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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629, >>NextTravel_Word_Problems/731247: There 429 people at a play. Admission was $8 each for adults and $4.50 each for children. The total receipts were $2641. How many adults and how many children attended?
1 solutions
Answer 447079 by ankor@dixie-net.com(15622)   on 2013-03-27 20:26:34 (Show Source):
You can put this solution on YOUR website!There 429 people at a play.
Admission was $8 each for adults and $4.50 each for children.
The total receipts were $2641.
How many adults and how many children attended
:
Let a = no. of adults
let c = no. of children
:
Write an equation for each statement
:
"There 429 people at a play."
a + c = 429
c = (429-a); use this form for substitution
:
" The total receipts were $2641."
8a + 4.50c = 2641
replace c with (429-a)
8a + 4.5(429-a) = 2641
8a + 1930.5 - 4.5a
8a - 4.5 a = 2641 - 1930.5
3.5a = 710.5
a = 710.5/3.5
a = 203 adults
:
I'll let you find the number of children, check the solutions in the
total$ equation
|
Exponents/731273: I don't understand how to complete this problem. The answer key says it should be 2 but I don't get that answer. Here's the problem(sorry I don't know how to type this stuff):
The cube root of 88 / the cube root of 11
I did 88^1/3 over 11^1/3 and then got 88/11 which then becomes 8. Please help! I don't know what I'm doing wrong. Thank you :)
1 solutions
Answer 447057 by ankor@dixie-net.com(15622) on 2013-03-27 19:11:42 (Show Source):
You can put this solution on YOUR website!The cube root of 88 / the cube root of 11
Factor inside the numerator radical to reveal a perfect cube
Extract the cube root of 8 and you have
 = 2
(cube root of 11 over cube root of 11 = 1)
|
Travel_Word_Problems/730947: andy track team decides to convert their running rates from miles per hour to kilometers per hour(1 mile<1.6 kilometers) A.which method would help you use to help the team do their converting:graph,table,or equation B.one of Andys teammates said that he could write an equation for his spreadsheet program that could convert any team members running rate from miles per hour to kilometers per hour. Write an equation that each member could use for this conversation
1 solutions
Answer 446980 by ankor@dixie-net.com(15622) on 2013-03-27 08:53:58 (Show Source):
You can put this solution on YOUR website! andy track team decides to convert their running rates from miles
per hour to kilometers per hour(1 mile<1.6 kilometers)
A.which method would help you use to help the team do their converting:graph,table,or equation
B.one of Andys teammates said that he could write an equation for his spreadsheet program that could convert any team members running rate
from miles per hour to kilometers per hour.
Write an equation that each member could use for this conversion
:
The actual conversion factor for mph to kmh is 1.609, an equation
k = 1.6m is probably close enough
:
Using this equation you can construct a table m=1 to m=10
m| k
-----
1|1.6
2|3.2
3|4.8
etc
|
Travel_Word_Problems/730910: There are 3 men riding bicycles all starting at the same time. They are on a 1/3 mile track. One is traveling 4 mph, one is traveling 6 mph and one is traveling 8 mph. How many minutes will it be until they are together at the starting point for the first time?
1 solutions
Answer 446936 by ankor@dixie-net.com(15622) on 2013-03-26 21:02:46 (Show Source):
You can put this solution on YOUR website!There are 3 men riding bicycles all starting at the same time.
They are on a 1/3 mile track.
One is traveling 4 mph, one is traveling 6 mph and one is traveling
8 mph. How many minutes will it be until they are together at the
starting point for the first time?
:
The first guy completes a lap in  * 3600 = 300 seconds
The 2nd guy completes a lap in  * 3600 = 200 seconds
The 3rd guy completes a lap in  * 3600 = 150 seconds
:
Least common multiple of all three lap times:
In 600 seconds which is 10 minutes, they should all be at the start
Guy 1 completes 2 laps
Guy 2 completes 3 laps
guy 3 completes 4 laps
|
Volume/730895: A hemispheric dome is needed to cover a circular region having an area of 1600 square feet. What will be the height of this dome? Answer to the nearest tenth of a foot.
1 solutions
Answer 446923 by ankor@dixie-net.com(15622) on 2013-03-26 20:07:54 (Show Source):
You can put this solution on YOUR website!A hemispheric dome is needed to cover a circular region having an area
of 1600 square feet.
What will be the height of this dome?
Answer to the nearest tenth of a foot.
:
Find the radius of the circular region, this is also the height of the
hemispheric dome
 = 1600
r = 
r = 22.56758 ~ 22.6 ft
|
Travel_Word_Problems/730781: a man travels x km at 3 km/h but does the return journey at 2 km/h. if the round trip took 5 hours find x
1 solutions
Answer 446891 by ankor@dixie-net.com(15622) on 2013-03-26 18:04:23 (Show Source):
You can put this solution on YOUR website! a man travels x km at 3 km/h but does the return journey at 2 km/h.
if the round trip took 5 hours find x
:
x/3 = time of the journey out
x/2 = time of the return
:
Write a time equation; time = dist/speed
out time + return time = 5 hrs
 +  = 5
multiply by 6 to get rid of the denominators, resulting in:
2x + 3x = 6(5)
5x = 30
x = 30/5
x = 6 km
:
:
Check solution in the original time equation
|
Geometry_Word_Problems/730805: A cable is run from the top of a tree to a stake located 4m away from the base of the tree. the length of the cable is 1m less than twice the height of the tree. find the length of the cable.
1 solutions
Answer 446868 by ankor@dixie-net.com(15622) on 2013-03-26 16:53:40 (Show Source):
You can put this solution on YOUR website!A cable is run from the top of a tree to a stake located 4m away from
the base of the tree.
the length of the cable is 1m less than twice the height of the tree.
find the length of the cable.
:
Let x = height of the tree
then
(2x-1) = length of the cable
:
Use pythag, a^2 + b^2 = c^2, where
a = 4
b = x
c = (2x-1)
4^2 + x^2 = (2x-1)^2
16 + x^2 = 4x^2 - 4x + 1
16 = 4x^2 - x^2 - 4x + 1
16 = 3x^2 - 4x + 1
0 = 3x^2 - 4x + 1 - 16
A quadratic equation
3x^2 - 4x - 15 = 0
Factors to
(3x + 5)(x - 3) = 0
the positive solution
x = 3 meters is the height of the tree
then
2(3) - 1 = 5 meters is the length of the cable
:
:
Check this 4^2 + 3^2 = 5^2
|
Geometry_Word_Problems/730819: hi, i just had a small question and i was wondering if you could just help me. My question is if a isosceles triangle has sides 4cm and 6cm what are two possible lengths for the third side?
Thanks for taking your time to help me plz reply asap.
1 solutions
Answer 446860 by ankor@dixie-net.com(15622) on 2013-03-26 16:27:57 (Show Source):
You can put this solution on YOUR website!My question is if a isosceles triangle has sides 4cm and 6cm what are two possible lengths for the third side?
:
An isosceles triangle has two equal side,
therefore third side could be either 4 or 6
1: 4, 4, 6
2: 6, 6, 4
|
Age_Word_Problems/730724: a father is ten times his daughter AGe now. in 5 years time he will be 5 times as old as his daughter. How old are each of them now?
1 solutions
Answer 446858 by ankor@dixie-net.com(15622) on 2013-03-26 16:21:52 (Show Source):
You can put this solution on YOUR website! a father is ten times his daughter AGe now.
f = 10d
in 5 years time he will be 5 times as old as his daughter.
f + 5 = 5(d+5)
f + 5 = 5d + 25
f = 5d + 25 - 5
f = 5d + 20
:
How old are each of them now?
replace f with 10d
10d = 5d + 20
10d - 5d = 20
5d = 20
d = 20/5
d = 4 yrs old is the daughter now
I'll let you find Dad's age
|
Graphs/730776: Please help with my question, I can catch on fast if I am explained how to do it
Find the equation of the line, both in point-slope and slope intercept form going through the point (3,5) and parallet to the line with the equation
y=-x+5
1 solutions
Answer 446852 by ankor@dixie-net.com(15622) on 2013-03-26 15:52:38 (Show Source):
You can put this solution on YOUR website!Find the equation of the line, both in point-slope and slope intercept
form going through the point (3,5) and parallel to the line with the
equation: y=-x+5
This is in the slope/intercept form
Parallel lines have the same slope, therefore the parallel line
y = -1x + b
Given points x=3, y=5, find b
5 = -1(3) + b
5 + 3 = b
b = 8
y = -x + 8 is the parallel line going thru 3,5
:
The point-slope form y - y1 = m(x - x1)
therefore
y - 5 = -1(x - 3)
|
Travel_Word_Problems/730738: Having problem figuring out this one. any help will be appreciated.
Myron corporation is sponsoring a walking race at its company outing. Leona Jackson and Sam Peterson love to walk. Leona walks at the rate of 5 miles per hour. Sam walks at the rate of 6 miles per hour.
Assume they start walking from the same place and walk in a straight line. Sam starts 1/2 hour after Leona.
A) how long will it take Sam to meet Leona ?
B) how many miles would each have walked?
1 solutions
Answer 446813 by ankor@dixie-net.com(15622) on 2013-03-26 14:02:49 (Show Source):
You can put this solution on YOUR website!Leona Jackson and Sam Peterson love to walk.
Leona walks at the rate of 5 miles per hour.
Sam walks at the rate of 6 miles per hour.
Assume they start walking from the same place and walk in a straight
line. Sam starts 1/2 hour after Leona.
A) how long will it take Sam to meet Leona ?
let t = S's walking time
then
(t + .5) = L's walking time
When S catches up with L, they will have walked the same distance
Write a distance equation: dist = speed * time
6t = 5(t+.5)
6t = 5t + 2.5
6t - 5t = 2.5
t = 2.5 hrs for S to catch up with L
:
(B) how many miles would each have walked?
Find S's distance
6 * 2.5 = 15 miles
check solution by finding L's dist
5 * (2.5+.5) = 15 mi
|
test/730504: What is the quadratic function that contains the points (0, 121), (1,116) & (2,101)?
1 solutions
Answer 446767 by ankor@dixie-net.com(15622) on 2013-03-26 08:48:21 (Show Source):
You can put this solution on YOUR website!What is the quadratic function that contains the points
(0, 121), (1,116) & (2,101)?
:
Using the form; ax^2 + bx + c = y; find a b and c
The first pair x=0, therefore we know that c = 121
Write equations for the other two pair
1, 116
1^2*a + 1b + 121 = 116
a + b = 116 - 121
a + b = -5
and
2, 101
2^2*a + 2b + 121 = 101
4a + 2b = 101 - 121
4a + 2b = -20
simplify divide by 2
2a + b = -10
:
Use elimination
2a + b = -10
a + b = - 5
--------------subtraction eliminates b, find a
a = -5
Find a
-5 + b = -5
b = 0
:
The equation: y = -5x^2 + 0b + 121 or just
y = -5x^2 + 121
:
Check this using the given x/y pairs
|
Graphs/730420: HELP!!! PLEASE!!! Been working on this for soo long and don't know what to do.
The ability of steel rod material to carry a load is related to the cross-sectional area of the rod. you can rewrite the expression that relates to the
cross-sectional area of the steel rod to the desired tension
(π (d^2))/4= (L)/(15,000 psi )
where d is the diameter of the steel rod in inches
and L is the load desired to be supported under tension, in pounds (L is divided by the safe working stress for medium steel rod, 15,000psi)
a. using the equation above, isolate the variable d to find an equation for the diameter of ateel rod needed for any load L.
b. draw a graph of your equation for loads from 0 to 100,000 pounds.
c. Is this graph linear or nonlinear?
THANK MUCH FOR THE HELP!!
1 solutions
Answer 446762 by ankor@dixie-net.com(15622) on 2013-03-26 07:56:09 (Show Source):
You can put this solution on YOUR website!The ability of steel rod material to carry a load is related to the
cross-sectional area of the rod.
you can rewrite the expression that relates to the cross-sectional
area of the steel rod to the desired tension:
(π (d^2))/4= (L)/(15,000 psi )
where d is the diameter of the steel rod in inches
and L is the load desired to be supported under tension, in pounds
(L is divided by the safe working stress for medium steel rod, 15,000psi)
 = 
a. using the equation above, isolate the variable d to find an equation
for the diameter of a steel rod needed for any load L.
Cross multiply
 = 4L
 = 
:
d = 
:
b. draw a graph of your equation for loads from 0 to 100,000 pounds.
Graph: y = 
looks like this
c. Is this graph linear or nonlinear? You can answer that from this graph
|
Miscellaneous_Word_Problems/730475: One pump can fill a water cistern twice as fast as a second pump. Working together, the two pumps can fill the cistern in 5 hours. Find how long it takes each pump to fill the cistern when working alone
1 solutions
Answer 446720 by ankor@dixie-net.com(15622) on 2013-03-25 21:45:09 (Show Source):
You can put this solution on YOUR website! One pump can fill a water cistern twice as fast as a second pump.
Working together, the two pumps can fill the cistern in 5 hours.
Find how long it takes each pump to fill the cistern when working alone
:
Let t = time required by one pump alone
then
2t = time required by the other pump
:
Let the completed job = 1 (a full cistern)
:
A typical shared work equation
Each will do a fraction of the work, the two fractions = 1
 +  = 1
multiply by 2t, resulting in
2(5) + 5 = 2t
10 + 5 = 2t
t = 15/2
t = 7.5 hrs for one pump
you can find the time for the other pump
|
Travel_Word_Problems/730328: If two cars start from 92 miles apart and travel directly towards each other, and one car starts at 11Am and the other starts at 11:15AM and goes 6 miles per hour faster, and they meet up at noon, what is the average speed of each car?
1 solutions
Answer 446713 by ankor@dixie-net.com(15622) on 2013-03-25 21:08:32 (Show Source):
You can put this solution on YOUR website! If two cars start from 92 miles apart and travel directly towards each other,
and one car starts at 11Am and the other starts at 11:15AM and goes 6 miles
per hour faster, and they meet up at noon, what is the average speed of each car?
:
Let s = speed of the Car1
then
(s+6) = speed of Car2
;
The travel time of each car from the information given
Car 1: 1 hr, Car 2: 45 min or .75 hr
:
Write a distance equation: dist = time * speed
:
Car 1 dist + Car 2 dist = 92 mi
1s + .75(s+6) = 92
s + .75s + 4.5 = 92
1.75s = 92 - 4.5
s = 
s = 50 mph is the speed of Car 1
then, obviously
56 mph is the speed of car 2
:
:
:
Check this by finding the actual distance each car went
1*50 = 50 mi
.75*56 = 42 mi
----------------
total dist: 92 mi
|
Bodies-in-space/730292: A cylinder of radius of 10cm. It already contains water to depth of 15cm. A metal sphere with volume 900cm^3 is placed in the water. Calculate the height that the water level rises
1 solutions
Answer 446635 by ankor@dixie-net.com(15622) on 2013-03-25 13:35:19 (Show Source):
You can put this solution on YOUR website! A cylinder of radius of 10cm.
It already contains water to depth of 15cm.
A metal sphere with volume 900cm^3 is placed in the water.
Calculate the height that the water level rises
:
Find the vol of water in the cylinder
V = 
V = 
V = 4712.4 cu/cm of water
:
Find the total volume of the water and the sphere
4712.4 + 900 = 5612.4 cu/cm
:
Find the height (h) of the water when displaced by the sphere
 = 5612.4
h = 
h = 17.8647 cm is the height
:
;
Check this by finding the vol of the water between 17.8647 - 15 = 2.8647cm
V = 
V = 899.97 ~ 900, the vol of the sphere
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Rectangles/730046: I have a rectangle with a perimeter equal to 16cm. I have to determine the value of x. One length(L) side of the rectangle is 3x. One width(W) side of the rectangle is 2x. Perimeter of this figure is equal to 16cm. At this time I cannot figure out the solution. I know that Perimeter = 2L+2W. Please help.
1 solutions
Answer 446488 by ankor@dixie-net.com(15622) on 2013-03-24 21:49:42 (Show Source):
You can put this solution on YOUR website! a rectangle with a perimeter equal to 16cm.
I have to determine the value of x.
One length(L) side of the rectangle is 3x.
One width(W) side of the rectangle is 2x.
Perimeter of this figure is equal to 16cm.
:
As you know that: 2L + 2W = 16
You also know that: L=3x, and W=2x
Replace L and W in the perimeter equation, then you have:
2(3x) + 2(2x) = 16
6x + 4x = 16
10x = 16
x = 16/10
x = 1.6 cm
:
check this by finding the perimeter when x=1.6
3(1.6) = 4.8 cm the length
and
2(1.6) = 3.2 cm the width
:
Perimeter:
2(4.8) + 2(3.2) = 16
9.6 + 6.4 = 16, confirms our solution of x=1.6
:
Did this make sense to you?
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Mixture_Word_Problems/729873: Hi I am trying to do some word problems by using a system of equations, for example using x and y that way when I set up the two equations I can use either the subsitution method or elimination method. Here are my word problems hope you can help. (:
1. A total of $12,000 is invested, part at 6% simmple interest and part at 3%. If the annual return from the two investments is the same, how much is invested at each rate?
2. A car travels 225 kilometers in the same time that a truck travels 195 kilometers. If the speed of the car is 10 kilometers per hour faster than the speed of the truck, find the speed of each vehicle.
1 solutions
Answer 446337 by ankor@dixie-net.com(15622) on 2013-03-24 16:44:57 (Show Source):
You can put this solution on YOUR website!1. A total of $12,000 is invested, part at 6% simple interest and part at 3%.
If the annual return from the two investments is the same, how much is invested at each rate?
let x = amt invested at 6%
let y = amt invested at 3%
Two equations
x + y = 12000
and
.06x = .03y
divide both sides by .03, results
2x = y
replace y with 2x in the 1st equation
x + 2x = 12000
3x = 12000
x = 12000/3
x = 4000
I'll let you find y, check the solutions in the interest equation
:
:
2. A car travels 225 kilometers in the same time that a truck travels 195 kilometers.
let x = car speed, let y = truck speed
write a time equation; time = dist/speed
 = 
Cross multiply
225y = 195x
divide both sides by 5, results:
45y = 39x
:
" If the speed of the car is 10 kilometers per hour faster than the speed of the truck,"
x - y = 10
x = y + 10
"find the speed of each vehicle."
replace x with (y+10) in the 1st simplified equation
45y = 39(y+10)
45y = 39y + 390
45y - 39y = 390
6y = 390
y = 390/6
y = 65 mph, the speed of the truck
I'll let you find the speed of the car, check your solutions in both equations
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Quadratic_Equations/729636: let k be an integer and p is a prime such that the quadratic equation x^2+kx+p=0 has two distinct positive integer solutions. The value of (k+p)=,,?
1 solutions
Answer 446220 by ankor@dixie-net.com(15622) on 2013-03-23 21:38:59 (Show Source):
You can put this solution on YOUR website!let k be an integer and p is a prime such that the quadratic equation
x^2 + kx + p = 0 has two distinct positive integer solutions.
The value of (k+p)=,,?
:
If p is prime and it has two integer solutions, one of the solutions has to be 1
therefore k = p + 1
x^2 + (p+1)x + p = 0
" The value of (k+p)="
(p+1) + p = 2p+1
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Rate-of-work-word-problems/729747: A,B,and C undertook a construction project. A and B worked together the first 6 days and finished 1/3 of the project, then B and C worked together for 2 days on 1/4 of the remaining. And the rest of the project was completed by A,B, and C working together for 5 days. They were paid $1800 in total. If each were to be paid fairly, according to how much work he contributed, how much should B receive?
1 solutions
Answer 446215 by ankor@dixie-net.com(15622) on 2013-03-23 21:18:41 (Show Source):
You can put this solution on YOUR website!A,B,and C undertook a construction project.
Let the completed project = 1800
then
A and B worked together the first 6 days and finished 1/3 of the project,
Their work is equal to 1/3 of 1800 or 600
Assuming they work at the same rate
A = 300
B = 300
:
then B and C worked together for 2 days on 1/4 of the remaining.
1/4 of the remaining (1200) = 300
B = 150
C = 150
:
And the rest of the project was completed by A,B, and C working together for 5 days.
The amt they did: 1800 - 600 - 300 = 900
A = 300
B = 300
C = 300
They were paid $1800 in total.
If each were to be paid fairly, according to how much work he contributed, how much should B receive?
B = 300 + 150 + 300 = $750 is B's share
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Equations/729754: A two digit number and the resulting number when the digits are reversed are in the ratio 2:9.If the sum of the digits is 9,Find the original number.
1 solutions
Answer 446208 by ankor@dixie-net.com(15622) on 2013-03-23 20:57:52 (Show Source):
You can put this solution on YOUR website!let a = the 10's digit of the original number
let b = the units
:
"A two digit number and the resulting number when the digits are reversed are in the ratio 2:9."
 = 
Cross multiply
9(10a+b) = 2(10b+a)
90a + 9b = 20b + 2a
90a - 2a = 20b - 9b
88a = 11b
Simplify divide by 11
8a = b
:
"If the sum of the digits is 9,
a + b = 9
replace b with 8a
a + 8a = 9
9a = 9
a = 1
then
b = 8
:
18 is the original number
:
:
:
Check this
 =
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