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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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>Next
Probability-and-statistics/102610: If three coins are tossed what is the probability of tossing two heads and one tail?
Thank you
1 solutions
Answer 74625 by stanbon(57203)   on 2007-10-06 12:41:18 (Show Source):
You can put this solution on YOUR website!If three coins are tossed what is the probability of tossing two heads and one tail?
----------
There are three ways to place the tail so those three are mutually
exclusive events. The probability of each event is (1/2)^2*(1/2)
because each coin is independent = 1/8
So the answer is 1/8 + 1/8 + 1/8 = 3/8
------------
Using the binomial formula you would get 3C2(1/2)^2(1/2) = 3(1/8) = 3/8
====================
Cheers,
Stan H.
|
Quadratic_Equations/102546: Solve each equation for x. Factor the left-hand side
x² +4x + 4 =7
1 solutions
Answer 74597 by stanbon(57203) on 2007-10-06 08:58:33 (Show Source):
You can put this solution on YOUR website!Solve each equation for x. Factor the left-hand side
x² +4x + 4 =7
-----------------
(x^2)^2 = 7
(x+2)^2-(sqrt7)^2 = 0
Factor:
(x+2-srt7)(x+2+sqrt7)=0
x=-2+sqrt7 or x= -2-sqrt7
==================
Cheers,
Stan H.
|
Trigonometry-basics/102562: This question is from textbook Algebra and Trigonometry
The degree three polynomial f(x) with real coefficients and leading coefficient 1 has -3 and 4i among its roots. Express f(x)as a porduct of linear and quadratic polynomials with real coefficients.
1 solutions
Answer 74596 by stanbon(57203) on 2007-10-06 08:55:21 (Show Source):
You can put this solution on YOUR website!The degree three polynomial f(x) with real coefficients and leading coefficient 1 has -3 and 4i among its roots. Express f(x)as a porduct of linear and quadratic polynomials with real coefficients.
----------
If f(x) has real coefficients and 4i is a root, then -4i is also a root.
------------
f(x) = (x+3)(x-4i)(x+4i)
f(x) = (x+3)(x^2+16)
f(x) = x^3+3x^2+16x+48
===========
Cheers,
Stan H.
|
Human-and-algebraic-language/102581: I am terrible at word problems. Please show me the formula to solve this question:
What is the exact height of a brick wall that is 44 courses high, when three courses of brick, plus their mortor joints are 8 inches (203.3 mm) high?
Thank you!
1 solutions
Answer 74592 by stanbon(57203) on 2007-10-06 08:37:33 (Show Source):
You can put this solution on YOUR website!What is the exact height of a brick wall that is 44 courses high, when three courses of brick, plus their mortor joints are 8 inches (203.3 mm) high?
-----------------
Find out how many "three courses of brick" there are in 44 courses:
44/3 is the answer
----------------------
since each of these is 8 inches high, multiply 44/3 by 8 to get:
117 1/3 inches or (44/3)*203.3 mm = 2981.733 mm
==================
Cheers,
Stan H.
|
Quadratic_Equations/102542: The demand and supply equations for a certain item are given by
D=-5p+40
S=-p^2+30p-8
Find the equilibrium price.
1 solutions
Answer 74573 by stanbon(57203) on 2007-10-05 22:28:32 (Show Source):
You can put this solution on YOUR website!D=-5p+40
S=-p^2+30p-8
Find the equilibrium price.
--------------------------------------
-5p+40 = -p^2+30p-8
p^2-35p+48=0
p = [35 +- sqrt(35^2-4*48)]/2
p = [35 +- sqrt(1033)]/2
p = [35 +- 32.14]/2
p = 33.57 or p = 1.43
========================
Cheers,
Stan H.
|
Trigonometry-basics/102520: A small company produces both doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets. Then graph the system of inequalities.
PLEASE help me with this again I am soo terribel with wrod problems like this.
1 solutions
Answer 74571 by stanbon(57203) on 2007-10-05 21:42:19 (Show Source):
You can put this solution on YOUR website!A small company produces both doll houses and sets of doll furniture.
Let x is the number of doll houses and y is the number of furniture sets.
-------------
The doll houses take 3 hours of labor to produce, and
the furniture sets take 8 hours.
The labor available is limited to 400 hours per week, and
the total production capacity is 100 items per week.
Labor Equation: 3x+8y<= 400
Production equation: x+y <=100
----------------------
Solve each for y; needed for graphing later
y <= (-3/8)x + 50
y <= -x+100
---------------------------
Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week.
x>=20
y>=10
Write a system of inequalities
Then graph the system of inequalities.
--------------
On an x/y coordinate system:
Draw a vertical line at x = 20 and at x=100
Draw a vertical line at y = 10 and at y=100
--------------
Comment
The resulting box limits the domain and the range.
-----------------------------------
Graph the Labor and the Production inequalities in the box.
=============
Cheers,
Stan H.
|
Trigonometry-basics/102506: Solve the system by graphing.
x + 2y = 4
x + 2y = –2
Please help with this graphing problem.
1 solutions
Answer 74544 by stanbon(57203) on 2007-10-05 20:05:47 (Show Source):
You can put this solution on YOUR website!Solve the system by graphing.
x + 2y = 4
x + 2y = –2
--------------------------
Comment: these lines are parallel; there is no solution for the system.
-------------------------
==================
Cheers,
Stan H.
|
Trigonometry-basics/102510: Solve the system by addition or substitution.
3x + 6y = 0
x = 2/3 (this is a fraction)
The 6y = 0 and
x = 2/3 are supposed to be lined up under each other if this helps anyone, it doesnt help me that is why I need your help.
Thank you.
1 solutions
Answer 74541 by stanbon(57203) on 2007-10-05 20:00:23 (Show Source):
You can put this solution on YOUR website!Solve the system by addition or substitution.
3x + 6y = 0
x = 2/3
------------
Substitute to solve for y:
3(2/3) + 6y = 0
2 + 6y = 0
y = -1/3
-------------
Solution: x = 2/3; y = -1/3
===================
Cheers,
Stan H.
|
Trigonometry-basics/102509: Please help me with this problem am having lots of problems with math especially graphing. Thank you.
Solve the system by graphing.
3x + y = –1
9x + 3y = –3
1 solutions
Answer 74538 by stanbon(57203) on 2007-10-05 19:55:25 (Show Source):
You can put this solution on YOUR website!Solve the system by graphing.
3x + y = –1
9x + 3y = –3
----------------
Put both equations in slope-intercept form.
-----------------
y = -3x-1
y = -3x-1
---------------------
Graph:
================
Solution: Since the two equations are the same every point
on the line y = -3x-1 is a solution for the system.
================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/102385: how much pure acid should be mixed with 7 gallons of a 40% acid solution in order to get a 70% acid solution?
1 solutions
Answer 74527 by stanbon(57203) on 2007-10-05 19:30:14 (Show Source):
You can put this solution on YOUR website!how much pure acid should be mixed with 7 gallons of a 40% acid solution in order to get a 70% acid solution?
------------------------
Comment: Follow the acid.
------------------------
40% solution DATA:
Amt = 7 gallons ; amt of acid = 0.07*7 = 0.49 gallons
---------------
100% solution DATA;
Amt = x gallos ; amt of acid = x gallons
-----------------------
70% mixture DATA:
amt = x+7 gallons ; amt of acid = 0.70(x+7)= (0.70x + 4.9) gallons
-----------------------------
EQUATION:
acid + acid = acid
0.49 + x = 0.70x + 4.9
0.30x = 4.41
x = 14.7 gallons (amt of 100% solution that must be added)
================
Cheers,
Stan H.
|
Graphs/102504: This question is from textbook Essentials of Intermediate Algebra for college students
What is the slope and y-intercept of the line whose equation is given. Then graph the linear function. y=2x+1
I do not understand this at all! Could someone please help me? I would greatly appreciate it. Thanks So Much.
1 solutions
Answer 74524 by stanbon(57203) on 2007-10-05 19:20:28 (Show Source):
You can put this solution on YOUR website!What is the slope and y-intercept of the line whose equation is given. Then graph the linear function. y=2x+1
-----------------------------
The slope is 2; the y-intercept is 1
-----------
Graph:
Cheers,
Stan H.
|
Travel_Word_Problems/102347: A plane is passing over the Taj at noon going 450 mile per hour and it's altitude is m feet. Write a function for the distance away from the Taj the plane is.
1 solutions
Answer 74522 by stanbon(57203) on 2007-10-05 19:14:51 (Show Source):
You can put this solution on YOUR website!A plane is passing over the Taj at noon going 450 mile per hour and it's altitude is m feet. Write a function for the distance away from the Taj the plane is.
|
Graphs/102495: I would so appreciate it if someone could help me, I don't understand the piecewise function thing. The problem says to graph the piecewise-defined function f(x)= {-4, if -5
{x^2+1, if x>0
1 solutions
Answer 74517 by stanbon(57203) on 2007-10-05 18:42:43 (Show Source):
|
Geometry_Word_Problems/102502: Geometry. The volume of the box is represented by (x^2+5x+6)(x+5). Find the polynomial that represents the area of the bottom of the box.
There is a picture of the box with x+2 next to it. Please help. Thank you.
1 solutions
Answer 74516 by stanbon(57203) on 2007-10-05 18:41:27 (Show Source):
You can put this solution on YOUR website!Geometry. The volume of the box is represented by (x^2+5x+6)(x+5). Find the polynomial that represents the area of the bottom of the box.
------------
x+5 is the height
x^2+5x+6 is the area of the base
=============
Cheers,
Stan H>
|
Quadratic_Equations/102486: 1
___ - 3= 8
x(squared) _____
x
1 solutions
Answer 74515 by stanbon(57203) on 2007-10-05 18:39:45 (Show Source):
You can put this solution on YOUR website!1
___ - 3= 8
x(squared) _____
x
------------------------
[1/x^2] - 3 = [8/x]
Multiply thru by x^2 to get:
1 -3x^2 = 8x
Rearrange:
3x^2+8x-1 = 0
Use the Quadratic formula:
x = [-8 +- sqrt(64-4*3*-1)]/6
x = [-8 +- sqrt(76)]/6
x = -(4/3) + (1/3)sqrt19 or x = -(4/3) - (1/3)sqrt19
====================
Cheers,
Stan H.
|
Graphs/102492: what is the domain and graph of this function: f(x)=2/3x-7
1 solutions
Answer 74512 by stanbon(57203) on 2007-10-05 18:23:42 (Show Source):
You can put this solution on YOUR website!what is the domain and graph of this function: f(x)=2/3x-7
-------------
Domain: All Real Numbers except x= 7/3
---------------
Graph:
=====================
Cheers,
Stan H.
|
Functions/102494: Can someone help me please!!! Determine whether the equation defines y as a function of x
x^3 y-2y=6
1 solutions
Answer 74510 by stanbon(57203) on 2007-10-05 18:14:26 (Show Source):
You can put this solution on YOUR website!x^3 y-2y=6
---------
Yes, each value of x will have one corresponding value for y.
-------------------
y(x^3-2) = 6
----------------
At this point each value of x has one corresponding value of y
so y still a function of x.
y = 6/(x^3-2)
----------------
Comment: At this point the equation does not have
the same domain as the original equation.
================
Cheers,
Stan H.
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Quadratic_Equations/102481: determine the equation of the parabola with x-intercepts -4 and 3, and that passes through (2,7)
1 solutions
Answer 74508 by stanbon(57203) on 2007-10-05 18:03:18 (Show Source):
You can put this solution on YOUR website!determine the equation of the parabola with x-intercepts -4 and 3, and that passes through (2,7)
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If -4 and 3 are x-intercepts, f(x) has factors (x+4) and (x-3)
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So, y = a(x+4)(x-3)
If the parabola passes thru (2,7)
7 = a(2+4)(2-3)
7 = a*6*-1
a = -7/6
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EQUATION:
y = (-7/6)(x+4)(x-3)
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Cheers,
Stan H.
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