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Recent problems solved by 'stanbon'
stanbon answered: 57135 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 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>Next
Matrices-and-determiminant/258939: For the following function f(x)=3x2-x+4 find
f(2)
F(2x)
F(2x+2)
1 solutions
Answer 190646 by stanbon(57203)   on 2010-01-20 17:48:52 (Show Source):
You can put this solution on YOUR website!For the following function
f(x)=3x^2-x+4 find
f(2)= 3*2^2 - 2 + 4 = 12+2 = 14
---------------------------
F(2x) = 3(2x)^2 - 2x + 4 = 12x^2 -2x +4
---------------------------
F(2x+2) = 3(2x+2)^2 + 2x+2 + 4
= 3(4x^2+8x+4) + 2x^2 + 4
---
= 6x^2 + 24x + 16
====================
Cheers,
Stan H.
|
Matrices-and-determiminant/258938: Determine whether the given points are all on the graph of the equation.
Equation: y= x3- 2
Points: (1, -1); (-1, -3); (0, -2)
1 solutions
Answer 190644 by stanbon(57203) on 2010-01-20 17:38:54 (Show Source):
You can put this solution on YOUR website!Determine whether the given points are all on the graph of the equation.
Equation: y= x^3- 2
Points: (1, -1); (-1, -3); (0, -2)
------------------------------
(1,-1): -1 = 1^3-2 = -1 ; on the graph
-----
(-1,-3): -3 = (-1)^3-2 = -1-2 = -3 ; on the graph
---------
(0,-2): -2 = 0^3-2 = -2 ; on the graph
==========================================
Cheers,
StanH.
|
Functions/258929: Here’s the problem:
For a car renting for $15 per day plus $.10 per mile, the cost for 1 day is
C(m)=15+o.10m (dollars)
where m is the number of miles driven. If the person paid $35.30 for 1 day’s rental, how far did the person drive?
Now I can look at this and know what the answer is, but I have to solve it using
L(a)=-2/3+150
I not only do not understand how to do it – I don’t understand the function.
Could you guide me through this please?
1 solutions
Answer 190635 by stanbon(57203) on 2010-01-20 17:23:45 (Show Source):
You can put this solution on YOUR website!For a car renting for $15 per day plus $.10 per mile, the cost for 1 day is
C(m)=15+0.10m (dollars) where m is the number of miles driven.
If the person paid $35.30 for 1 day’s rental, how far did the person drive?
-----
Solve 15 + 0.10m = 35 for "m"
Subtract 15 from both sides to get:
0.10m = 20
m = 20/(0.10)
m = 20/(1/10)
m = 20 miles
====================
Cheers,
Stan H.
|
Polygons/258926: How many sides does a regular polygon have when each exterior angle measure is one eighth the measure of the interior angle?
1 solutions
Answer 190630 by stanbon(57203) on 2010-01-20 17:16:38 (Show Source):
You can put this solution on YOUR website!How many sides does a regular polygon have when each exterior angle measure is one eighth the measure of the interior angle?
---------------------------
Let the interior be "x"
Then the exterior is (1/8)x
-------------
Equation:
x + (1/8)x = 180
8x + x = 8*180
9x = 8*180
x = 8*20 = 160 degrees (measure of one of the interior angles)
---
(1/8)x = (1/8)160 = 20 degrees (measure of one of the exterior angles)
--------------
Fact: The sum of the exterior angles is 360
--------------
Equation:
# of exterior angles = # of sides = 360/20 = 18
================================
Cheers,
Stan H.
|
Numbers_Word_Problems/258916: find two consecutive odd integers whose product is 195
1 solutions
Answer 190627 by stanbon(57203) on 2010-01-20 17:09:47 (Show Source):
You can put this solution on YOUR website!find two consecutive odd integers whose product is 195
===
1st: 2x+1
2nd: 2x+3
-----
Equation:
(2x+1)(2x+3) = 195
4x^2 +8x + 3 = 195
4x^2 + 8x - 192 = 0
4(x^2 + 2x - 48)
(x-6)(x+8) = 0
---
Positive solution:
x = 6
1st: 2x+1 = 13
2nd: 2x+3 = 15
-------------------
Negative solution:
x = -8
1st: 2x+1 = -15
2nd: 2x+3 = -13
======================
Cheers,
Stan H.
======================
|
Linear-equations/258919: The slope of the line below is -1. Write the point-slope equation of the line using the coordinates of the labeled point. The coordinate it (4,-9)
1 solutions
Answer 190622 by stanbon(57203) on 2010-01-20 16:52:16 (Show Source):
You can put this solution on YOUR website!The slope of the line below is -1. Write the point-slope equation of the line using the coordinates of the labeled point. The coordinate it (4,-9)
-----------------
Equation Form: y = mx + b
Find "b"
-9 = -1*4 + b
b = -5
-------
Equation:
y = -x - 5
===============
Cheers,
Stan H.
|
Equations/258918: if 2x+15=27-4x what does x equal
1 solutions
Answer 190620 by stanbon(57203) on 2010-01-20 16:49:02 (Show Source):
You can put this solution on YOUR website!if 2x+15=27-4x what does x equal
---
Add 4x to both sides of the equation to get:
6x + 15 = 27
Subtract 15 from both sides to get:
6x = 12
Divide both sides by 6 to solve for "x":
x = 2
----------------
Cheers,
Stan H.
|
Money_Word_Problems/258836: How many years does Steven need to invest his $3,000 at 7% to earn $210 in simple interest?
1 solutions
Answer 190566 by stanbon(57203) on 2010-01-20 14:36:30 (Show Source):
You can put this solution on YOUR website!How many years does Steven need to invest his $3,000 at 7% to earn $210 in simple interest?
------
Interest = Prt
210 = 3000*0.07t
t = 210/(210)
time = 1 year
========================
Cheers,
Stan H.
|
Systems-of-equations/258795: determine if the following system of equations is independent, dependent, or inconsistent:
-7x -5y = -4
-35x -25y =13
1 solutions
Answer 190513 by stanbon(57203) on 2010-01-20 12:11:37 (Show Source):
You can put this solution on YOUR website!determine if the following system of equations is independent, dependent, or inconsistent:
-7x -5y = -4
-35x -25y =13
-----------------------
Multiply thru the 1st equation by 5 to get:
-35x - 25y = -20
-35x - 25y = 13
--------------------------
Subtract the 1st from the 2nd to get:
0 = 33
---
That is a contraction which resulted because we assumed
the x and the y variable stood for the same numbers in
the two equations.
They do not, so the system of equations is inconsistent.
===================
If you graphed the two equations you would see the lines
are parallel; they do not share a point.
===================
Cheers,
Stan H.
|
Radicals/258800: Hi
Simplify the radical by rationalizing the denominator. Variables are assumed to be positive.
square root sign over the following: 3x to the 6th power over 2y to the 4th power. The square root sign is over the whole fraction with a small 5 to the left of the square root sign. All to the 5th power.
I'm having trouble figuring out what to do.
Thanks
R
1 solutions
Answer 190512 by stanbon(57203) on 2010-01-20 12:07:40 (Show Source):
You can put this solution on YOUR website!Simplify the radical by rationalizing the denominator. Variables are assumed to be positive.
square root sign over the following: 3x to the 6th power over 2y to the 4th power. The square root sign is over the whole fraction with a small 5 to the left of the square root sign. All to the 5th power.
-------------
[5th root of(3x^6/2y^4]^5
---------------------------
Note: [the 5th root of anything]^5 is just the "anything".
Are you sure that is what your problem calls for?????
---------------------------
Ans. to your problem: 3x^6/2y^4
====================================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/258797: Janet invested $27,000, part at 15% and part at 9%. If the total interest at the end of the year is $3,390, how much did she invest at 15%?
1 solutions
Answer 190510 by stanbon(57203) on 2010-01-20 12:03:06 (Show Source):
You can put this solution on YOUR website!Janet invested $27,000, part at 15% and part at 9%. If the total interest at the end of the year is $3,390, how much did she invest at 15%?
---------------------
Using two variables:
Equations:
Quantity Equation: x + y = 27000
Interest Equation:0.15x + 0.09y = 3390
----------------------------------------
Multiply thru the 1st equation by 9
Multiply thru the 2nd equation by 100
-----
9x + 9y = 9*27000
15x+ 9y = 339000
------------------------
Subtract the 1st from the 2nd and solve for "x":
6x = 96000
x = $16,000 (amt. invested at 15 %
------------------------------
Cheers,
Stan H.
|
Probability-and-statistics/258784: Amniocentesis tests result in miscarriage 0.5% of the time. Assuming each test is independent and follows a Bernoulli random variable, then what is the variance of one test? What is the variance of 400 tests? I found the equation for variance p(1-p), but it doesn't take into account the number of tests.
1 solutions
Answer 190509 by stanbon(57203) on 2010-01-20 11:55:51 (Show Source):
You can put this solution on YOUR website!Amniocentesis tests result in miscarriage 0.5% of the time. Assuming each test is independent and follows a Bernoulli random variable, then what is the variance of one test? What is the variance of 400 tests? I found the equation for variance p(1-p), but it doesn't take into account the number of tests.
-------------------
For a binomial distribution variance = npq
----
Your problem:
variance = 400*0.05*0.95 = 19
====================================
Cheers,
Stan H.
|
Travel_Word_Problems/258761: jacqui commutes 30 miles to her job each day. She finds that if she drives 10 miles/hour faster, it takes her 6 minutes less to get to work .find her new speed
1 solutions
Answer 190483 by stanbon(57203) on 2010-01-20 10:10:41 (Show Source):
You can put this solution on YOUR website!jacqui commutes 30 miles to her job each day. She finds that if she drives 10 miles/hour faster, it takes her 6 minutes less to get to work.
find her new speed
------------------------
Old DATA:
distance = 30 miles ; rate = x mph ; time = d/r = 30/x hrs.
--------------------------------------------------
New DATA:
distance = 30 miles ; rate = (x+10) mph ; time = d/r = 30/(x+10) hrs
------------------------------------------------------
Equation:
old time - new time = 1/10 hr
30/x - 30/(x+10) = 1/10
Multiply thru by 10x(x+10)
300(x+10) - 300x = x(x+10)
3000 = x^2 + 10x
---
x^2 + 10x - 3000 = 0
(x+60)(x-50) = 0
---
Positive solution:
x = 50 mph (old speed)
---
x+10 = 60 mph (her new speed)
==================================
Cheers,
Stan H.
|
Numbers_Word_Problems/258774: Solve the following equation:
4ax+by=11ab
8ax-5by=ab
1 solutions
Answer 190480 by stanbon(57203) on 2010-01-20 10:01:22 (Show Source):
You can put this solution on YOUR website!4ax+by=11ab
8ax-5by=ab
---------------
Multiply the 1st eq by 2 to get:
8ax + 2by = 22ab
8ax-5by = ab
-----------------
Subtract the 2nd from the 1st and solve for "y":
7by = 21ab
y = 3a
---------------
Substitute into 4ax+by = 11ab to solve for "x":
4ax + b(3a) = 11ab
Divide thru by a to get:
4x + 3b = 11b
4x = 8b
x = 2b
------------------
Solution: (2b,3a)
========================
Cheers,
Stan H.
|
Rectangles/258772: the perimeter of a rectangle is 64 cm. The length is 4 cm less than twice the width.
1 solutions
Answer 190478 by stanbon(57203) on 2010-01-20 09:55:58 (Show Source):
You can put this solution on YOUR website!the perimeter of a rectangle is 64 cm. The length is 4 cm less than twice the width.
-----------
Perimeter = 2(L + W)
64 = 2(2W-4 + W)
32 = 3W-4
3W = 36
W = 12 cm (width of the rectangle)
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Since the length = 2W-4, L = 2*12-4 = 20 cm (length of the rectangle)
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Cheers,
Stan H.
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Sequences-and-series/258765: The sum of the first n terms in a sequence is always 1/n. Find the product of the first 2007 terms.
1 solutions
Answer 190477 by stanbon(57203) on 2010-01-20 09:53:19 (Show Source):
You can put this solution on YOUR website!The sum of the first n terms in a sequence is always 1/n. Find the product of the first 2007 terms.
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2007/n is the number of times you have n terms in 2007
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Each of those n terms sets adds up to 1/n
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So the sum is (2007/n)(1/n) = 2007/n^2
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Cheers,
Stan H.
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logarithm/258773: how would you answer a log question when it asks for the value of a letter(x) in simultaneous form????
1 solutions
Answer 190471 by stanbon(57203) on 2010-01-20 09:47:31 (Show Source):
You can put this solution on YOUR website!how would you answer a log question when it asks for the value of a letter(x) in simultaneous form?
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Maybe it is asking for the value of x in exponential form?
Example:
If log2(x) = 3
Then the exponential form is x = 2^3
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In general:
If log(x) = y, then x = 10^y
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If ln(x) = y, then x = e^y
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Cheers,
Stan H.
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Linear-equations/258768: Describe the transformation from the graph of f(x)=4x to the graph of g(x)1/2x
1 solutions
Answer 190469 by stanbon(57203) on 2010-01-20 09:44:18 (Show Source):
You can put this solution on YOUR website!Describe the transformation from the graph of
f(x)=4x to the graph of g(x)= (1/2)x
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Find h(x) if h[f(x)] = (1/2)x
h[f(x)] = h(4x) = (1/2)x
h(x) = (1/8)x
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Let h(x) = (1/8)x
Then h[f(x)] = h(4x) = (1/8)(4x) = (1/2)x
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Ans: h(x) = (1/8)x
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Cheers,
Stan H.
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Probability-and-statistics/258722: Normal Distribution
The scores for the intelligence quotient (IQ) test are normally distributed with mean 100 and standard deviation 16.
(a) What is the probability that at least two of five randomly selected people have IQ test score higher than 120?
(b) A person is randomly selected from all people whose IQ are higher than 110. What is the probability that this person has IQ higher than 120?
(c) One thousand people are randomly selected. Approximately what is the probability that fewer than 90 of them have IQ score higher than 120?
1 solutions
Answer 190464 by stanbon(57203) on 2010-01-20 09:26:13 (Show Source):
You can put this solution on YOUR website!Normal Distribution
The scores for the intelligence quotient (IQ) test are normally distributed with mean 100 and standard deviation 16.
(a) What is the probability that at least two of five randomly selected people have IQ test score higher than 120?
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Find the z-score of 120:
z(120) = (120-100)/16 = 1.25
P(z>1.25) = normalcdf(1.25,100) = 0.1056
Find P(2<= x <=5 with n = 5 and p = 0.1056) = 1-binomcdf(5,0.1056,1) = 0.0899..
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(b) A person is randomly selected from all people whose IQ are higher than 110. What is the probability that this person has IQ higher than 120?
z(110) = 10/16 = 0.625
P(x>110) = P(z> 0.625) = 0.26598..
P(x>120 | x>110) = P(x > 120)/P(x>110) = 0.1056/0.26598 = 0.3970..
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(c) One thousand people are randomly selected. Approximately what is the probability that fewer than 90 of them have IQ score higher than 120?
P(x>120) = 0.1056
P(k< 90) = binomcdf(1000,0.1056,89) = 0.04624.....
Cheers,
Stan H.
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Quadratic_Equations/258645: The length of a rectangle is twice the width. The area is 98yd^2. Find the length and the width.
The length is ? yd.
(Simplify your answer)
The width is ? yd.
(Simplify your answer)
Thank you very much for your help with this problem.
1 solutions
Answer 190418 by stanbon(57203) on 2010-01-19 21:05:36 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is twice the width. The area is 98yd^2. Find the length and the width.
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L = 2W
Area = LW
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98 = (2W)W
49 = w^2
W = 7 yds (width)
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L = 2W = 14 yds (length)
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Cheers,
Stan H.
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The length is ? yd.
(Simplify your answer)
The width is ? yd.
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percentage/258644: chris has a basket of apples,40%red, and the rest green apples. there are six red apples ,how many green apples does it contain?
1 solutions
Answer 190417 by stanbon(57203) on 2010-01-19 21:02:13 (Show Source):
You can put this solution on YOUR website!chris has a basket of apples, 40%red, and the rest green apples. there are six red apples ,how many green apples does it contain?
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Let "x" be the number of apples.
0.40x = 6
x = 6/0.4 = 15
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# of green apples = 0.6*15 = 9
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Cheers,
Stan H.
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Age_Word_Problems/258631: a father is four times as old as his son. in twenty years he will be twice as old. how old are they now?
1 solutions
Answer 190411 by stanbon(57203) on 2010-01-19 20:47:07 (Show Source):
You can put this solution on YOUR website!a father is four times as old as his son. in twenty years he will be twice as old. how old are they now?
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F = 4S
(F+20) = 2(S+20)
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Substitute for "F" and solve for "S":
(4S+20) = 2S+40
2S = 20
S= 10 yrs old (the son's age)
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F= 4S = 40 yrs old (the father's age)
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Cheers,
Stan H.
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Geometry_Word_Problems/258630: i have no type of idea how to find out to solve nothing i appreciate n thank you
a stake is to be driven into the ground away from the base of a 50foot pole,a wire from the stake on the ground to the top of the pole is to be installed at an angle of elevation of 52degrees.
This is like the triangle on the paper being that b is 5o foot pole,A is 52 degress and C is the wire
how far away from the base of the pole should the stake be driven in,to the NEAREST foot? what will be the length of the wire from the stake to the top of the pole, to the NEAREST foot?
1 solutions
Answer 190409 by stanbon(57203) on 2010-01-19 20:43:27 (Show Source):
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