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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 , 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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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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, >>NextLinear-equations/153846: I need help with this word problem
during the 2003 NBA playoffs, the top-scoring player was Kobe Bryant of the Los Angeles Lakers. Bryant scored a totals of 385 points during the playoffs. The number of free throws (each worth one point) he made was 11 more than three times the number of three-point field goals he made. Bryant also made 26 fewer free throws than two-point field goals. How many free throaw, two point field goals. and three point field goals did Kobe Bryant make during the 2003 playoffs?
please help me with this equation
thanks
1 solutions
Answer 113206 by stanbon(57203)   on 2008-08-27 20:18:20 (Show Source):
You can put this solution on YOUR website!Bryant scored a totals of 385 points during the playoffs. The number of free throws (each worth one point) he made was 11 more than three times the number of three-point field goals he made. Bryant also made 26 fewer free throws than two-point field goals. How many free throws, two point field goals. and three point field goals did Kobe Bryant make during the 2003 playoffs?
--------------------------------
EQUATIONS:
f = 3r + 11
f = t - 26
f + 2t + 3r=385
-------------------------
Rearrange:
f + 2t + 3r = 385
f + 0t - 3r = 11
f - t + 0r = -26
-------------------------
Solve the system of equations by any method to get:
# of free throws = 86
# of two-pointers = 112
# of three-pointers = 25
-------------------------
Cheers,
Stan H.
|
Linear-equations/153841: I need help working through this word problem.
In 1998, 1.7 million electronic bill statements were delivered and payments occured. In 2002, that number rose to 9.9 million.
a) write two ordered pairs of the form (years after 1998, millions of electronic bills).
b) the relationship between years after 1998 and 2002 is approximately linear over this period. Use the ordered pairs from part a to write an equation of the line relating to electronic bills.
c) Use the linear equation from part (b) to estimate the lectronic bills to be delivered and pain in 2006.
please help me with this problem
thank you
1 solutions
Answer 113199 by stanbon(57203) on 2008-08-27 19:54:52 (Show Source):
You can put this solution on YOUR website!In 1998, 1.7 million electronic bill statements were delivered and payments occured. In 2002, that number rose to 9.9 million.
--------------------------------------
a) write two ordered pairs of the form (years after 1998, millions of electronic bills).
(0,1.7 mil); (4,9.9 mil)
--------------------------------------
b) the relationship between years after 1998 and 2002 is approximately linear over this period. Use the ordered pairs from part a to write an equation of the line relating to electronic bills.
slope = (9.9-1.7)/(4-0) = 8.2/4 = 2.05
intercept: (0,1.7 mil)
EQUATION:
# of bills = 2.05*years since 1998 + 1.7 million electric statements
b = 2.05x + 1.7
--------------------------------------
c) Use the linear equation from part (b) to estimate the lectronic bills to be delivered and pain in 2006.
b(2) = 2.05*8 + 1.7
b(2) = 18.1 million
=====================================
Cheers,
Stan H.
|
Geometry_proofs/153820: the problem is:
________
M N O P
I am given that MN is equal to OP i have to prove that NP is equal to MO and have to give the steps and reasons. So far I have: 1. MN = OP given
2. OP + ON = NP segment addition
MN + NO = MO
3. MO = NP substitution
But, I think I have missed a step. Have I ?
1 solutions
Answer 113194 by stanbon(57203) on 2008-08-27 18:46:31 (Show Source):
|
Polynomials-and-rational-expressions/153670: This question is from textbook College Algebra
Find the qoutient and the remainder. Check your work by verifying that
(Qoutient)(Divisor)+Remainder=Divedend
Page 49 #96. 3x5-x2+x-2 divided by 3x3-1
This should read 3x to the 5th power-x squared +x-2 divided by 3x cubed -1. I am not sure how to get the numbers in the proper place on the keyboard to show "powers".
I got an answer of (x squared with remainder x-2). This is one of the first division problems I have done, so I am just trying to check to make sure I am doing it right.
1 solutions
Answer 113119 by stanbon(57203) on 2008-08-27 09:56:50 (Show Source):
You can put this solution on YOUR website!3x^5-x^2+x-2 divided by 3x^3-1
-----------------------------------
Quotient: x^2
Remainder: x-2
===================
You are correct.
===================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/153673: This question is from textbook elementary and intermediate algebra
I'm, stuck can you help? #80. Buried Treasure. Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock,walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information then they can find x and save a lot of digging. What is x?
1 solutions
Answer 113116 by stanbon(57203) on 2008-08-27 09:39:02 (Show Source):
You can put this solution on YOUR website!Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock,walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information then they can find x and save a lot of digging. What is x?
---------------------
To see the problem draw an x/y coordinate system.
Put Castle Rock (CR) at the intersection of the x and y axis.
Mark a point "x" up the vertical axis from CR.
From that point mark a point 2x+4 to the right.
Use Pythagoras to find the distance that point is from CR:
d = sqrt(x^2 + (2x+4)^2) = sqrt(5x^2+16x+16)
----------
That point is also 2x+6 from CR according to Ahmed's map.
-----------
EQUATION:
sqrt(5x^2 + 16x + 16) = 2x+6
5x^2 + 16x + 16 = 4x^2+ 24x + 36
x^2 - 8x -20 = 0
(x-10)(x+2) = 0
Positive solution:
x = 10
=============
Cheers,
Stan H.
|
Numbers_Word_Problems/153642: At 11 am Kate left clinton tollbooth travelling west at 809 km/h. At 12 pm, Juan left the tollbooth traveling west at 72 km/h. At what time will they be 98 km apart
1 solutions
Answer 113088 by stanbon(57203) on 2008-08-26 22:44:10 (Show Source):
You can put this solution on YOUR website!At 11 am Kate left clinton tollbooth travelling west at 809 km/h. At 12 pm, Juan left the tollbooth traveling west at 72 km/h. At what time will they be 98 km apart
----------
Kate DATA:
rate = 809 km/h ; time = x + 1 hrs ; distance = 809(x+1) km
------------------------------
Juan DATA:
rate = 72 km/h ; time = x hrs ; distance = 72x km
--------------------
EQUATION:
distance + distance = 98 km
809(x+1) + 72x = 98
809x + 809 + 72x = 98
---------------
These numbers give a negative answer.
Most probably the 809 km/h rate for Kate is wrong.
------------------------------
Cheers,
Stan H.
|
Word_Problems_With_Coins/153636: Sandy held a garage sale during which she charged a dime for everything, but accepted a nickel if the buyer bargained well. At the end of the day she realized she had sold all 12 items and raked in a grand total of 95 cents. She had only dimes and nickels. How many of each did she have? (please show work) Thank you so much
1 solutions
Answer 113085 by stanbon(57203) on 2008-08-26 22:15:13 (Show Source):
You can put this solution on YOUR website!Sandy held a garage sale during which she charged a dime for everything, but accepted a nickel if the buyer bargained well. At the end of the day she realized she had sold all 12 items and raked in a grand total of 95 cents. She had only dimes and nickels. How many of each did she have? (please show work) Thank you so much
-------------------------------------------------
Quantity: d + n = 12
Value: 10d + 5n = 95
------------------------
Multiply the 1st equation by 10 to get:
10d + 10n = 120
10d + 5n = 95
---------------
Subtract 2nd from 1st to get:
5n = 25
n = 5 (# of nickels)
Since d+n + 12, d= 12-5; d = 7 (# of dimes)
===============================================
Cheers,
Stan H.
|
expressions/153640: This question is from textbook
worksheet problem -- not in book -- could not find edition no., but the year is 1995
what order do I solve this equation
{8[12(10 +6) - 88 ] + 168} /125
1 solutions
Answer 113084 by stanbon(57203) on 2008-08-26 22:05:15 (Show Source):
You can put this solution on YOUR website!{8[12(10 +6) - 88 ] + 168} /125
= {8[12*16 - 88] + 168} / 125
= {8[104] + 168} / 125
= {10816 + 168} / 125
= {10984}/125
= 87.872
==============
Cheers,
Stan H.
|
Inequalities/153638: Can i get some help with these problems?
Use an inequality to describe the interval of real numbers.
1. [-1,1) and 2. (-infinite,4]
Thanks
1 solutions
Answer 113083 by stanbon(57203) on 2008-08-26 21:59:17 (Show Source):
You can put this solution on YOUR website!Use an inequality to describe the interval of real numbers.
1. [-1,1)
----------------
-1 <= x < 1
====================
2. (-infinite,4]
----------------
x <= 4
====================
Cheers,
Stan H.
|
Inequalities/153639: What would be the set builder notation fo the following representation:
{-2, -4, -6, -8...}
is it {xI -8< x <= -2 and x is EVEN}
1 solutions
Answer 113082 by stanbon(57203) on 2008-08-26 21:55:54 (Show Source):
You can put this solution on YOUR website!the set builder notation fo the following representation:
{-2, -4, -6, -8...}
is it {xI -8<= x <= -2 and x is EVEN}
--------------
I added an equal sign by the -8.
Cheers,
Stan H.
|
Travel_Word_Problems/153630: A truck enters a highway driving 60 mph. A car enters the same highway 13 minutes later and driving 71 mph. How long does it take the car to pass the truck?
1 solutions
Answer 113077 by stanbon(57203) on 2008-08-26 20:49:58 (Show Source):
You can put this solution on YOUR website!A truck enters a highway driving 60 mph. A car enters the same highway 13 minutes later and driving 71 mph. How long does it take the car to pass the truck?
---------------------
Car DATA:
distance = x miles ; rate = 71 mph ; time = d/r = x/71 hrs
---------------------
Truck DATA:
distance = x miles ; rate = 60 mph ; time = x/60 hrs
-----------------
EQUATION:
truck time - car time = 13 min = (13/60) hrs.
----------------------------------------------
x/60 - x/71 = 13/60
Multiply thru by 71*60:
71x - 60x = 71*13
11x = 71*13
x = 83.91 miles (distance required for the car to catch the truck)
==============================
Cheers,
Stan H.
|
Exponents/153629: This question is from textbook Intermediate Algebra
This problem is new to me, so if someone can help me, I would appreciate it. This deals with radical exponents; exponential and logarithmic functions.
My problem is to simplify each expression. All variables represent positive real numbers.
sqrt of 25b^2 with 4 as the cube root
Thanks a lot!
1 solutions
Answer 113074 by stanbon(57203) on 2008-08-26 20:41:09 (Show Source):
You can put this solution on YOUR website!What do you mean by this?
"sqrt of 25b^2 with 4 as the cube root"?
---------------------------
Is it a square root or is it a cube root?
or is it a mixture?
Cheers,
Stan H.
|
absolute-value/141307: Find the solutions to: -|x|<0
Find the solutions to: |x|<0
Find the solutions to: |x|not equal to 0
1 solutions
Answer 113072 by stanbon(57203) on 2008-08-26 20:35:17 (Show Source):
You can put this solution on YOUR website!Find the solutions : -|x|<0 for all values of x except x = 0
--------------------------------------
Find the solutions : |x|<0 for no values of x
--------------------------------------
Find the solutions : |x| not equal to 0 for all values of x except x=0
===========================================
Cheers,
Stan H.
|
Equations/153613: This question is from textbook algebra1
hi,
my name is jay, and i am struggling with this question. the question is:
if a pitcher throws a baseball 90 miles per hour, how many seconds does it take for the ball to reach home plate?
here's what i've tried:
time equals distance divided by speed
i divide 60.5 feet by 90 mph, and i get .6722 seconds.
Then i thought, can i really solve this equation this way? can i use feet in distance as the numerator and miles per hour in divisor. I'm not sure how to solve this.
thank you so much for your time. Jay
1 solutions
Answer 113068 by stanbon(57203) on 2008-08-26 20:21:24 (Show Source):
You can put this solution on YOUR website!if a pitcher throws a baseball 90 miles per hour, how many seconds does it take for the ball to reach home plate?
-------------------------
Convert miles per hour to feet per second:
[90 miles/1 hour]
= [90 * 1 * 5280] / [1* 3600 * 1] ft./sec.
= 132 ft./sec
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To cover 60 ft:
(60 ft/132 ft/sec) = 0.454545... seconds
==================================
Cheers,
Stan H.
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Travel_Word_Problems/153602: The distance between Maggie's house and Rashmee's house is 1,600. If it takes Maggie 3 seconds to walk 10 feet, how long will it take her to walk to Rashmee's house? (please show steps!)
1 solutions
Answer 113061 by stanbon(57203) on 2008-08-26 19:51:22 (Show Source):
You can put this solution on YOUR website!The distance between Maggie's house and Rashmee's house is 1,600 ft. If it takes Maggie 3 seconds to walk 10 feet, how long will it take her to walk to Rashmee's house? (please show steps!)
--------------------------
1600 ft / 10 ft = 160
160 * 3 seconds = 480 seconds
480 seconds * (1 min/60 seconds) = 8 minutes
It will take her 8 minutes to walk to Rashmee's house.
=========================
Cheers,
Stan H.
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Linear-equations/153589: I need help solving this linear equation in three variables
5y -7z = 14
2x + y + 4z = 10
2x + 6y - 3z = 30
please help me solve this equation.\
thanks
megan
1 solutions
Answer 113058 by stanbon(57203) on 2008-08-26 19:26:53 (Show Source):
You can put this solution on YOUR website!0x + 5y -7z = 14
2x + y + 4z = 10
2x + 6y - 3z = 30
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Switch line 1 and line 2 to get:
-------------------------
2x + y + 4z = 10
0x + 5y -7z = 14
2x + 6y - 3z = 30
-------------------------
Subtract line 1 from line 3:
2x + y + 4z = 10
0x + 5y -7z = 14
0x + 5y -7z = 20
-------------------------
2x + y + 4z = 10
0x + 5y -7z = 14
0x + 0y -0z = 6
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The 3rd line is a contradiction and indicates there is no
solution to the system of three equations.
===========================
Cheers,
Stan H.
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Travel_Word_Problems/153549: When operating at full capacity, an electric generator can produce 3000 kilowatts of electrical power. If the same generator is currently producing 2010 kilowatts, at what percentage of its full capacity is it running?
1 solutions
Answer 113035 by stanbon(57203) on 2008-08-26 15:55:43 (Show Source):
You can put this solution on YOUR website!When operating at full capacity, an electric generator can produce 3000 kilowatts of electrical power. If the same generator is currently producing 2010 kilowatts, at what percentage of its full capacity is it running?
--------------
You are getting 2010 kw when you could be getting 3000 kw.
Percent means "how many you are getting out of 100".
EQUATION:
2010 / 3000 = x / 100
x = 201000/3000
x = 67
----------------
The generator is running at 67% of capacity.
======================
Cheers,
Stan H.
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Mixture_Word_Problems/153543: How many kilograms of water must be evaporated from 50 kg of a 10% salt solution to obtain a 15% salt solution?
1 solutions
Answer 113029 by stanbon(57203) on 2008-08-26 15:34:30 (Show Source):
You can put this solution on YOUR website!How many kilograms of water must be evaporated from 50 kg of a 10% salt solution to obtain a 15% salt solution?
--------------------
EQUATION:
salt: 0.10*50 -0*x = 0.15(50-x)
Multiply thru by 100 to get rid of the decimals:
10*50 = 15(50-x)
500 = 750 - x
x = 250 kg (amount of water that must be evaporated)
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Notice that this answer makes no sense; you cannot evaporate
250 kg when you only have 50 kg.
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Why the nonsense?
Notice that you started with a 10% solution, evaporated water,
and ended up with a 15% solution. That cannot happen.
==========================
Cheers,
Stan H.
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Numbers_Word_Problems/153547: How many 9 digit numbers can be made from the set 1-9. No repeat digits so that all even digits remain adjacent?
1 solutions
Answer 113026 by stanbon(57203) on 2008-08-26 15:25:18 (Show Source):
You can put this solution on YOUR website!How many 9 digit numbers can be made from the set 1-9. No repeat digits so that all even digits remain adjacent?
------------------------------------
The adjacent even digits can be arranged in 4! ways.
Considering the 4-even as one clump, you have 5 odd and a clump to arrange.
-----------------
Total # of arrangements is 4! * 6! = 17280
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Cheers,
Stan H.
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Expressions-with-variables/153544: Please help me solve the following problem:
Simplify the expression (x^2 - 9)/(x^2 + 3x)
My attempt to this problem was to cancel out the x^2 because they divided each other, and then i simplified -9/3x to -3x. But when i check to see if my work is correct by substituting x for 2, the answers did not match.
1 solutions
Answer 113025 by stanbon(57203) on 2008-08-26 15:20:50 (Show Source):
You can put this solution on YOUR website!Simplify the expression (x^2 - 9)/(x^2 + 3x)
My attempt to this problem was to cancel out the x^2 because they divided each other, and then i simplified -9/3x to -3x. But when i check to see if my work is correct by substituting x for 2, the answers did not match.
---------------
You may only cancel "factors" that are common to the numerator and to the
denominator.
x^2 is a "term" in the numerator and a "term" in the denominator and
may not be cancelled.
Example (2 + 3)/(2 + 5)
If you cancelled the "2" you would get 3/5; but the answer should be 5/7.
Don't cancel terms.
------------------------
Simplify the expression (x^2 - 9)/(x^2 + 3x)
Factor where you can to get:
[(x-3)(x+3)] / [x(x + 3)]
Notice that the (x+3) is a factor of the numberator and of the denominator
so you may cancel it to get:
= (x-3)/(x)
Notice that you cannot cancel the "x" because it is a "term" and not a factor in the numerator.
===============
Cheers,
Stan H.
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Exponential-and-logarithmic-functions/152698: In studying the frictional effects on a flywheel, the revolutions per minute R that it makes as a function of the time t (in min) is given by R = 4520(0.750)^2.50t. Find t for R = 1950 r/min
1 solutions
Answer 113018 by stanbon(57203) on 2008-08-26 14:56:15 (Show Source):
You can put this solution on YOUR website!In studying the frictional effects on a flywheel, the revolutions per minute R that it makes as a function of the time t (in min) is given by R = 4520(0.750)^2.50t. Find t for R = 1950 r/min
--------------------------------
R = 4520(0.750)^2.50t
1950 r/min = 4520(3/4)^(2.5t)
0.431416 = (3/4)^(2.5t)
Take the log of both sides to get:
(2.5t) = log(0.431416)/log(3/4)
2.5t = -0.365104
t = -0.146042
Comment: This answer doesn't make any sense.
The time should not be negative.
==================================
Cheers,
Stan H.
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