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Recent problems solved by 'stanbon'
stanbon answered: 57911 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 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899 , 57900..57929, >>NextAngles/100348: the complement of an angle is five times the measure of the angle itself. find the angle and its complement.
1 solutions
Answer 73076 by stanbon(57984)   on 2007-09-25 17:35:24 (Show Source):
You can put this solution on YOUR website!the complement of an angle is five times the measure of the angle itself. find the angle and its complement.
---------------
Let the angle be x; then its complement = "90-x".
EQUATION:
90-x = 5x
6x = 90
x = 15 (the angle)
90-x = 75 (the complement)
=============
Cheers,
Stan H.
|
Inverses/100336: I kind of understand how to do these f◦g and g◦f problems, but I dont know how to do this one because the fraction throws me off. Please help me!!! Thank you!!!! The problem is:
For  and  , show that f ◦ g ( x ) = x and g ◦ f ( x) = x.
1 solutions
Answer 73074 by stanbon(57984) on 2007-09-25 17:31:01 (Show Source):
You can put this solution on YOUR website!f(x)=2x+1 and g(x)=(x-1)/2
show that f ◦ g ( x ) = x and g ◦ f ( x) = x.
--------------
fog(x)= f[g(x)] = f[(x-1)/2] = 2[(x-1)/2]+1 = (x-1)+1 = x
---------
gof(x) = g[f(x)] = g[2x+1] = ((2x+1)-1)/2 = 2x/2 = x
==============
Cheers,
Stan H.
|
Coordinate-system/100344: This question is from textbook cpm
Complete the table below for the equation y=2x-1 and draw a graph.
b)Estimate the x-value snd corresponding to y=2
c)find the x intercept.
d)find the y intercept.
1 solutions
Answer 73073 by stanbon(57984) on 2007-09-25 17:23:11 (Show Source):
You can put this solution on YOUR website!Complete the table below for the equation y=2x-1 and draw a graph.
b)Estimate the x-value snd corresponding to y=2
2= 2x-1; 2x = 3; x =3/2
-----------------------
c)find the x intercept.
If y=0, 2x-1=0 ; x = 1/2 is the x-intercept
------------------------
d)find the y intercept.
If x=0, y = -1 is the y-intercept
===============
Cheers,
Stan H.
|
Inverses/100338: I have no idea how to solve this problem:
If y is inversely proportional to the square of x, and y=1 when x=4, find y when x=8.
1 solutions
Answer 73069 by stanbon(57984) on 2007-09-25 17:13:48 (Show Source):
You can put this solution on YOUR website!If y is inversely proportional to the square of x
y = k/x^2
-------
and y=1 when x=4
1 = k/4^2
k= 16
-------------------
find y when x=8.
y = 16/x^2
y = 16/8^2
y = 1/4
============
Cheers,
Stan H.
|
Probability-and-statistics/99789: If i drive through 3 sets of traffic lights and the probablity of any one being green is 0.3 and the probability of one not being green is 0.7 how do i find what the probability of all being green and the probability that at least one light will not be green? Also how do i calculate the theoretical probability that all three sets of lights will be green.
1 solutions
Answer 73057 by stanbon(57984) on 2007-09-25 16:18:15 (Show Source):
You can put this solution on YOUR website!If i drive through 3 sets of traffic lights and the probablity of any one being green is 0.3 and the probability of one not being green is 0.7
--------------------------------------
how do i find what the probability of all being green?
= 0.3^3 = 0.027
---------------------
and the probability that at least one light will not be green?
= 1 - P(all are green) = 1-0.027 = 0.973
-----------------------
Also how do i calculate the theoretical probability that all three sets of lights will be green.
You multiply 0.3*0.3*0.3 to get 0,027
==============
Cheers,
Stan H.
|
Linear-systems/100310: This is my question...
Answer the following information about this line: y = 2x-3
m=_______
b=_______
Find the x or y for the following points on the above line:
(0,__) , (___, 0) , (1,___0 , (____, 9)
I am clueless how to anwser this...HELP!!!!!!
1 solutions
Answer 73049 by stanbon(57984) on 2007-09-25 15:31:39 (Show Source):
You can put this solution on YOUR website!Answer the following information about this line: y = 2x-3
m=2______
b=-3_______
Find the x or y for the following points on the above line:
(0,-3__) , (3/2___, 0) , (1,-1___) , (6____, 9)
------------------
Cheers,
Stan H.
|
test/100255: From the information in the table providing values of f(x) and g(x), evaluate (f o g)^-1 (2)
x 1 2 3 4 5
f(x) 3 4 5 1 2
g(x) 5 4 2 3 1
1 solutions
Answer 73048 by stanbon(57984) on 2007-09-25 15:29:10 (Show Source):
You can put this solution on YOUR website!From the information in the table providing values of f(x) and g(x), evaluate (f o g)^-1 (2)
x 1 2 3 4 5
f(x) 3 4 5 1 2
g(x) 5 4 2 3 1
-----------------
(fog)^-1(x) = (g^-1of^-1)(x)
Your Problem
= g^-1[f^-1(2)]
= g^-1[5]
= 1
=============
Cheers,
Stan H.
|
Systems-of-equations/100303: Please help me solve this equation - It is in fractions- I keep getting lost in my work
5+ x/3 = 2x/5 -7
X=
at one point I had it set up and worked as
75 + 15x/5 = 30x/15 - 105
75x = 2X -105 If I am on the right path I am lost on what to do next- If I am completely wrong then I need help from the beginning. Please advise
1 solutions
Answer 73047 by stanbon(57984) on 2007-09-25 15:24:36 (Show Source):
You can put this solution on YOUR website!5+ x/3 = 2x/5 -7
-------------------
x/3 - 2x/5 = -12
Multiply thru by 15 to get:
5x - 3*2x = -12*15
-x = -12*15
x = 150+30 = 180
=================
Cheers,
Stan H.
Cheers,
Stan H.
|
Equations/100308: In Ajax Corporation, the first shift produced 4 1/2 times as many lightbulbs as the second shift. If the number of lightbulbs was 55,000 how many lightbulbs were produced on each shift?
Solve the unknown
1 solutions
Answer 73046 by stanbon(57984) on 2007-09-25 15:20:30 (Show Source):
You can put this solution on YOUR website!In Ajax Corporation, the first shift produced 4 1/2 times as many lightbulbs as the second shift. If the number of lightbulbs was 55,000 how many lightbulbs were produced on each shift?
-----------
Let # produced by 2nd shift be "x".
Then # produced by 1st shift = 4.5 x
-------------
EQUATION:
x + 4.5x = 55000
5.5x = 55000
x = 10,000 (# produced by 2nd shift)
4.5x = 45000 (# produced by 1st shift)
===============
Cheers,
Stan H.
|
Equations/100266: This question is from textbook College Algebra and Trigonometry
A sewage treatment plant has two inlet pipes to its settling pond. One can fill the pond in 10 hr, the other in 12 hr. If the first pipe is open for 5 hr and then the second pipe is opened, how long will it take to fill the pond?
1 solutions
Answer 73045 by stanbon(57984) on 2007-09-25 15:16:59 (Show Source):
You can put this solution on YOUR website!A sewage treatment plant has two inlet pipes to its settling pond. One can fill the pond in 10 hr, the other in 12 hr. If the first pipe is open for 5 hr and then the second pipe is opened, how long will it take to fill the pond?
-----------------
1st pipe DATA:
Time to fill = 10 hr/job ; Rate = 1/10 job/hr
-----------------
2nd pipe DATA:
Time to fill = 12 hr/job ; Rate = 1/12 job/hr
----------------
EQUATION:(since half of the pond has already been filled)
Let x = time for the two pipe together to fill half the pond
x(1/10 + 1/12) = 1/2
x(22/120)= 1/2
x(11/60) = 1/2
x(11/30) = 1
x = 30/11 = 2 hrs (8/11) hr
(8/11)*60 = 43.6 minutes
Total time for the two pipes to fill half the pond = 2 hrs 43.6 minutes
===================
Cheers,
Stan H.
|
Linear-equations/100284: x y
3 56
4 42
growth rate ?
percent decrease ?
My professor told me to use slope formula but I do not know what they are asking.
1 solutions
Answer 73042 by stanbon(57984) on 2007-09-25 14:53:28 (Show Source):
You can put this solution on YOUR website!x y
3 56
4 42
growth rate ?
percent decrease ?
------------------
growth rate is the slope from (3,56) to (4,42)
slope = [42-56]/[4-3]= -14
--------------------
percent decrease is -14*100/100 = -1400 %
================
Cheers,
Stan H.
|
Rational-functions/100256: Hello,
I am having a hard time finding domains. For example:
f(x) = 1/x-2? This makes no sense to me. Please help.
1 solutions
Answer 73005 by stanbon(57984) on 2007-09-25 09:01:47 (Show Source):
You can put this solution on YOUR website!x cannot be "2"because x=2 would make the denominator zero
which would make f(x) meaningless.
Therefore the Domain is "all Real Numbers except x=2".
Cheers,
Stan H.
|
Square-cubic-other-roots/100209: Tutor I was wondering if you could help me with these two problems?
1.) Sqrt of 50 (use property 1 to simplify each radical expression. Assume all variables represent positive real numbers.) I got 5 sqrt of 10 is this correct?
2.) sqrt of 72x^3 is the answer 3x sqrt of x?
Thank you for helping me with these problems I appreciate the help.
1 solutions
Answer 72976 by stanbon(57984) on 2007-09-24 22:42:12 (Show Source):
You can put this solution on YOUR website!1.) Sqrt of 50 (use property 1 to simplify each radical expression. Assume all variables represent positive real numbers.) I got 5 sqrt of 10 is this correct?
sqrt(50) = sqrt(25)*sqrt(2) = 5sqrt(2)
=====================
2.) sqrt of 72x^3 is the answer 3x sqrt of x?
sqrt(72x^3) = sqrt(36x^2)*sqrt(2x)= 6xsqrt(2x)
==================
Cheers,
Stan H.
|
Graphs/100206: This question is from textbook Intermediate Algebra through Applications
I just took a quiz online and I knew everything, but for some reason this question stumped me. I looked in the chapter to find a problem like this and there were none. How do you solve this:
(4,-3) (3,b) m= -4/5 find b
the answer was something like -34/5
???????? Thanks a lot!!!
1 solutions
Answer 72971 by stanbon(57984) on 2007-09-24 22:18:45 (Show Source):
You can put this solution on YOUR website!(4,-3) (3,b) m= -4/5 find b
-----------------
slope = change in y / change in x
slope = [b--3]/[3-4] = [b+3]/[-1]
Since m= -4/5 and since m is the slope
you get the following equation:
(b+3)/-1 = -4/5
b+3 = 4/5
b = -3 + 4/5
b = -15/5 + 4/5
b = -11/5
==============
Cheers,
Stan H.
|
percentage/100196: this year,75%of a graduating class had taken at least 8 mth courses. Of the remaining class members,60% had taken 6 or 7 math courses.what percent of the graduating class had taken fewer than 6 math courses?
1 solutions
Answer 72969 by stanbon(57984) on 2007-09-24 22:06:05 (Show Source):
You can put this solution on YOUR website!75% had more than 8
0.6*25% had 6 or 7
0.4*25% had less than 6
---------
0.4*0.25 = 0.10 = 10% had less than 6 math classes
======================
Cheers,
Stan H.
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Expressions-with-variables/100197: This question is from textbook middle grades math
Please help show me where i am going wrong; On the two days before a swim meet, jesse swan a total of 2050 meters. The second day she swam 250 meeters more than the first day. How many meters did she swim on each day?
m+250=2050 m=1800
1800-250=500
500+250=750 1st day
2050-750=1600 2nd day
I know this to be wrong, book says 900 and 1150
1 solutions
Answer 72966 by stanbon(57984) on 2007-09-24 21:48:46 (Show Source):
You can put this solution on YOUR website!On the two days before a swim meet, jesse swan a total of 2050 meters. The second day she swam 250 meeters more than the first day. How many meters did she swim on each day?
----------------
1st day she swam "x" miles
2nd day she sham "x+250" miles
EQUATION:
x + x+250 = 2050
2x = 1800
x = 900 (distance she swam on the 1st day)
x+250 = 1150 ( distance she swam on the 2nd day)
================
Cheers,
Stan H.
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Expressions-with-variables/100191: This question is from textbook Algebra Structure and Method
A discount store bought 12 dozen radios. Each to be sold at $15.00 above cost. The store sold X of the radios at that price. Each of the remaining radios was sold at $4.00 below cost. IF the store paid $11.00 for each radio, what was the total income from the sale?
1 solutions
Answer 72963 by stanbon(57984) on 2007-09-24 21:38:22 (Show Source):
You can put this solution on YOUR website!A discount store bought 12 dozen radios. Each to be sold at $15.00 above cost. The store sold X of the radios at that price. Each of the remaining radios was sold at $4.00 below cost. IF the store paid $11.00 for each radio, what was the total income from the sale?
-------------------------------------------
Cost of the radios = 144*11 = $1584
Income from selling = (11+15)X + (11-4)(144-X)
Total Profit= Income - Cost = 26x+7(144-x)-1584
==========================
Cheers,
Stan H.
|
Surface-area/100160: This question is from textbook Pre-algebra
Problem: 2 by 5 rectangle find area : 20in (9-24-07)
question: When you come up with your answer on an area problem would the answer be
squared??? sorry it has completely escaped my mind.
request: If you could I kind of need the answer before school tomorrow.
8th grade Pre-algebra
1 solutions
Answer 72939 by stanbon(57984) on 2007-09-24 19:30:10 (Show Source):
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Inequalities/100148: Can someone please help me to simplify this without negative exponents?
(xy^5 / x^-4y^2)^-2
1 solutions
Answer 72930 by stanbon(57984) on 2007-09-24 18:56:30 (Show Source):
You can put this solution on YOUR website!(xy^5 / x^-4y^2)^-2
-----------------
Comment: The negative sign means "invert"; the 2 means "square"
1st: Invert to get:
(x^-4y^2/xy^5)^2
2nd: Square to get:
(x^-8 y^4 / x^2 y^10)
3rd: Simplify:
(y^4 / x^10 y^10)
==================
Cheers,
Stan H.
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Expressions-with-variables/100138: This question is from textbook Glenco Algebra I
The Yankee Clipper leaves the pier at 9:00 AM at 8 knots. A half hour later, The River Rover leaves the same pier in the same direction traveling at 10 knots. At what time will The River Rover overtake The Yankee Clipper?
I'm not sure how to solve this when both time and distance are missing. Thanks.
1 solutions
Answer 72926 by stanbon(57984) on 2007-09-24 18:50:58 (Show Source):
You can put this solution on YOUR website!The Yankee Clipper leaves the pier at 9:00 AM at 8 knots. A half hour later, The River Rover leaves the same pier in the same direction traveling at 10 knots. At what time will The River Rover overtake The Yankee Clipper?
---------------
Comment: That is what algebra is all about; if something is missing,
call it "x" and solve for it.
-------------------------
Clipper DATA:
Rate = 8 knots ; Distance = x miles ; time = d/r = x/8 hrs.
-----------------
Rover DATA:
Rate = 10 knots; Distance = x miles ; time = d/r = x/10 hrs.
-----------------
EQUATION:
Cipper time = Rover time + (1/2) hr.
x/8 = x/10 + (1/2)
Multiply thru by 40 to get:
5x = 4x + 20
x = 20 miles
Clipper time = 20/8= 5/2 hrs.
9:00 plus (5/2) hrs = 11:30 AM
Rover will over take Clipper at 11:30 AM
==================
Cheers,
Stan H.
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Functions/100140: What is the domain of the function:
f(x) = 2x + 3 when the range is {5,7,9}?
f(x) = 1/4x + 3 when the range is {3, -17, 27}?
f(x) = -3x - 5 when the range is {-2, 0, 3}?
1 solutions
Answer 72923 by stanbon(57984) on 2007-09-24 18:42:57 (Show Source):
You can put this solution on YOUR website!What is the domain of the function:
f(x) = 2x + 3 when the range is {5,7,9}?
In three separate steps, set f(x) = 5, then 7, then 9
and solve for x:
x =1 , 2, 3
Domain: {1,2,3}
-------------------------------
f(x) = 1/4x + 3 when the range is {3, -17, 27}?
x = 0, -80, 120
Domain: {0,80,120}
f(x) = -3x - 5 when the range is {-2, 0, 3}?
x = -1, -5/3, -8/3
----------------------------
Cheers,
Stan H.
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Miscellaneous_Word_Problems/100139: A club charters a plane at a cost of $15840 to take a group of members on a trip. At the last minute, 6 people in the group canceled, increasing the cost per person by $20. How many people originally intended to take this trip?
I set the original # of people = P
Cost/person = 15840/P
The people that went were = (P-6)
Final cost/person = 15840/(P-6)= 15840/P + 20
I did do a methodical 'guess and check' and did get what I think is the right answer (72), but how do I really work it out. On a test, that will be too time
consuming and in the real work, it is not practical.
Help! Also what would you classify this problem as?
Thanks
1 solutions
Answer 72920 by stanbon(57984) on 2007-09-24 18:36:21 (Show Source):
You can put this solution on YOUR website!15840/(P-6)= 15840/P + 20
Multiply thru by P(P-6) to get:
15840P = 15840(P-6) + 20P(P-6)
15840P -15840P +15840*6 = 20P^2-120P
20P^2-120P-15840*6 = 0
Divide thru by 20 to get:
P^2 - 6P -792*6 = 0
(P - 72)(P + 66) = 0
Positive answer:
P = 72
=================
Cheers,
Stan H.
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Money_Word_Problems/100096: An aid in the mathematical department office gets paid $3 per hour for clerical work and $8 per hour for tutoring. If she wants to work a total of 20 hours and earn at least $145, what is the maximum number of hours X she can spend on clerical work?
1 solutions
Answer 72882 by stanbon(57984) on 2007-09-24 16:16:55 (Show Source):
You can put this solution on YOUR website!An aid in the mathematical department office gets paid $3 per hour for clerical work and $8 per hour for tutoring. If she wants to work a total of 20 hours and earn at least $145, what is the maximum number of hours X she can spend on clerical work?
------------------
Let number of hours of clerical work be "x" ; pay for this is 3x dollars
Number of hours of tutoring is "20-x"; pay for this is 8(20-x)= 160-8x dollars
-----------------------
EQUATION:
pay + pay =145 dollars
3x + 160-8x = 145
-5x = -15
x = 3 (number of clerical hours)
20-x = 17 (number of tutoring hours)
================
Cheers,
Stan H.
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Numbers_Word_Problems/100098: This question is from textbook Sullivan College Algebra
A builder of tract homes reduced the price of a model by 15%. If the new price is $425,000, what was it's original price? How much can be saved by purchasing thr model?
1 solutions
Answer 72880 by stanbon(57984) on 2007-09-24 16:10:33 (Show Source):
You can put this solution on YOUR website!A builder of tract homes reduced the price of a model by 15%. If the new price is $425,000, what was it's original price? How much can be saved by purchasing thr model?
-----------------
Let the original price be "x".
EQUATION:
x - 0.15x = 425,000
0.85x = 425,000
x= $500,000
Cheers,
Stan H.
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