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Recent problems solved by 'stanbon'
stanbon answered: 57227 problems
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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 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next
Miscellaneous_Word_Problems/170479: Jack usually mows his lawn in 7 hours. Marilyn can mow the same yard in 4 hours. How much time would it take for them to mow the lawn together?
(Simplify your answer. Type and integer, proper fraction, or mixed number.)
1 solutions
Answer 125863 by stanbon(57295)   on 2008-12-01 10:06:16 (Show Source):
You can put this solution on YOUR website!Jack usually mows his lawn in 7 hours. Marilyn can mow the same yard in 4 hours. How much time would it take for them to mow the lawn together?
------------------------------------
Jack DATA:
Time = 7 hrs/job ; rate = 1/7 job/hr
----------------------------------------
Marilyn = 4 hrs/job ; rate = 1/4 job/hr
-----------------------------------------
Together DATA:
Time = x hrs/job ; rate = 1/x job/hr
----------------------------------------
EQUATION:
rate + rate = together rate
1/7 + 1/4 = 1/x
11/28 = 1/x
x = 28/11 = 2.545454... hrs
===============================
Cheers,
Stan H.
|
logarithm/170478: Solve the logarithmic equation:
log5x=log6 + (x+6)
1 solutions
Answer 125861 by stanbon(57295) on 2008-12-01 10:00:35 (Show Source):
You can put this solution on YOUR website!log5x=log6 + (x+6)
log(5x/6) = x+6
5x/6 = 10^(x+6)
-------------------
Comment: I suspect you have not posted this problem correctly.
If you have you can find a solution by graphing separately the
left side and the right side of this equation, and finding
intersection of the two.
=============================
Cheers,
Stan H.
|
Rational-functions/170471: This question is from textbook Saxon Algebra 2
There are 6 places to sit at a table. How many ways can 6 people be seated at the table?
1 solutions
Answer 125858 by stanbon(57295) on 2008-12-01 09:40:25 (Show Source):
You can put this solution on YOUR website!There are 6 places to sit at a table. How many ways can 6 people be seated at the table?
---------------------
Assuming the table is round, or the seats are arranged without two ends,
the answer is 6!/6 = 5!= 120
==================================
Cheers,
Stan H.
|
Rational-functions/170473: Find all numbers for which the rational expression is undefined.
9/7v+6
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type N is the answer is never undefined.)
1 solutions
Answer 125857 by stanbon(57295) on 2008-12-01 09:35:28 (Show Source):
You can put this solution on YOUR website! Find all numbers for which the rational expression is undefined.
9/7v+6
-----------
7y+6 = 0 when y = -6/7
============================
Cheers,
Stan H.
|
Rational-functions/170474: Find all numbers for which the rational expression is undefined.
2/6y+5
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type N is the answer is never undefined.)
1 solutions
Answer 125856 by stanbon(57295) on 2008-12-01 09:32:14 (Show Source):
You can put this solution on YOUR website!Find all numbers for which the rational expression is undefined.
2/6y+5
------------
When the denominator is zero, the rational expression is undefined.
6y+5 = 0
y = -5/6
(undefined when y = -5/6)
=============
Cheers,
Stan H.
|
Travel_Word_Problems/170472: Two trains are traveling on parallel tracks. Train A is traveling at 80 mph and train B is traveling at 88 mph. Train A passes the train station at 9:25. Train B passes the same station at 9:55. What time will it be when train B catches up with train A?
1 solutions
Answer 125855 by stanbon(57295) on 2008-12-01 09:28:54 (Show Source):
You can put this solution on YOUR website!Two trains are traveling on parallel tracks. Train A is traveling at 80 mph and train B is traveling at 88 mph. Train A passes the train station at 9:25. Train B passes the same station at 9:55. What time will it be when train B catches up with train A?
------------------
Train A DATA:
rate = 80 mph; time = x hrs ; distance = 80x miles
--------------------------------
Train B DATA:
rate = 88 mph; time = (x-(1/12)) hr. ; distance = 88(x-(1/12)) miles
------------------------------
EQUATION:
distance = distance
80x = 88(x-(1/12))
80x = 88x - (22/3)
8x = 22/3
x = 11/12 hr
x = 55 minutes
Ans: 9:25 + 55 minutes = 10:20
====================================
Cheers,
Stan H.
|
Trigonometry-basics/170420: hello, my question is concerning parabolas. I have to find the equation of the parabola whose vertex is (4, -2) and focus at (6,-2). my teacher rushed through this section and failed to explain what exactly the focus, vertex, and directrix is. If you could please explain to me them and the equations you use for them i would really appreciate it.
Thanks!!
1 solutions
Answer 125816 by stanbon(57295) on 2008-11-30 22:50:25 (Show Source):
You can put this solution on YOUR website!I have to find the equation of the parabola whose vertex is (4, -2) and focus at (6,-2). my teacher rushed through this section and failed to explain what exactly the focus, vertex, and directrix is.
-----------------
Plot those two points and sketch the parabola opening to the right
starting at the vertex.
----------------
The distance from the vertex to the focus is 6-4=2
That means p = 2,
And you already have the vertex, so h=6 and k=-2
-----------------------------------------------------
EQUATION Form:
(y-k)^2 = 4p(x-h)
Your Equation:
(y+2)^2 = 8(x-6)
----------------------
Comment: Using google on the internet will get you all the information
you need and illustrations so you can see what the vertex, directrix,
and focus are.
===================
Cheers,
Stan H.
|
Permutations/170323: Find the term not involving y in the expansion of
bracket( 1 over y exponent 3 + y exponent 2 closed bracket) exponent 5
1 solutions
Answer 125815 by stanbon(57295) on 2008-11-30 22:43:40 (Show Source):
You can put this solution on YOUR website!Find the term not involving y in the expansion of
bracket( 1 over y exponent 3 + y exponent 2 closed bracket) exponent 5
------------------
[(1/y^3) + y^2]^5
= [[y^5+1]^5]/y^15
Let m = y^5
= [m+1]^5/m^3
= [m^5 + 5m^4 + 10m^3+.....]/m^3
Comment: Here you can see that if you divide thru by m^3 you will
have a term 10m^3/m^3 = 10
----------------------------
That is the term that has no "m" in it and therefore no "y".
That term is 10m^3/m^3 = 10y^15/y^15
============================
Cheers,
Stan H.
|
real-numbers/170416: g(x) = 5X/x squared + 25. Please expain to me how to go about finding the domain for this equation, I want to be able to do additional questions myself so a thorough explaination would be greatly appreceiated.
Thank You
1 solutions
Answer 125813 by stanbon(57295) on 2008-11-30 22:33:45 (Show Source):
You can put this solution on YOUR website!g(x) = 5X/(x^2 + 25). Please explain to me how to go about finding the domain for this equation,
-------------------------
If some value of x can make the denominator be zero that value of x is
excluded from the domain.
---------
Your problem. Since x^2+25 cannot be zero for any Real Number value of "x",
the domain of the function is "all Real Numbers".
------------------------
Notice that in determining the domain you do not try to FIND the domain.
You try to determine if there are values which are EXCLUDED from the
domain. If you cannot find any excluded values, the domain is "all
Real Numbers".
===================
cheers,
Stan H.
|
Miscellaneous_Word_Problems/170417: BILL CAN BUILD A BOOKCASE IN 6 HOURS, BUT IT TAKES HIS FRIEND, DAVID, ONLY 4 HOURS TO BUILD THE SAME BOOKCASE. HOW LONG WILL IT TAKE THEM TO BUILD THE BOOKCASE IF THEY WORK TOGETHER?
GIVE THE ANSWER IN HOURS AND MINUTES
1 solutions
Answer 125812 by stanbon(57295) on 2008-11-30 22:24:01 (Show Source):
You can put this solution on YOUR website!BILL CAN BUILD A BOOKCASE IN 6 HOURS, BUT IT TAKES HIS FRIEND, DAVID, ONLY 4 HOURS TO BUILD THE SAME BOOKCASE. HOW LONG WILL IT TAKE THEM TO BUILD THE BOOKCASE IF THEY WORK TOGETHER?
-----------------------------
Bill DATA:
Time = 6hrs/job ; rate = 1/6 job/hr
--------------------------------------
Davis DATA::
Time = 4 hrs/job ; rate = 1/4 job/hr
---------------------------------------
Together DATA:
Time = x hrs/job ; rate = 1/x job/hr
----------------------------------------
EQUATION:
rate + rate = together rate
1/6 + 1/4 = 1/x
(10/24) = 1/x
x = 24/10 = 2.4 hrs
--------
0.4 hrs = 0.4*60 minutes = 24 minutes
----------
Answer: 2 hrs and 24 minutes (time they need to do the job together)
====================================
Cheers,
Stan H.
|
Numbers_Word_Problems/170406: The least of 3 consecutive integers is divided by 10, the next is divided by 17, and the greatest is divided by 26. What are the numbers if the sum of the quotient is 10?
1 solutions
Answer 125804 by stanbon(57295) on 2008-11-30 21:28:23 (Show Source):
You can put this solution on YOUR website!The least of 3 consecutive integers is divided by 10, the next is divided by 17, and the greatest is divided by 26. What are the numbers if the sum of the quotient is 10?
--------------------
1st: x-1
2nd: x
3rd: x+1
---------------
EQUATION:
(x-1)/10 + x/17 + (x+1)/26 = 10
17*26(x-1) + 10*26x + 10*17(x+1) + 10*10*17*26
872x -272 = 44200
872x = 44472
x = 51 (2nd)
x-1= 50 (1st)
x+1 = 52 (3rd)
====================
Cheers,
Stan H.
|
Exponential-and-logarithmic-functions/170404: A bacteria culture starts with 120 bacteria and after three hours the population consists of 200 bacteria. assuming that the culture grows exponentially, find the poplation after 5 hours.
1 solutions
Answer 125803 by stanbon(57295) on 2008-11-30 21:19:45 (Show Source):
You can put this solution on YOUR website!A bacteria culture starts with 120 bacteria and after three hours the population consists of 200 bacteria. assuming that the culture grows exponentially, find the poplation after 5 hours.
---------------------------------------------------
A(t) = ab^t
---------------------
200 = 120b^3
b^3 = 200/120 = 5/3
b = 1.047197551....
-----------
Equation:
A(5) = 120(1.047197551)^5
A(5) = 151.12
Rounding down, A(5) = 151
=============================
Cheers,
Stan H.
|
Numbers_Word_Problems/170399: A certian radioactive substance decays according to the formula A(t)=e^-0.0063t where t is time in days. What is the half life of this substance (to the nearest day)?
1 solutions
Answer 125802 by stanbon(57295) on 2008-11-30 21:10:57 (Show Source):
You can put this solution on YOUR website!A certian radioactive substance decays according to the formula
A(t) = Aoe^-0.0063t where t is time in days. What is the half life
of this substance (to the nearest day)?
--------------------------------
If you start with Ao then A(t) = (1/2)Ao will determine the halflife.
------------------
(1/2)Ao = Aoe^-0.0063t
(1/2) = e^-0.0063t
Take the natural log to get:
-0.0063t = ln(0.5)
t = ln(0.5)/-0.0063
t = 110.0233620 years
0.0233620*365 days = 8.527.. days
--------------------
Ans: Halflife = 110 yrs + 8.527 days
========================================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/170398: A local elementary school is taking orders for a craf they will make. After calculating the cost of supplies the profit associated with making the craft is represented by P(x)=-x^2+130x-3000, where x represents the number of crafts sold and P represents the profilt. Determine the number of orders that could be acepted in order to make a profit. (Give the entire interval of solutions where a profit would be made)
1 solutions
Answer 125791 by stanbon(57295) on 2008-11-30 20:44:34 (Show Source):
You can put this solution on YOUR website!the profit associated with making the craft is represented by P(x)=-x^2+130x-3000, where x represents the number of crafts sold and P represents the profilt. Determine the number of orders that could be acepted in order to make a profit.
------------------
Determine when P is > 0
--------------------------
Solve -x^2+130x -3000 = 0
-(x^2-130x+3000) = 0
(x-30)(x-100) = 0
----------------------
Profit interval: 30 < x < 100
=============================
Cheers,
Stan H.
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Money_Word_Problems/170396: Sarah invested $5000 in two funds, paying 7% and 9% annual interest respectively. If the total interest earned for the year was $375, how much was invested at each rate?
1 solutions
Answer 125785 by stanbon(57295) on 2008-11-30 20:31:22 (Show Source):
You can put this solution on YOUR website!Sarah invested $5000 in two funds, paying 7% and 9% annual interest respectively. If the total interest earned for the year was $375, how much was invested at each rate?
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Interest Equation: 0.07x + 0.09(5000-x) = 375 dollars
7x + 9(5000-x) = 37500
7x + 45000 -9x = 37500
-2x = -7500
x = $3750.00 (amt. invested at 7%
5000-3750 = $1250 (amt. invested at 9%)
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Cheers,
Stan H.
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Mixture_Word_Problems/170377: Normal sea water is about 3.5% solids. This is about the same as saying "There are nearly 300 pounds of dissolved solid matter per thousand gallons of sea water" Using this information, find the weight of a gallon of sea water.
THANK YOU SO MUCH!
1 solutions
Answer 125783 by stanbon(57295) on 2008-11-30 20:23:49 (Show Source):
You can put this solution on YOUR website!"There are nearly 300 pounds of dissolved solid matter per thousand gallons of sea water" Using this information, find the weight of a gallon of sea water.
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x lbs/1 gallon = 300 lbs/1000 gallons
x = 0.3 lbs
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Cheers,
Stan H.
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Probability-and-statistics/170394: This is bothering me, I answered a math problem, This one
.
Bill has been given a 20 question mulitple choice test. He hasnt attended class recently, and there are 5 answers to each question, but only one is correct...what is the probability that he will answer more than five questions on the test correctly?..explain your answer
.
I think the answer is  , because you multiply the probability of getting one right, and multiply it 6 times,  or 
.
Am I right?
1 solutions
Answer 125780 by stanbon(57295) on 2008-11-30 20:17:34 (Show Source):
You can put this solution on YOUR website!Bill has been given a 20 question mulitple choice test. He hasnt attended class recently, and there are 5 answers to each question, but only one is correct...what is the probability that he will answer more than five questions on the test correctly?..explain your answer
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No, that is not the correct answer.
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It is a binomial problem with n= 20, p = 1/5; x>5
n is the number of trials
p is the probability of success on each trial
x is the number of successes
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P(x>5) = 1 - binomcdf(20,(1/5),4) = 0.37035...
This, from using a TI-83 calculator.
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Cheers,
Stan H.
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Expressions-with-variables/170289: This question is from textbook
This problem has to be solved algebraically. I am quite confused by this.
y=1.2x - 32.7
y=-0.7x + 46.15
1 solutions
Answer 125708 by stanbon(57295) on 2008-11-30 14:34:08 (Show Source):
You can put this solution on YOUR website!y=1.2x - 32.7
y=-0.7x + 46.15
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Since they both equal "y" they must equal each other:
1.2x - 32.7 = -0.7x + 46.15
1.9x = 78.85
x = 41.5
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Cheers,
Stan H.
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Quadratic_Equations/170286: I need help with this word problem I have tried and so has a tutor at school.
Malikka takes a paddleboat 1km upriver against a 4km/hr current then returns downriver with the current, back to starting point. Her whole trip takes 2 hours, write a quadratic equation describing this situation. The unknown is the speed, v, that Mallika would paddle with no current present. Solve. What speed (in km/hr) would Mallika paddle by herself with no current present?
1 solutions
Answer 125698 by stanbon(57295) on 2008-11-30 13:57:51 (Show Source):
You can put this solution on YOUR website!Malikka takes a paddleboat 1km upriver against a 4km/hr current then returns downriver with the current, back to starting point. Her whole trip takes 2 hours, write a quadratic equation describing this situation. The unknown is the speed, v, that Mallika would paddle with no current present. Solve. What speed (in km/hr) would Mallika paddle by herself with no current present?
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Upriver DATA:
Distance = 1 km ; rate = v-4 km/h ; time = d/r = 1/(v-4) hr.
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Downriver DATA:
Distance = 1 km ; rate = v+4 km/h ; time = d/r = 1/(v+4) hr.
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EQUATION:
time up + time down = 2 hrs
1/(v-4) + 1/(v+4) = 2
v+4 + v-4 = 2(v^2-16)
v = v^2-16
v^2 - v - 16 = 0
v = [1 +- sqrt(1 - 4*-16)]/2
v = [1 +- sqrt(65)]/2
Positive solution:
v = 4.53 km/h
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Cheers,
Stan H.
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Quadratic-relations-and-conic-sections/170276: I can never get this!!! Please Help!!!
For Each Of The Conics in standard form, list all Applical Information. If the Information isnt needed for the conic, write N/A. Then Graph Equation on a graph. Labeling Graph Completley.
Center:
Covertices:
Focus/Foci:
Asymptopes:
Major Axis:
Transverse:
Directrix:
Vertices/Vertex:
Radius:
Eccentricity:
Minor Axis:
Conjugate Axis:
Axis Of Symmetry:
1 solutions
Answer 125696 by stanbon(57295) on 2008-11-30 13:43:33 (Show Source):
You can put this solution on YOUR website!For Each Of The Conics in standard form, list all Applical Information. If the Information isnt needed for the conic, write N/A. Then Graph Equation on a graph. Labeling Graph Completley.
(y+1)^2/4-(x-4)^2/16=1
This is an ellipse with center at (4,-1)
a = 4;b=2;c=sqrt(16+4)=2sqrt5
Foci: (4,-1+-2sqrt(5))
Major axis: x = -1
Vertices: (4,-1+-4)
Covertices: (4+-2,-1)
Eccemtricity: ?
All others are NA
Center: listed
Covertices:
Focus/Foci:
Asymptopes:
Major Axis:
Transverse:
Directrix:
Vertices/Vertex:
Radius:
Eccentricity:
Minor Axis:
Conjugate Axis:
Axis Of Symmetry:
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Quadratic-relations-and-conic-sections/170279: I can never get this!!! Please Help!!!
For Each Of The Conics in standard form, list all Applical Information. If the Information isnt needed for the conic, write N/A. Then Graph Equation on a graph. Labeling Graph Completley.
Center:
Covertices:
Focus/Foci:
Asymptopes:
Major Axis:
Transverse:
Directrix:
Vertices/Vertex:
Radius:
Eccentricity:
Minor Axis:
Conjugate Axis:
Axis Of Symmetry:
1 solutions
Answer 125694 by stanbon(57295) on 2008-11-30 13:24:43 (Show Source):
You can put this solution on YOUR website!For Each Of The Conics in standard form, list all Applical Information. If the Information isnt needed for the conic, write N/A. Then Graph Equation on a graph. Labeling Graph Completley.
y^2-8y-8x+64=0
Complete the square with the y-terms:
y^2-8y+16 = 8x-64+16
(y-4)^2 = 8(x-6)
This is a parabola with vertex at (6.4) opening to the right ;axis of symmetry y = 4; p = 2; focus at (8,4); directrix of x=4.
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Center: NA
Covertices:NA
Focus/Foci: listed
Asymptopes: NA
Major Axis:NA
Transverse: NA
Directrix: listed
Vertices/Vertex: listed
Radius: NA
Eccentricity: always 1 for a parabola
Minor Axis:NA
Conjugate Axis: NA
Axis Of Symmetry: listed
===========================
Cheers,
Stan H.
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Human-and-algebraic-language/170226: 2. Find the product of the cube of (-4/3) and square of (-3/2).
1 solutions
Answer 125662 by stanbon(57295) on 2008-11-30 08:07:45 (Show Source):
You can put this solution on YOUR website!2. Find the product of the cube of (-4/3) and square of (-3/2).
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= (-4/3)^3*(-3/2)^2
= -64/3^3 * 3^2/4
Cancel 3^2 in the numerator and the denominator to get:
= -64/3 * 1/4
Cancel 4 in the numerator and the denominator to get:
= -16
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Cheers,
Stan H.
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Quadratic_Equations/170220: square root sign 9x+67=x+5 (solve)
Rewrite with a rational exponent small 6 square root sign 19.
Convert to decimal notation 8.87*10^7. I had 8870000000. (I know this is incorrect)
Use rational exponents to write xy small 5*y small 1|6 (1&6 are small numbers)*2 small 1|3 (1&3 are small numbers)
I thank you in advance, for all your help.
I am a student and I am in need of help.
1 solutions
Answer 125659 by stanbon(57295) on 2008-11-30 07:56:57 (Show Source):
You can put this solution on YOUR website!square root sign 9x+67=x+5 (solve)
sqrt(9x+67) = x+5
Square both sides to get:
9x+67 = x^2+10x+25
Rearrange:
x^2+x-42 = 0
Factor:
(x-7)(x+6) = 0
x = 7 or x = -6
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Rewrite with a rational exponent small 6 square root sign 19.
Ans: 19^(1/6)
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Convert to decimal notation 8.87*10^7. I had 8870000000. (I know this is incorrect)
Ans: 8.87*10^7= 887*10^5 = 88700000
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Use rational exponents to write xy small 5*y small 1|6 (1&6 are small numbers)*2 small 1|3 (1&3 are small numbers)
Comment: That is too confusing for me.
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Cheers,
Stan H.
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