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1 solutions
Answer 154168 by ankor@dixie-net.com(15746)   on 2009-07-25 19:12:06 (Show Source):
You can put this solution on YOUR website!A thief is 20 steps ahead of a cop , and takes 6 steps while the cop takes 5,
but 5 of the cop's steps equal 8 of the thief's; how far will the thief run
before he is caught?
:
:
Let x = distance of 1 step by the thief
Then
 = 1.6x; the cop's step distance
:
Write a distance equation:
5(1.6x) = 6x + 20
8x - 6x = 20
2x = 20
x = 10 units; distance of 1 step
:
6(10) = 60 units traveled by the thief, when he is caught
5(1.6*10)) = 80 units traveled by the cop (started out 20 steps behind)
;
:
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Money_Word_Problems/204176: The amount Estella invested in a 6% savings is $3500 less than the amount she invested in a 10% savings account. At the end of the year,she received $75o in simple interest. Find the amount invested in each account?
I think you set the probelm up like this .06(x-3500).10+x=1500?
Can anyone confirm this?
1 solutions
Answer 154140 by ankor@dixie-net.com(15746) on 2009-07-25 12:51:43 (Show Source):
You can put this solution on YOUR website!The amount Estella invested in a 6% savings is $3500 less than the amount she invested in a 10% savings account. At the end of the year,she received $75o in simple interest. Find the amount invested in each account?
I think you set the probelm up like this .06(x-3500).10+x=1500?
:
I think it would be:
.06(x-3500) + .10x = 750
|
Quadratic_Equations/204170: I need help putting this word problem into equation form, can someone help me?
A business invests $8000 in a savings account for 2 years. At the beginning of the second year, an additional $2500 is invested. At the end of the second year, the account balance is $11445. What was the annual interest rate?
1 solutions
Answer 154138 by ankor@dixie-net.com(15746) on 2009-07-25 12:31:08 (Show Source):
You can put this solution on YOUR website!A business invests $8000 in a savings account for 2 years.
At the beginning of the second year, an additional $2500 is invested.
At the end of the second year, the account balance is $11445.
What was the annual interest rate?
:
let x = interest rate (in decimal form)
:
An equation for this:
:
(1+x)((8000(1+x))+2500)) = 11445
:
(1+x)(8000 + 8000x + 2500) = 11445
:
(1+x)(8000x + 10500) = 11445
;
8000x + 10500 + 8000x^2 + 10500x = 11445
:
8000x^2 + 8000x + 10500x + 10500 - 11445 = 0
Simplify divide by 5:
8000x^2 + 18500x - 945 = 0
:
1600x^2 + 3700x - 189 = 0
:
Use the quadratic formula
in this equation: a=1600, b=3700, c= -189
:
:
:
The positive solution
:
x = .05; 5% is the interest rate
;
;
See if this is true
1st year: 1.05*8000 = 8400
Add 2500 after the 1st year = 10900
End of 2nd yr: 1.05(10900) = 11445
|
Quadratic_Equations/204134: This question is from textbook
Hi. I really need help with an equation that needs to be graphed, also I need to find the coordinates of the vertex. The equation is y= -x^2 - 8x - 7
1 solutions
Answer 154089 by ankor@dixie-net.com(15746) on 2009-07-24 21:41:19 (Show Source):
You can put this solution on YOUR website!i. I really need help with an equation that needs to be graphed,
also I need to find the coordinates of the vertex.
The equation is y= -x^2 - 8x - 7
:
Plot the graph from x=-8 to x= 0; should look like this:
:
Find the vertex by finding the axis of symmetry; x = -b/(2a)
in the equation a=-1, b=-8
x = 
:
x = 
:
x = -4 is the x coordinate of the vertex
:
Find y, substitute -4 for x in the equation
y = -(-4^2) - 8(-4) - 7
y = -16 + 32 - 7
y = +9
;
Vertex: -4,+9 as shown on the graph
|
Equations/204094: Option 1-$42.00 monthly fee plus $5.00/hour for court rental
option 2-no monthly fee but$8.50/hour for court rental
Let x=hour per month of court rental time
write a mathematical model representing the total monthly cost, C, in terms of x for the following:
option1 C=
option2 C=
How many hour would you have to rent the court so the monthly cost of option 1 is less than option 2? Set up an inequality and show your work algebraically using the info in part A
1 solutions
Answer 154080 by ankor@dixie-net.com(15746) on 2009-07-24 18:58:42 (Show Source):
You can put this solution on YOUR website!): Option 1-$42.00 monthly fee plus $5.00/hour for court rental
option 2-no monthly fee but$8.50/hour for court rental
Let x=hour per month of court rental time
write a mathematical model representing the total monthly cost, C, in terms of x for the following:
:
option1 C = 5x + 42
option2 C = 8.5x
:
How many hour would you have to rent the court so the monthly cost of option 1
is less than option 2?
Set up an inequality and show your work algebraically using the info in part A
:
8.5x > 5x + 42
:
8.5x - 5x > 42
:
3.5x > 42
x > 
x > 12 hrs, the monthly cost of option 1 is less than option 2
:
Test this with 13 hrs
Opt 1: 5(13) + 42 = $107
Opt 2: 8.5(13) = $110.50
|
Travel_Word_Problems/204108: This question is from textbook
Gone fishing. Debbie traveled by boat 5 miles upstream to
fish in her favorite spot. Because of the 4-mph current, it
took her 20 minutes longer to get there than to return. How
fast will her boat go in still water?
Thank you for your help
1 solutions
Answer 154074 by ankor@dixie-net.com(15746) on 2009-07-24 18:12:28 (Show Source):
You can put this solution on YOUR website!Debbie traveled by boat 5 miles upstream to fish in her favorite spot.
Because of the 4 mph current, it took her 20 minutes longer to get there
than to return.
How fast will her boat go in still water?
:
Let s = boat speed in still water
then
(s-4) = speed upstream
and
(s+4) = speed down stream
:
Convert 20 min to hrs: 20/60 =  hr
:
Write a time equation: time = 
Upstream time = downstream time + 20 minutes (1/3 hr)
 =  +
:
To clear out these denominators, multiply equation by 3(s+4)(s-4)
3(s+4)(s-4)* = 3(s+4)(s-4)* + *3(s+4)(s-4)
Results in
:
15(s+4) = 15(s-4) + (s+4)(s-4)
:
15s + 60 = 15s - 60 + s^2 - 16
:
0 = 15s - 15s - 60 - 60 + s^2 - 16
:
0 = s^2 - 136
:
s^2 = 136
s = 
s = 11.66 mph speed in still water
:
:
Check solution on calc: (speed up = 7.66 and speed down = 15.66)
5/7.66 - 5/15.66 = .3333 which is 1/3 of an hr
|
Volume/204056: Find the area of the shaded portion of the circle. Use 3.14 for π. Figure not drawn to scale.
The figure is an uncircumscribed circle with a square in it that says 10cm inside the square.The shaded portion is everything outside of the square, so portions of(in) the circle. I do not know if this question can be answered without the figure, but I have tried to figure this out and I have given up, it is over my head. Or if you could just give an example of an uncircumscribed circle and the shaded portion, would be helpful also. Thank you very much for your time.
1 solutions
Answer 154032 by ankor@dixie-net.com(15746) on 2009-07-24 11:08:25 (Show Source):
You can put this solution on YOUR website!Find the area of the shaded portion of the circle. Use 3.14 for π. Figure not drawn to scale.
The figure is an uncircumscribed circle with a square in it that says 10cm inside the square.The shaded portion is everything outside of the square, so portions of(in) the circle. I do not know if this question can be answered without the figure, but I have tried to figure this out and I have given up, it is over my head. Or if you could just give an example of an uncircumscribed circle and the shaded portion, would be helpful also. Thank you very much for your time
:
From the given information, I understand that it is a square that fits exactly
inside the circle, the 10 cm is the diagonal of the square and would also be
the diameter of the circle, if this is correct here's how to do it:
Find the area of the circle
A = pi*r^2
Remember r = 10/2 = 5 cm
A = 3.14 * 5^2
A = 3.14 * 25
A = 78.5 sq/cm is the area of the circle
:
The diagonal of the square is also 10 cm, find the area of the square by
finding the length of the side of the square, call it x:
Using pythag a^2 + b^2 = c^2
a & b = x (it's a square)
c = 10
:
x^2 + x^2 = 10^2
2x^2 = 100
Remember x^2 = is also the area of the square
x^2 = 
x^2 = 50 sq/cm is the area of the square
:
Circle area - square area
78.5 - 50 = 28.5 sq/cm is the area outside the square
:
:
Did this help?
|
Quadratic_Equations/204078: Please help me solve this problem.
Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle.
1 solutions
Answer 154012 by ankor@dixie-net.com(15746) on 2009-07-24 09:44:01 (Show Source):
You can put this solution on YOUR website!Steve traveled 150 miles at a certain speed.
Had he gone 20 mph faster, the trip would have taken 2 hours less.
Find the speed of his vehicle.
:
Let s = the speed of the car
then
(x+20) = the faster speed
:
Write a time equation: Time 
:
 =  + 2
:
Multiply this equation by s(s+20) and solve for s, and you have it
|
Numbers_Word_Problems/204036: The difference of two numbers is 16. Three-fourths of the larger number is 14 larger than one-half of the smaller number. Find the numbers.
1 solutions
Answer 153981 by ankor@dixie-net.com(15746) on 2009-07-23 20:55:29 (Show Source):
You can put this solution on YOUR website!Two numbers, x & y
;
The difference of two numbers is 16.
x - y = 16
x = (y+16)
:
Three-fourths of the larger number is 14 larger than one-half of the smaller number.
.75x = .5y + 14
:
Replace x with (y+16)
.75(y + 16) = .5y + 14
:
.75y + 12 = .5y + 14
:
.75y - .5y = 14 - 12
:
.25y = 2
y = 
y = 8
then
x = 8 + 16
x = 24
|
Geometry_Word_Problems/204031: The perimeter of a swimming pool is 96m. The width is 3m more than half the length of the pool. find the length and breadth of the pool.
1 solutions
Answer 153971 by ankor@dixie-net.com(15746) on 2009-07-23 16:40:25 (Show Source):
You can put this solution on YOUR website!The perimeter of a swimming pool is 96 m.
The width is 3m more than half the length of the pool.
Find the length and breadth of the pool.
:
Let x = the length of the pool
It says,"The width is 3m more than half the length of the pool.", therefore
(.5x + 3) = the width
;
Perimeter equation: 2L + 2W = 96, therefore:
2x + 2(.5x+3) = 96
2x + x + 6 = 96
3x = 96 - 6
3x = 90
x = 
x = 30 m is the length
therefore
.5(30) + 3 = 18 m is the width
;
;
Check solution, find the perimeter
2(30) + 2(18) = 96
|
Miscellaneous_Word_Problems/203837: A diagonal of a square connects the points (-4,3) and (2,-3). Find the area and perimeter of the square.
1 solutions
Answer 153963 by ankor@dixie-net.com(15746) on 2009-07-23 15:08:48 (Show Source):
You can put this solution on YOUR website!A diagonal of a square connects the points (-4,3) and (2,-3).
Find the area and perimeter of the square.
:
If you draw this on graph paper you can see this is a square 6 by 6
You can do it in your head: 4*6 = 24 is the perimeter and 6^2 = 36 is the area
|
Equations/203958: Hi all, I was hoping someone could help me in answering the following 2 problems. They are two similiar problems bbut they are seperate problems and are not related to eachother.
1. Make t the subject of the equation y = sqrt(8t + 3)
2. Make x the subject of the equation y = 3e^(2x).
Any help with steps would be most appreciated.
Thanks, -Nick.
1 solutions
Answer 153955 by ankor@dixie-net.com(15746) on 2009-07-23 14:21:32 (Show Source):
You can put this solution on YOUR website!1. Make t the subject of the equation y = sqrt(8t + 3)
y = 
Square both sides:
y^2 = 8t + 3
Subtract 3 from both sides
y^2 - 3 = 8t
Divide both sides by 8
 = t
:
:
2. Make x the subject of the equation y = 3e^(2x)
y = 
Divide both sides by 3
 = 
find the natural log of both sides
 = 
log equiv of exponents:
= 
natural log of e is 1
= 2x
divide both sides by 2
 = x
|
Linear_Equations_And_Systems_Word_Problems/203995: Four times the sum of the digits of a two-digit number is equal to the number. It the digits are reversed, the resulting number is 27 greater than the original number. What is the number?
1 solutions
Answer 153933 by ankor@dixie-net.com(15746) on 2009-07-23 12:22:05 (Show Source):
You can put this solution on YOUR website!Four times the sum of the digits of a two-digit number is equal to the number.
It the digits are reversed, the resulting number is 27 greater than the original number.
What is the number?
:
Let x = the 10's digit
Let y = the units digit
then
10x + y = "the number"
:
Write an equation for each statement:
:
"Four times the sum of the digits of a two-digit number is equal to the number."
4(x+y) = 10x + y
4x + 4y = 10x + y
4y - y = 10x - 4x
3y = 6x
Simplify, divide by 3
y = 2x
:
"If the digits are reversed, the resulting number is 27 greater than the original number."
10y + x = 10x + y + 27
10y - y = 10x - x + 27
9y = 9x + 27
Simplify divide by 9
y = x + 3
:
From the 1st statement equation, replace y with 2x
2x = x + 3
2x - x = 3
x = 3
then
y = 2(3)
y = 6
:
36 = " the number"
:
:
Check solutions in the statement:
"If the digits are reversed, the resulting number is 27 greater than the original number."
63 = 36 + 27
|
Miscellaneous_Word_Problems/203841: Jean goes to a movie theater where a ticket costs $7 and any snack item-candy,popcorn,or drink-sells for $1.50 each. Frank goes to a theater where the ticket costs $4 and candy, popcorn, or drinks sell for $2.50 each. How many snack items would jean and Frank need to buy, so that they each pay the same amount at the theater?
1 solutions
Answer 153880 by ankor@dixie-net.com(15746) on 2009-07-22 21:22:08 (Show Source):
You can put this solution on YOUR website!Jean goes to a movie theater where a ticket costs $7 and any snack
item-candy,popcorn,or drink-sells for $1.50 each.
Frank goes to a theater where the ticket costs $4 and candy, popcorn,
or drinks sell for $2.50 each.
How many snack items would jean and Frank need to buy, so that they
each pay the same amount at the theater?
:
Let n = number of snack items bought for equal amts
:
Franks$ = Jeans%
2.50n + 4 = 1.50n + 7
2.5n - 1.5n = 7 - 4
n = 3 snack items
:
:
Check solution in original equation
2.5(3) + 4 = 1.5(3) + 7
7.50 + 4 = 4.50 + 7
|
Miscellaneous_Word_Problems/203843: When 6 students show up for the Swift River Cleanup Day, they can pick up all of the bottles and trash on their section of the riverfront in 2 1/2 hr. If 9 students show up, how long will the same cleanup take?
1 solutions
Answer 153879 by ankor@dixie-net.com(15746) on 2009-07-22 21:10:21 (Show Source):
You can put this solution on YOUR website!When 6 students show up for the Swift River Cleanup Day, they can pick up
all of the bottles and trash on their section of the riverfront in 2 1/2 hr.
If 9 students show up, how long will the same cleanup take?
:
Let t = time required using 9 students
;
You can solve this using man-hrs, given:
6 * 2.5 = 15 man-hrs required to do the job
Then
9t = 15
t = 
t = 1  hrs if 9 students work
:
|
Functions/203846: Find the numbers C and D such that (-4,-7) is a solution of the following system:
-4x + Cy =-3
Dx - 2y =24
1 solutions
Answer 153837 by ankor@dixie-net.com(15746) on 2009-07-22 14:49:33 (Show Source):
You can put this solution on YOUR website!Find the numbers C and D such that (-4,-7) is a solution of the following system:
-4x + Cy =-3
Dx - 2y = 24
:
Substitute -4 for x and -7 for y
-4(-4) + C(-7) = -3
D(-4) - 2(-7) = 24
:
+16 - 7C = -3
-4D + 14 = 24
:
-7C = -3 - 16
7C = 3 + 16
C = 
and
-4D = 24 - 14
-4D = 10
D = 
D = 
|
Miscellaneous_Word_Problems/203852: You are in line at a ticket window. There are two more people ahead of you in line than there are behind you. In the entire line, there are three times as many people as there are behind you. how many are in the line?
1 solutions
Answer 153823 by ankor@dixie-net.com(15746) on 2009-07-22 12:54:18 (Show Source):
You can put this solution on YOUR website!You are in line at a ticket window. There are two more people ahead of you in
line than there are behind you.
In the entire line, there are three times as many people as there are behind you.
how many are in the line?
:
Let x = no. behind you
then
(x=2) = no. ahead of you
:
Write an equation for the statement:
"there are three times as many people as there are behind you."
x + 1 + (x+2) = 3x
2x + 3 = 3x
3 = 3x - 2x
x = 3 people behind you
then
3 + 2 = 5 people ahead
:
Total: ahead + you + behind:
5 + 1 + 3 = 9 folks in line
:
|
Volume/203829: A cylinder can of cleaner holds 1 liter of liquid. What is its height if the diameter of the base is 10cm.
I am failing my geomerty class, I just do not get it, but trying. I did not get to give a reply of a "thank you" to a tutor(Stan) that answered 2 questions of mine a couple of weeks ago because it would not let me send it for some reason- So just in case-Thanks so much for your time in helping me.
1 solutions
Answer 153814 by ankor@dixie-net.com(15746) on 2009-07-22 11:24:34 (Show Source):
You can put this solution on YOUR website!A cylinder can of cleaner holds 1 liter of liquid.
What is its height if the diameter of the base is 10 cm.
:
Change 1 liter to cu/cm: 1 liter = 1000 cu/cm
:
Volume of a cylinder: V = 
Find the radius: a 10 cm diameter = 5 cm radius
:
 = 1000
:
 = 1000
:
h = 
h = 12.73 cm is the height
:
:
Check solution on a calc: enter pi*5^2*12.73 = 999.8 ~ 1000, which is 1 liter
|
logarithm/203739: A certain strain on bacteria divides every three hours. If a colony is started with 30 bacteria, then the time(t, in hours) required for the colony to groww to N bacteria is given by the following formula. Find the time required for the colony to grow to a million bacteria.(Give your answer to the nearest tenth)
t= 3(log(n/30))/log 2
1 solutions
Answer 153756 by ankor@dixie-net.com(15746) on 2009-07-21 16:17:12 (Show Source):
You can put this solution on YOUR website!A certain strain on bacteria divides every three hours.
If a colony is started with 30 bacteria, then the time(t, in hours) required
for the colony to groww to N bacteria is given by the following formula.
Find the time required for the colony to grow to a million bacteria.
(Give your answer to the nearest tenth)
;
t= 
:
t= 
:
t= 
:
t= 
t = 45.1 hrs
|
Mixture_Word_Problems/203665: Angela needs 20 quarts of 50%
antifreeze solution in her radiator. She plans to obtain this
by mixing some pure antifreeze with an appropriate
amount of a 40% antifreeze solution. How many quarts of
each should she use?
1 solutions
Answer 153669 by ankor@dixie-net.com(15746) on 2009-07-20 19:51:58 (Show Source):
You can put this solution on YOUR website!needs 20 quarts of 50% antifreeze solution in her radiator.
plans to obtain this by mixing some pure antifreeze with an appropriate
amount of a 40% antifreeze solution. How many quarts of antifreeze?
:
Let x = amt of pure antifreeze
The resulting amt is to be 20 qts, therefore
(20-x) = amt of 40% solution required
:
A typical mixture problem
:
x + .40(20-x) = .50(20)
;
x + 8 - .4x = 10
:
x - .4x = 10 - 8
:
.6x = 2
x = 
x = 3 qts of pure anti-freeze
and
20 - 3 = 16 qts of 40% mixture
|
Numeric_Fractions/203662: I am having a hard time with Algebra. Here's one I do not get. I do not get what the letters stand for. Please help.....
Solve for w: 3w - 10 = 4w +5
1 solutions
Answer 153668 by ankor@dixie-net.com(15746) on 2009-07-20 19:41:14 (Show Source):
You can put this solution on YOUR website! 3w - 10 = 4w + 5
You want to isolate the unknown (w) on one side, and numerical value on the other side
:
Subtract 5 from both sides
3w - 10 - 5 = 4w + 5 - 5
;
and you have
3w - 15 = 4w
;
Subtract 3w from both sides:
3w - 3w - 15 = 4w - 3w
;
and you have
-15 = w
:
:
Check your solution by substituting -15 for w in the original equation
3w - 10 = 4w + 5
3(-15) - 10 = 4(-15) + 5
-45 - 10 = -60 + 5
-55 = -55; equality reigns, confirms your solution of w = 15
|
Percentage-and-ratio-word-problems/203597: This question is from textbook mathematics for igcse
if an employer reduce the working week from 40 hours to 35 hours with no loss of weekly pay,calculate the percentage increase in the hourly rate of pay
1 solutions
Answer 153634 by ankor@dixie-net.com(15746) on 2009-07-20 13:38:31 (Show Source):
You can put this solution on YOUR website! an employer reduce the working week from 40 hours to 35 hours with no loss
of weekly pay, calculate the percentage increase in the hourly rate of pay
:
Let the weekly pay = 400
:
 = $10 per/hr original hourly pay
:
 = $11.43 increased hourly pay
:
Pay increase divided by original pay = Per cent increase
:
 = 1.43/10 = .143 * 100 = 14.3% increase in pay
|
Volume/203576: Suppose you are designing a cardboard box that must have a volume of 34 cubic feet. The cost of the cardboard is $9 per square ft. How much will the material for each box cost?
1 solutions
Answer 153586 by ankor@dixie-net.com(15746) on 2009-07-19 21:10:32 (Show Source):
You can put this solution on YOUR website!Suppose you are designing a cardboard box that must have a volume of 34 cubic feet.
The cost of the cardboard is $9 per square ft.
How much will the material for each box cost?
:
If it is a square box the dimension (s) will be:
s = cube root(34)
s ~ 3.24 ft
:
Find the cost using the Surface area:
6(3.24^2) * $9 = $566.87
|
Quadratic_Equations/203510: Could someone help me with this one? I have trouble with word problems? You are greatly appreciated.
An express train and a local train both leave Gray’s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it. Find the speed of each train.
1 solutions
Answer 153583 by ankor@dixie-net.com(15746) on 2009-07-19 19:41:07 (Show Source):
You can put this solution on YOUR website!An express train and a local train both leave Gray’s Lake at 12:00 noon and head
for Chicago 60 miles away. The express travels twice as fast as the local and
arrives 2 hours ahead of it. Find the speed of each train.
:
Let s = speed of the freight
then
2s = speed of the express
:
Write a time equation: Time =
Freight time = Express time + 2 hrs
 =  + 2
Multiply equation by 2s, results:
2(60) = 60 + 2(2s)
120 = 60 + 4s
120 - 60 = 4s
60 = 4s
s = 
s = 15 mph is the freight,
then
2(15) = 30 mph is express
;
:
Check solution by finding the time of each train
60/15 = 4 hr
60/30 = 2 hr
------------
differ = 2 hrs
|
Quadratic_Equations/203530: A bridge is the shape of a parabola. It is 10 m wide and the highest point of the bridge is 6m above ground. A transport truck is 4.5 m tal and 3 m wide. The road is centered on the axis of symmetry and the transport truck must stay on its own side of the road. Will the trick fit under the bridge? Justify your decision.
1 solutions
Answer 153577 by ankor@dixie-net.com(15746) on 2009-07-19 19:02:09 (Show Source):
You can put this solution on YOUR website!A bridge is the shape of a parabola. It is 10 m wide and the highest point of
the bridge is 6m above ground. A transport truck is 4.5 m tal and 3 m wide.
The road is centered on the axis of symmetry and the transport truck must stay
on its own side of the road. Will the truck fit under the bridge?
Justify your decision.
:
Find the parabola equation using the form ax^2 + bx = y
x = 5; y = 6
25a + 5b = 6
and
x = 10; y = 0
100a + 10b = 0
:
Multiply the 1st equation by 2 and subtract from th above equation
100a + 10b = 0
50a + 10b = 12
----------------
50a = -12
a = 
a = -.24
;
Find b using 100a + 10b = 0
100(-.24) + 10b = 0
-24 + 10b = 0
10b = 24
b = 2.4
:
The equation y = -.24x^2 + 2.4x which we can plot:
Assuming the truck will be just at the right of the centerline,
a 3 m wide truck will be at x = 8>
Find the height of the parabola where x = 8
y = -.24(8^2) + 2.4(8)
y = -15.36 + 19.2
y = +3.84, so 4.5 is too high
|
Rate-of-work-word-problems/203558: Five workers paint four houses in six days. Working at the same rate as these workers, how many workers are needed to paint 12 houses in three days?
1 solutions
Answer 153571 by ankor@dixie-net.com(15746) on 2009-07-19 18:26:11 (Show Source):
You can put this solution on YOUR website!Five workers paint four houses in six days. Working at the same rate as these
workers, how many workers are needed to paint 12 houses in three days?
:
Use Man-days (no.of men * no. of days)
:
Let x = the no. of man-days required to paint 1 house
:
x = 
x = 
x = 7.5 man-days per house
:
"how many workers are needed to paint 12 houses in three days?"
Let w = no. of workers
3w = 12(7.5)
3w = 90
w =
w = 30 workers to paint 12 house in 3 days.
|
Proportions/203409: The ratio of domestic stamps to foreign stamps in John’s stamp collection is 3:1. If John sold thirty of his domestic stamps, the ratio of domestic stamps to foreign stamps would be 1:2. How many foreign stamps does John have in his collection?
1 solutions
Answer 153553 by ankor@dixie-net.com(15746) on 2009-07-19 15:39:50 (Show Source):
You can put this solution on YOUR website!The ratio of domestic stamps to foreign stamps in John’s stamp collection is 3:1.
If John sold thirty of his domestic stamps, the ratio of domestic stamps to foreign stamps would be 1:2.
How many foreign stamps does John have in his collection?
:
"The ratio of domestic stamps to foreign stamps in John’s stamp collection is 3:1."
 = 
d = 3f
:
"If John sold thirty of his domestic stamps, the ratio of domestic stamps to foreign stamps would be 1:2."
:
 = 
f = 2(d-30)
f = 2d - 60
replace d with 3f
f = 2(3f) - 60
f = 6f - 60
60 = 6f - f
60 = 5f
f = 
f = 12 foreign stamps
;
:
Check solution
d = 3(12
d = 36 domestic stamps
:
Check in statement:
" John sold thirty of his domestic stamps, the ratio of domestic stamps to foreign stamps would be 1:2."
36 - 30 = 6 stamps
6/12 = 1/2
|
Quadratic_Equations/203509: Could someone help me with this one? I have difficulty with word problems. You are greatly appreciated.
Joe has a collection of nickels and dimes that is worth $6.05. If the number of dimes was doubled and the number of nickels was decreased by 10, the value of the coins would be $9.85. How many dimes does he have?
1 solutions
Answer 153551 by ankor@dixie-net.com(15746) on 2009-07-19 15:15:12 (Show Source):
You can put this solution on YOUR website!Joe has a collection of nickels and dimes that is worth $6.05.
If the number of dimes was doubled and the number of nickels was decreased by 10,
the value of the coins would be $9.85. How many dimes does he have?
:
Let d = no. of dimes
Let n = no. of nickels
:
Write an equation for each statement:
:
"a collection of nickels and dimes that is worth $6.05."
.05n + .10d = 6.05
:
"If the number of dimes was doubled and the number of nickels was decreased by 10, the value of the coins would be $9.85."
.05(n-10) + .10(2d) = 9.85
:
.05n - .50 + .20d = 9.85
:
.05n + .20d = 9.85 + .50
:
.05n + .20d = 9.35
:
Subtract the 1st equation from the above equation:
.05n + .20d = 9.35
.05n + .10d = 6.05
---------------------Subtraction eliminate n, find d
0n + .10d = 3.30
d = 
d = 33 dimes
:
:
Check solution
Find n:
.05n + .10d = 6.05
.05n + .10(33) = 6.05
.05n + 3.30 = 6.05
.05n = 6.05 - 3.30
.05n = 2.75
n = 
n = 55 nickels
:
.05(55) + .20(33) = 9.35
2.75 + 6.60 = 9.35
|
Polynomials-and-rational-expressions/203406: Five grams of sugar are added to a 45 gram serving of a breakfast cereal that is is 10% sugar. What is the percent concentration in the resulting mixture?
1 solutions
Answer 153544 by ankor@dixie-net.com(15746) on 2009-07-19 14:33:18 (Show Source):
You can put this solution on YOUR website!Five grams of sugar are added to a 45 gram serving of a breakfast cereal that
is is 10% sugar. What is the percent concentration in the resulting mixture?
:
Let x = the decimal equiv of percent of sugar of the resulting mixture
.10(45) + 5 = x(45+5)
:
4.5 + 5 = 50x
:
9.5 = 50x
x = 
x = .19 * 100 = 19% sugar concentration
|
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