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Recent problems solved by 'stanbon'
stanbon answered: 57281 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 , 57240..57269 , 57270..57299, >>NextTrigonometry-basics/93514: This question is from textbook Algebra and Trigonometry
If a piece of real estate purchased for $75,000 in 1998 appreciates at the rate og 6% per year, then its value t years after the purchase will be f(f)=75,000(1.06^t). According to this model, by how much will the value of this piece of property increase between the years 2005 and 2008?
1 solutions
Answer 68088 by stanbon(57354)   on 2007-08-20 20:04:23 (Show Source):
You can put this solution on YOUR website!If a piece of real estate purchased for $75,000 in 1998 appreciates at the rate og 6% per year, then its value t years after the purchase will be f(t)=75,000(1.06^t). According to this model, by how much will the value of this piece of property increase between the years 2005 and 2008?
---------------------
Value in 2008: 75000(1.06)^10
Value in 2005: 75000(1.06)^7
-------------
Increase between 2005 and 2008:
75000(1.06^10 - 1.06^7) = 75000*0.2872174376... = $21,541.31
==============
Cheers,
Stan H.
|
Trigonometry-basics/93513: This question is from textbook Algebra and Trigonometry
Write the expression log lower case a (y+5)+2log lower case a(x+1) as one logarithm.
1 solutions
Answer 68086 by stanbon(57354) on 2007-08-20 19:57:49 (Show Source):
You can put this solution on YOUR website!Write the expression log lower case a (y+5)+2log lower case a(x+1) as one logarithm.
Rule log A + log B = log AB
That means "when you add exponents you are multiplying"
------------------
Your Problem:
log(y+5) + 2 log(x+1)
= log (y+5) + log (x+1)^2
= log [(y+5)(x+1)^2]
Note: The base on all of these is "a"
============================
Cheers,
Stan H.
|
logarithm/93484: This question is from textbook
write in exponential form and simplify this is really hard to explian so please try follow along carefully (the little 3)then the sqrt a^5 (then the little 5) then sqrt a
1 solutions
Answer 68068 by stanbon(57354) on 2007-08-20 18:17:32 (Show Source):
You can put this solution on YOUR website!(the little 3)then the sqrt a^5 (then the little 5) then sqrt a
[a^5]^(1/3)^(1/5)
= a^(5/3)* a^(1/5)
= a^[(5/3) + (1/5)]
= a^[(28/15)
==================
Cheers,
Stan H.
|
Length-and-distance/93486: This question is from textbook GEOMETRY
Find the distance bewteen the two cities using the information given in the table, which is from a coordinate system used for calculating long-distance telephone rates.
48. Buffalo and Dallas
Buffalo = (5075, 2326)
Dallas = (8436, 4034)
1 solutions
Answer 68066 by stanbon(57354) on 2007-08-20 18:09:19 (Show Source):
You can put this solution on YOUR website!Buffalo = (5075, 2326)
Dallas = (8436, 4034)
----------------------------
d = sqrt[(change in x)^2 + (change in y)^2]
d = sqrt[ 3361^2 + 1708^2]
d = sqrt[14213585]
d = 3770.09
================================================
Cheers,
Stan H.
|
logarithm/93483: This question is from textbook
REALLY HARD TO EXPLAIN please help ,.... write in exponential form and simplify
(the little 3)sqrt x^2y
1 solutions
Answer 68064 by stanbon(57354) on 2007-08-20 17:57:23 (Show Source):
You can put this solution on YOUR website!write in exponential form and simplify
(the little 3)sqrt x^2y
------------------------
(x^2 y)^(1/3)
There is no "simplifying" you can do.
================
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/93472: This question is from textbook
Find the what what and the what? please help me!!! Find (a)the directrix,
(b) the focus and (c) the roots of the parabola y = x^2 - 5x + 4
(a)_________________
(b)_________________
(c)_________________
1 solutions
Answer 68059 by stanbon(57354) on 2007-08-20 17:35:43 (Show Source):
You can put this solution on YOUR website!Find (a)the directrix,
(b) the focus and (c) the roots of the parabola y = x^2 - 5x + 4
----------------------
Complete the square on the x terms and keep the equation balanced:
x^2 - 5x + 4 = y
x^2 -5x + ? = y-4 + ?
x^2 + 5x + (5/2)^2 = y - 16/4 + (25/4)
Factor and simplify to get:
(x+(5/2))^2 = (y+9/4)
Note: This follows the form (x-h)^2 = 4P(y-k)
--------------------------------
a) directrix is x = -5/2
------------------
b) 4P=1; p=1/4
Vertex is (-5/2 , -9/4)
Focus is (-5/2 , -9/4 + 1/4) = (-5/2 , -2)
---------------------
c) Roots:
y = x^2 - 5x + 4
Let y=0 and solve for x:
x^2-5x+4 = 0
(x-4)(x-1) = 0
x=4 or x=1
==========================
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/93473: please help me do this!!!!
(a) graph x^2/16 - y^2/25 = 1 show how you arrived at the graph by determining the (b) x-intercepts, (c) extent of the graph and the (d)asymptotes.
(a)_____________
(b)_____________
(c)_____________
(d)_____________
1 solutions
Answer 68057 by stanbon(57354) on 2007-08-20 17:16:19 (Show Source):
You can put this solution on YOUR website!a) graph x^2/16 - y^2/25 = 1 show how you arrived at the graph by determining the (b) x-intercepts, (c) extent of the graph and the (d)asymptotes
-------------------------
x-intercepts:
Let y = 0, then x^2 = 16; x=4 or x=-4
-------------------------
y-intercept:
Let x = 0, then y^2 = -1; y is imaginary so no y intercepts
--------------------
Extent of the graph:
It is a hyperbola with center at the origin; vertices are the x-intercepts;
opening to the left and to the right.
-------------------------------
Asymptotes:
a = 4 ; b = 5
y = (b/a)x = (5/4)x
y = (-b/a)x = (-5/4)x
====================
Cheers,
Stan H.
|
Equations/93469: stan has 52 quarters and nickels combined. if he has three times as many nickels as quarters, how much money does he have?
1 solutions
Answer 68051 by stanbon(57354) on 2007-08-20 17:01:23 (Show Source):
You can put this solution on YOUR website!stan has 52 quarters and nickels combined. if he has three times as many nickels as quarters, how much money does he have?
------------
Let # of quarters be "x"
------------
# of nickels is "3x"
-------------
EQUATIOn:
x + 3x = 52
4x = 52
x = 13 (# of quarters; value of these is 25*13 = $3.25
3x = 39 (# of nickels; value of these is 39*5 = $1.95
---------------
He has $5.20
=================
Cheers,
Stan H.
------------
|
Quadratic_Equations/93446: This question is from textbook
Use synthetic division to find the value of f (-2) for f (x) =
x ^3 - 3x^2 - x - 9.
1 solutions
Answer 68027 by stanbon(57354) on 2007-08-20 16:08:01 (Show Source):
You can put this solution on YOUR website! Use synthetic division to find the value of f (-2) for f (x) =
x ^3 - 3x^2 - x - 9.
-----------------------------
-2)....1....-3....-1....-9
.........1....-5....9...|..-27
=============================
Remainder: f(-2) = -27
Quotient: x^2-5x+9
=========================
Cheers,
Stan H.
|
Expressions-with-variables/93421: This question is from textbook addison-wesley
hello,
I would be extremely grateful for any help or advice for this problem. It has been extremely difficult for me as there is no fore-explanation on how to solve this type of problem.
it is in the section of Maximum and Minimum problems, I was not sure where to put it, I hope I got the right topic.
QUESTION:
A straight section of railroad track crosses two highways at points that are 400m and 600m, respectively, from an intersection.
Determine the Dimensions of the largest rectangular lot that can be laid out in the triangle formed by the railroad and highways.
now, I worked a few hours on this problem, coming to absolutely nothing.
I found the remaining side of the right triangle, at 721.1,
I tried any number of equations using variables, in the end coming up with 4(x-1/4L)²-1/2 meaning zilch without knowing L.
I tried graphing it and solving from there, coming up with a rough esimate of the answer.
I Know how to deal with turning into standard form and all that, but I just cannot seem to grasp which numbers I can use to come up with the (x²+1x+1)format, ... as you can see, I am very confused, any help that you can give will a lifesaver
yours truly,
Michael Demski
ps The answer from the book is 200m by 300m, I just don't know how to get there
1 solutions
Answer 68025 by stanbon(57354) on 2007-08-20 16:04:03 (Show Source):
You can put this solution on YOUR website!Put the intersection on the origin of an xy coordinate system.
Mark the point (600,0) on the x axis.
Mark the point (0,400) on the y axis.
Draw a line thru those two points.
That line is the railroad track.
---------------
Find the equation of that line using the two points.
You get slope = -400/600 = -2/3
You have the y-intercept at 400
The equation is y = (-2/3)x+400
---------------------
Sketch a rectangle inside the figure touching the railroad line at (x,y),
with other vertices, (0,0), (0,y), (x,0)
-----------------------
The area of that rectangle is x*y
A = xy
But y = (-2/3)x+400, so you get
A = x[(-2/3)x+400]
A = (-2/3)x^2 + 400x
------------------
The maximum value for A occurs when x = -b/2a
x = -(400/[2(-2/3)]
x = 200/(2/3)
x = 300
Substitute that into y = (-2/3)x + 400 to get:
y = (-2/3)*300 + 400
y = -200 + 400
y = 200
----------------
The dimensions of the rectangle with maximum area are 300 by 200
===================
Cheers,
Stan H.
|
Numeric_Fractions/93368: The median age at first marriage for females increased from 24.5 years in 1995 to 25.1 years in 2000. Let 1995 be 5 and 2000 be year 10
a) Find the equation of the line through (5, 24.5) and (10, 25.1)
b) What do x and y represent in your equation?
c) Interpret the slope of this line
d) In what year will the median age be 30.
Your help is moslty appreciate, when I am in need. Thank you.
1 solutions
Answer 67989 by stanbon(57354) on 2007-08-19 22:24:56 (Show Source):
You can put this solution on YOUR website!The median age at first marriage for females increased from 24.5 years in 1995 to 25.1 years in 2000. Let 1995 be 5 and 2000 be year 10
a) Find the equation of the line through (5, 24.5) and (10, 25.1)
slope = [25.1-24.5] / [10-5] = 0.6 / 5 = 3/25
------------------------
The form is y = mx+b where m=3/25 and y=24.5 when x=5
24.5 = (3/25)(5) +b
b = 239/10
----------
EQUATION:
y = (3/25)x + 239/10
-----------------------------
b) What do x and y represent in your equation?
x is # of years after 1990
y is median age at which women married
-------------------------
c) Interpret the slope of this line
For every 25 years after 1990 the median age at which wormen marry increases
by 3 years.
------------------------
d) In what year will the median age be 30.
30 = (3/25)x + (239/10)
(3/25)x = 6.1
x=50.83333
1990 + 50.8333.. = 2040.3333...
Rounding you get the year 2040
=================
Cheers,
Stan H.
|
Numeric_Fractions/93366: The percentage of workers receiving direct deposit of their paychecks went from 32% in 1994 to 60% in 2004. Let 1994 be year 0 and 2004 be year 10.
a)write the equation of the line through (0,32) and (10,60) to model the growth of direct deposit.
I am having trouble producing an equation. Kindly help.
1 solutions
Answer 67987 by stanbon(57354) on 2007-08-19 22:08:47 (Show Source):
You can put this solution on YOUR website!a)write the equation of the line through (0,32) and (10,60) to model the growth of direct deposit.
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The y-intercept is 32.
The slope = [60-32] / [10-0] = 28/10 = 14/5
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EQUATION:
growth = (14/5)(years since 1994) + 32
y = (14/5)x + 32
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Cheers,
Stan H.
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Expressions-with-variables/93369: the number of gallons in q quarts? How would i write an expression for this?
1 solutions
Answer 67986 by stanbon(57354) on 2007-08-19 21:58:57 (Show Source):
You can put this solution on YOUR website!the number of gallons in q quarts?
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There are 4 quarts in a gallon.
Each quart is (1/4) gallon.
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EQUATION:
1 qt. = (1/4) gal.
Multiply both sides by "q" to get:
q qts = (1/4)q gallons
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Cheers,
Stan H.
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Mixture_Word_Problems/93324: In a city the percent of moisture that falls a snow rather than rain is approximated by P=86.3 Ln - 680 where P is the percent of moisture as snow at an altitude of h feet. At what altitude os 50% of the moisture snow?
Thanks in advance
1 solutions
Answer 67936 by stanbon(57354) on 2007-08-19 16:55:02 (Show Source):
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Graphs/93204: Graph y >- 3 - x.
1 solutions
Answer 67935 by stanbon(57354) on 2007-08-19 16:51:24 (Show Source):
You can put this solution on YOUR website!Graph y >- 3 - x.
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1st: Graph the boundary of the inequality
which is y=-3-x
Plot two points and draw a dashed line thru them:
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2nd: Pick a test point to see where the graph of the INEQUALITY
lies. For example pick (0,0)
Test that in the inequality y>-3-x
You get 0 > -3-0
That is true so (0,0) is in the half-plane solution of the inequality.
Darken the half-plane above the line which contains the test point (0,0).
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Cheer,
Stan H.
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Expressions-with-variables/93319: Can you help me with this problem? Solve for x. x+2y= -1
3x-4y= 27
I think I am supposed to solve for y in one problem, then substitute it in the next one... but I'm not sure. Thanks in advance!!!
1 solutions
Answer 67932 by stanbon(57354) on 2007-08-19 16:07:32 (Show Source):
You can put this solution on YOUR website!Solve for x.
1st: x+2y= -1
2nd: 3x-4y= 27
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Solve 1st for x:
x = -2y-1
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Substitute that into 2nd and solve for y:
3(-2y-1) - 4y = 27
-6y-3 -4y = 27
-10y = 30
y = -3
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Substitute that into x = -2y-1 and solve for x:
x = -2*-3-1
x = 5
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System solution:
x=5; y=-3
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Cheers,
Stan H.
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Functions/93143: 5) Suppose that the function P=13+45ln x represents the percentage of inbound e-mail in the U.S. that is considered 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.
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.
1 solutions
Answer 67921 by stanbon(57354) on 2007-08-19 13:42:37 (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 considered 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.
P=13+45ln x
P(3) = 13 + 45ln3 = 62.437553 %
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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 + 45lnx
82 = 45lnx
lnx = (82/45)
x = e^(82/45)
x = 6.185589
2000 + 6.185589 = 2006.185589
Rounding to the nearest whole number you get the year 2006
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Cheers,
Stan H.
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Permutations/93300: The menu at a restaurant has 11 appetizers, 15 entrees, 10 desserts, and 8 beverages. The restaurant offers a dinner special that includes 1 appetizer, 1 entree, 1 dessert, and 1 beverage. In how many ways can a person order a dinner special at this restaurant?
1 solutions
Answer 67918 by stanbon(57354) on 2007-08-19 13:35:16 (Show Source):
You can put this solution on YOUR website!The menu at a restaurant has 11 appetizers, 15 entrees, 10 desserts, and 8 beverages. The restaurant offers a dinner special that includes 1 appetizer, 1 entree, 1 dessert, and 1 beverage. In how many ways can a person order a dinner special at this restaurant?
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11*15*10*8 = 13200 ways to order a meal
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Cheers,
Stan H.
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Exponential-and-logarithmic-functions/93295: I need help with these - PLEASE!!!!
okay
1. log4 7 = x ( the 4 should be lower - you know!!!)
2. log0.8 10 = x (same thing)
3. logx 343 = 3
Hope these make sense
Thanks
Llo
1 solutions
Answer 67916 by stanbon(57354) on 2007-08-19 13:32:00 (Show Source):
You can put this solution on YOUR website!1. log4 7 = x
x = [log7] / [log4] = 1.403677461...
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2. log0.8 10 = x
x = [log10] / [log0.8] = 1/(-0.09691013...)= -10.31885116...
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3. logx 343 = 3
x^3 = 343
x = 343^(1/3)
x = 7
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Cheers,
Stan H.
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Rate-of-work-word-problems/93298: One pipe alone will fill a tank in 7 1/2 hrs. A second pipe will fill it alone in 10 hrs. I the second pipe were open for 8 hrs. and then closed, how long would the first pipe take to finish filling the tank?
1 solutions
Answer 67915 by stanbon(57354) on 2007-08-19 13:26:24 (Show Source):
You can put this solution on YOUR website!One pipe alone will fill a tank in 7 1/2 hrs. A second pipe will fill it alone in 10 hrs. If the second pipe were open for 8 hrs. and then closed, how long would the first pipe take to finish filling the tank?
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1st pipe DATA:
Time = 15/2 hr/job ;Rate = 2/15 job/hr
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2nd pipe DATA:
Time = 10 hr/job ; Rate = 1/10 job/hr
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2nd for 8 hrs + 1st for x hrs = 1 job
8(1/10) + (2/15)x = 1
Multiply thru by 30 to get:
24 + 4x = 30
4x = 6
x= 3/2 hrs (time the 2nd pipe will take to finish the job)
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Cheers,
Stan H.
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Miscellaneous_Word_Problems/93136: susan liked her ceiling so much she decided to carpet her room.it measures 8ft,5ft,10ft,12ft. she found carpet she liked at $16.50 a square yard. how much will she have to payfor the carpet? i came up with $583.00 is that right im not sure
1 solutions
Answer 67913 by stanbon(57354) on 2007-08-19 13:18:05 (Show Source):
You can put this solution on YOUR website!8ft,5ft,10ft,12ft
What do these 4 dimensions describe?
Is she going to carpet the floor only; if so what are its length and width?
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Cheers,
Stan H.
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Rational-functions/93085: This question is from textbook
Please help me with this equation:
It is a rational expression and the directions are: Perform the operation and simplify completely:
(3) divided by (x-1) plus (5x) divided by (3x+4)
1 solutions
Answer 67912 by stanbon(57354) on 2007-08-19 13:09:57 (Show Source):
You can put this solution on YOUR website!(3) / (x-1) + (5x) / (3x+4)
You need a common denominator if you are going to add the fractions.
[3(3x+4) + 5x(x-1)] / [(x-1)(3x+4)]
[9x + 12 + 5x^2-5x] / [(x-1)(3x-4)]
[5x^2+4x+12] / [(x-1)(3x-4)]
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Note: Neither x-1 nor 3x-4 divides the numerator so there
is no use trying to factor the numerator.
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Cheers,
Stan H.
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Trigonometry-basics/93274: An airplane is flying 8,000 feet above the level ground. The angle of depression from the plane to the base of the tree is 16.4 degrees. How far horizontally must the plane fly to be directly above the tree?
1 solutions
Answer 67911 by stanbon(57354) on 2007-08-19 12:59:12 (Show Source):
You can put this solution on YOUR website!An airplane is flying 8,000 feet above the level ground. The angle of depression from the plane to the base of the tree is 16.4 degrees. How far horizontally must the plane fly to be directly above the tree?
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Draw the picture;label the parts of the triangle
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The angle of elevation of the plane from the ground is the same
as the angle of depression of the tree from the plane.
Let horizontal distance from the plane to the tree be "x"
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EQUATION:
tan(16.4 degrees) = 6000/x
x = 6000/(tan(16.4))
x = 20386.25 ft.
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Cheers,
Stan H.
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Matrices-and-determiminant/93270: Many college graduates who are employed full-
time have longer than 40-hour work weeks. Suppose that we wish to estimate the mean number of hours
, , worked per week by college graduates employed full-time. We'll choose a random sample of college
graduates employed full-time and use the mean of this sample to estimate . Assuming that the
standard deviation of the number of hours worked by college graduates is 6.00 hours per week,
what is the minimum sample size needed in order for us to be 95%confident that our estimate is
within 1.2 hours per week of ?
1 solutions
Answer 67910 by stanbon(57354) on 2007-08-19 12:54:17 (Show Source):
You can put this solution on YOUR website!Assuming that the standard deviation of the number of hours worked by college graduates is 6.00 hours per week, what is the minimum sample size needed in order for us to be 95%confident that our estimate is within 1.2 hours per week of ?
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n = [z's/E]^2
For 95% confidence z' = 1.96
s is the sample standard deviation = 6
E is the standard error = 1.2
n is the desired sample size
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n = [1.96*6/1.2]^2 = 96
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Cheers,
Stan H.
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