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Recent problems solved by 'stanbon'
stanbon answered: 57304 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329, >>NextMixture_Word_Problems/148284: A student mixes distilled water with a 90% solution of acid to produce a 50% solution. If 5 liters of water is used how much 50% solution is produced?
I know the answer is 11.25 but I am unable to figure out how they got to that answer.
I have tried setting water as x and 5 then acid as 90% and solution as 50% but any way I try does not get to the answer.
Help please!
1 solutions
Answer 108695 by stanbon(57377)   on 2008-07-14 22:59:33 (Show Source):
You can put this solution on YOUR website!A student mixes distilled water with a 90% solution of acid to produce a 50% solution. If 5 liters of water is used how much 50% solution is produced?
--------------------------
Your equation should track the water OR track the acid.
----------------
Water EQUATION: 5 + 0.10x = 0.50(5+x)
5+0.10x = 2.5+0.5x
0.4x = 2.5
x = 6.25 liters of 50% solution
-------------------------------------
Acid EQUATION:
0*5 + 0.9x = 0.50(5+x)
0.9x = 2.5 + 0.5x
0.4x = 2.5
x = 6.25 liters of 50% solution
--------------------------------------
You don't have to do both; one or the other.
=======================================
Cheers,
Stan H.
|
Trigonometry-basics/148293: Hi,
Question is solve the equation on the interval [0,2Pi0.
2cos^2x+sinx-2=0
Since cos^2x= 1-sin^2x I substituded this:
2(1-sin^2x) + sinx-2=0 to get
-2sin^2x + sinx=0 since -2 and +2 cancel eachother out. I am lost after this and the calculator hmm don't know whats worse figuring out the calculator or the math problem.
1 solutions
Answer 108694 by stanbon(57377) on 2008-07-14 22:48:47 (Show Source):
You can put this solution on YOUR website!Question is solve the equation on the interval [0,2Pi].
2cos^2x+sinx-2=0
Since cos^2x= 1-sin^2x I substituded this:
2(1-sin^2x) + sinx-2=0 to get
-2sin^2x + sinx=0 since -2 and +2 cancel each other out.
2sin^2x - sinx = 0
Now factor to get:
sinx(2sinx-1) = 0
sinx = 0 or 2sinx = 1
sinx = 0 or sinx = 1/2
x = 0,pi,2pi or x = pi/6,(5/6)pi
===============
Cheers,
Stan H.
|
Linear-equations/148294: Hello. I ran across a problem that left me baffled. It is not a hard one but I just did not retain it whe nI learned algebra if I learned it at all. Here goes:
The constraint 5x+2y<=0 passes through (20,50), (10,0), (20,0), (0,-5). Why and how?
Also, the constraint 2x-3y>=0 passes through (10,50), (30, 20), (0, 30) (-10, 0)
Why and how?
1 solutions
Answer 108693 by stanbon(57377) on 2008-07-14 22:37:54 (Show Source):
You can put this solution on YOUR website!The constraint 5x+2y<=0 passes through (20,50), (10,0), (20,0), (0,-5). Why and how?
Substitute x and y in the inequality with the numbers in each numbered pair
to see if you get a true statement.
Example: using (20,50) you get
5*20+2*50 <= 0
100 + 100 <= 0
200 <= 0
That is false.
---------------
It is true only for (0,-5)
------------------------
Also, the constraint 2x-3y>=0 passes through (10,50), (30, 20), (0, 30) (-10, 0)
Why and how?
==============================
Cheers,
Stan H.
|
Geometry_Word_Problems/148221: A spacelab circles Earth at an altitude of 380 miles. When an astronaut views the horizon of Earth, the angle θ is 65.8 dgrees. Use this information to estimate the radius of the Earth.
1 solutions
Answer 108640 by stanbon(57377) on 2008-07-14 14:23:54 (Show Source):
You can put this solution on YOUR website!A spacelab circles Earth at an altitude of 380 miles. When an astronaut views the horizon of Earth, the angle θ is 65.8 dgrees. Use this information to estimate the radius of the Earth.
--------------------------------------
Draw an arc of the earth; Draw a radius from the center then thru the arc
to a point 380 miles above the arc.
Draw a tangent from the top of the previous segment to a point that
is tangent to the arc.
Draw a radius from the center to the point of tangency (that should form
a right angle at the point of tangency).
Label the angle of depression from the spacelab 65.8 degrees.
-------------------------
EQUATION:
sin(65.8) = r / (r+380)
0.91212(r+380) = r
0.91212r + 346.6056 = r
346.6056 = 0.08788r
r = 3944.078.. miles
=========================
Cheers,
Stan H.
|
Money_Word_Problems/148224: One video rental club charges $25 to become a member and $2.50 to rent each video. Another charges no membership fee, but charges $3.25 to rent each video. How many videos must you rent to make the first club more economical?
1 solutions
Answer 108638 by stanbon(57377) on 2008-07-14 14:06:30 (Show Source):
You can put this solution on YOUR website!One video rental club charges $25 to become a member and $2.50 to rent each video. Another charges no membership fee, but charges $3.25 to rent each video.
---------------
1st rental club cost: C(x) = 25 + 2.5x
2nd rental club cost: C(x) = 3.25x
-------------------------------------------
How many videos must you rent to make the first club more economical?
EQUATION: 25 + 2.5x < 3.25x
25 < 0.75x
x > 33.3333
You must rent at least 34 videos
=====================
Cheers,
Stan H.
|
Mixture_Word_Problems/148225: A 5% acid solution is mixed with a 9% acid solution. How many ounces of the 5% acid solution must you mix with the 10 ounces of 9% acid solution to obtain 40ounces of 6%acid solution?
1 solutions
Answer 108634 by stanbon(57377) on 2008-07-14 13:59:38 (Show Source):
You can put this solution on YOUR website! A 5% acid solution is mixed with a 9% acid solution. How many ounces of the 5% acid solution must you mix with the 10 ounces of 9% acid solution to obtain 40ounces of 6%acid solution?
----------
Acid EQUATION: 0.05x + 0.09*10 = 0.06*40
0.05x + 0.9 = 2.4
0.05x = 1.5
5x = 150
x = 30 oz(amount of 5% that must be added)
================
Cheers,
Stan H.
|
Mixture_Word_Problems/148228: A box contains 5 green, 2 yellow, and 3 purple balls. Find the probability of obtaining a green or a yellow or a purple ball in a single draw.
1 solutions
Answer 108633 by stanbon(57377) on 2008-07-14 13:53:32 (Show Source):
You can put this solution on YOUR website!A box contains 5 green, 2 yellow, and 3 purple balls. Find the probability of obtaining a green or a yellow or a purple ball in a single draw.
-------------------
You can't miss. The probability is 10/10 = 1
=================
Cheers,
Stan H.
|
Rectangles/148231: The length of a rectangle is 2ft more than the width. The perimeter is 20ft. Find length.
1 solutions
Answer 108629 by stanbon(57377) on 2008-07-14 13:50:11 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is 2ft more than the width. The perimeter is 20ft. Find length
----------------
Let length be "x"; then width = "x-2"
Perimeter = 2(length + width)
20 = 2(x + x-2)
10 = 2x-2
2x = 12
x = 6 ft (length)
x-2 = 4 ft (width)
-------------------
Cheers,
Stan H.
|
Mixture_Word_Problems/148230: The Fahrenheit and Celsius scales are related by the equation F= 9/5 C+32. What temperature Celcius would give the body temperature of 98.6 degrees F?
1 solutions
Answer 108628 by stanbon(57377) on 2008-07-14 13:47:06 (Show Source):
You can put this solution on YOUR website!The Fahrenheit and Celsius scales are related by the equation F= (9/5)C+32. What temperature Celcius would give the body temperature of 98.6 degrees F?
---------------
98.6 =(9/5)C + 32
(9/5)C = 66.6
C = 37 degrees Celsius
=========================
Cheers,
Stan H.
|
test/148181: 7) Tickets for a play at the community theater cost $20 for an adult and $8 for a child. If 220 tickets were sold and the total receipts were $3200, how many of each type of ticket were sold?
Can someone please help?
v/r
Jess
1 solutions
Answer 108579 by stanbon(57377) on 2008-07-14 09:45:08 (Show Source):
You can put this solution on YOUR website!Tickets for a play at the community theater cost $20 for an adult and $8 for a child. If 220 tickets were sold and the total receipts were $3200, how many of each type of ticket were sold?
----------
Using two variables
Quantity Equation: a + c = 220
Value EQUATION: 20a + 8c = 3200
---------------------
Modify to use elimination:
20a + 20c = 4400
20a + 8c = 3200
-------------------
Subtract to solve for "c"
12c = 1200
c = 100 (# of child tickets)
--------
Substitute to solve for "a":
a+c = a+100 = 220
a = 120 (# of adult tickets)
=============
Cheers,
Stan H.
|
Unit_Conversion_Word_Problems/148178: pls. help!! I can't understand this question. I have to get the diameter and the given is only the mass and the height.
here is the word problem:
A cylindrical water tank holds 1000 L of water. Determine it's diameter if it's 1.5 m tall.
What could be the formula to get the Diameter. Please help.
1 solutions
Answer 108578 by stanbon(57377) on 2008-07-14 09:33:54 (Show Source):
You can put this solution on YOUR website!I can't understand this question. I have to get the diameter and the given is only the mass and the height.
here is the word problem:
A cylindrical water tank holds 1000 L of water. Determine it's diameter if it's 1.5 m tall.
What could be the formula to get the Diameter
-----------------------
V = (pi)dh
1000 = (pi)d*1.5
d = 212.20... m
Cheers,
Stan H.
|
Graphs/148179: Hope that you can help me with this problem.
Problem: A result of Kepler’s harmonic law is that the mass of a planet (M) with a satellite is directly proportional to the cube of the mean distance (d) from the satellite to the planet and inversely proportional to the square of the period of revolution (p). Early astronomers estimated the mass of the earth to be The mass of the earth is 5.976 x 10 to the 24th power. kg and observed that the moon orbited the earth with a period of 27.322 days at a mean distance of km.
(1) Write a formula for the mass of a planet according to Kepler.
(2) Find the proportionality constant using the observations and estimates for the earth and moon.
(3) Extend your knowledge across the solar system to find the mass of Mars based on observations that Phobos orbits Mars in 7.65 hours at a mean distance of 9330 km.
(1) What is the approximate ratio of the mass of the earth to the mass of Mars?
1 solutions
Answer 108577 by stanbon(57377) on 2008-07-14 09:29:57 (Show Source):
You can put this solution on YOUR website!Problem: A result of Kepler’s harmonic law is that the mass of a planet (M) with a satellite is directly proportional to the cube of the mean distance (d) from the satellite to the planet and inversely proportional to the square of the period of revolution (p).
-----------------------------
Early astronomers estimated the mass of the earth to be 5.976 x 10 to the 24th power. kg and observed that the moon orbited the earth with a period of 27.322 days at a mean distance of 384,403 km.
(1) Write a formula for the mass of a planet according to Kepler.
Equation: M = k[d^3/p^2]
----------------------------
(2) Find the proportionality constant (k) using the observations and estimates for the earth and moon.
5.978x10^24 = k[384,403^3/27.322^2]
5.978x10^24/7.609135732x1013 = k
k = 7.85635..x10^10
----------------------------
(3) Extend your knowledge across the solar system to find the mass of Mars based on observations that Phobos orbits Mars in 7.65 hours at a mean distance of 9330 km.
M = k[d^3/p^2]
M = (7.85635x10^10)[9330^3/7.65^2]
M = 1.09029...x10^21 kg
(1) What is the approximate ratio of the mass of the earth to the mass of Mars?
r = (5.976 x 10^24th power. kg)/(1.09029...x10^21 kg) = 5481.1028:1
========================
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/148180: The sum of two numbers is 73. The second is 7 more than 5 times the first. What are the two numbers?
Can some please help out with this question.
v/r
Jess
1 solutions
Answer 108576 by stanbon(57377) on 2008-07-14 09:27:56 (Show Source):
You can put this solution on YOUR website!The sum of two numbers is 73. The second is 7 more than 5 times the first. What are the two numbers?
----------------------
Using two variables:
EQUATIONS:
x + y = 73
y = 5x + 7
-------------
Substitute the 2nd into the 1st to get:
x + (5x+7) = 73
6x = 66
x = 11
-------
Substitute into y = 5x+7 to solve for "y":
y = 5*11+7
y = 62
===================
Using one variable:
Let 1st be "x";
then 2nd = 5x+7
EQUATION:
x + 5x+7 = 73
6x + 7 = 73
6x = 66
x = 11
then y = 62
=============
Cheers,
Stan H.
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Trigonometry-basics/148136: Hi,
looking for help with Trig functions.
1: Which is equilvalent to SinӨ+CotӨ+CosӨ=?
2: Find all vertical asymptotes of... F(X)=X/X^2-9
3: Find all solutions in [0,2pi) for the trigonometric equation Cos2x=-1
If you can help thank you!
1 solutions
Answer 108574 by stanbon(57377) on 2008-07-14 07:26:13 (Show Source):
You can put this solution on YOUR website!1: Which is equilvalent to SinӨ+CotӨ+CosӨ=?
There are many, many equivalents.
------------------------------------------
2: Find all vertical asymptotes of... F(X)=X/X^2-9
They occur when the denominator is zero and the numerator is not zero.
Vertical asymptotes at x = 3 and at x = -3
------------------------------------------
3: Find all solutions in [0,2pi) for the trigonometric equation Cos2x=-1
If cos(2x) = -1
then 2x = pi or 3pi
then x = pi/2 or (3/2)pi
===============
Cheers,
Stan H.
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Proportions/148140: Three individuals form a partnership and agree to divide the profits equally. X invests $9,000, Y invests $7,000, Z invests $4,000. If the profits are $4,800, how much less does X receive than if the profits were divided in proportion to the amount invested?
1 solutions
Answer 108573 by stanbon(57377) on 2008-07-14 07:20:16 (Show Source):
You can put this solution on YOUR website!Three individuals form a partnership and agree to divide the profits equally. X invests $9,000, Y invests $7,000, Z invests $4,000. If the profits are $4,800, how much less does X receive than if the profits were divided in proportion to the amount invested?
---------
Equal amount received by each 4800/3 = $1600 for each
--------------------------
Proportional amount received by each:
Proportion: 9:7:4
9x + 7x + 4x = 4800
20x = 4800
x = 240
x amount: 9x = 2160
y amount: 7x = 1680
z amount: 4x = 960
---------------------
how much less does X receive than if the profits were divided in proportion to the amount invested?
2160 - 1600 = $560
=======================
Cheers,
Stan H.
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Trigonometry-basics/148144: Hi,
Looking for help with these problems.
1: The equation of the line passing through the point (1,-2) and perpendicular to the line Y=(-2/3X)+(4/3)is?
2: Simplify the expression below (leave answer with positive exponents)
(7X^3Y/14XY^-2)^2 both numerator & denominator squared.
3: The trigonometric expression SinӨ+CotӨCosӨ
4: If SinӨ=(3/5) and Ө is in quadrant2 find Sin2Ө (Hint Sin2Ө=SinӨCosӨ)
Last one for trig! yes!
5: The point (-2,3) lies on the terminal side of an angle Ө in standard position. Find the exact value of Ө.
Thank YOU!!!!!!!!!!!!!!!!!!
1 solutions
Answer 108554 by stanbon(57377) on 2008-07-13 22:20:10 (Show Source):
You can put this solution on YOUR website!1: The equation of the line passing through the point (1,-2) and perpendicular to the line Y=(-2/3X)+(4/3)is?
-----------------------------------
slope = 3/2
Form: y = mx + b
You know m=3/2 and y = -2 when x = 1 ; solve for "b":
-2 = (3/2)*1 + b
b = -7/2
EQUATION: y = (3/2)x - (7/2)
===================================
2: Simplify the expression below (leave answer with positive exponents)
(7X^3Y/14XY^-2)^2 both numerator & denominator squared.
Cancel the common factors: 7, X
= (X^2Y^5/2)^2
= (X^4 y^10 / 4)
============================
3: The trigonometric expression
SinӨ+CotӨCosӨ = sin(theta) + [cos(theta)/sin(theta)]*cos(theta)
= sin(theta) + cos^2(theta)/sin(theta)
= [sin^2(theta) + cos^2(theta)]/sin(theta)
= 1/sin(theta)
= csc(theta)
============================
4: If SinӨ=(3/5) and Ө is in quadrant2 find Sin2Ө (Hint Sin2Ө=SinӨCosӨ)
In 2nd Quadrant, if sin=43/5, cos=-4/5
Then sin(2theta)= (3/5)(-4/5) = -12/25
============================
5: The point (-2,3) lies on the terminal side of an angle Ө in standard position. Find the exact value of Ө.
theta = tan^-1(-3/2) = -56.31 degrees = 180 = 123.31 degrees
=======================================
Cheers,
Stan H.
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Expressions-with-variables/148147: Hello, I am trying to get this algebra down, and right now it is still not clicking. I am having trouble with solving by elimination.
5x + 5y = -13
7x - 2y = 19
Thank you so much for any help you can offer.
Paula
1 solutions
Answer 108544 by stanbon(57377) on 2008-07-13 21:16:14 (Show Source):
You can put this solution on YOUR website!I am having trouble with solving by elimination.
5x + 5y = -13
7x - 2y = 19
------------------
Multiply thru 1st equation by 2 ; Multiply thru 2nd by 5.
10x + 10y = -26
35x - 10y = 95
--------------------
By add the two equation you can eliminate the y-terms:
45x = 69
x = 23/15
---------------
Substitute that value of x into one or other of the original equations
to solve for "y":
5(23/15) + 5y = -13
23/3 + 5y = -13
23/3 + 5y = -39/3
5y = -62/3
y = -62/15
---------------
Check the answer in the other original equation (7x - 2y = 19) :
7(23/15) -2(-62/15) = 19
161/15 + 124/15 = 19
285/15 = 19
19 = 19
=============
Cheers,
Stan H.
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Miscellaneous_Word_Problems/148153: Hi, could someone please help me to understand this problem?
A wood company can convert logs into lumber or plywood. The mill turns out three times as many units of plywood as lumber. A profit of $20 on a untit of lumber and $50 on plywood. How many of each unit must be produced and sold in order to make a profit of $17,680?
Math is my worst subject and I have a very hard time understanding it.
Thanks
1 solutions
Answer 108542 by stanbon(57377) on 2008-07-13 20:57:27 (Show Source):
You can put this solution on YOUR website!A wood company can convert logs into lumber or plywood.
The mill turns out three times as many units of plywood as lumber.
P and L are the number of units of Plywood and of Lumber.
Quantity EQUATION: P = 3L
---------------
A profit of $20 on a unit of lumber and $50 on plywood. How many of each unit must be produced and sold in order to make a profit of $17,680?
Value EQUATION: 50P + 20L = 17680
------------------------------------
Rearrange:
P - 3L = 0
50P + 20L = 17680
--------------------
Modify to allow elimination:
50P - 150L = 0
50P + 20L = 17680
-----------------------
Subtract 1st from 2nd so you can solve for "L":
170L = 17680
L = 104 (number of units of Lumber)
Since P = 3L, P = 312 (number of units of Plywood)
==========================
Cheers,
Stan H.
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Equations/148111: Having problems simplifying (-R2/R2CS+1)/R1. Any assistance in the explanation would be greatly appreciated.
1 solutions
Answer 108529 by stanbon(57377) on 2008-07-13 18:55:05 (Show Source):
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Quadratic-relations-and-conic-sections/148125: Could someone please help me with this question?
Thanks in advance..
Michael
The edge of my kitchen counter top is the shape of an ellipse. Since my tiles were 18" squares, the deepest part is 18 inches deep and the edge tapers to 12 inches deep. The counter will be 6 feet long. You can see the counter outlined below if you look at the area that is both inside the blue ellipse and inside the brown rectangle at the same time.
What is the equation of this ellipse if everything is figured in inches?
Where do the foci of my “tacks” need to be placed to draw my counter edge?
How long should the “string” be to generate this curve?
1 solutions
Answer 108526 by stanbon(57377) on 2008-07-13 18:51:35 (Show Source):
You can put this solution on YOUR website!It sounds like the ellipse is 6 ft wide and 18 inches deep.
Is that true?
Cheers,
Stan H.
Yes Stan,
This is true..
Thanks
Michael
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Finance/147822: Solve the system eqation by graphing. then classify the system as consistent or inconsistant and equation as dependent or independent.
What is the solution of the system equation?
3x + y =16
4x + 5y =14
B. Snookers lumber can convert logs into either lumber or plywood. In a given day, the mills turns twice as many units of plywood as lumber. It makes a profit of $20. on a unit of lumber and $50. on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $12480?
Snookers lumber must product and sell ?? units of lumber and ?? units of plywood in order to make a profit of $12480.
1 solutions
Answer 108522 by stanbon(57377) on 2008-07-13 18:38:56 (Show Source):
You can put this solution on YOUR website!3x + y =16
4x + 5y =14
-------------
-----------
Solution: x = 6 and y = -2
=================
B. Snookers lumber can convert logs into either lumber or plywood. In a given day, the mills turns twice as many units of plywood as lumber.
Quantitity EQUATION: P = 2L
-----------------
It makes a profit of $20. on a unit of lumber and $50. on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $12480?
Value EQUATION: 50P + 20L = 12480
---------------------------------------
Snookers lumber must product and sell ?? units of lumber and ?? units of plywood in order to make a profit of $12480.
---------------------
P - 2L = 0
50P + 20L = 12480
-----------------------------
50P -100L = 0
50P + 20L = 12480
----------------
120L = 12480
L = 104 (units of Lunber)
------------
P = 2L = 208 (units of plywood)
=================================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/148120: Solve: 0 = x^3 - x^2 - 11x - 10
1 solutions
Answer 108514 by stanbon(57377) on 2008-07-13 18:12:27 (Show Source):
You can put this solution on YOUR website!Solve: 0 = x^3 - x^2 - 11x - 10
--------------
I graphed to find solutions:
------------------
Using synthetic division to find the remaining zeroes:
-2)....1....-1....-11....-10
........1.....-3.....-5...|..0
Quotient = x^2-3x-5
x = [3 +- sqrt(9 - 4*-5)]/2
x = [3 +- sqrt(29)]/2
x = [3+sqrt(29)]/2 or x = [3-sqrt(29)]/2
x = 4.1925824.. or x = -1.192582...
==================
Cheers,
Stan H.
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Graphs/148076: Graph 6x + 4y ≤ 24
1 solutions
Answer 108482 by stanbon(57377) on 2008-07-13 12:14:24 (Show Source):
You can put this solution on YOUR website!Graph 6x + 4y ≤ 24
-----------
1st: graph the equality as a solid line:
y = (-3/2)x + 6
---------
2nd: Since your inequality is "less than" shade the
half-plane "below" the line.
-------------
The union of the line and the half-plane is the graph of your problem.
Cheers,
Stan H.
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Radicals/148082: What is x in the equation:
 =
1 solutions
Answer 108481 by stanbon(57377) on 2008-07-13 12:11:01 (Show Source):
You can put this solution on YOUR website!x^2-x-4 = sqrt(x^2-x-2)
Square both sides to get:
x^2 - x -2 = (x^2-(x+4)*(x^2-(x+4))
x^2 - x -2 = x^4 -2x^2(x+4)+(x+4)^2
x^2 -x -2 = x^4 -2x^3-8x^2+x^2+8x+16
x^2 -x -2 = x^4 -2x^3 -7x^2 + 8x + 16
x^4 -2x^3 -8x^2 + 9x + 18 = 0
x=-2 or x = -1.3027756.. or x = 2.3027756 or x = 3
=============
Cheers,
Stan H.
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