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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629, >>NextMixture_Word_Problems/376412: For extremely cold temperatures, an automobile manufacturer recommends that a 80% antifreeze and 20% water mix be used in the cooling system of a car. How many quarts of pure (100%) antifreeze and 50% antifreeze and 50% water mix should be combined to make 11 quarts of 80% antifreeze and 20% water mix?
1 solutions
Answer 267826 by ankor@dixie-net.com(15624)   on 2010-11-27 09:42:11 (Show Source):
You can put this solution on YOUR website!an automobile manufacturer recommends that a 80% antifreeze and 20% water
mix be used in the cooling system of a car.
How many quarts of pure (100%) antifreeze and 50% antifreeze and 50% water
mix should be combined to make 11 quarts of 80% antifreeze and 20% water mix?
:
Let x = amt of pure antifreeze
Then
(11-x) = amt of 50% antifreeze required
:
.50(11-x) + x = .80(11)
5.5 - .5x + x = 8.8
.5x = 8.8 - 5.5
.5x = 3.3
Multiply by 2
x = 6.6 qt of pure antifreeze
and
11 - 6.6 = 4.4 quarts of 50% antifreeze
;
:
Check this in the original equation
.5(4.4) + 6.6 = .8(11)
2.2 + 6.6 = 8.8; Confirms our answers
|
Polynomials-and-rational-expressions/376386: Can someone please help me with this problen because I am totaly confused and please show all work?
Consider that the age, x, of a unicorn in human equivalent years can be given by the formula (x) = - 0.0021718x^4 + 0.027326x^3 – 0.3367x^2 + 12.46x + 2.914. When a unicorn is 2.5 years old, what is its age in human equivalent years? What about when it is 12 years old? Is it similar to a dog’s approximation of multiplying by 7 to get the age in human equivalent years? Why or why not?
1 solutions
Answer 267823 by ankor@dixie-net.com(15624) on 2010-11-27 08:36:21 (Show Source):
You can put this solution on YOUR website!Consider that the age, x, of a unicorn in human equivalent years can be given
by the formula (x) = - 0.0021718x^4 + 0.027326x^3 – 0.3367x^2 + 12.46x + 2.914.
When a unicorn is 2.5 years old, what is its age in human equivalent years?
What about when it is 12 years old?
:
Just substitute 2.5 yrs for x in the given formula and do the tedious math:
f(x) = - 0.0021718(2.5^4) + 0.027326(2.5^3) – 0.3367(2.5^2) + 12.46(2.5) + 2.914
f(x) = - 0.0021718(39.0625) + 0.027326(15.625) – 0.3367(6.25) + 12.46(2.5) + 2.914
f(x) = - .085 + .427 – 2.104 + 31.15 + 2.914
f(x) = 32.3 yrs
:
You can check the math, a lot chances to make a mistake here.
:
" What about when it is 12 years old?"
Substitute 12 for x, and do the same thing
:
Is it similar to a dog’s approximation of multiplying by 7 to get the age in
human equivalent years? Why or why not?
:
I don't think it is. The dog's age formula is linear
|
Linear_Equations_And_Systems_Word_Problems/376371: The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning, when graphed, the function gives a line with a slope of -0.6. Suppose that the height of the candle after 20 hrs is 12 centimeters. What was the height of the candle after 15 hrs?
1 solutions
Answer 267783 by ankor@dixie-net.com(15624) on 2010-11-26 22:05:45 (Show Source):
You can put this solution on YOUR website!The height (in centimeters) of a candle is a linear function of the amount of
time (in hours) it has been burning, when graphed, the function gives a line
with a slope of -0.6.
Suppose that the height of the candle after 20 hrs is 12 centimeters.
:
Use the point/slope equation: y - y1 = m(x - x1)
where m =-.6; x = 20; y = 12
:
y - 12 = -.6(x - 20)
y - 12 = -.6x + 12
y = -.6x + 12 + 12
y = -.6x + 24, is the equation (y = length after x hours)
:
"What was the height of the candle after 15 hrs?"
y = -.6(15) + 24
y = -9 + 24
y = 15 inches after 15 hrs
|
Evaluation_Word_Problems/375986: A ladder is two feet longer than the height of a certain wall. When the top of the ladder is placed against the top of the wall, the distance from the base of the ladder to the bottom of the wall is equal to the height of the wall. How high is the wall?
1 solutions
Answer 267781 by ankor@dixie-net.com(15624) on 2010-11-26 21:50:02 (Show Source):
You can put this solution on YOUR website!A ladder is two feet longer than the height of a certain wall.
When the top of the ladder is placed against the top of the wall, the distance
from the base of the ladder to the bottom of the wall is equal to the height of the wall.
How high is the wall?
:
This is a right triangle problem, a^2 + b^2 = c^2
The distance from the base to the wall, and the height of the wall are given
as equal: a = b, the ladder is the hypotenuse, c = a+2
:
We can write the equation:
a^2 + a^2 = (a+2)^2
:
2a^2 = a^2 + 4a + 4
Combine on the left
2a^2 - a^2 - 4a - 4 = 0
a^2 - 4a - 4 = 0
Solve this using the quadratic formula
Positive solution; a = 4.828 ft height of the wall
:
6.828 ft = length of ladder
Seems kind of short, check solution by finding the ladder length
Ladder =  enter into a calc
Ladder = 6.828; confirms our solution
|
Exponential-and-logarithmic-functions/375830: Stopping an Oil Tanker: It has been shown that if an oil tanker stops its engines, then its velocity will decrease exponentially. Suppose that captin shuts off the engines when the speed of the tanker is 20 mph and one minute later the speed of the tanker is 18 mph. What is the speed of the tanker after one hour?
1 solutions
Answer 267773 by ankor@dixie-net.com(15624) on 2010-11-26 21:23:37 (Show Source):
You can put this solution on YOUR website!Stopping an Oil Tanker:
It has been shown that if an oil tanker stops its engines, then its velocity will decrease exponentially.
Suppose that captain shuts off the engines when the speed of the tanker is
20 mph and one minute later the speed of the tanker is 18 mph.
What is the speed of the tanker after one hour?
:
Using the decay equation
20(2^(-1/k)) = 18
2^(-1/k) = 
2^(-1/k) = .9
 = 
= -.152
k = 
k = 6.579:
:
Find the speed (s) of the tanker, when t = 60 min
s = 20(2^(-60/6.579))
s = 20 * .0018
s = .036 mph
|
Quadratic_Equations/376255: A window washer accidentally drops a bucket from the top of a 144 meter building. The height h of the bucket after t seconds is given by the formula . When will the bucket hit the ground?
1 solutions
Answer 267741 by ankor@dixie-net.com(15624) on 2010-11-26 19:41:42 (Show Source):
You can put this solution on YOUR website!A window washer accidentally drops a bucket from the top of a 144 meter building.
The height h of the bucket after t seconds is given by the formula:
h = -16t^2 + 144
h = 0 when it hits the ground
-16t^2 + 144 = 0
-16t^2 = -144
Divide both sides by -16
t^2 = 9
t = 
t = 3 seconds to hit the ground
.
|
test/376311: Soybean meal is 12% protein. Cornmeal I'd 6% protein. How many pounds of each should be mixed to get a 240 pound mixture that is 10% protein?
1 solutions
Answer 267731 by ankor@dixie-net.com(15624) on 2010-11-26 19:15:37 (Show Source):
You can put this solution on YOUR website!Soybean meal is 12% protein. Cornmeal is 6% protein.
How many pounds of each should be mixed to get a 240 pound mixture that is 10% protein?
:
Let x = amt of 12% protein
then
(240-x) = amt of 6% protein
:
At typical mixture equation:
.12x + .06(240 - x) = .10(240)
.12x + 14.4 - .06x = 24
.12x - .06x = 24 - 14.4
.06x = 24 - 14.4
.06x = 9.6
x = 9.6/.06
x = 160 lb of soy meal
and
240 - 160 = 80 lb of corn meal
:
:
Check solution
.12(160) + .06(80) = .10(240)
|
Circles/376227: A large circular garden is surrounded by a stone wall that is 6 inches wide. The circumferance of teh OUTSIDE of teh stone wall measures 54 feet.
A. Find the radius of the garden INCLUDING the stone wall.
B. Find the radius of the garden WITHOUT the stone wass.
C. Find the area of teh garden (not including the stone wall) in square feet.
I can find the answer to A. 27ft/Pie
I think the answer to B is 26ft/Pie
But I can't figure out part C.
1 solutions
Answer 267724 by ankor@dixie-net.com(15624) on 2010-11-26 18:56:15 (Show Source):
You can put this solution on YOUR website!A large circular garden is surrounded by a stone wall that is 6 inches wide.
The circumference of the OUTSIDE of the stone wall measures 54 feet.
:
A. Find the radius of the garden INCLUDING the stone wall.
The equation: 2*pi*r = C
2*pi*r = 54
r = 
r = 8.6 ft is the radius including the wall
:
B. Find the radius of the garden WITHOUT the stone wall.
6 inches = .5 ft
8.6 - .5 = 8.1 ft radius inside the stone wall
:
C. Find the area of the garden (not including the stone wall) in square feet.
A = pi*8.1^2
A = 206.12 sq/ft, area inside the stone wall
:
:
|
Quadratic_Equations/376236: Hi Everyone, stuck in again on a weekend doing my maths !, having problems with this one please can someone help
A circular-cylindrical oil drum is required to have a given surface area S (including its lid and base), ie S is a constant. Find the proportions of the design which contain the greatest volume V .
Thank You
John
1 solutions
Answer 267721 by ankor@dixie-net.com(15624) on 2010-11-26 18:43:10 (Show Source):
You can put this solution on YOUR website!A circular-cylindrical oil drum is required to have a given surface area S
(including its lid and base), ie S is a constant.
Find the proportions of the design which contain the greatest volume V .
:
Surface area: S = 2(pi*r^2) + (2*pi*h)
:
Volume: V = pi*r^2*h
:
Find the relationship between the surface area and the volume
:
 =  = 
Cancel pi*r
= 
Therefore
S = 2*(h+r)
Assume a value: S = 120
2h + 2r = 120
h + r = 60
h = (60-r)
:
V = pi*r^2*(60-r): replace h with (60-r)
Find Max volume. graph the equation y = 3.14*x^2*(60-x)
Max volume occurs when r = 40
then h = 60 - 40
h = 20
:
The proportion:
 =  ,
we can say max volume when radius:height = 2:1
|
logarithm/375902: Its a word problem and i am not sure how to solve it?
A forensic specialist took the temperature of a victim's body lying in a street at 2:10 a.m. and found it to be 85.7'F. At 2:40 a.m., the temperature of the body was 84.8'F. When was the murder committed if the air temperature during the night was 55'F? [Remember, normal body temperature is 98.6'F.]
HELP! Please and Thank You
1 solutions
Answer 267666 by ankor@dixie-net.com(15624) on 2010-11-26 16:11:14 (Show Source):
You can put this solution on YOUR website!A forensic specialist took the temperature of a victim's body lying in a street
at 2:10 a.m. and found it to be 85.7'F.
At 2:40 a.m., the temperature of the body was 84.8'F.
When was the murder committed if the air temperature during the night was 55'F?
[Remember, normal body temperature is 98.6'F.]
:
Find the body temp loss rate in 30 min, convert to degrees/hr
85.7 - 84.8 = .9 * 2 = 1.8 degrees/hr
:
Let t = no. of hrs from 98.6 (temp at death) until temp = 84.8
98.6 - 1.8t = 84.8
-1.8t = 84.8 - 98.6
-1.8t = -13.8
t = 
t = 7.67 hrs or 7 hr 40 min prior to 2:40 am
That would place the time at 7 pm on the previous day
|
Travel_Word_Problems/376209: if someone is traveling 40mph on the way to work
Traveled 30mph on the way home traveling the same route
What is the total miles they traveled round trip
1 solutions
Answer 267641 by ankor@dixie-net.com(15624) on 2010-11-26 13:12:40 (Show Source):
You can put this solution on YOUR website!Not enough information given here, you have to know the time it takes to make
one way trip, or the time relationship between the two trips, or the time required
to make a round trip.
|
Evaluation_Word_Problems/375989: Runners Aaron and Ben leave the same oint P at a right angle to one another. Aaron runs 4 km/hr faster than Ben. After 2 hours they are 40km apart. Find the speed of each.
1 solutions
Answer 267634 by ankor@dixie-net.com(15624) on 2010-11-26 11:12:55 (Show Source):
You can put this solution on YOUR website!Runners Aaron and Ben leave the same point P at a right angle to one another.
Aaron runs 4 km/hr faster than Ben.
After 2 hours they are 40km apart.
Find the speed of each.
:
We will use a^2 + b^2 = c^2, to solve this problem
Let a = Aaron's running speed
In two hrs, he will have run 2a km
then
(a-4) = Ben's running speed
In two hrs, he will have run (2a-8)km
:
c = 40
:
(2a)^2 + (2a-8)^2 = 40^2
4a^2 + 4a^2 - 32a + 64 = 1600
8a^2 - 32a + 64 - 1600 = 0
8a^2 - 32a - 1536 = 0; our old friend, the quadratic equation!
Simplify, divide by 8
a^2 - 4a - 192 = 0
Factor this to
(a-16)(a+12) = 0
positive solution
a = 16 km/hr is Aaron's speed
and
12 km/hr is Ben's speed
;
:
Check this out
32^2 + 24^2 = 40^2
1024 + 576 = 1600
|
Graphs/375845: A local travel agent can sell up to 1200 travel packages for a concert. The packages will include airfare, hotel, and two types of flights: non-stop or two stop. The non-stop flight carries 150 passengers and the two stop flight carries 100 passengers. The travel agency can use no more than 10 planes. The non-stop package sells for $1200 and the two stop flight sells for $900. Assume that each plane will contain the maximum number of passengers.
a) Write the constraints
b) Find the maximum revenue for the constraints.
1 solutions
Answer 267616 by ankor@dixie-net.com(15624) on 2010-11-26 09:39:27 (Show Source):
You can put this solution on YOUR website!A local travel agent can sell up to 1200 travel packages for a concert.
The packages will include airfare, hotel, and two types of flights: non-stop or two stop.
The non-stop flight carries 150 passengers and the two stop flight carries 100 passengers.
The travel agency can use no more than 10 planes.
The non-stop package sells for $1200 and the two stop flight sells for $900.
Assume that each plane will contain the maximum number of passengers.
:
a) Write the constraints
b) Find the maximum revenue for the constraints.
:
Let x = number of 150 passenger planes
Let y = number of 100 passenger planes
:
Number of airplanes:
x + y =< 10
Put in the general (y=) form, to plot on a graph
y =< 10 - x; (purple line)
:
Number of travel packages sold:
150x + 100y =< 1200
100y =< 1200 - 150x
y =< 1200/100 - (150/100)x
y =< 12 - 1.5x; (green line)
:
The graph:
:
Feasibility region is at or below the purple or green lines whichever is lowest
:
The vertices:
x = 8, y = 0
x = 0, y = 10
Solve the two equation system to find the other vertici
150x + 100y = 1200
Simplify, divide by 100
1.5x + y = 12
x + y = 10
----------------subtract, find x
.5x = 2
x = 2/.5
x = 4
:
Find y:
4 + y = 10
y = 6
The 3rd vertici is x = 4, y = 6, 4 ea 150 pass planes, 6 ea 100 pass planes
:
Revenue:
4*150*1200 = $720,000
6*100*900 = $540,000
--------------------
total is $1,260,000 for 4 ea 150 pass planes and 6 ea 100 pass planes
:
Max revenue would be 8 full 150 pass planes at $1,440,000
|
Exponential-and-logarithmic-functions/375796: Height of tsunami waves: when waves generated by tsunamis approach shore, the height of the waves gennerally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk.
Greens law tells us how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location of water depth d, then the new height h of the wave is given by h= HR^0.25, where R is the water depth ratio given by R=D/d.
A.) Calculate the height of a tsunami wave in water 25 feet deep if its height is a 3 feetat its point of orgin in water 15,000 feet deep.
B.) If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?
Helpful hints:
a power function has a form of: f(x)= cx^k
Please help;)
1 solutions
Answer 267610 by ankor@dixie-net.com(15624) on 2010-11-26 09:26:06 (Show Source):
You can put this solution on YOUR website!Height of tsunami waves: when waves generated by tsunamis approach shore,
the height of the waves generally increases.
Understanding the factors that contribute to this increase can aid in
controlling potential damage to areas at risk.
:
Greens law tells us how water depth affects the height of a tsunami wave.
If a tsunami wave has height H at an ocean depth D, and the wave travels
to a location of water depth d, then the new height h of the wave is given
by h= HR^0.25, where R is the water depth ratio given by R=D/d.
:
A.) Calculate the height of a tsunami wave in water 25 feet deep if its
height is 3 feet at its point of origin in water 15,000 feet deep.
:
H=3, D=15000, d=25
:
h = 3(15000/25)^.25
h = 3*600^.25
h = 3*5.0
h = 15 ft
:
B.) If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?
In the above equation
h = 3*1200^.25
h = 3*5.9
h = 17.657 ft
:
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Miscellaneous_Word_Problems/376162: 20 people are coming for thanksgiving dinner. Aunt Rose has sent you out to buy a turkey and she wants leftovers for everyone. A cookbook said a turkey under 12 pounds will allow 1 pound per serving and for heavier birds 1/2 lb. per serving. Aunt Rose (Who I hate) says buy a turkey four pounds larger than you figure. The turkeys are on sale for .89 cents per pound. How much will it cost? And how big is it?
1 solutions
Answer 267597 by ankor@dixie-net.com(15624) on 2010-11-26 09:05:12 (Show Source):
You can put this solution on YOUR website!20 people are coming for thanksgiving dinner.
Aunt Rose has sent you out to buy a turkey and she wants leftovers for everyone.
A cookbook said a turkey under 12 pounds will allow 1 pound per serving and
for heavier birds 1/2 lb. per serving.
Aunt Rose (Who I hate) says buy a turkey four pounds larger than you figure.
The turkeys are on sale for .89 cents per pound.
How much will it cost? And how big is it?
:
The small size (12 lb) won't work
:
Will calculate using the large size
20(.5) + 4 = 14 lb
14 * .89 = $12.46
:
But why do you hate poor Aunt Rose, who is just trying to share her vast
knowledge on Turkey preparation?
|
Quadratic_Equations/375890: Pauline wants to sell stainless steel water bottles as a school fundraiser. She knows that she will maximze prophits and raise 1024 dollars if she sells the bottles for 28 dollars each. she also knows that she will lose 4160 dollars if she sells the bottles for only 10 dollars each.
a) Write a quadratic relation to model her profit. P in dollars if she sells the bottles for x dollars each
b) What selling price will ensure that she breaks even
1 solutions
Answer 267587 by ankor@dixie-net.com(15624) on 2010-11-26 08:50:12 (Show Source):
You can put this solution on YOUR website!She knows that she will maximze prophits and raise 1024 dollars if she sells
the bottles for 28 dollars each.
she also knows that she will lose 4160 dollars if she sells the bottles for only 10 dollars each.
:
Find how many bottles are being sold. Let n = no. of bottles sold
28n = 1024
10n = -4160
-------------subtract
18n - 5184
n = 5184/18
n = 288 bottles
Find the profit made on each bottle
1084/288 = $3.76
find the cost of each bottle
28 - 3.76 = $24.24
:
a) Write a quadratic relation to model her profit.
P in dollars if she sells the bottles for x dollars each
:
P = 288(x - 24.24)
:
b) What selling price will ensure that she breaks even
288(x - 24.24) = 0
288x - 6981.12 = 0
288x = 6981.12
x = 
x = $24.24, will break even (obviously)
|
Functions/375863: Thank you so much!!
Write an equation of the line containing the given point and parallel to the given line. Express in y = mx+b.
(-6,2;) 6x = 5y+4
1 solutions
Answer 267560 by ankor@dixie-net.com(15624) on 2010-11-25 21:29:31 (Show Source):
You can put this solution on YOUR website!Write an equation of the line containing the given point and parallel to the given line.
Express in y = mx+b.
(-6,2;) 6x = 5y+4
:
Find the slope of the given equation, put it in the slope intercept form y = mx+b:
6x = 5y + 4
-5y = -6x + 4
y has to be positive, multiply by -1
5y = 6x - 4
divide by 5
y =  x - 
:
The slope = , a parallel line will have the same slope
Use the point/slope form y - y1 - m(x - x1)
:
y - 2 = (x - (-6))
y - 2 = (x + 6)
y - 2 = x + 
y = x + + 2
y = x + + 
y = x +  ; is the parallel line
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Graphs/376144: One canned juice drink is 30% orange juice, another is 5% orange juice. How many liters of each should be mixed together in order to get 25 liters that is 9% of orange juice.
I tried this problem and came up with some whacky numbers, i think im missing a step, any help would be great.
1 solutions
Answer 267550 by ankor@dixie-net.com(15624) on 2010-11-25 20:32:48 (Show Source):
You can put this solution on YOUR website!One canned juice drink is 30% orange juice, another is 5% orange juice.
How many liters of each should be mixed together in order to get 25 liters that is 9% of orange juice.
:
Let x = amt of 30% juice required
then
(25-x) = amt of 5% juice
:
.30x + .05(25-x) = .09(25)
:
.30x + 1.25 - .05x = 2.25
:
.30x - .05x = 2.25 - 1.25
.25x = 1
x = 
x = 4 liters of 30% required
then
25 - 4 = 21 liters of 5% juice
:
:
You can check these values in the original equation
|
Linear-equations/376082: help me with this:
write an equation in standard form of the line that contains the point (-1, 2) and is perpendicular to the line y=3x-1
1 solutions
Answer 267546 by ankor@dixie-net.com(15624) on 2010-11-25 20:24:18 (Show Source):
You can put this solution on YOUR website!write an equation in standard form of the line that contains the
point (-1, 2) and is perpendicular to the line y=3x-1
:
slope of the equation, m1 = 3
:
The relationship of slopes of perpendicular lines: m1*m2 = -1
3*m2 = -1
m2 =  is the slope of the perpendicular line
:
Use point slope form to find the equation of the line, y - y1 = m(x - x1)
where m2= , x1=-1, y1=2
:
y - 2 = (x - (-1))
y - 2 = (x + 1)
y - 2 = x - 
y = x - + 2
y = x - + 
y = x +  ; is the equation of the perpendicular line
But they want it in the standard form
Multiply equation by 3, to get rid of the denominators
3y = -x + 5
x + 3y = 5; is the standard form
:
looks like this
|
Numeric_Fractions/376102: A food contains three major ingredients : carbohydrate 50g, fats 15g and proteins 25g.
(a) What fraction of food is carbohydrate?
(b) What percentage of food is carbohydrate?
(c) What fraction of food is not fat?
(d) What percentage of food is fat?
(e) What mass of fat is there in 60g of the food?
1 solutions
Answer 267543 by ankor@dixie-net.com(15624) on 2010-11-25 20:01:01 (Show Source):
You can put this solution on YOUR website!A food contains three major ingredients : carbohydrate 50g, fats 15g and proteins 25g.
:
Find total weight: 50 + 15 + 25 = 90g
:
(a) What fraction of food is carbohydrate?
 = 
:
(b) What percentage of food is carbohydrate?
* 100 = 55.56%
:
(c) What fraction of food is not fat?
 =  = 
:
(d) What percentage of food is fat?
 * 100 = 16.67%
:
(e) What mass of fat is there in 60g of the food?
.1667 * 60 = 10 grams of fat
|
Rate-of-work-word-problems/376118: two machines work at the same rate. after they work together for 7 h, one machine breaks down. the second machine requires 14 h more to finish the boxes. how long would it have taken one of the machines to fill the boxes?
1 solutions
Answer 267517 by ankor@dixie-net.com(15624) on 2010-11-25 18:07:55 (Show Source):
You can put this solution on YOUR website!two machines work at the same rate. after they work together for 7 h,
one machine breaks down. the second machine requires 14 h more to finish the boxes.
how long would it have taken one of the machines to fill the boxes?
:
Let x = time required by one machine to do the job
:
Let the completed job = 1
:
One machine works a total of 21 hrs, the other machine works 7 hrs
:
A shared work equation:
 +  = 1
Multiply thru by x, results:
21 + 7 = x
x = 28 hrs, one machine working alone
|
Equations/376031: A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $15,248 , and the variable costs will be $25.50 per book. With the other method, the one-time fixed costs will total $71,570 , and the variable costs will be $12.00 per book. For how many books produced will the costs from the two methods be the same?
1 solutions
Answer 267511 by ankor@dixie-net.com(15624) on 2010-11-25 16:50:51 (Show Source):
You can put this solution on YOUR website!A small publishing company is planning to publish a new book.
The production costs will include one-time fixed costs (such as editing)
and variable costs (such as printing).
There are two production methods it could use.
With one method, the one-time fixed costs will total $15,248 , and the
variable costs will be $25.50 per book.
With the other method, the one-time fixed costs will total $71,570, and the
variable costs will be $12.00 per book.
For how many books produced will the costs from the two methods be the same?
:
Let n = number of books produced
:
Write an equation for the Cost (C) of each method:
:
1: C = 25.50n + 15248
and
2: C = 12N + 71570
:
Method 1 cost = Method 2 cost
25.50n + 15248 = 12n + 71570
25.50n - 12n = 71570 - 15248
13.5n = 56322
n = 
n = 4172 books will have the same cost
|
Miscellaneous_Word_Problems/376108: The length of a poster is 10cm longer than its width. If the area of the poster is 1200cm2, what is the width of the poster.
Please can someone help this quad word problem is driving me nuts.
1 solutions
Answer 267510 by ankor@dixie-net.com(15624) on 2010-11-25 16:27:51 (Show Source):
You can put this solution on YOUR website!The length of a poster is 10cm longer than its width.
:
If the area of the poster is 1200cm2, what is the width of the poster.
:
L = the length
W = the width
:
Write an equation for each statement;
:
"The length of a poster is 10cm longer than its width."
L = W+10
:
"the area of the poster is 1200cm2,"
L * W = 1200
:
what is the width of the poster.
: Using the 1st equation replace L with (W+10) in the 2nd equation
(W+10) * W = 1200
W^2 + 10W = 1200
A quadratic equation
W^2 + 10W - 1200 = 0
This can be factored to
(w+40)(w-30) = 0
The positive solution
w = 30 cm is the width
then
L = 30 + 10
L = 40 cm is the length
:
:
Confirms this with the area: 40 * 30 = 1200
|
Equations/376093: Find measure of am angle whose compliment is 8 times its measure. I have no idea how to solve this.
1 solutions
Answer 267509 by ankor@dixie-net.com(15624) on 2010-11-25 16:17:26 (Show Source):
You can put this solution on YOUR website!Let x = the measure of the angle
:
Find measure of am angle whose compliment is 8 times its measure.
:
We know that the compliment of angle x = (90 - x)
:
Write an equation for the statement:
"Find measure of an angle whose compliment is 8 times its measure."
8x = 90 - x
8x + x = 90
9x = 90
x = 
x = 10 degrees is the angle
:
:
You can see that it's complement will be 8(10) which is 80 degrees
90 - 10 = 80
:
This is not very hard, right?
|
Travel_Word_Problems/376091: Billy and Joe are separated by 6.6 miles when they begin to walk in the same direction. It takes Billy 11 hours to overtake Joe. If they had begun to walk towards each other rather than in the same direction, they would meet up in 1 hour. What are Billy and Joe's speeds?
1 solutions
Answer 267508 by ankor@dixie-net.com(15624) on 2010-11-25 16:07:42 (Show Source):
You can put this solution on YOUR website!Billy and Joe are separated by 6.6 miles when they begin to walk in the
same direction, it takes Billy 11 hours to overtake Joe.
If they had begun to walk towards each other rather than in the same
direction, they would meet up in 1 hour.
What are Billy and Joe's speeds?
:
Let b = Bill's speed
Let j = Joe's speed
:
Write a distance equation for each scenario, Dist = time * speed
:
11(b - j) = 6.6
and
1(b + j) = 6.6
:
Divide the 1st equation by 11, add to the 2nd equation
b - j = .6
b + j = 6.6
---------------adding eliminates j, find b
2b = 7.2
b = 
b = 3.6 mph is Bill's speed
then using the 2nd equation find j
3.6 + j = 6.6
j = 6.6 - 3.6
j = 2 mph is Joe's speed
:
:
Check solution in the 1st equation
11(3.6 - 3) = 6.6
11(.6) = 6.6; confirms our solutions
|
Equations/374977: Hello, i need help on solving this equation. I dont even know where to start.
t-2/t-1= t+17/t^(2)-1 - 1/t+1
Im kind of new at this but the problem is read: t minus 2 over t minus 1 equals t plus 17 over t squared minus 1 over t plus one.
1 solutions
Answer 267053 by ankor@dixie-net.com(15624) on 2010-11-23 15:40:11 (Show Source):
You can put this solution on YOUR website! =  - 
Factoring (t^2-1) as the difference of squares, reveals the common denominator of (t-1)(t+1
=  -
:
Multiply thru by (t+1)(t-1) and you have:
(t+1)(t-2) = t + 17 - (t-1)
:
FOIL the left side remove the brackets on the right side
t^2 - t - 2 = t + 17 - t + 1
:
t^2 - t - 2 = 18
:
t^2 - t - 2 - 18 = 0
:
t^2 - t - 20 = 0
Factors to
(x-5)(x+4) = 0
two solutions
x = -4
x = +5
:
You can check both solutions in the original problem
|
Rational-functions/374795: A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 15 minutes?
1 solutions
Answer 266837 by ankor@dixie-net.com(15624) on 2010-11-22 21:57:40 (Show Source):
You can put this solution on YOUR website!A camel can drink 15 gallons of water in 10 minutes.
At this rate, how much water can the camel drink in 15 minutes?
:
You can do this as a ratio equation,
let x = amt of water in 15 min
:
 = 
10x = 15 * 15
10x = 225
x = 22.5 gal in 15 min
:
:
Check this another way, he drinks 1.5 gal in 1 min, then 1.5 * 15 = 22.5
|
Polynomials-and-rational-expressions/375205: I have a problem solving a word problem.
The polynominal 0.041h-0.018a-2.69 can be used to estimate the lung capacity, in liters, of a female with height h, in centimeters, and age a, in years. Find the lung capacity of a 20-year-old women who is 190 centimeters tall.
Her lung capacity is approximately liters.
Do i start this problem with it reading 0.041h(190)-0.018(20)-2.69, I am confused.
1 solutions
Answer 266833 by ankor@dixie-net.com(15624) on 2010-11-22 21:47:04 (Show Source):
You can put this solution on YOUR website!he polynominal 0.041h-0.018a-2.69 can be used to estimate the lung capacity,
in liters, of a female with height h, in centimeters, and age a, in years.
Find the lung capacity of a 20-year-old women who is 190 centimeters tall.
Her lung capacity is approximately liters.
Do i start this problem with it reading 0.041h(190)-0.018(20)-2.69,
:
Let L = Lung Capacity in liter
:
Replace h with, 190 and a with 20, just like you did, except you left the h in there.
L = 0.041(190)-0.018(20)-2.69
just do the math
L = 7.79 - .36 - 2.69
L = 4.74 liters
:
but why are you confused?
|
Miscellaneous_Word_Problems/375078: Find the height of a flagpole that sits atop a hill, if it makes an angle of 122 degrees with the hillside, and the angle of elevation between the side of the hill to the top of the flagpole is 35 degrees at a distance of 120 feet.
1 solutions
Answer 266832 by ankor@dixie-net.com(15624) on 2010-11-22 21:37:39 (Show Source):
You can put this solution on YOUR website!Find the height of a flagpole that sits atop a hill, if it makes an angle
of 122 degrees with the hillside, and the angle of elevation between the
side of the hill to the top of the flagpole is 35 degrees at a distance of 120 feet.
:
We are going to use the law of Sines,
:
Let the angle at the top of the pole to a point on the hillside = A
Then the side opposite this angle = a, which is given as 120'
:
Let the angle between the hillside point to the top of the pole = B (35 degrees)
Then the side opposite this angle = b (the height of the pole
:
The angle between the pole and the hillside, C = 122 degrees
:
Find angle A: 180 - 122 - 35 = 23 degrees
:
 = 
Using our values
 = 
Cross multiply
sin(23)*b = sin(35)*120
Which is
.39073b = .573576*120
.39073b = 68.829
b = 
b = 176.155 ft is the height of pole above the top of the hill
|
Evaluation_Word_Problems/374881: I am really struggling in math right now. I am working on word problems for linear systems, and Unfortunately I don't have a clue what to do, so i need some answers from you, to look them over and examine them to get a clue of what i'm trying to do.
1. Find the equation of the line that passes through the point of intersection of -2x + 4y = 14 and 5x - 3y = -14 and is perpendicular to 2x - 3y + 6 = 0.
1 solutions
Answer 266799 by ankor@dixie-net.com(15624) on 2010-11-22 20:06:59 (Show Source):
You can put this solution on YOUR website!1. Find the equation of the line that passes through the point of intersection of -2x + 4y = 14 and 5x - 3y = -14 and is perpendicular to 2x - 3y + 6 = 0.
:
First of all find the point of intersection by solving the system, x & y
-2x + 4y = 14
+5x - 3y = -14
:
Multiply the 1st equation by 5, the 2nd equation by 2, results:
-10x + 20y = 70
+10x - 6y = -28
------------------adding eliminates x, find y
14y = 42
y = 
y = 3
:
Find x using the 2nd equation: +5x - 3y = -14; replace y with 3
5x - 3(3) = -14
5x - 9 = -14
5x = -14 + 9
5x = -5
x = -1
:
The point of intersection: x=-1, y=3
:
We want the equation of a line that is perpendicular to 2x - 3y + 6 = 0
and pass thru the point x=-1, y=3
:
Find the slope of the equation 2x - 3y + 6 = 0, put it in the slope/intercept form, namely: y = mx + b
2x - 3y + 6 = 0
subtract 2x and 6 from both sides
-3y = -2x - 6
Y has to be positive, mult by -1
3y = 2x + 6
Divide both sides by 3
y =  x + 2
The slope: m1 =
:
The relationship of the slopes of perpendicular lines is m1*m2 = -1
we know m1, find m2
*m2 = -1
divide both sides by 3/2
m2 = -1* 
m2 = 
:
Using the point/slope form: y - y1 = m(x - x1)
x1=-1; y1=3 (the point of intersection)
m =
so we have:
y - 3 = [x - (-1)]
y - 3 = [x + 1]
y - 3 = x -
add 3 to both sides
y = x - + 3
which is
y = x - + 
y = x +
Put in the standard form, multiply by 2
2y = -3x + 3
Add 3x to both sides
3x + 2y = 3; is the equation of a line that passes thru the intersecting point -1,3
and is perpendicular to the line 2x - 3y + 6 = 0.
|
Percentage-and-ratio-word-problems/374680: How do I solve this word problem. --> for every two widgets i buy at regular price, i can buy a third widget for $4. i bought 9 widgets for a total of $909. find, in dollars, the regular price of a widget.
1 solutions
Answer 266608 by ankor@dixie-net.com(15624) on 2010-11-22 12:12:11 (Show Source):
You can put this solution on YOUR website!> for every two widgets i buy at regular price, i can buy a third widget for $4. i bought 9 widgets for a total of $909. find, in dollars, the regular price of a widget.
:
If you bought a total of 9, then 3 of the nine will cost only $4
Therefore you bought 6 at the regular price
:
6w = 909 - 3(4)
6w = 897
w = 
w = $149.50 is the reg price
|
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