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Recent problems solved by 'stanbon'
stanbon answered: 57259 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269, >>NextEquations/123674: This question is from textbook Trigonometry
Find an equation of the line that passes through the points (0,0), (0,10).
I get 0 as a slope so it's undefined and I don't know what to do next.
Thanks!
1 solutions
Answer 90715 by stanbon(57332)   on 2008-01-30 13:45:50 (Show Source):
You can put this solution on YOUR website!Find an equation of the line that passes through the points (0,0), (0,10).
------------
You are given the y-intercept as (0,10)
The slope is (10-0)/(0-0) = 10/0 which is "undefined".
----------
If the slope is undefined, the line is vertical.
It passes thru two points where x=0 so it must
pass thru all the points where x=0
It's equation is x=0.
Cheers,
Stan H.
|
Human-and-algebraic-language/123665: Please just don't get it....Suppose that the function?
Suppose that the function P=13+45ln x represents the percentage of inbound e-mail in the U.S. that is consideed spam, where x is the number of years after 2000.
Carry all calculations to six decimals on each intermediate step, when necessary.
a) Use this model to approximate the percentage of spam in the year 2003.
Answer:
b) Use this model to approximate the year that the percent of spam will reach 95% provided that law enforcement regarding spammers does not change?
Answer:
1 solutions
Answer 90713 by stanbon(57332) on 2008-01-30 13:42:18 (Show Source):
You can put this solution on YOUR website!Suppose that the function P=13+45ln x represents the percentage of inbound e-mail in the U.S. that is consideed spam, where x is the number of years after 2000.
Carry all calculations to six decimals on each intermediate step, when necessary.
a) Use this model to approximate the percentage of spam in the year 2003.
Answer: P(2003-2000) = 13+45ln(3) = 62.4376%
----------------------
b) Use this model to approximate the year that the percent of spam will reach 95% provided that law enforcement regarding spammers does not change?
95 = 13 + 45ln(x)
82 = 45ln(x)
ln(x) = 1.8222
x = e^1.8222 = 6.1856
------------------
95% spam will be reached in 2000+6.1856 or in the year 2007
==================
Cheers,
Stan H.
|
Proportions/123670: Please help with this problem...it's a handful. Any help is appreciated. Thanks.
Question:
Solve for y
3(y+7)/7y - (4y-7)/6 = (7y+10)/3y - 2(7y-1)/21
1 solutions
Answer 90711 by stanbon(57332) on 2008-01-30 13:33:45 (Show Source):
You can put this solution on YOUR website!Solve for y
3(y+7)/7y - (4y-7)/6 = (7y+10)/3y - 2(7y-1)/21
Multiply thru by 42y to get rid of the denominators:
18(y+7) - 7y(4y-7) = 14(7y+10) - 4y(7y-1)
18y+ 126 -28y^2 + 49y = 98y+140 -28y^2+4y
67y+126 = 102y+140
26 = 35y
y = 26/35
=============
Cheers,
Stan H.
|
Probability-and-statistics/123517: The number of blocking pansies increased by 160% overnight. If they numbered 117 in the morning how many pansies had bloomed before nightfall?
1 solutions
Answer 90691 by stanbon(57332) on 2008-01-30 12:13:11 (Show Source):
You can put this solution on YOUR website!The number of blocking pansies increased by 160% overnight. If they numbered 117 in the morning how many pansies had bloomed before nightfall?
-----------------
This is a bit ambiguous. If the increase was 160% you
have original amt. + 1.60(original amt.) = 117
------------
Let original amt be "x".
EQUATION"
x + 1.60x = 117
2.6x = 117
x = 45 (original number of blooms)
117-45 = 72 (number that bloomed before nighfall or overnight or whatever)
==============
Cheers,
Stan H.
|
Quadratic_Equations/123615: Find the value(s) of k if the equation 3k^2+5x+2=0 have no real roots.
1 solutions
Answer 90681 by stanbon(57332) on 2008-01-30 09:57:48 (Show Source):
You can put this solution on YOUR website!Find the value(s) of k if the equation 3k^2+5x+2=0 have no real roots.
--------------
No real roots means the discriminant is negative.
-------------
b^2-4ac < 0
25 -4*3k*2 <0
25 -24k < 0
24k > 25
k > 25/24
==============
Cheers,
Stan H.
|
Quadratic_Equations/123618: A certain radioactive element decays to 1/2 of its original amount every 20 years. If there was 100mg to start with, how much will be present after 200 years? Set up an equation and solve the problem. Can someone please help me ??
1 solutions
Answer 90680 by stanbon(57332) on 2008-01-30 09:53:08 (Show Source):
You can put this solution on YOUR website!A certain radioactive element decays to 1/2 of its original amount every 20 years. If there was 100mg to start with, how much will be present after 200 years? Set up an equation and solve the problem.
------------------
A(t)=A(0)*(1/2)^(t/20)
A(t) is the amount you have at a certain time.
A(0) is the amount you have when you start.
---------------------------
A(200)=100*(1/2)^(200/20)
A(200) = 100*0.0313
A(200) = 31.3 mg
===================
Cheers,
Stan H.
|
Distributive-associative-commutative-properties/123626: The formula for the area of a rectangle is a= lw.Find possible algebraic expressions for l and w if A= 6x + 5x-4
***** The 1st x is to the 4th, 2nd sq.
1 solutions
Answer 90678 by stanbon(57332) on 2008-01-30 09:48:51 (Show Source):
You can put this solution on YOUR website!The formula for the area of a rectangle is a= lw.Find possible algebraic expressions for l and w if A= 6x + 5x-4
--------------
The 1st x is to the 4th, 2nd sq.
---------------
Area = 6x^4 + 5x^2 -4
Factor to get:
= 6x^4+8x^2-3x^2-4
= 2x^2(3x^2+4)-(3x^2+4)
= (3x^2+4)(2x^2-1)
-----------
Either factor could be an expression for length or width.
=============
Cheers,
Stan H.
|
Percentage-and-ratio-word-problems/123627: If 53% of the college students are woman and there are 2096 women, How many men are there?
1 solutions
Answer 90676 by stanbon(57332) on 2008-01-30 09:43:50 (Show Source):
You can put this solution on YOUR website!If 53% of the college students are woman and there are 2096 women, How many men are there?
-----------------
Let the total number of students be "x":
EQUATION:
0.53x = 2096
x = 3955 when rounded off to a whole number.
-----------
# of men = 3955-2096 = 1859
=============
Cheers,
Stan H.
|
Linear-equations/123620: I am suppose to draw the graph of each line using its y-intercept and its slope..I have gone over the chapter and am just confused on how exactly i find that using this equation.  I am so ready to tear my hair out...can someone help?
thank you
1 solutions
Answer 90672 by stanbon(57332) on 2008-01-30 09:35:23 (Show Source):
You can put this solution on YOUR website!4x+3y=9
------------
Solve for y : 3y=-4x+9
y = (-4/3)x+3
-----------------
The y-intercept is the point (0,3)
The slope is -4/3
-----------------
slope means "change in y"/"change in x"
Your change in x is +3;
Your change in y is -4
--------------------------
Put your pencil point on the y-intercept: put a dot there.
Move your pencil point +3 to the right, then 4 down; to the
point (3,-1); put a dot there.
Now draw a line thru the two points. That is the graph you want.
=================
Cheers,
Stan H.
|
Distributive-associative-commutative-properties/123624: find an algebraic expression for the length of a side of a square with area of
a+14ab+49b
1st a to the 6ht , 2nd a cubed, b to the 9th, last b to the 18th
1 solutions
Answer 90670 by stanbon(57332) on 2008-01-30 09:27:36 (Show Source):
You can put this solution on YOUR website!find an algebraic expression for the length of a side of a square with area of
a+14ab+49b
1st a to the 6ht , 2nd a cubed, b to the 9th, last b to the 18th
---------------
a^6 + 14a^3b^9 + 49b^18
= (a^3+7b^9)(a^3+7b^9)
======================
Each side is a^3+7b^9
========================
Cheers,
Stan H.
|
Functions/123559: I am practicing finding the domain of an expression in interval notation. A particular problem has brought confusion
radical x(square)-7x-18/x-12
I know that the denomenator cannot be zero, otherwise it would be undefined. So would the answer be [-9,2] U [2,infinity) and x cannot =12 ?
Am I on the right track with this?
1 solutions
Answer 90634 by stanbon(57332) on 2008-01-29 23:39:47 (Show Source):
You can put this solution on YOUR website!radical x(square)-7x-18/x-12
--------------------------------
Comment: It is difficult to tell what your numerator is.
Maybe it is sqrt(x^2-7x-18)
If that is true, x^2-7x-18 must not be negative
(x-9)(x+2) < 0
Draw a number line; plot the points x=-2 and x=9
Find which interval contains the solution set:
If x=-3 you get (-3-9)(-3+2)< 0 which is false
If x=0 you get (0-9)(0+2)< 0 which is true
If x= 10 you get (10-9)(10+2)< 0 which is false
-------------------------------------------
So, the domain cannot be 12 and it cannot be in the interval (-2,9)
The domain is all Real Numbers except 12 or -2 < x < 9
====================
Cheers,
Stan H.
|
Expressions-with-variables/123545: i cant figure this one out either
bruce invested in stock paying 10 1/2% dividend, maya invested $4000 more than bruce in tax free bonds paying 7 1/2% annual simple interest. If mayas income from investment is $75 more than bruces find how much money each invested. (NOTE: 10 1/2=10.5 not 101/2!!!!!!!!)
THAnkYOU VERY MUCH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1 solutions
Answer 90628 by stanbon(57332) on 2008-01-29 22:34:39 (Show Source):
You can put this solution on YOUR website!bruce invested in stock paying 10 1/2% dividend,
maya invested $4000 more than bruce in tax free bonds paying 7 1/2% annual simple interest.
If mayas income from investment is $75 more than bruces find how much money each invested.
------------------------
Bruce DATA:
Amt invested = x dollars ; interest = 0.105x dollars
---------------
Maya DATA:
Amt invested = x+4000 ; interest = 0.075(x+4000)= 0.075x+300 dollars
---------------
EQUATIon:
Maya interest = Bruce interest + 75
0.075x+300 = 0.105x + 75
75x + 300000 = 105x + 75000
30x = 225000
x = $7500 (amount Bruce invested)
x+4000= $11,500 (amount Maya invested)
======================
Cheers,
Stan H.
|
Expressions-with-variables/123542: I cant figure this out
the number of students at westwood high school with a drivers license is 558. this is 24% more than last year. how many students had a drivers license last year.
THANKS
1 solutions
Answer 90626 by stanbon(57332) on 2008-01-29 22:24:02 (Show Source):
You can put this solution on YOUR website!the number of students at westwood high school with a drivers license is 558. this is 24% more than last year. how many students had a drivers license last year.
-----------------
Let # with a drivers license last year be "x".
x + 0.24x = 558
1.24x = 558
x = 450
===========================
Cheers,
Stan H.
|
Expressions-with-variables/123541: i cant figure this out
Emily Ling is a real estate broker who earns 12% commision on each house she sells. if she earns $21,600 on the sale fo a house, what was the selling price of the house?
THANKS
1 solutions
Answer 90625 by stanbon(57332) on 2008-01-29 22:18:27 (Show Source):
You can put this solution on YOUR website!Emily Ling is a real estate broker who earns 12% commision on each house she sells. if she earns $21,600 on the sale fo a house, what was the selling price of the house?
-----------------
Let the selling price of the house be "x".
EQUATION:
0.12x = 21,600
x = $180,000
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Cheers,
Stan H.
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Travel_Word_Problems/123539: The rate of the bicyclist is 7 mph faster than the rate of a long-distance runner. The bicyclist travels 30 miles in the same amount of time that the runner travles 16 miles. Find the rate of the runner.
I know you can find rate R= d/t i have 30/x+7 for cyclist and 16/x for runner. I don't know what to do with these numbers now.
Please help
THANK you
1 solutions
Answer 90621 by stanbon(57332) on 2008-01-29 22:12:57 (Show Source):
You can put this solution on YOUR website!The rate of the bicyclist is 7 mph faster than the rate of a long-distance runner.
The bicyclist travels 30 miles in the same amount of time that the runner travles 16 miles.
Find the rate of the runner.
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Bicyclist DATA:
Distance = 30 miles ; Rate = x+7 mph ; Time = d/r = 30/(x+7) hrs.
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Runner DATA:
Distance = 16 miles ; Rate = x mph ; Time = d/r = 16/x hrs
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EQUATION:
cyclist time = runner time
30/(x+7) = 16/x
30x = 16x+112
14x = 112
x = 8 mph (runner rate)
===========================
Cheers,
Stan H.
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Probability-and-statistics/123377: Please help solve:
A survey was sent to a group of randomly chosen people over the internet. It poses questions about the importance of technology in america. What factors might bias the results of this survey?
1) Internet sites can only handle a limited number of users at a time.
2) Internet use is avaiable internationally, not just in america.
3) Internet surfers would not spend the time to complete the surveys.
4) Internet acess is avaiable at all times, day and night.
5) Internet acess is often not as avaiable to disadvantage people.
I chosen the answers: 2, 3, and 5. Is this correct.
thanks.
1 solutions
Answer 90620 by stanbon(57332) on 2008-01-29 22:04:40 (Show Source):
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Distributive-associative-commutative-properties/123536: This question is from textbook Elementary and intermediate Algebra
Skydiving. If there were no air resistance, then the height (in feet) above the earth for a skydiver t seconds after jumping from an airplane at 10,000 feet would be given by h(t)= -16t^2 + 10,000
a) find the time that it would take to fall to earth with no air resistance: that is, find t for which (t)= 0.A skydiveractually gets about twice as much free fall time due to air resistance.
b)Use the accompanying graph to determine whether the skydiver(with no air resistance ) falls farther in the first 5 seconds or the last 5 seconds of the fall.
c) Is the skydiver's velocity increasing or decreasing as she falls?
1 solutions
Answer 90618 by stanbon(57332) on 2008-01-29 21:52:15 (Show Source):
You can put this solution on YOUR website!If there were no air resistance, then the height (in feet) above the earth for a skydiver t seconds after jumping from an airplane at 10,000 feet would be given by h(t)= -16t^2 + 10,000
a) find the time that it would take to fall to earth with no air resistance: that is, find t for which (t)= 0.A skydiveractually gets about twice as much free fall time due to air resistance.
When on earth the height is zero.
-16t^2+10,000=0
-16t^2 = -10,000
t^2 = 625
t = 25 seconds
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b)Use the accompanying graph to determine whether the skydiver(with no air resistance ) falls farther in the first 5 seconds or the last 5 seconds of the fall.
Height after 5 seconds = h(5)=-16(5^2)+10000 = 9600 ft
The skydiver falls 400 ft in the 1st 5 seconds.
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Height after 20 seconds = h(20)=-16(20^2)+10000= 3600 ft
Height aftrer 25 seconds is zero
The skydiver falls 3600 ft in the last 5 seconds.
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c) Is the skydiver's velocity increasing or decreasing as she falls?
increasing.
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Cheers,
Stan H.
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Miscellaneous_Word_Problems/123535: A purchase of 5 oranges and 6 bananas is 2.05 and a purchase of 7 oranges and 8 bananas is 2.79. What is the cost of each orange?
1 solutions
Answer 90616 by stanbon(57332) on 2008-01-29 21:41:12 (Show Source):
You can put this solution on YOUR website!A purchase of 5 oranges and 6 bananas is 2.05 and a purchase of 7 oranges and 8 bananas is 2.79. What is the cost of each orange?
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EQUATIONS:
5o+6b = 2.05
7o+8b = 2.79
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Multiply 1st equation by 7: Multiply 2nd equation by 5
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35o+42b = 7*2.05
35o+40b = 5*2.79
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Subtract 2nd from 1st to get:
2b = 0.4
b = 0.20 (price of a banana)
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Substitute into one of the 1st two equations to solve for "o":
5o+6*0.20 = 2.05
5o+1.20 = 2.05
5o = 0.85
o = 0.17 (price of an orange)
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Cheers,
stan H.
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Polynomials-and-rational-expressions/123501: I am just trying to check over my answer to this question. I have that it is PRIME so therefore the polynomial is NOT factorable. The equation in question is 10-9y-2y^2
1 solutions
Answer 90608 by stanbon(57332) on 2008-01-29 21:12:19 (Show Source):
You can put this solution on YOUR website!The equation in question is 10-9y-2y^2
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Rearrange: -2y^2-9y+10
y = [9 +- sqrt(81-4*-2*10)]/(-4)
y = [9 +- sqrt(161)]/(-4)
y = (-9/4) -(1/4)sqrt(161) or y = (-9/4)+(1/4)sqrt(161)
(y+[(+9/4)+(1/4)sqrt(161)])(y+[(9/4)+(-1/4)sqrt(161)])
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These are factors of the polynomial but I would not
disagree with you; the polynomial is prime by most
normal standards.
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Cheers,
Stan H.
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Functions/123345: Find the domain of the function express in set builder notation.
f(x)= 4/x-3
1 solutions
Answer 90544 by stanbon(57332) on 2008-01-29 12:22:20 (Show Source):
You can put this solution on YOUR website!The domain is all Real numbers except x=3
In set-builder notation this is :
{x|-inf
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Comment: The word "or" could replace "union".
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Cheers,
Stan H.
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