Percent that fail after three tests = x*0.39*0.37*0.58 = 0.0837 = 8%
(Round the answer to the nearest whole number.)
===================
Cheers,
Stan H.
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Geometry_Word_Problems/263610: An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 inches from each corner and turning up the edges. If the box is to hold 294 cubic inches, what should be the dimensions of the sheet metal?
1 solutions
Answer 194266 by stanbon(57307) on 2010-01-31 19:44:47 (Show Source):
You can put this solution on YOUR website!An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 inches from each corner and turning up the edges.
If the box is to hold 294 cubic inches, what should be the dimensions of the sheet metal?
---------------------------------------
Let the sheet metal be x" by x".
Sketch a square that is x by x.
sketch 6 by 6 squares in each of its corners.
Imagine cutting out those four squares.
Imagine folding up the four sides to form a box.
---------
The base of the box is (x-2*6)^2 sq in.
The height of the box is 6 in
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Volume = 6(x-12)^2 = 294
(x-12)^2 = 49
x-12 = 7
x = 19"
====================
Cheers,
Stan H.
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Linear-systems/263606: I need to graph on a plane. y>-1. Where do I begin?
1 solutions
Answer 194256 by stanbon(57307) on 2010-01-31 19:26:02 (Show Source):
You can put this solution on YOUR website!I need to graph on a plane. y>-1
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You never directly graph an inequality.
You graph the boundary of the inequality which is the EQUALITY.
Graph y = -1 as a line passing thru all points where y = -1
Graph that boundary line as a dashed line because it is not
the graph of your problem.
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Your problem says y is Greater than the boundary y-values.
So, shade the half-plane ABOVE the boundary line.
---
That shaded area is the graph of your problem.
-----------
Cheers,
Stan H.
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Radicals/263603: I don't even know where to begin on this one! Please help!?!? Thank you!
A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 5 questions on the survey?
1 solutions
Answer 194253 by stanbon(57307) on 2010-01-31 19:18:14 (Show Source):
You can put this solution on YOUR website!A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 5 questions on the survey?
---
ways to pick the 1st question: 5
ways to pick the 2nd question: 4
ways to pick the 3rd-----------3
ways to pick the 2nd-----------2
ways to pick the 1st-----------1
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Total number of arrangements = 5*4*3*2*1 = 120
==============================================
Cheers,
Stan H.
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Graphs/263602: Please help me. I have to write an equation in point-slope form of the line that passes through the given points. My points are (1,5) and (-1,-5). I understand how to plot the points, but not how to put them in this formula
y= mx+b
1 solutions
Answer 194251 by stanbon(57307) on 2010-01-31 19:14:27 (Show Source):
You can put this solution on YOUR website!I have to write an equation in point-slope form of the line that passes through the given points. My points are (1,5) and (-1,-5).
----
slope = (5--5)/(1--1) = 10/2 = 5
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Form is y = mx +b
You know m and that y = 5 when x = 1
Solve for "b":
5 = 5*1 + b
b = 0
--------------------
Equation:
y = 5x
==============
Cheers,
Stan H.
I understand how to plot the points, but not how to put them in this formula
y= mx+b
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Linear_Equations_And_Systems_Word_Problems/263584: Meg traveled 7 miles yesterday walking for one half-hour and biking for one half-hour. Today traveling at the same rates she traveled a total of 6 miles by walking for 40 mintues and biking for 20 mintues. What was her walking and biking rates? The answer is walking 4mph and biking 10mph. Please help me set up the equations.
1 solutions
Answer 194248 by stanbon(57307) on 2010-01-31 19:09:53 (Show Source):
You can put this solution on YOUR website!Meg traveled 7 miles yesterday walking for one half-hour and biking for one half-hour. Today traveling at the same rates she traveled a total of 6 miles by walking for 40 mintues and biking for 20 mintues. What was her walking and biking rates? The answer is walking 4mph and biking 10mph.
Let walking rate be "w": let biking rate be "b":
Equations:
(1/2)w + (1/2)b = 7
(2/3)w + (1/3)b = 6
---------------------------
Modify the equations:
w + b = 14
2w + b = 18
-------------------
Subtract 1st from 2nd equation to get:
w = 4 mph (walking rate)
---
Since w + b = 14, w = 10 mph (walking rate)
==============================================
Cheers,
Stan H.
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Numeric_Fractions/263579: Esperanto Corporation wants to determine a linear function relating price, p(x), to demand where x = number of doodads sold. They sold 900 doodads per week when price was 94 dollars for each doodad. The number of doodads sold dropped to 400 doodads per week when price was raised to 104 dollars for each doodad. Write the function that models price as a function of number of doodads sold
1 solutions
Answer 194238 by stanbon(57307) on 2010-01-31 18:45:10 (Show Source):
You can put this solution on YOUR website!Esperanto Corporation wants to determine a linear function relating price, p(x), to demand where x = number of doodads sold.
They sold 900 doodads per week when price was 94 dollars for each doodad.
The number of doodads sold dropped to 400 doodads per week when price was raised to 104 dollars for each doodad.
----------------------------------------------
Write the function that models price as a function of number of doodads sold
---
You have two points: (900,94) and (400,104)
slope = (104-94)/(-500)= -1/50
---
The linear form is y = mx + b
104 = (-1/50)*400 + b
b = 104 + 8
b = 112
----------------
Linear Equation:
p(x) = (-1/50)x + 112
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Cheers,
Stan H.
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Triangles/263576: If a triangle has the measures 85 and 69 degrees how would figure out which side is the shortest?
1 solutions
Answer 194229 by stanbon(57307) on 2010-01-31 18:18:43 (Show Source):
You can put this solution on YOUR website!If a triangle has the measures 85 and 69 degrees how would figure out which side is the shortest?
---
The 3rd angle must be 180-(85+69) = 26 degrees.
---------------------------------------------------
The shortest side is the side opposite the smallest angle.
=========================
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/263564: Ellen wishes to mix candy worth $1.80 per pound with candy worth $2.40 per pound to form 48 pounds of a mixture worth $2.00 per pound. How many pounds of the more expensive candy should she use?
1 solutions
Answer 194222 by stanbon(57307) on 2010-01-31 18:09:05 (Show Source):
You can put this solution on YOUR website!Ellen wishes to mix candy worth $1.80 per pound with candy worth $2.40 per pound to form 48 pounds of a mixture worth $2.00 per pound. How many pounds of the more expensive candy should she use?
--------------------
Equation:
value + value = value
1.8x + 2.4(48-x) = 2*48
Multiply thru by 10 to get:
18x + 24*48 - 24x = 20*48
-6x = -4*48
x = 4*8 = 32 (amount of $1.80 candy needed in the mixture)
---------------------------------
48-32 = 16 lbs (amount of $2.40 candy needed in the mixture)
=========================================================
Cheers,
Stan H.
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Probability-and-statistics/263548: HI! I saw this on a webpage:
Tutorial on the Use of Significant Figures, page 7
--------------------------------------------------------------------------------
General guidelines for using calculators
When using a calculator, if you work the entirety of a long calculation without writing down any intermediate results, you may not be able to tell if an error is made. Further, even if you realize that one has occurred, you may not be able to tell where the error is.
In a long calculation involving mixed operations, carry as many digits as possible through the entire set of calculations and then round the final result appropriately. For example,
(5.00 / 1.235) + 3.000 + (6.35 / 4.0)=4.04858... + 3.000 + 1.5875=8.630829...
The first division should result in 3 significant figures. The last division should result in 2 significant figures. The three numbers added together should result in a number that is rounded off to the last common significant digit occurring furthest to the right; in this case, the final result should be rounded with 1 digit after the decimal. Thus, the correct rounded final result should be 8.6. This final result has been limited by the accuracy in the last division.
Warning: carrying all digits through to the final result before rounding is critical for many mathematical operations in statistics. Rounding intermediate results when calculating sums of squares can seriously compromise the accuracy of the result.
This is on a chemistry webpage dealing with significant figures. What do the two sentences after the word warning mean exactly? I don't understand this.
1 solutions
Answer 194210 by stanbon(57307) on 2010-01-31 17:44:44 (Show Source):
You can put this solution on YOUR website!It means "just be careful".
---
To comply with the sentences you should carry out your
work with at least 6 decimal places at each step if
you are asked to arrive at an answer that is good to
the 3rd decimal place. Don't round off your decimals
to the 3rd place every step along the line while you
are working the problem.
---
Hope that helps.
Cheers,
Stan H.
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Inequalities/263516: cant seem to figure this one out :/
1 solutions
Answer 194200 by stanbon(57307) on 2010-01-31 17:27:32 (Show Source):
You can put this solution on YOUR website!x/2 > x/(x+4) + 4
---
Solve the equality:
(x/2) = x/(x+4) + 4
Multiply thru by 2(x+4) to get:
x(x+4) = 2x + 8(x+4)
x^2+4x = 2x + 8x + 32
x^2 -6x - 32 = 0
x = [6 +- sqrt(36 -4*-32)]/2
x = [6 +- sqrt(164)]/2
x = 9.403 or x = -3.403
---
These cannot be in the solution of the inequality.
x = -4 can also not be a solution.
--------------------------
Draw a number line and plot -4, -3.403 and 9.403
That breaks the number line into four intervals that
may or may not contain solutions for the INEQUALITY.
------------------------
Test a value from each interval in x/2 > x/(x+4) + 4
Test x = -5: -5/2 > -5/-1 + 4 ; false
Test x = 1: 1/2 > 1/5 + 4 ; false
Test x = 10: 5 > (10/14) + 4 : true
==========================================
Solution: x> 9.403
==========================================
Cheers,
Stan H.
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Rate-of-work-word-problems/263510: A bank lends out $9000 at 7% simple intrest. At the end of 1 year, how much interest is owed on the lone?
I solved this problem like this: I =PRT
=(9000)(.07) (1)
=630 IS THE INTEREST OWED ON THE LONE AT THE END OF THE YEAR.
Is this answer correct? Please let me know.
1 solutions
Answer 194184 by stanbon(57307) on 2010-01-31 16:18:56 (Show Source):
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Rate-of-work-word-problems/263507: A flash of Lightning is seen, and the resulting thunderclap is heard 3 seconds later. If the speed of sound averages 1,100 feet per second, how far away is the storm?
I solved this problem like this: 1100=1 sec
x= 3 sec
1100(3)= 1x
3300=1x
x= 3300 ft away is the storm.
Is this correct?
1 solutions
Answer 194182 by stanbon(57307) on 2010-01-31 16:17:01 (Show Source):
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Radicals/263503: I saw a statement:
If a is negative and n is odd then there is just one n-th root, and it is negative also. For example, 3 cube root(-1) = 5th root (-1) = -1.
What is the reasoning for those three numbers above to be equal?
1 solutions
Answer 194180 by stanbon(57307) on 2010-01-31 16:12:13 (Show Source):
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Percentage-and-ratio-word-problems/263495: Automobiles and small trucks account for 84% of the travel to and from work in the united states. What fraction represents all other means of travel to and from work in the United States?
1 solutions
Answer 194173 by stanbon(57307) on 2010-01-31 15:59:55 (Show Source):
You can put this solution on YOUR website!Automobiles and small trucks account for 84% of the travel to and from work in the united states. What fraction represents all other means of travel to and from work in the United States?
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100%-84% = 16% = 16/100 = 4/25
==================================
Cheers,
Stan H.
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