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Recent problems solved by 'stanbon'
stanbon answered: 57135 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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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, >>NextProbability-and-statistics/338606: A train leaves the station at 12:00 travling 90 mph and travels 450 miles to its destination. Another train leaves at 12:15 traveling 100 mph from the 1st train's destination. What time will they possibly pass each other? 1 solutions
Answer 242713 by stanbon(57203) on 2010-09-03 14:05:33 (Show Source):
You can put this solution on YOUR website!A train leaves the station at 12:00 travling 90 mph and travels 450 miles to its destination. Another train leaves at 12:15 traveling 100 mph from the 1st train's destination. What time will they possibly pass each other?
------------------------------
1st train DATA:
rate = 90 mph ; distance = x miles ; time = x/90 hrs.
----------------------
2nd train DATA:
rate = 100 mph ; distance = 450-x miles ; time = (450-x)/100 hrs
--------------------------
Equation:
1st train time - 2nd train time = 1/4 hr.
------
x/90 - (450-x)/100 = 1/4
------
Multiply thru by 900 to get:
10x - 9(450-x) = 225
10x - 9*450 + 9x = 225
19x = 19*225
x = 225 miles (1st train distance)
1st train time = 225/90 = 2.5 hrs
----
Clock time when they pass one-another: 2:30 PM
==============================
Cheers,
Stan H.
|
Money_Word_Problems/338395: a coin bank contains 25 coins in nickels,dimes,and quarters. There are four times as many dimes as quarters.The value of the coins is $2.05. How many dimes are in the bank?
please and thank you... i cant figure it out my book says its supose to be 8 dimes but im not getting how it got that answer. 1 solutions
Answer 242557 by stanbon(57203) on 2010-09-02 20:45:48 (Show Source):
You can put this solution on YOUR website!a coin bank contains 25 coins in nickels,dimes,and quarters. There are four times as many dimes as quarters.The value of the coins is $2.05. How many dimes are in the bank?
-------
Equations:
Quantity Eq:::: n + d + q = 25
Quantity Eq:::: d = 4q
Value Eq:::::::5n +10d+25q = 205
-------
Rearrange:
n + d + q = 25
0 + d -4q = 0
5n+10d+25q= 205
----------------------
Use any method you know to solve the system to get:
# of nickels = 15
# of dimes = 8
# of quarters= 2
=====================
Cheers,
Stan H.
|
test/338412: How do you find the hypotenuse of a right triangle and how do you find the angles of a right triangle? 1 solutions
Answer 242556 by stanbon(57203) on 2010-09-02 20:34:37 (Show Source):
You can put this solution on YOUR website! How do you find the hypotenuse of a right triangle and how do you find the angles of a right triangle?
--------------
Use Pythgoras to find the hypotenuse.
---
Use trigonometry to find the angles.
---
Cheers,
Stan H.
|
Probability-and-statistics/338312: PROBABILITY:
Choose one of the outcomes listed above. Based on the sample space above, what is the theoretical probability that the outcome will occur? (write the probability as a fraction and as a decimal.)
Outcome:______TT3______ Probability: _____1/24 ; 0.0417______
(over)
EXPERIMENTAL (Empirical) PROBABILITY:
Using the same outcome you chose at the bottom of the previous page, conduct the experiment and record the number of times the outcome occurs.
Outcome: ______________
In the table below, “success” means that the above outcome occurred. You will conduct the experiment a total of 100 times.
# of successes for this set of 10 trials Cumulative number of successes Proportion of successes based on all trials Decimal estimate of successes based on all trials
First set of 10 trials /10
Second set of 10 trials /20
Third set of 10 trials /30
Fourth set of 10 trials /40
Fifth set of 10 trials /50
Sixth set of 10 trials /60
Seventh set of 10 trials /70
Eighth set of 10 trials /80
Ninth set of 10 trials /90
Tenth set of 10 trials /100
Look at the far right column of the table. How does the empirical probability compare to the theoretical probability as the total number of trials increases? What would happen to the numbers in the far right column if you repeated the experiment 1000 times?
1 solutions
Answer 242549 by stanbon(57203) on 2010-09-02 20:22:34 (Show Source):
You can put this solution on YOUR website!PROBABILITY:
Choose one of the outcomes listed above. Based on the sample space above, what is the theoretical probability that the outcome will occur? (write the probability as a fraction and as a decimal.)
Outcome:______TT3______ Probability: _____1/24 ; 0.0417______
(over)
EXPERIMENTAL (Empirical) PROBABILITY:
Using the same outcome you chose at the bottom of the previous page, conduct the experiment and record the number of times the outcome occurs.
---
Comment: This tells you to flip the coin one, then flip it again, then
roll a dice once. That would constitute one trial of the experiment.
Let's assume you perform the experiment 24 times.
You are to keep track of how many time tt3 occurs and record that
number below.
-----
Outcome: put your number here______________
--------------------------------
In the table below, “success” means that the above outcome occurred.
===
You will conduct the experiment a total of 100 times.
# of successes for each set of 10 trials
Cumulative number of successes
Proportion of successes based on all trials
Decimal estimate of successes based on all trials
---
Comment: Now you are perform the experiment 10 times and list the number of tt3.
Do it again for 10 trials.
And again
And again
etc.
Add up the number of successes as you go through each set of 10 trials.
First set of 10 trials /10
Second set of 10 trials /20
Third set of 10 trials /30
Fourth set of 10 trials /40
Fifth set of 10 trials /50
Sixth set of 10 trials /60
Seventh set of 10 trials /70
Eighth set of 10 trials /80
Ninth set of 10 trials /90
Tenth set of 10 trials /100
Look at the far right column of the table.
Comment: The far right column contains the cumulative sum of the decimal equivalents of the number of tt3's as you perform the trial more and more times.
How does the empirical probability compare to the theoretical probability as the total number of trials increases? What would happen to the numbers in the far right column if you repeated the experiment 1000 times?
====
Comment: As you increase the number of trials the emperical proportion of
tt3 results will get closer and closer to the theoretical proportion of
1 out of 24 = 0.0417
==========================
Cheers,
Stan H.
|
Probability-and-statistics/338302:
EXPERIMENTAL (Empirical) PROBABILITY:
Using the same outcome you chose at the bottom of the previous page, conduct the experiment and record the number of times the outcome occurs.
Outcome: ______________
In the table below, “success” means that the above outcome occurred. You will conduct the experiment a total of 100 times.
1.# of successes for this set of 10 trials
2. Cumulative number of successes
3. Proportion of successes based on all trials
4 Decimal estimate of successes based on all trials
First set of 10 trials /10
Second set of 10 trials /20
Third set of 10 trials /30
Fourth set of 10 trials /40
Fifth set of 10 trials /50
Sixth set of 10 trials /60
Seventh set of 10 trials /70
Eighth set of 10 trials /80
Ninth set of 10 trials /90
Tenth set of 10 trials /100
Look at the far right column of the table. How does the empirical probability compare to the theoretical probability as the total number of trials increases? What would happen to the numbers in the far right column if you repeated the experiment 1000 times?
1 solutions
Answer 242483 by stanbon(57203) on 2010-09-02 17:33:01 (Show Source):
|
absolute-value/338269: how can you rewrite expressions without absolute value bars my problem is x^2/x/ if x<0 1 solutions
Answer 242458 by stanbon(57203) on 2010-09-02 15:49:19 (Show Source):
You can put this solution on YOUR website!how can you rewrite expressions without absolute value bars my problem is x^2/x/ if x<0
-----
Since x<0, |x| = -x
-----
x^2*|x| = (x^2)(-x) = -x^3 if x<0
==============================
Cheers,
Stan H.
|
Equations/338261: I have a table and have to find the value of the variable
c=(5/9)(F-32)
this is the table
F C
-40
14
32
59
86
Could some please help me solve this table? 1 solutions
Answer 242456 by stanbon(57203) on 2010-09-02 15:43:09 (Show Source):
You can put this solution on YOUR website!I have a table and have to find the value of the variable
c=(5/9)(F-32)
this is the table
F C
-40
14
32
59
86
Could someone please help me solve this table?
---
A couple of examples:
C(-40) = (5/9)(-40-32) = (5/9)(-72) = 5*-8 = -40
----
C(32) = (5/9)(32-32) = (5/9)(0) = 0
etc.
=======================
Cheers,
Stan H.
|
Coordinate-system/338258: how do you solve and graph y=(x-2)^2-3 ? 1 solutions
Answer 242455 by stanbon(57203) on 2010-09-02 15:30:23 (Show Source):
You can put this solution on YOUR website!how do you solve and graph y=(x-2)^2-3 ?
---
If you have studied vertical and horizontal
shifts you might see that the basic y = x^2
curve has been moved 2 units to the right
and 3 units down.
------------------------
That puts the vertex at (2,-3) and hopefully
you see that the parabola is opening up.

----
If all that does not make sense your only
alternative is to plot points.
------------------------------
Cheers,
Stan H.
|
Permutations/338207: Use induction to show
1+2n_<3^n for n_>1
I'm really having a hard time understanding this process . I think if I see some examples it will help me solve it on my own 1 solutions
Answer 242417 by stanbon(57203) on 2010-09-02 13:12:30 (Show Source):
You can put this solution on YOUR website!1+2n_<3^n for n_>1
---------------------------------
You show it is true for n = 1.
Then you assume it is true for n = k
and prove that is is true for n = k+1.
----
If you can do that, you know it is true
for 1+1 = 2, 2+1=3, 3+1=4, etc.
==============
Your Problem
True for n = 1 ?
1+2*1 <= 3^1
1+2 <= 3
3<=3
True
------------------
Assume true for n = k
1+2k <= 3^k
Note: We know it is true for k=1 because we did that above.
-------------------
Prove it is true for n = k+1
1+2(k+1) = (1+2k)+2
substitute 3^k for 1+2k to get
<= 3^k+2 <= 3^k+3 = 3^k*3 = 3^(k+1)
So 1+2(k+1) <= 3^(k+1)
--------
And that is what you were trying to prove
--------
So, 1+2n <= 3^n for all n>=1
=================================
Cheers,
Stan H.
|
absolute-value/338206: Please assist me in helping to solve the following problem:
3x + 2y = 3
4x -3y = -13
Your analysis and comments are appreciated. Thank you. 1 solutions
Answer 242415 by stanbon(57203) on 2010-09-02 12:58:04 (Show Source):
You can put this solution on YOUR website!solve the following problem:
3x + 2y = 3
4x -3y = -13
--------------------
If you want to solve by elimination you need to
have the same number of some variable in the
numerator and in the denominator.
You can pick either of the two variables but
you must create the same number in both equations.
---
Lets say you pick "x".
-----
Multiply thru the 1st equation by 4
Multiply thru the 2nd equation by 3
-----
12x + 8y = 4*3
12x - 9y = 3*-13
----------------------
Subtract the 2nd equation from the 1st to get:
17y = 12--39
17y = 51
Divide both sides by 16 to get:
y = 3
---
Substitute that into either of the original equations
and solve for "x":
3x + 2y = 3
3x + 2*3 = 3
3x + 6 = 3
3x = -3
x = -1
-------
Check the solution in the "other" original equation:
4x -3y = -13
4(-1)-3(3) = -13
-4-9 = -13
-13 = -13
===============
Solution:
x = -1 ; y = 3
=======================
Cheers,
Stan H.
|
Expressions-with-variables/338204: how can i solve (Z+5)-7=(Z-7)+5
and
-(Y+5)-(2+7y)+8y=3y-8
tha parenthesis gets me off track can you please give me the steps to similar problems?
thank you so much 1 solutions
Answer 242414 by stanbon(57203) on 2010-09-02 12:49:51 (Show Source):
You can put this solution on YOUR website!solve
(Z+5)-7=(Z-7)+5
Z+5-7 = Z-7+5
Z-2 = Z-2
Z = Z
--
The original equation is an identity and
is true for all values of Z.
-------------------------------------
and
-(Y+5)-(2+7y)+8y=3y-8
-Y-5 -2-7y+8y = 3y-8
-7 = 3y-8
3y = 1
y = 1/3
==============
Cheers,
Stan H.
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Probability-and-statistics/338077: A and B are independent events. Find the missing probability.
P(B) = 1/5, P(A and B) = 2/13, Find P(A) 1 solutions
Answer 242412 by stanbon(57203) on 2010-09-02 12:43:54 (Show Source):
You can put this solution on YOUR website!A and B are independent events. Find the missing probability.
P(B) = 1/5, P(A and B) = 2/13, Find P(A)
------------
P(A and B)
= P(A)*P(B) = 2/13
= P(A)*(1/5) = 2/13
P(A) = (2/13)/(1/5) = (2/13)*(5/1) = 10/13
=============================================
Cheers,
Stan H.
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Triangles/338151: A triangle is made from a rope. The sides of the triangle are 25 cm, 11 cm and 31 cm. What will be the area of the square made from the same rope 1 solutions
Answer 242383 by stanbon(57203) on 2010-09-02 10:11:51 (Show Source):
You can put this solution on YOUR website!A triangle is made from a rope. The sides of the triangle are 25 cm, 11 cm and 31 cm. What will be the area of the square made from the same rope
---------------
The longest "side" must be the hypotenuse.
So the legs are 25 and 11
---
Area = (1/2)*11*25 = 137.5 sq. cm.
==================================
The length of the rope = 11+31+25 = 67 cm
---
Divide the length by 4 to find the length
of a side of a square made with the rope.
side = 67/4
--
Then area of the square would be (67/4)^2 = 280.56 sq. cm
============================================================
Cheers,
Stan H.
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absolute-value/338138: After solving an absolute value do you write is like this:
|x<10|
x<10 or x<-10
(infinity sign,10) or (-infinity sign, -10) 1 solutions
Answer 242381 by stanbon(57203) on 2010-09-02 10:08:49 (Show Source):
You can put this solution on YOUR website!After solving an absolute value do you write is like this:
x<|10|
---
x<10 or x<-10
-----
No.
You write as
-10 < x < 10
---------------------
If the problem is
x > |10| you would get
x >10 or x < -10
======================
Remember: You can always check
your answers in the original
equation.
======================
Cheers,
Stan H.
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Travel_Word_Problems/337971: evaluate the expressions 3x to the second power and (3x)to the second power when x=4? 1 solutions
Answer 242285 by stanbon(57203) on 2010-09-01 20:45:34 (Show Source):
You can put this solution on YOUR website!evaluate the expressions 3x to the second power and (3x)to the second power when x=4?
-----------------------
3x^2 + (3x)^2
---
3*4^2 + (12)^2
---
3*16 + 144
---
48 + 144
---
= 192
============
Cheers,
Stan H.
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Travel_Word_Problems/337961: okay my question is ; you drove 200 miles in 3 hours and 20 minutes. Which expression represents your average speed if d represents distance and t represents time?
1 solutions
Answer 242278 by stanbon(57203) on 2010-09-01 20:41:44 (Show Source):
You can put this solution on YOUR website!okay my question is ; you drove 200 miles in 3 hours and 20 minutes. Which expression represents your average speed if d represents distance and t represents time?
------------------------
speed = distance/time
----
speed = 200 mi/(3 1/3 hrs = 200/(10/3) = 200(3/10) = 60 mph
==========================================
Cheers,
Stan H.
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Linear-equations/337898: The question is which line is steeper, Line 1: y=3/5x-2 or Line 2: y=2/3x=3?
This is my attempt at the problem.
Line 1: y=3/5x-2
-3/5x -3/5x
y-3/5x=2
Thats as far as I got and I know its wrong. We just learned how to find which line is steeper but we've done it with whole numbers not fractions. Ex: Line 1: (2,3) and (4,7) or Line 2 (-1,2) and (4,5). I am so lost so if you could explain this to me that would be great. Thank you! :) 1 solutions
Answer 242242 by stanbon(57203) on 2010-09-01 18:47:45 (Show Source):
You can put this solution on YOUR website!The question is which line is steeper,
Line 1: y=(3/5)x-2 or Line 2: y=(2/3)x=3 ?
------
The slope of the 1st line is 3/5.
---
The slope of the 2nd line is 2/3
---
Convert both fractions to a common denominator:
3/5 = 9/15
---
2/3 = 10/15
---
So, 2/3 is the steeper slope.
So, Line 2 is the steeper line.
=====================================
Cheers,
Stan H.
=============
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Complex_Numbers/337896: the state tax in new york is 0.0425 (or 4.25%) your total bill at the department store included $2.21 in sales tax. one half of the merchandise purchased was nontaxable. what was the total bill? 1 solutions
Answer 242240 by stanbon(57203) on 2010-09-01 18:43:03 (Show Source):
You can put this solution on YOUR website!the state tax in new york is 0.0425 (or 4.25%) your total bill at the department store included $2.21 in sales tax. one half of the merchandise purchased was nontaxable. what was the total bill?
--------------
Let half of the total bill be "x":
Solve 0.0425x = 2.21
x = 52.00 (that is half of the total bill)
----
Total bill = 2*52.00 = $104.00
================================
Cheers,
Stan H.
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Travel_Word_Problems/337879: If two trains leave New Haven traveling in opposite directions one is traveling at 75 miles per hour and they are 405 miles apart in 3 hours what speed is the second train traveling at. 1 solutions
Answer 242239 by stanbon(57203) on 2010-09-01 18:39:24 (Show Source):
You can put this solution on YOUR website!If two trains leave New Haven traveling in opposite directions one is traveling at 75 miles per hour and they are 405 miles apart in 3 hours what speed is the second train traveling at.
-------------
Let the rate of the 2nd train be "x mph".
---
The separation rate of the two trains is "75+x" mph
------------------------------------------------------
Equation:
3(75+x) = 405
75+x = 135
x = 60 mph (speed of the 2nd train)
=========================================
Cheers,
Stan H.
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Geometry_Word_Problems/337877: The length of a rectangle is 6 times longer than the width. The perimeter is 42. What is the width? 1 solutions
Answer 242217 by stanbon(57203) on 2010-09-01 17:56:15 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is 6 times longer than the width. The perimeter is 42. What is the width?
---
Let width be "x".
The length is "6x".
---
Perimeter = 2(width + length)
42 = 2(x+6x)
21 = 7x
x = 3 units (width)
----
6x = 18 units (length)
==========================
Cheers,
Stan H.
============================
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Miscellaneous_Word_Problems/337866: A cellular phone company charges $50 for each phone plus $25 per month under a special sale plan. The total cost C (in dollars) of operating the phone is given by the linear model C=50+25t where t represents the number of months of operation of a cellular phone.
How many months has the phone been in service if the total cost is $250.00?
What is the cost of the service after 18 months?
Thank You!!! 1 solutions
Answer 242208 by stanbon(57203) on 2010-09-01 17:43:28 (Show Source):
You can put this solution on YOUR website!C=50+25t where t represents the number of months of operation of a cellular phone.
How many months has the phone been in service if the total cost is $250.00?
---------------
Solve 50+25t = 250.00
25t = 200
t = 8
-----------------------------
What is the cost of the service after 18 months?
C(18) = 50+25*18 = $500
==========================
Cheers,
Stan H.
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