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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
Graphs/91299: Find the horizontal asymptote of F(x) =5x^2+1/ x^2+2x+1
1 solutions
Answer 66270 by stanbon(57203)   on 2007-08-02 21:12:36 (Show Source):
You can put this solution on YOUR website!Find the horizontal asymptote of F(x) =5x^2+1/ x^2+2x+1
---------
To find the horizontal asymptote of a rational function:
1st: Find the highest power term; it doesn't matter if this term
is in the numerator or in the denominator. For your problem the
highest power term is x^2.
---------
2nd: Write down the coefficient of that highest power term as it
appears in the numerator and as it appears in the denominator.
For your problem that would be 5/1
------------
3rd: The horizontal asymptote is y= that number. For your problem
that would be y=5
=================
Cheers,
Stan H.
|
Surface-area/91206: this is a problem i would like to ask that if i know the circumference of an oval
which is 1000m, how to find the area of this oval. please help me with this question. thanks.
1 solutions
Answer 66268 by stanbon(57203) on 2007-08-02 21:05:57 (Show Source):
|
Polynomials-and-rational-expressions/91296: I need help with this Word Problem.
Ed and Dave are going to divide a cash prize of $14,000 in a ratio of 2 to 5. How much will Dave receive?
How do you know who gets what amount? Here is how I worked it but confused on who gets what.
x/14000-x=2/5
5x=2(14000-x)
5x=28000-2x
5x+2x=28000-2x+2x
7x=28000
7x/x=28000/7
x=4000
14000-x
14000-4000=10000
1 solutions
Answer 66267 by stanbon(57203) on 2007-08-02 21:04:29 (Show Source):
You can put this solution on YOUR website!Ed and Dave are going to divide a cash prize of $14,000 in a ratio of 2 to 5. How much will Dave receive?
--------------
2 to 5 is the same as 2x to 5x
Ed has 2x; Dave has 5x
EQUATION:
2x+5x = 14000
7x = 14000
x=2000
Ed has 2x= $4000
Dave has 5x= $10000
==========
Cheers,
Stan H.
|
Graphs/90552: Please help me with this:
It asks to have the inequality solved and to state and graph the solution set???
x/x-3<=-8/x-6 HELP PLEASE!!!
1 solutions
Answer 66266 by stanbon(57203) on 2007-08-02 21:00:55 (Show Source):
You can put this solution on YOUR website!state and graph the solution set???
x/(x-3)<=-8/(x-6)
Find the values x CANNOT take.
x cannot be 3 and x cannot be 6.
----------------
Draw a number line; plot 3 and 6 on that number line.
You now have three intervals of points that may be solution points.
Pick a test point from each interval to determine if the selected
interval is part of the solution set.
--------------
Interval (-inf,3); select x=0; 0/(0-3)<=-8/(0-6) ; true so (-inf,3) is part of the solution.
-----------
Interval (3,6); select x= 5; 5/(5-3)<=-8/(5-6) ; true so (3,6) is part of the
solution.
------------
Interval (6,inf); select x= 7; 7/(7-3)<=-8/(7-6); false so no solution here
---------------
Final solution: (-inf,3)U(3,6)
===============
Cheers,
Stan H.
|
real-numbers/91237: 1. y(y*5)(wy)
2. |6-3.7|+|7-(5-2)|
3. 8-3|5-16+1|
This is my first Algebra course. Kindly assist me. Thank you
1 solutions
Answer 66227 by stanbon(57203) on 2007-08-02 15:38:29 (Show Source):
You can put this solution on YOUR website!1. y(y*5)(wy) = 5y^2(wy) = 5wy^3
2. |6-3.7|+|7-(5-2)| = |2.3] + |7-3| = 2.3 + 4 = 6.3
3. 8-3|5-16+1| = 8-3(10) = -22
================
Cheers,
Stan H.
|
real-numbers/91236: Susan and Joan are diving for golf balls in a large trap. Susan recovers a golf ball every 0,016 hours while Joan recovers a ball every 0,025 hour. If both are working then at what rate(in golf balls per hour) are they recovering golf balls?
Kindly help me.
1 solutions
Answer 66226 by stanbon(57203) on 2007-08-02 15:33:58 (Show Source):
You can put this solution on YOUR website!Susan and Joan are diving for golf balls in a large trap. Susan recovers a golf ball every 0,016 hours while Joan recovers a ball every 0,025 hour. If both are working then at what rate(in golf balls per hour) are they recovering golf balls?
------------------
Susan DATA:
Time = 0.016 hrs/job ; Rate = 1/0.016 job/hr
-------------------
Joan DATA:
Time = 0.025 hrs/job ; Rate = 1/0.025 job/hr
------------------------
Their together rate is 1/0.016 + 1/0.025 = 62.5 + 40 = 102.5/hr
==========================
Cheers,
Stan H.
|
Quadratic_Equations/91230: The value 'V'(in dollars per acre) of a wheat crop 'd' days after planting is given by V=12d-0.5d^2 for 201 solutions
Answer 66225 by stanbon(57203) on 2007-08-02 15:22:49 (Show Source):
You can put this solution on YOUR website!The value 'V'(in dollars per acre) of a wheat crop 'd' days after planting is
given by V=12d-0.5d^2 for 20 < d < 80.
Find the maximum value of an acre of wheat.
How many days after it was planted will it take to achieve this maximum value?
----------------
Maximum occurs at d = -b/2a = -12/(2*-0.5) = 12
V(d) = 12*12 - 0.5(12^2) = $72 per acre
=========================
Cheers,
Stan H.
|
Mixture_Word_Problems/91234: This question is from textbook
The directions on a concentrated cleaner state that 3 tablespoons of concentrate make 345 ounces of fluid. How many ounces of cleaning fluid will 2 tablespoons of cleaner make?
Thank you!
1 solutions
Answer 66223 by stanbon(57203) on 2007-08-02 14:59:13 (Show Source):
You can put this solution on YOUR website!The directions on a concentrated cleaner state that 3 tablespoons of concentrate make 345 ounces of fluid. How many ounces of cleaning fluid will 2 tablespoons of cleaner make?
--------------------------
Let x be the number of counces of cleaning fluid made by 2 taglespoons.
x/2 = 345/3
x = (2*345)/3
x = 690/3 = 230 ounces of cleaning fluid
====================
Cheers,
Stan H.
|
Functions/91232: Please help with this THANKS
f(x)=-4x +2
g(x)= 6x^2 + 4x -5
NEED TO FIND:
(got)(x)
Do not understand
HELP
llo
1 solutions
Answer 66221 by stanbon(57203) on 2007-08-02 14:53:25 (Show Source):
You can put this solution on YOUR website!f(x)=-4x +2
g(x)= 6x^2 + 4x -5
NEED TO FIND:
(gof)(x) = g[f(x)] = g[-4x+2] = 6(-4x+2)^2 + 4(-4x+2) -5
= 6(16x^2-8x+4) -16x-8 -5
= 96x^2-48x+24-16x-13
= 96x^2-64x+11
===================
Cheers,
Stan H.
|
Equations/91233: This question is from textbook
what is the greastest commonn fator of 24 and 72 and also what is
the answer to this 7a+16+(-4a)+(-4a) i tryed many times and its never the right answer i get -a + 16
1 solutions
Answer 66220 by stanbon(57203) on 2007-08-02 14:48:38 (Show Source):
You can put this solution on YOUR website!what is the greatest common factor of 24 and 72
24 = (2^3)*3
72 = (2^3)*(3^2)
The gcf is each prime raised to the lowest power present in either number:
Your gcf is 2^3 * 3 = 24
---------------------
what is the answer to this 7a+16+(-4a)+(-4a)
= 7a + 16 -8a
=-a + 16
===================
Cheers,
Stan H.
|
Quadratic_Equations/91217: factoring a quadratic with leading coefficient greater than one
2y^2+15y+28
1 solutions
Answer 66197 by stanbon(57203) on 2007-08-02 10:34:24 (Show Source):
You can put this solution on YOUR website!factoring a quadratic with leading coefficient greater than one
2y^2+15y+28
ac=2*28=56
b=15
Think of two numbers whose product is 56 and whose sum is 15
The numbers are 7 and 8
Replace 15y by 7y+8y to get:
2y^2+7y+8y+28
Factor to get:
y(2y+7)+4(2y+7)
Factor again to get:
(2y+7)(y+4)
=============
Cheers,
Stan H.
|
Radicals/91216: I need help with this problem
Determine whether square root of 4 is rational or irrational
Thank you
1 solutions
Answer 66195 by stanbon(57203) on 2007-08-02 10:31:14 (Show Source):
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Travel_Word_Problems/91212: A sailboat travels 20 miles downstream in 3 hours. It returns in 4 hours. Find the speed of the sailboat in still water and the rate of the current. (using the 5- step method )
1 solutions
Answer 66194 by stanbon(57203) on 2007-08-02 10:29:52 (Show Source):
You can put this solution on YOUR website!A sailboat travels 20 miles downstream in 3 hours. It returns in 4 hours. Find the speed of the sailboat in still water and the rate of the current.
---------
Draw the picture:
Symbolize the DATA:
Downstream DATA:
distance= 20 miles; time = 3 hrs ; rate = 20/3 hrs
--------
Upstream DATA:
distance = 20 miles; time = 4 hrs ; rate = 20/4 = 5 hrs
---------------
Let speed in still water be "b"
Let speed of the current be "c"
-----------------
EQUATION:
b+c=20/3
b-c=5
-----------
Add the two equations:
2b = 35/3
b = 35/6 mph (speed of the boat in still water)
Solve for c:
35/6 + c = 40/6
c=5/6 mph (speed of the current)
===============
Cheers,
Stan H.
|
Triangles/91214: this is a type of problem i was unable to solve. i was given the perimeter of a scalene triangle which was 1000m and asked to find its area. please can you help me solve this problem.thanks.
1 solutions
Answer 66193 by stanbon(57203) on 2007-08-02 10:22:34 (Show Source):
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Graphs/91188: Find the equation of the line that goes through the given point and has the given slope. Write the answer in slope-intercept form.
(-1,-5), -8
1 solutions
Answer 66192 by stanbon(57203) on 2007-08-02 10:20:18 (Show Source):
You can put this solution on YOUR website!Find the equation of the line that goes through the given point and has the given slope. Write the answer in slope-intercept form.
(-1,-5), -8
-------------
The equation has the form y=mx+b
You know m=-8 and y=-5 when x=-1 so you can solve for b as follows:
-5 = (-8)(-1)+b
b=3
EQUATION:
y = -8x + 3
=================
Cheers,
Stan H.
|
real-numbers/91198: Prove that cube root of 7 is an IRRATIONAL number ?
1 solutions
Answer 66191 by stanbon(57203) on 2007-08-02 10:16:05 (Show Source):
You can put this solution on YOUR website!Prove that cube root of 7 is an IRRATIONAL number ?
Assume that cube rt 7 is rational.
Then (7)^(1/3) = a/b where a and b are integers and a/b is reduced to lowest terms.
Then a=b[7^(1/3)]
Since a is a multiple of b and a is an integer, b divides a.
Since b divides a, a = nb and n is an integer.
Therefore 7^(1/3) = a/b = nb/b, so a/b is not reduced to lowest terms.
-----------
What led to this contradiction?
The assumption that 7^(1/3) was rational.
The assumption must be wrong.
Therefore 7^(1/3) if irrational.
================
Cheers,
Stan H.
|
Linear-equations/91213: Solve each system by graphing. y=-2/3x
2x+3y=5
I tried to use the formula y=mx+b. Can you show me line by line instructions so I can get the steps straight in my head. Thanks for your help.
1 solutions
Answer 66190 by stanbon(57203) on 2007-08-02 10:04:34 (Show Source):
You can put this solution on YOUR website!Solve each system by graphing. y=-2/3x
2x+3y=5
-------------
Put both in slope-intercept form and graph them:
y=-2/3x
y=(-2/3)x+(5/3)
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The lines are parallel so there is no solution for the system of equations.
==============
Cheers,
Stan H.
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Probability-and-statistics/91195: A bag contains 52 tickets numbered 1,2...52 of which 5 are drawn at random and arranged in ascending order t1>t2>t3>t4>t5.find the probability that t4 being 42.
1 solutions
Answer 66188 by stanbon(57203) on 2007-08-02 09:11:40 (Show Source):
You can put this solution on YOUR website!A bag contains 52 tickets numbered 1,2...52 of which 5 are drawn at random and arranged in ascending order t1>t2>t3>t4>t5.find the probability that t4 being 42.
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To get the 42 on the 4th card you have to NOT get the 42 on the 1st, the
2nd, or the 3rd card. Once you get the 42 on the 4th card the next card
can be any of the remaining cards.
Prob(no 42 on 1st draw)= 51/52
Prob(no 42 on 2nd draw) = 50/51
Prob(no 42 on 3rd draw) = 49/50
Prob(42 on the 4th draw) = 1/49
Prob(any card on the 5th draw) = 48/48
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P(42 on 4th draw) = (51/52)(50/51)(49/50)(1/49)(48/48)
= (1/52)(1/49)
= 1/2548
==========
Cheers,
Stan H.
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percentage/91180: The question is:
This year, 75% of the graduating class of Harriot Tubman High School had taken at least 8 math courses. Of the remaining members, 60% had taken 6 or 7 math courses. What percent of the graduating class had taken fewer than 6 math courses?
---I know it's 60% of 25% but how do you get that? What does "of" stand for?
1 solutions
Answer 66185 by stanbon(57203) on 2007-08-01 22:55:08 (Show Source):
You can put this solution on YOUR website!This year, 75% of the graduating class of Harriot Tubman High School had taken at least 8 math courses. Of the remaining members, 60% had taken 6 or 7 math courses. What percent of the graduating class had taken fewer than 6 math courses?
---I know it's 60% of 25% but how do you get that? What does "of" stand for?
------------
What does (1/3) of 6 mean? It means 2. How do you get that? You multiply.
"of" means multiply.
-------------------
75% take at least 8 math courses.
--------------------
That leaves 25% who did not take at least 8 math courses.
60% of those 25% took 6 or 7 math courses:
0.60*0.25 = 0.15 = 15% took 6 or 7 math courses.
-----------
Summarizing;
75% take at least 8 math course
15% take 6 or math classes
That leaves 10% who took fewer than 6 math courses.
=================
Cheers,
Stan H.
.
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real-numbers/91179: 3(x-2)+2=2(x-4)
-7x=-26+6x
7x+3>9x-5
I=Prt solve for r
This is from Beginning Algebra by John Tobey, Jeffrey Slater
6th edition
1 solutions
Answer 66184 by stanbon(57203) on 2007-08-01 22:43:57 (Show Source):
You can put this solution on YOUR website!3(x-2)+2=2(x-4)
3x-6+2 = 2x-8
3x-4 = 2x-8
x = -4
----------------------
-7x=-26+6x
13x = 26
x=2
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7x+3>9x-5
8> 2x
x<4
----------------
I=Prt solve for r
r = I/(Pt)
=========================
Cheers,
Stan H.
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Graphs/91176: 2) By looking at the equation for a rational function, how can you tell if there will be "y-values" which will never occur? How might this be represented on the graph?
1 solutions
Answer 66183 by stanbon(57203) on 2007-08-01 22:35:11 (Show Source):
You can put this solution on YOUR website!The denominator of the rational function cannot have a value of zero.
If there are radicals in the denominator the radicand must not be negative.
----------------
Cheers,
Stan H.
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Numeric_Fractions/91178: Sarah spends 1/4 of her income for transportation, 1/6 of her income for food, and 1/3 of her income for rent and utilities. What fractional part of Sarah's income is left for all of her other expenses?
1 solutions
Answer 66182 by stanbon(57203) on 2007-08-01 22:30:19 (Show Source):
You can put this solution on YOUR website!Sarah spends 1/4 of her income for transportation, 1/6 of her income for food, and 1/3 of her income for rent and utilities. What fractional part of Sarah's income is left for all of her other expenses?
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1-1/4-1/6-1/3
Lcd is 12
= 12/12 - 3/12 -2/12 -4/12
= (12-9)/12
= 3/12
= 1/4 is left for all her other expenses
=======================
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/91167: The percentage of women in the 20-24 age group who have never married went from 55% in the 1970 to 73% in 2000 (Census Bureau, www.census.gov) Let 1970 be year 0 and 200 be year 30.
a.) Find the interpret the slope of the line through the points (0,55) and (30,73).
b.) Find the equation of the line in part (a).
c.) What is the meaning of the y-intercept?
d.) Use the equation to predict the percentage in 2010.
e.) If this trend continues, then in what year will the percentages of women in the 20-24 age group who have never married reach 100%?
1 solutions
Answer 66180 by stanbon(57203) on 2007-08-01 21:57:49 (Show Source):
You can put this solution on YOUR website!The percentage of women in the 20-24 age group who have never married went from 55% in the 1970 to 73% in 2000 (Census Bureau, www.census.gov) Let 1970 be year 0 and 2000 be year 30.
a.) Find the interpret the slope of the line through the points (0,55) and (30,73).
slope = [73-55]/[30-0] = 18/30 = 9/15
slopw means "for each 15 years gone by the percent of women in the designated
group who have never married increased 9%"
-----------------------------
b.) Find the equation of the line in part (a).
m= (9/15) and y = 55 when x= 0
EQUATION: y = (9/15)x+55
-----------------------------
c.) What is the meaning of the y-intercept?
y-intercept occurs when x = 0 means that in 1970 the percentage was 55
----------------------------------
d.) Use the equation to predict the percentage in 2010.
In 2010 x= 2010-1970 = 40
Let x=40 and solve for y:
y = (9/15)40+55 = 24+55 =79%
-------------------------------
e.) If this trend continues, then in what year will the percentages of women in the 20-24 age group who have never married reach 100%?
Let y= 100 and solve for x:
100 = (9/15)x+55
45 = (9/15)x
x = 75
1970+75= 2045
================
Cheers,
Stan H.
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expressions/91175: This question is from textbook Mathematics course 3
Would you be able to tell me what "absolute value" stands for in a word phrase algebraic expression?
15 more than the absolute value of a number
Would this be written as 15+x?
1 solutions
Answer 66179 by stanbon(57203) on 2007-08-01 21:46:44 (Show Source):
You can put this solution on YOUR website!|x|+15
----------
absolute value of a number means the distance the number is from 0 on a number line.
Examples: |-3| = 3
|5| = 5
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Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/91171: A bookstore manager plans to spend $60.00 on pens at 30 cents each and pencils at 10 cents each. The equation 0.10x + 0.30y = 60 can be used to model this situation.
a.) What do x and y represent?
b.) Graph th equation.
c.) Write the equation in slope-intercept form.
d.) What is the slope of the line?
e.) What does the slope tell you?
1 solutions
Answer 66177 by stanbon(57203) on 2007-08-01 21:43:50 (Show Source):
You can put this solution on YOUR website!A bookstore manager plans to spend $60.00 on pens at 30 cents each and pencils at 10 cents each. The equation 0.10x + 0.30y = 60 can be used to model this situation.
a.) What do x and y represent?
x is the # of pencils; y is the number of pens
-----------------
b.) Graph th equation.
Solve for y, as follows:
y = (-1/3)x + 200
-------------------------
c.) Write the equation in slope-intercept form.
y=(-1/3)x+200
----------------------
d.) What is the slope of the line?
slope = -1/3
-----------------
e.) What does the slope tell you?
As the number of pens sold decreases 1 the number of percils sold increases
by 3
=================
Cheers,
Stan H.
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real-numbers/91150: Help Me Please
23 Which of the following datasets is a straight-line graph? Explain (or draw its graph).
a.
x y
4 5
5 3
7 2
b.
r t
66 330
29 145
41 205
c.
h k
450 230
348 266
590 110
1 solutions
Answer 66175 by stanbon(57203) on 2007-08-01 21:31:52 (Show Source):
You can put this solution on YOUR website!Set "b" is three points that are on a straight line because the
slope between the points is the same = 5.
============
Cheers,
Stan H.
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logarithm/91152: What is the formula for solving this problem
Solve the equation two ways: by equating bases and using the uniqueness properties, and by applying a base-10 or base-e Logarithm and using the power property of Logarithms.
243/64=16(3/4)^n-1
1 solutions
Answer 66173 by stanbon(57203) on 2007-08-01 21:26:51 (Show Source):
You can put this solution on YOUR website!243/64 = 16(3/4)^n-1
Divide both sides by 16 to get:
(3/4)^(n-1) = 243/[64*16]
Take the log of both sides to get:
(n-1)log(3/4) = log243-[log64+log16]
(n-1)log(3/4) = -0.624693683...
Divide both sides by log(3/4) to get:
n-1 = 5
n = 6
==========
Cheers,
Stan H.
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