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Recent problems solved by 'stanbon'
stanbon answered: 57146 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, >>NextPercentage-and-ratio-word-problems/72477: Science and Medicine. Fungicides account for 1/10 of the pesticides used in the United States. Insecticides account for 1/4 of all the pesticides used in the United States. The ratio of fungicides to insecicides used in the United States can be written as 1/10 divided by 1/4. Write this ratio in simplest form.
I am trying to figure this out and came up with 1/40. Is this correct. I think I simplified wrong. Thanks 1 solutions
Answer 51813 by stanbon(57214) on 2007-02-27 13:34:33 (Show Source):
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Graphs/72476: This question is from textbook Intermediate Algebra
Solve the system of equations using the addition (elimination) method. If the answer is a unique solution, present it as an ordered pair: (x,y). If not, specify whether the answer is "no solution" or "infinitely many solutions."
3x - 2y = 7
-9x + 6y = -21 1 solutions
Answer 51810 by stanbon(57214) on 2007-02-27 13:02:22 (Show Source):
You can put this solution on YOUR website!3x - 2y = 7
-9x + 6y = -21
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Multiply the 1st equation by 3 to get:
9x - 6x = 21
Add that to the 2nd equation to get:
0+0 =0
------------
That means the two equations are the equation for the same line.
It means every point on the line is a solution, so there are
infinitely many solutions to the system of equations. The equatios
are said to be dependent, meaning, one is a multiple of the other.
-------
Cheers,
Stan H.
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Miscellaneous_Word_Problems/72442: This question is from textbook For All Practical Purposes
Criticize the following claims, which were cited in the New York Times of September 25, 1987 and October 21, 1987:
a) A new dental rinse "reduces plaque on teeth by over 300%"
b) An airline working to decrease lost baggage has "already improved 100% in the last six months."
c) "If interest rates drop from 10% to 5%, that is a 100% reduction." 1 solutions
Answer 51787 by stanbon(57214) on 2007-02-27 10:42:16 (Show Source):
You can put this solution on YOUR website!a) A new dental rinse "reduces plaque on teeth by over 300%"
A 100% reduction would result in "no plaque". 300% reduction
is meaningless.
-----------------
b) An airline working to decrease lost baggage has "already improved 100% in the last six months."
They can stop working; lost baggage has already been reduced to "zero
bags lost".
---------------
c) "If interest rates drop from 10% to 5%, that is a 100% reduction."
A 100% reduction would mean " a zero interest rate".
They should have said there was a 50% drop in the interest rate; that
would really get people confused.
=========
Cheers,
Stan H.
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Money_Word_Problems/72456: This question is from textbook For All Practical Purposes
I asked this question a few days ago and I am waiting for an answer. I hope I will get one today.
Suppose that you save for retirement by contributing the same amount each month from your 23rd birthday until your 65th birthday, in an account that pays a steady 5% annual interest compounded monthly.
a) How much will be in your fund at age 65 if you save $ 100 a month?
b) How much will be in your fund if you get a steady return of 7.5% compounded monthly?
c) How much will be in your fund if you get a steady return of 10% compounded monthly? (This is comparable to the average annual return of about 11% for all stocks on the New York Stock Exchange from 1950 to 2000) 1 solutions
Answer 51786 by stanbon(57214) on 2007-02-27 10:36:51 (Show Source):
You can put this solution on YOUR website!Suppose that you save for retirement by contributing the same amount each month from your 23rd birthday until your 65th birthday, in an account that pays a steady 5% annual interest compounded monthly.
a) How much will be in your fund at age 65 if you save $ 100 a month?
Formula for "future value of an annuity":
S = R[(1+i)^n -1]/i
S = 100[(1+(0.05/12))^(32*12) -1]/(0.05/12)
S = 100[23.3699]/0.004
S = $584,247.50
================
b) How much will be in your fund if you get a steady return of 7.5% compounded monthly? Don't have a formula for this; suggest you post it separately.
-
c) How much will be in your fund if you get a steady return of 10% compounded monthly? Don't have a formula for this; suggest you post it separaely.
========
Cheers,
Stan H.
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Permutations/72458: Determine the eight term (simplified) in the expansion of (4a+7b)^15.
Thank you
Kristen 1 solutions
Answer 51784 by stanbon(57214) on 2007-02-27 10:26:00 (Show Source):
You can put this solution on YOUR website!Determine the eight term (simplified) in the expansion of (4a+7b)^15.
8th term = 15C8(4a)^8(7b)^7 = 6435*65636*a^8*823543b^7=(3.4784x10^14)a^8b^7
-------
Cheers,
Stan H.
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Permutations/72460: Determine the coefficent of the term containing a^5 in the expansion of
(a - 1/a)^5
I got 1 for the coefficent of a^5. However, I can not read my teachers writing and I think that the the question could be, "Determine the coefficent of the term containing a in the expansion of (a - 1/a)^5". If this is the case I am not sure of the coefficent since there are two a's and when you expand using binomial expansion, there are two possible terms that have a values (either multipy the a's together to get a or there is just an a in one of the terms).
Thank you,
Kristen
1 solutions
Answer 51783 by stanbon(57214) on 2007-02-27 10:19:53 (Show Source):
You can put this solution on YOUR website!Determine the coefficent of the term containing a^5 in the expansion of
(a - 1/a)^5
= (a - a^-1)^5
1st term of the expansion is 5C5a^5(a^-1)^0 = a^5
==========
Cheers,
Stan H.
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Money_Word_Problems/72459: From Table 21.5, you can determine the rate of inflation from one year to the next. For example, you find the rate of inflation from 1991 to 1992 by subtracting the two index numbers and dividing the earlier one: (140.6-136.2)/136.2=0.032=3.2%. Similarly, knowing the rate of inflation, you can compute one index number from another.
a) What was the rate of inflation from 1980 to 1981
b) For a 3% rate of inflation per year from 2003 on, what would the Co nsumer Price Index be in 2006?
Table 21.5 figures
1980-82.4
1981-90.0
1982-96.5
1983-99.6
1984-103.9
1985-107.6
1986-109.6
1987-113.6
1988-118.3
1989-124.0
1990-130.7
1991-136.2
1992-140.3
1993-144.5
1994-148.2
1995-152.4
1996-156.9
1997-160.5
1998-163.0
1999-166.6
2000-172.2
2001-177.1
2002-179.9
2003-184.0
2004-189.5
2005(EST)-195.0
2006 (EST)-200.5 1 solutions
Answer 51782 by stanbon(57214) on 2007-02-27 10:15:34 (Show Source):
You can put this solution on YOUR website!From Table 21.5, you can determine the rate of inflation from one year to the next. For example, you find the rate of inflation from 1991 to 1992 by subtracting the two index numbers and dividing the earlier one: (140.6-136.2)/136.2=0.032=3.2%. Similarly, knowing the rate of inflation, you can compute one index number from another.
a) What was the rate of inflation from 1980 to 1981
b) For a 3% rate of inflation per year from 2003 on, what would the Co nsumer Price Index be in 2006?
Table 21.5 figures
1980-82.4
1981-90.0
1982-96.5
1983-99.6
1984-103.9
1985-107.6
1986-109.6
1987-113.6
1988-118.3
1989-124.0
1990-130.7
1991-136.2
1992-140.3
1993-144.5
1994-148.2
1995-152.4
1996-156.9
1997-160.5
1998-163.0
1999-166.6
2000-172.2
2001-177.1
2002-179.9
2003-184.0
2004-189.5
2005(EST)-195.0
2006 (EST)-200.5
a) rate of inflation 80' to 81'= (90.0-82.40/82.4 = 0.09
b) rate from 2003 to 2006 is 0.03, find index for 2006
Let indes for 2006 be "x":
Then (x-184)/184 = 0.03
Multiply both sides by 184 to get:
x-184=5.52
x=189.52 (This is the index for 2006)
=============
Cheers,
Stan H.
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Inequalities/72399: Please help....thanks!
Solve: X is greater than or equal to 10 or X is less than or equal to 10.
Is this the answer? (-infinity,10) union (10, infinity)....Please explain, I think I understand a little, but not quite sure. 1 solutions
Answer 51739 by stanbon(57214) on 2007-02-26 22:30:34 (Show Source):
You can put this solution on YOUR website!X is greater than OR equal to 10 or X is less than or equal to 10.
If you have to put the answer in interval notation you need to take
account of the "equal" words.
X is greater than or equal to 10 is [10,inf)
X is less than or equal to 10 is (-inf,10]
--------
You want the union of these which is (-inf,inf)
Cheers,
Stan H.
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Linear-equations/72389: This question is from textbook algebra 1
what type of equation do i use to give the slope-intercept of an equation of the line that is perpendicular to 8x+5y=4 and contains (-9,1)? 1 solutions
Answer 51737 by stanbon(57214) on 2007-02-26 22:21:50 (Show Source):
You can put this solution on YOUR website!what type of equation do i use to give the slope-intercept of an equation of the line that is perpendicular to 8x+5y=4 and contains (-9,1)?
---------
Put the given equation in slope-intercept form:
y = -(8/5)x + (4/5)
The slope of this line is -8/5
-----------
The perpendicular line must have a slope of +5/8
The equation you want will have the form y=mx+b where
m=5/8 and y=1 when x=-9.
1 = (5/8)(-9)+b
b= 45/8 + 8/8
b=53/8
EQUATIOn:
y=(5/8)x + 51/8
Cheers,
Stan H.
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Functions/72391: Can you help me find F(4)and the domain for the function:
F(x)=10x + 1 / x squared - 9x 1 solutions
Answer 51735 by stanbon(57214) on 2007-02-26 22:13:13 (Show Source):
You can put this solution on YOUR website!find F(4)and the domain for the function:
F(x)=(10x + 1) /( x squared - 9x)
F(x) = (10x+1)/(x(x-9))
The denominator cannot be zero; so x cannot be 0 and x cannot be 9.
Therefore the domain is all real number except x=0 and x=9.
---------------
F(4) = (10*4 +1)/(4^2-9*4)
F(4) = 41/-20
----------
Cheers,
Stan H.
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Miscellaneous_Word_Problems/72392: I submitted this problem quite a few days ago and did not get a response. I am resubmitting in hopes to get some help.
Solve the following application.
Business and finance. Ms. Jordan has been given a loan of $2500 for 1 year. If the interest charged is $275, what is the interest rate on the loan?
This is what I have so far.
loan=$2500
interest=$275
interest rate=x 1 solutions
Answer 51734 by stanbon(57214) on 2007-02-26 22:08:01 (Show Source):
You can put this solution on YOUR website!Ms. Jordan has been given a loan of $2500 for 1 year. If the interest charged is $275, what is the interest rate on the loan?
--------
Interest = P*r*t
2Ms. Jordan has been given a loan of $2500 for 1 year. If the interest charged is $275, what is the interest rate on the loan?
275 = 2500*r*1
r = 275/2500
r = 0.11
r = 11%
--------
Cheers,
Stan H.
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Inequalities/72393: Please help me understand how to work this problem, I believe the answer is
(0,1,3,4,7,8,9,11} but I'm not sure why! Thanks!
Let A = {0,3,4,7,8} and B = {1,3,7,9,11}. Find A union B 1 solutions
Answer 51732 by stanbon(57214) on 2007-02-26 22:04:19 (Show Source):
You can put this solution on YOUR website!You have it right.
You "unite" A and B but do not duplicate elements that appear in both A and B;
you list each separate element once.
Cheers,
Stan H.
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Probability-and-statistics/72377: The Hudson Valley Bottling Company distributes root beer in bottles labeled 32 ounces. The Bureau of Weights and Measures randomly selects 50 of these bottles, measures their contents and obtains a sample mean of 31.80 ounces with a standard deviation of 0.75 ounces (assume population values for mean and standard deviation). Using a 0.01 significance level, test the Bureaus claim that the company is cheating consumers. Indicate whether you would use a z score or t score, give the value of that score and the critical value to 2 decimal places, and state whether you "Reject" or "Fail to Reject" the null hypothesis. 1 solutions
Answer 51726 by stanbon(57214) on 2007-02-26 21:47:22 (Show Source):
You can put this solution on YOUR website!The Hudson Valley Bottling Company distributes root beer in bottles labeled 32 ounces. The Bureau of Weights and Measures randomly selects 50 of these bottles, measures their contents and obtains a sample mean of 31.80 ounces with a standard deviation of 0.75 ounces (assume population values for mean and standard deviation). Using a 0.01 significance level, test the Bureaus claim that the company is cheating consumers. Indicate whether you would use a z score or t score, give the value of that score and the critical value to 2 decimal places, and state whether you "Reject" or "Fail to Reject" the null hypothesis
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Ho: u = 32
H1: u < 32 (Claim)
x-bar=31.8; s=0.75
COMMENT: Whether you use a t or z depends on your text.
If you use a t-score for 31.8 you get t= -1.8856
If you use a z-score for 31.8 you get z= -1.8856
The critical z value of alpha = 1% is -2.326
Fail to reject Ho.
Cheers,
Stan H.
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Probability-and-statistics/72378: In 1990, 5.8% of job applicants who were tested for drugs failed the test. At the 0.01 level, test the claim that the failure rate is now lower if a random sample of 1,520 current job applicants results in 58 failures. Does the result suggest that fewer job applicants now use drugs? Give the z score to 2 decimal places to, p(hat) to three decimal places, and the corresponding value of p to 4 decimal places. Also, do you conclude that fewer use drugs (Yes or No)? 1 solutions
Answer 51723 by stanbon(57214) on 2007-02-26 21:25:17 (Show Source):
You can put this solution on YOUR website!In 1990, 5.8% of job applicants who were tested for drugs failed the test. At the 0.01 level, test the claim that the failure rate is now lower if a random sample of 1,520 current job applicants results in 58 failures. Does the result suggest that fewer job applicants now use drugs? Give the z score to 2 decimal places to, p(hat) to three decimal places, and the corresponding value of p to 4 decimal places. Also, do you conclude that fewer use drugs (Yes or No)?
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Ho: p = 0.058
H1: p < 0.058
x=58; n=1520; p-hat = 58/1520= 0.038
z(0.038) = (0.038=0.058)/sqrt[(0.058)*(0.942)/1520] = -3.34
p-value = 0.0004
Yes, few use drugs.
Cheers,
Stan H.
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Equations/72358: Working as a team ,8 mathletes can solve 20 problems in 10 minutes. At this rate, how many mathletes are needed in order to solve 30 problems in 5 minutes. 1 solutions
Answer 51715 by stanbon(57214) on 2007-02-26 20:35:33 (Show Source):
You can put this solution on YOUR website!8 men / 20 probs in 10 min
Divide probs and minutes by 2 to get
8 men / 10 probs in 5 min
Multiply men and probs by 3 to get
24 men / 30 probs in 5 min
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Cheers,
Stan H.
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Polynomials-and-rational-expressions/72344: This question is from textbook
for the polynominal, one zero is given. Find all the others:
f(x)= x^4 + 10x^3 + 27x^2 + 10x + 26; i 1 solutions
Answer 51707 by stanbon(57214) on 2007-02-26 18:52:13 (Show Source):
You can put this solution on YOUR website!for the polynominal, one zero is given. Find all the others:
f(x)= x^4 + 10x^3 + 27x^2 + 10x + 26; i
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If "i" is a zero, then "-i" is also a zero.
Therefore (x-i)(x+i)=x^2+1 is a factor.
Dividing by x^2+1 the quotient is x^2+10x+26
The roots of this quadratic are:
x=[-10+-sqrt(100-4*26)]/2
x=[-10+-sqrt(-4)]/2
x=[-5+-i]
x=5+i or x=5-i or x=i or x=-i
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Cheers,
Stan H.
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Polynomials-and-rational-expressions/72349: This question is from textbook
Determine whether each pair of functions as graphed or defined are inverse of each other:
f(x)+ 8x - 7, g (x)= x + 8
______
7 1 solutions
Answer 51703 by stanbon(57214) on 2007-02-26 17:59:12 (Show Source):
You can put this solution on YOUR website!f(x)= 8x - 7, g (x)= (x + 8)/7
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If f and g are inverse to one-another f(g(x))=x
and g(f(x))=x
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g(f(x)) = g[8x-7] = (8x-7+8)/7 = (8x+1)/7
Therefore g and f are not inverse of one-another.
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Cheers,
Stan H.
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Polynomials-and-rational-expressions/72348: This question is from textbook
for each function as defined that is one on one (a) write an equation for the inverse function in the form y= f-1(x) (b), graph f and f-1 on the same axes and (c) give the domain and the range of f and fi-1. If the function is not one on one, say so.
y + 4/x 1 solutions
Answer 51701 by stanbon(57214) on 2007-02-26 17:49:02 (Show Source):
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Polynomials-and-rational-expressions/72346: This question is from textbook
The number of long-dsitance phone calls between two cities in a certain time perio varies directly as the population p1 and p2 of the cities and inversely as the distane between them. If 10,000 calls are made between two cities 500 mi apart, having populations of 50,000 and 125,000, find the number of calls between two cities 800 mi apart, having populations of 20,000 and 80,000 1 solutions
Answer 51700 by stanbon(57214) on 2007-02-26 17:41:59 (Show Source):
You can put this solution on YOUR website!The number of long-dsitance phone calls between two cities in a certain time perio varies directly as the population p1 and p2 of the cities and inversely as the distane between them. If 10,000 calls are made between two cities 500 mi apart, having populations of 50,000 and 125,000, find the number of calls between two cities 800 mi apart, having populations of 20,000 and 80,000
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Formula: # of calls = k p1*p2/d where d is the distance from p1 to p2
10000 = k 50000*125000/500
k = 0.0008
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EQUATION:
number = (0.0008)P1*p2/d
number = 0.0008*20000*80000/800
number = 1600
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Cheers,
Stan H>
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Exponential-and-logarithmic-functions/72299: The amount of a radioactive tracer remaining after t days is given
by A = A0 e–0.058t, where A0 is the starting amount at the beginning of
the time period. How many days will it take for one half of the
original amount to decay? 1 solutions
Answer 51697 by stanbon(57214) on 2007-02-26 16:52:38 (Show Source):
You can put this solution on YOUR website!The amount of a radioactive tracer remaining after t days is given
by A = A0 e–0.058t, where A0 is the starting amount at the beginning of
the time period. How many days will it take for one half of the
original amount to decay?
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If half decays that leaves (1/2)Ao.
EQUATION:
(1/2)Ao = Ao e^(-0.058t)
Divide both sides by Ao to get:
1/2 = e^(-0.058t)
Take the natural log of both sides to get:
ln(1/2) = -0.058t
t= ln*1/2) / -0.058
t=11.95 days
The half-life of the tracer is 11.95 days.
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Cheers,
Stan H.
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Surface-area/72166: How would I figure out how to find the circumference of the circle. When the formula is v=2/3 pi squared h. Then I have to round to the nearst hundredth? 1 solutions
Answer 51670 by stanbon(57214) on 2007-02-26 09:11:15 (Show Source):
You can put this solution on YOUR website!How would I figure out how to find the circumference of the circle. When the formula is v=2/3 pi squared h. Then I have to round to the nearst hundredth?
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To find the circumference you need the radius or the diameter of the circle.
Your formula, v=(2/3)pi^2h does not contain either the radius or the diameter.
Are you sure that is all the information you are given?
Cheers,
Stan H.
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Proportions/72190: This question is from textbook Algebra 2
I need help with this problem
In Exercises 14-29, y varies directly as x. Find the constant of variation, and write an equation of direct variation that relates the two variables.
16. y= -16 when x = 2
1 solutions
Answer 51669 by stanbon(57214) on 2007-02-26 09:07:04 (Show Source):
You can put this solution on YOUR website!y varies directly as x.
Therefore y=kx
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Find the constant of variation, and write an equation of direct variation that relates the two variables.
16. y= -16 when x = 2
If y=-16 when x=2 then:
-16 = k(2)
k=-8
k is the constant of variation.
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Cheers,
Stan H.
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Money_Word_Problems/72247: A wheelbarrow manufacturer uses handles made of hardwood. Find the amount of wood that is necessary to make 182 handles. The longest dimension shown is the handle length. The following information was provided.
6.0 cubic Ft WheelBarrow
* steel construction with hardwood handles
* 14" tubeless pneumatic tire
* fully rolled edge for added tray strength
* overall dimensions: 61 1/2"L x 27"W x 24.9"H 1 solutions
Answer 51666 by stanbon(57214) on 2007-02-26 08:52:30 (Show Source):
You can put this solution on YOUR website!You have to assume the handles are 61 1/2 inches long.
182 of them would be 182*(123/2)" = 91*123 =11193 inches of wood
or 932.75 ft of wood
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Cheers,
Stan H.
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