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Recent problems solved by 'stanbon'
stanbon answered: 57222 problems
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53010..53039 , 53040..53069 , 53070..53099 , 53100..53129 , 53130..53159 , 53160..53189 , 53190..53219 , 53220..53249 , 53250..53279 , 53280..53309 , 53310..53339 , 53340..53369 , 53370..53399 , 53400..53429 , 53430..53459 , 53460..53489 , 53490..53519 , 53520..53549 , 53550..53579 , 53580..53609 , 53610..53639 , 53640..53669 , 53670..53699 , 53700..53729 , 53730..53759 , 53760..53789 , 53790..53819 , 53820..53849 , 53850..53879 , 53880..53909 , 53910..53939 , 53940..53969 , 53970..53999 , 54000..54029 , 54030..54059 , 54060..54089 , 54090..54119 , 54120..54149 , 54150..54179 , 54180..54209 , 54210..54239 , 54240..54269 , 54270..54299 , 54300..54329 , 54330..54359 , 54360..54389 , 54390..54419 , 54420..54449 , 54450..54479 , 54480..54509 , 54510..54539 , 54540..54569 , 54570..54599 , 54600..54629 , 54630..54659 , 54660..54689 , 54690..54719 , 54720..54749 , 54750..54779 , 54780..54809 , 54810..54839 , 54840..54869 , 54870..54899 , 54900..54929 , 54930..54959 , 54960..54989 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next
Angles/104671: a triangle with the angles of 50 degrees, 95 degrees, and 35 degrees what type of triangle would this be and why?
1 solutions
Answer 76164 by stanbon(57290)   on 2007-10-17 06:26:54 (Show Source):
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Linear-equations/104639: Write an equation in slope-intercept form for the line that satisfies each set of conditions.
slope 2, passes through (-3,0)
1 solutions
Answer 76151 by stanbon(57290) on 2007-10-16 22:09:27 (Show Source):
You can put this solution on YOUR website!Write an equation in slope-intercept form for the line that satisfies each set of conditions.
slope 2, passes through (-3,0)
------------------------------------
Equation form is y = mx+b
m = 2
Need to find "b":
0 = 2*-3 + b
b = 6
----------------
EQUATION:
y = 2x + 6
=================
Cheers,
Stan H.
|
Graphs/104632: This question is from textbook Algebra I
This is from 4.7 Challenge: Skills and Applications
Questions 5 & 6
In 1992, 7.6 million music videos were shipped and in 1996, 16.9 million were shipped.
Write an equation you can solve to find the year that the model predicts 25 million music videos will be shipped.
Then solve the equation graphically. Interpret the result.
Things I know: rate of change is 2.325 million per year.
Tried this equation:
25 =2.325x +7.6 (knowing all numbers in millions)
so to graph I got y=2.325x - 17.4
but now I have a negative graph and I know that is wrong.
So I am thinking what I got is x=years later, not the year. How do I get the year in one equation instead of 2?
Thanks for any help.
1 solutions
Answer 76150 by stanbon(57290) on 2007-10-16 22:05:00 (Show Source):
You can put this solution on YOUR website!In 1992, 7.6 million music videos were shipped and in 1996, 16.9 million were shipped.
Write an equation you can solve to find the year that the model predicts 25 million music videos will be shipped.
-------------
You have two points: (2, 7.6) and (6, 16.9)
slope = [16.9-7.6]/[6-2] = 2.325
-----------------
Equation form is # of videos = 2.325(year) + b
Nedd to solve for "b":
7.6 = 2.325*2 + b
7.6 = 4.65 + b
b = 7.6-4.65
b = -2.95
---------------
EQUATION:
# of videos = 2.325(year) - 2.95
-----------------
find the year that the model predicts 25 million music videos will be shipped.
25 = 2.325(year) - 2.95
27.95 = 2.325(year)
year = 12.02...
The year will be 1990+12 = 2002
==================
Cheers,
Stan H.
|
Linear-equations/104633: This question is from textbook McDougal Littel Algebra 1
my class is working on the standard form of a linear equation. i was absent for a long period of time and unfortunatley missed some things. so here is the problem.
i need to get 4x-y-7=0 to be y=mx+b so far i've got it down to -y=7-4x
now i have this gut feeling that that's wrong. is it? and if it isn't, then how do you do it. thanks for your time.
1 solutions
Answer 76143 by stanbon(57290) on 2007-10-16 21:44:18 (Show Source):
You can put this solution on YOUR website!4x-y-7=0 to be y=mx+b
Add y to both sides to get:
4x-7 = y
Rearrange:
y = 4x-7
--------
Comment: This is the slope-intercept form
The standard form is 4x-y=7
===============
Cheers,
Stan H.
|
Travel_Word_Problems/104624: marla begins walking at 3 mi/h toward the library. her friend meets her at the halfway point and drives her the rest of the way to the library. the distance to the library is 4 miles. how many hours did marla walk?
1 solutions
Answer 76141 by stanbon(57290) on 2007-10-16 21:39:55 (Show Source):
You can put this solution on YOUR website!marla begins walking at 3 mi/h toward the library. her friend meets her at the halfway point and drives her the rest of the way to the library. the distance to the library is 4 miles. how many hours did marla walk?
--------------------------
Marla walking DATA:
Rate = 3 mph ; distance = 2 miles ; time = d/r = 2/3 hour
--------------------
Marla walked for 2/3 hour
===================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/104515: A car rental company increases daily rental fees 15% in the summer to cover increased fuel costs. They then have a "25% off" promotion for the fall. If a car rented for $36.00 per day before the summer, what would the per day rental cost be during the fall promotion?
1 solutions
Answer 76137 by stanbon(57290) on 2007-10-16 21:17:23 (Show Source):
You can put this solution on YOUR website!A car rental company increases daily rental fees 15% in the summer to cover increased fuel costs. They then have a "25% off" promotion for the fall. If a car rented for $36.00 per day before the summer, what would the per day rental cost be during the fall promotion?
-------------------------
Fall rental cost = 36*1.15*0.75 = $31.05
==============
Cheers,
Stan H.
|
Linear-equations/104615: Could someone please show me how to find the equation of a line that passes through (6,10) (8,7) I am really struggling with how to set this up and solve. Any help would greatly be appreciated.
1 solutions
Answer 76135 by stanbon(57290) on 2007-10-16 21:12:23 (Show Source):
You can put this solution on YOUR website!Could someone please show me how to find the equation of a line that passes through (6,10) (8,7) I am really struggling with how to set this up and solve. Any help would greatly be appreciated.
------------------
The equation form is y = mx + b
You need to find "m" and "b".
--------------
m = slope = [10-7]/[6-8] = -3/2
-------------------------
Substitute m, x, and y into y=mx+b to find "b":
10 = (-3/2)(6)+b
10 = -9 + b
b = 19
--------------
EQUATION:
y = (-3/2)x + 19
===================
==================
Cheers,
Stan H.
|
Average/104612: I am having a hard time with this problem. Can you help me?
Mr. Bedell has 107 fiction books in his classrooom. Mr Bedell's fiction collection is 27 more than a third of his non-fiction collection. How many non-fiction books does Mr. Bedell have? Thank you..
1 solutions
Answer 76132 by stanbon(57290) on 2007-10-16 20:36:13 (Show Source):
You can put this solution on YOUR website!Mr. Bedell has 107 fiction books in his classrooom. Mr Bedell's fiction collection is 27 more than a third of his non-fiction collection. How many non-fiction books does Mr. Bedell have?
-----------------------
Let number of non-fiction books be "x".
Then # of fiction books is (1/3)x+27
---------------------
EQUATION:
(1/3)x+27 = 107
(1/3)x = 80
x = 240 (# of non-fiction books)
=======================================
Cheers,
Stan H.
|
Expressions-with-variables/104604: This question is from textbook prentice hall mathematics algebra 1
May rides her bike the same distance that Leah walks. May rides her bike 10 km/h faster than Leah walks. If it takes May 1 h and Leah 3 h to travel that distance, how fast does each travel?
1 solutions
Answer 76128 by stanbon(57290) on 2007-10-16 20:14:10 (Show Source):
You can put this solution on YOUR website!May rides her bike the same distance that Leah walks. May rides her bike 10 km/h faster than Leah walks. If it takes May 1 h and Leah 3 h to travel that distance, how fast does each travel?
------------------------
Leah DATA:
Rate = x km/hr ; Time = 3 hr ; distance =rt = 3x km
---------------------------
May DATA:
Rate = (x+10) km/h ; Time = 1 hr; distance = (x+10) km/hr
----------------------------
EQUATION:
distance = distance
3x = x+10
2x = 10
x = 5 km/hr (Leah's Rate)
x+10 = 15 km/hr (May's Rate)
==================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/104578: pLEASE HELP WITH THE FOLLOWING
THE STUDENT TEACHER RATIO FOR WASHINGTON HIGH WAS REPORTED TO BE 27.5 TO 1. IF THERE ARE 42 TEACHERS, THEN HOW MANY STUDENTS ARE THERE?
i GET 9,982 IS THIS CORRECT?
1 solutions
Answer 76114 by stanbon(57290) on 2007-10-16 18:59:22 (Show Source):
You can put this solution on YOUR website!THE STUDENT TEACHER RATIO FOR WASHINGTON HIGH WAS REPORTED TO BE 27.5 TO 1. IF THERE ARE 42 TEACHERS, THEN HOW MANY STUDENTS ARE THERE?
i GET 9,982 IS THIS CORRECT?
-----------------------
27.5 to 1 is the same as 27.5x to x where 27.5 is # of students and x the number of teachers.
-------------
EQUATION:
If x = 42, 27.5x = 1155
# of students = 1155
=========================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/104582: FIND A TRINOMIAL THAT REPRESENTS THE AREA OF A PARALLELOGRAM WHOSE BASE IS3X + 2 METERS AND WHOSE HEIGHT IS 2X + 3 METERS
1 solutions
Answer 76108 by stanbon(57290) on 2007-10-16 18:33:36 (Show Source):
You can put this solution on YOUR website!FIND A TRINOMIAL THAT REPRESENTS THE AREA OF A PARALLELOGRAM WHOSE BASE IS 3X + 2 METERS AND WHOSE HEIGHT IS 2X + 3 METERS
------------------------------------
Area = (3x+2)(2x+3)
Area = 6x^2+13x+6
==================
Cheers,
Stan H.
|
Expressions-with-variables/104577: This question is from textbook algebra Structure and Method
Here is another problem!
Jo has 37 coins(all nickles, dimes and quarters) worth $5.50. She has 4 more quarters than nickles. How many dimes does Jo have? I can't figure out what the variable for dimes is.
Thanks!
1 solutions
Answer 76106 by stanbon(57290) on 2007-10-16 18:23:55 (Show Source):
You can put this solution on YOUR website!Jo has 37 coins(all nickles, dimes and quarters) worth $5.50. She has 4 more quarters than nickles. How many dimes does Jo have? I can't figure out what the variable for dimes is.
-------------------------
Let number of nickels be "x" ; value of these is 5x cents
# of quarters is "x+4" ; value of these is 25(x+4) = 25x+100 cents
# of dimes = 37-(x+x+4)="33-2x"; value is 10(33-2x)=330-20x cents
-------------------------
EQUATION:
value + value + value = 550 cents
5x + 25x+100 + 330-20x = 550
10x = 120
x = 12 (# of nickels)
x+4 = 16 (# of quarters)
33-2x= 9 (# of dimes)
========================
Cheers,
Stan H.
|
Quadratic_Equations/104537: Find the axis of symmetry.
y = x^2 + x – 3
1 solutions
Answer 76101 by stanbon(57290) on 2007-10-16 18:00:36 (Show Source):
You can put this solution on YOUR website!Find the axis of symmetry.
y = x^2 + x – 3
----------------------
x^2+x+? = y+3+?
x^2+x+(1/2)^2 = y+3+(1/2)^2
(x+(1/2))^2 = y+(13/4)
-------------------
Vertex: (-1/2, -13/4)
Axis of symmetry: x = -1/2
====================
Cheers,
Stan H.
|
Sequences-and-series/104572: prove that:
Sum of n numbers in a sequence is n/2[2a+(n-1)d].
1 solutions
Answer 76099 by stanbon(57290) on 2007-10-16 17:49:45 (Show Source):
You can put this solution on YOUR website!prove that:
Sum of n numbers in a sequence is n/2[2a+(n-1)d].
----------------
Write the sequence : S(n)=a ,a+d ,a+2d ,.....a+(n-1)d
Write the sequence backwards: S(n)=a+(n-1)d, a+(n-2d) ,a+(n-3d) ,a
-----------------
Add the two sequences to get: 2S(n)= n[a+a+(n-1)d]
2S(n) = n[2a+(n-1)d]
S(n) = (n/2)[2a+(n-1)d]
============
Cheers,
Stan H.
|
Linear-systems/104573: Multiply both sides of each equation by a common denominator to eliminate the fractions. then solve the system
x/2 + y/3 = 8
2x/3 + 3y/2 = 17
1 solutions
Answer 76095 by stanbon(57290) on 2007-10-16 17:27:37 (Show Source):
You can put this solution on YOUR website!solve the system
x/2 + y/3 = 8
Multiply thru by by 6 to get:
1st: 3x + 2y = 48
----------------
2x/3 + 3y/2 = 17
Multiply thru by 6 to get:
2nd: 4x + 9y = 102
------------------
Multiply 1st by 4 and 2nd by 3 to get:
3rd: 12x + 8y = 192
4th: 12x +27y = 306
-----------------------
Subtract 3rd from 4th to solve for y:
19y = 114
y = 6
--------------
Substitute into 3x+2y=48 to solve for "x".
3x + 12 = 48
3x = 36
x = 12
---------------
Final solution:
x=12; y=6
=======================
Cheers,
Stan H.
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Probability-and-statistics/104477: This question is from textbook
Find the probability that 2 friends never agree on two seperate topics out of 100. The probability that they agree on any given topic is 0.02, and ifthey did agree they would consider it a coincidence, and any two topics are independent events.
1 solutions
Answer 76093 by stanbon(57290) on 2007-10-16 17:19:01 (Show Source):
You can put this solution on YOUR website!Find the probability that 2 friends never agree on two seperate topics out of 100. The probability that they agree on any given topic is 0.02, and ifthey did agree they would consider it a coincidence, and any two topics are independent events.
=============
P(they do not agree on any given topic) = 0.98
P(they do not agree on any of 100 topics) = 0.98^100 = 0.1326...
===============
Cheers,
Stan H.
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Graphs/104551: write the equation of the line passing through each of the given points with the indicated slope. (rewrite in standard from) Give your results in slope-intercept form, where possible.
(0,5), m= -3/5
1 solutions
Answer 76070 by stanbon(57290) on 2007-10-16 15:33:21 (Show Source):
You can put this solution on YOUR website!Give your results in slope-intercept form, where possible.
(0,5), m= -3/5
-------------------
The form is y = mx + b
You are told the slope is -3/5 and the b is 5
EQUATION:
y = (-3/5)x + 5
=============
Cheers,
Stan H.
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Equations/104511: im reall yreally stuck on this one, can you please help me, so anyway, the problem is to find the value of x.
5/x = 10
HELP PLEASE!!
1 solutions
Answer 76067 by stanbon(57290) on 2007-10-16 15:29:52 (Show Source):
You can put this solution on YOUR website!5/x = 10
Multiply both sides by x to get:
5 = 10x
Divide both sides by 10 to get
x = 5/10
Simplify:
x = 1/2
===============
Cheers,
Stan H.
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Exponents/104541: Nlog base 2 N=3500 I tried base changes
log 3500=log N^N/(log 2)
(log 3500) (log 2)=log N^N
(3.54)(.301)=log N^N
1.066=log N^N
10^1.066=N^N
11.62=N^N
N is about 3.4
It doesn't check out Help please
1 solutions
Answer 76066 by stanbon(57290) on 2007-10-16 15:27:21 (Show Source):
You can put this solution on YOUR website!Nlog base 2 N=3500 I tried base changes
log 3500=log N^N/(log 2)
(log 3500) (log 2)=log N^N
(3.54)(.301)=log N^N
1.066=log N^N
10^1.066=N^N
11.62=N^N
N= 11.62^(1/N)
Nlog base 2 N=3500 I tried base changes
log 3500=log N^N/(log 2)
(log 3500) (log 2)=log N^N
(3.54)(.301)=log N^N
1.066=log N^N
10^1.066=N^N
11.62=N^N
N = 11.62^(1/N)
------------
I graphed y=x and y=11.62^(1/x) on the same screen and
found their intersection at x = 2.5838137
---------------
Checking:
11.62 = 2.5838137^2.5838137
11.62 = 11.61999999999...
==========
Cheers,
Stan H.
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Complex_Numbers/104440: 1) Is the following function linear? Can you evaluate the function for the given value of x.
f(x)=1 - x^2 ; f(0)
2)Can you help me write an equation of the line that passes through the given point and satisfies the given condition for the foolowing two problems:
a)(1,3) ; parallele to y=2x-1
b) (3,2) ; perpendicular to y= -3x
3)What is the property that the statement 4(2 + 3)=4(2) + 4(3) illustrates?
1 solutions
Answer 75987 by stanbon(57290) on 2007-10-15 23:15:47 (Show Source):
You can put this solution on YOUR website!1) Is the following function linear?
Ans: No, it is a quadratic equation.
--------------
Can you evaluate the function for the given value of x.
f(x)=1 - x^2 ;
Ans: f(0) = 1-0^2 = 1
----------------------------
2)Can you help me write an equation of the line that passes through the given point and satisfies the given condition for the foolowing two problems:
a)(1,3) ; parallel to y=2x-1
Equation form: y=mx+b; you need m and b
m=2 because the line you want is parallel to y=2x-1 which has slope = 2
Solve for b: 3 = 2*1+b ; b = 1
EQUATIOn:
y = 2x+1
------------------
b) (3,2) ; perpendicular to y= -3x
m = 1/3
2=(1/3)3+b ; b = 1
EQUATION:
y = (1/3)x + 1
--------------------
3)What is the property that the statement 4(2 + 3)=4(2) + 4(3) illustrates?
The distributive property.
====================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/104460: hi was wondering if i could get some help with this question please and thank you.
Brook Winfield operates a snowmobile lodge. Last year it had 95 guests, each of which paid $160 per night.The lodge accountant estimates that for every $1 reduction in the price five additional customers will rent a room.
a)write a function representing the revenue of the lodge.
b)what is the maximum projected revenue?
thanks again
1 solutions
Answer 75985 by stanbon(57290) on 2007-10-15 23:06:27 (Show Source):
You can put this solution on YOUR website!Last year it had 95 guests, each of which paid $160 per night.The lodge accountant estimates that for every $1 reduction in the price five additional customers will rent a room.
a)write a function representing the revenue of the lodge.
b)what is the maximum projected revenue?
---------------------
Let "x" be the amount of reduction in price per room below 160.
------------------
Revenue = price * # of guests
Revenue = (160-x)(95+5x)
R(x) = -5x^2+705x+15200
--------------
Maximum occurs when x=-b/2a = -705/(-10) = 70.5
Maximum revenue = R(70.5)
R(70.5) = -5(70.5)^2+705(70.5)+15200
R(70.5) = $40,051.25
================
Cheers,
Stan H.
|
Expressions-with-variables/104435: The problem reads 0.9y-18=0.3y
Step 1 Substract .9y from each side
Step 2 -18=-.6y
Step 3 Divide by -.6
Step 4 Answer is ? I got the answer as 30, but not sur eif I am right.
1 solutions
Answer 75970 by stanbon(57290) on 2007-10-15 22:14:17 (Show Source):
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Radicals/104401: Hello,
I need help solving this problem:
Two buildings are separated by a three-foot alleyway. Fatima wants to use a 16-foot ladder to reach a window in the wall of one of these buildings. If she places the foot of the ladder against the base of the other building, how far up the wall will the top of the ladder reach?
Thank you
1 solutions
Answer 75965 by stanbon(57290) on 2007-10-15 22:06:30 (Show Source):
You can put this solution on YOUR website!Two buildings are separated by a three-foot alleyway. Fatima wants to use a 16-foot ladder to reach a window in the wall of one of these buildings. If she places the foot of the ladder against the base of the other building, how far up the wall will the top of the ladder reach?
---------------------
The ladder is the hypotenuse of a right triangle whose base is 3'
Find the 3rd side using Pythagoras.
-------------------
16^2 = 3^2 + x^2
x^2 = 256 - 9
x = sqrt247
x = 15.716 ft
=====================
Cheers,
Stan H.
|
Geometric_formulas/104400: Hello,
The geometric mean of a number and 3 is 9. I need help finding the number using the formula g=(sqrt)ab.
Thank you
1 solutions
Answer 75961 by stanbon(57290) on 2007-10-15 22:01:46 (Show Source):
You can put this solution on YOUR website!The geometric mean of a number and 3 is 9. I need help finding the number using the formula g=(sqrt)ab.
---------------------------The geometric mean of a number and 3 is 9. I need help finding the number using the formula g=(sqrt)ab.
geometric mean = sqrt[3*9] = 3sqrt(3)
==================
Cheers,
Stan H.
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