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Recent problems solved by 'stanbon'
stanbon answered: 57274 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 , 54990..55019 , 55020..55049 , 55050..55079 , 55080..55109 , 55110..55139 , 55140..55169 , 55170..55199 , 55200..55229 , 55230..55259 , 55260..55289 , 55290..55319 , 55320..55349 , 55350..55379 , 55380..55409 , 55410..55439 , 55440..55469 , 55470..55499 , 55500..55529 , 55530..55559 , 55560..55589 , 55590..55619 , 55620..55649 , 55650..55679 , 55680..55709 , 55710..55739 , 55740..55769 , 55770..55799 , 55800..55829 , 55830..55859 , 55860..55889 , 55890..55919 , 55920..55949 , 55950..55979 , 55980..56009 , 56010..56039 , 56040..56069 , 56070..56099 , 56100..56129 , 56130..56159 , 56160..56189 , 56190..56219 , 56220..56249 , 56250..56279 , 56280..56309 , 56310..56339 , 56340..56369 , 56370..56399 , 56400..56429 , 56430..56459 , 56460..56489 , 56490..56519 , 56520..56549 , 56550..56579 , 56580..56609 , 56610..56639 , 56640..56669 , 56670..56699 , 56700..56729 , 56730..56759 , 56760..56789 , 56790..56819 , 56820..56849 , 56850..56879 , 56880..56909 , 56910..56939 , 56940..56969 , 56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299, >>NextEquations/454681: How do I simplify this?
10x^2-30x+20
___________ =
x^2-1
1 solutions
Answer 312169 by stanbon(57347)   on 2011-05-27 06:12:42 (Show Source):
You can put this solution on YOUR website!How do I simplify this?
10x^2-30x+20
___________ =
x^2-1
---
Factor:
= [10(x^2-3x+2)]/[(x-1)(x+1)]
----
= [10(x-2)(x-1)]/[(x-1)(x+1)
---------
Cancel the common (x-1) factor to get:
----
= [10(x-2)]/[x+1]
==========================
Cheers,
Stan H.
|
test/454683: One card is selected at random from a deck of cards. Determine the probability that the card is a red 10.
1 solutions
Answer 312168 by stanbon(57347) on 2011-05-27 06:09:12 (Show Source):
You can put this solution on YOUR website!One card is selected at random from a deck of cards. Determine the probability that the card is a red 10.
---
There are 2 red 10's
----
P(select a red 10) = 2/52 = 1/26
=================================
Cheers,
Stan H.
|
Equations/454682: How do I add this problem?
b + 2b
____ _________
b-1 b^2-1
1 solutions
Answer 312167 by stanbon(57347) on 2011-05-27 06:07:20 (Show Source):
You can put this solution on YOUR website!How do I add this problem?
b + 2b
____ _________
b-1 b^2-1
-----------
To add or subtract fractions you need to
have a common denominator on the fractions.
------------
least commondenominator is (b-1)(b+1) = b^2-1
------------
Rewrite each fraction with the lcd as its denominator:
[b(b+1)/lcd] + [2b/(lcd]
----
Combine the numerators over the lcd:
---
[b^2+b+2b]/lcd
---
Simplify:
---
= [b^2+3b]/[b^2-1]
==================
Cheers,
Stan H.
|
Mixture_Word_Problems/454633: 10 Liters of a 20% acid solution are mixed with 30 Liters of a 30% acid solution. What is the concentration of acid in the final mixture?
Remember:
Concentration = (the number of Liters of pure acid) / (total number of Liters in the mixture)
1 solutions
Answer 312146 by stanbon(57347) on 2011-05-26 22:32:26 (Show Source):
You can put this solution on YOUR website!10 Liters of a 20% acid solution are mixed with 30 Liters of a 30% acid solution. What is the concentration of acid in the final mixture?
----
Equation:
acid + acid = acid
0.20*10 + 0.30*30 = x(40)
---
Multiply thru by 100 to get:
20*10 + 30*30 = 4000x
200 + 900 = 4000x
x = 1100/4000
x = 0.275 or 27.5%
=======================
Cheers,
Stan H.
=============
|
Permutations/454631: 4 red, 3 yellow, 2 green marbles
How many arrangements of 5 marbles possible if there is to be at least one of each colour.
1 solutions
Answer 312144 by stanbon(57347) on 2011-05-26 22:27:51 (Show Source):
You can put this solution on YOUR website!This answer is wrong as I calculate the
# of 9-long arrangements when I got 1260.
----------------
I should have calculated the # of 5-log
arrangements that are unrestricted as
to color combinations.
---------------------
Cheers,
Stan H.
|
Pythagorean-theorem/454624: The hypotenuse of a 30- 60- 90 triangle has length 17. What is the length of the side opposite the 60 angle? If necessary, round your answer to two decimal places.
1 solutions
Answer 312140 by stanbon(57347) on 2011-05-26 22:03:29 (Show Source):
You can put this solution on YOUR website!The hypotenuse of a 30- 60- 90 triangle has length 17. What is the length of the side opposite the 60 angle? If necessary, round your answer to two decimal places.
----------------------
Draw the figure.
The side opposite the 30 degree angle is (1/2)17
The side opposite the 60 degree angle = [sqrt(3)/2]17 = 14.72
============
Cheers,
Stan H.
============
|
Probability-and-statistics/454467: 9) The time spent by students on a particular E270 homework assignment follows a normal distribution with a mean μ = 150 minutes and standard deviation σ = 40 minutes. Then 90% of student finish the assignment within ± _____ minutes from the mean time period.
a 41.6
b 51.2
c 65.6
d 78.6
10) On a different homework assignment the standard deviation of the time spent is 30 minutes. If 20% of students finish the assignment under 115 minutes, then the mean time spent on this assignment is _____ minutes.
a 157
b 153
c 146
d 140
1 solutions
Answer 312137 by stanbon(57347) on 2011-05-26 21:21:13 (Show Source):
You can put this solution on YOUR website!The time spent by students on a particular E270 homework assignment follows a normal distribution with a mean μ = 150 minutes and standard deviation σ = 40 minutes. Then 90% of student finish the assignment within ± _____ minutes from the mean time period.
---
Draw the picture of a normal curve.
Center 90% around the mean.
That leaves a right and a left tail or 5%.
---
The z-value cutoffs are +/-1.645
The corresponding minute values are:
x = 1.645*40 = 65.8 minutes
------------------------------------
a 41.6
b 51.2
c 65.6
d 78.6
------------------------------------
10) On a different homework assignment the standard deviation of the time spent is 30 minutes. If 20% of students finish the assignment under 115 minutes, then the mean time spent on this assignment is _____ minutes.
---
Find the z-value with a 20% left tail.
z = -0.8416
------
Using x = zs+u
115 = -0.8416*30 + u
u = 115 + 25.25
u = 140.25 mminutes
================================
Cheers,
Stan H.
===============
a 157
b 153
c 146
d 140
|
Probability-and-statistics/454457: A coin is tossed 3 times. What is the probability of obtaining at least 1 head?
1 solutions
Answer 312045 by stanbon(57347) on 2011-05-26 15:42:56 (Show Source):
You can put this solution on YOUR website!A coin is tossed 3 times. What is the probability of obtaining at least 1 head?
---
P(at least one head) = 1 - P(no heads in 3 tosses)
---
= 1 - (1/2)^3
---
= 1 - 1/8
---
= 7/8
=============
Cheers,
Stan H.
===============
|
Exponents/454429: use the laws of exponents
5^3/5 * 5^5/10 =
please help.
Thank you
Gina
1 solutions
Answer 312036 by stanbon(57347) on 2011-05-26 13:43:16 (Show Source):
You can put this solution on YOUR website!use the laws of exponents
5^(3/5) * 5^(5/10)
----------------------------------
= 5^[6/10 + 5/10]
----
= 5^[11/10]
----
= 5*5^(1/10)
---
===========
Cheers,
Stan H.
|
Linear-equations/454426: I need help solving the system listed below using the elimination method. I have a particulary hard time when I have to substitute the value of x in the equations.
5x + 5y = -7
7x - 3y = 11
1 solutions
Answer 312034 by stanbon(57347) on 2011-05-26 13:35:48 (Show Source):
You can put this solution on YOUR website!5x + 5y = -7
7x - 3y = 11
----------------
Multiply 1st equation by 7
Multiply 2nd equation by 5
-----
35x + 35y = -49
35x - 15y = 55
----
Subtract and solve for "y":
50y = -104
y = -52/25
-----
Solve for "x":
5x + 5(-52/25) = -7
5x - 52/5 = -35/5
---
5x = 17/5
---
x = 17/25
================
Cheers,
Stan H.
|
Probability-and-statistics/454415: A restaurant offers a choice of 3 salads, 2 entrees, and 4 desserts. How many different meals consisting of a salad, an entrée, and a dessert are possible?
1 solutions
Answer 312031 by stanbon(57347) on 2011-05-26 13:21:13 (Show Source):
You can put this solution on YOUR website!A restaurant offers a choice of 3 salads, 2 entrees, and 4 desserts. How many different meals consisting of a salad, an entrée, and a dessert are possible?
--------------------------
# of meals = 3*2*4 = 24
============================
Cheers,
Stan H.
|
Probability-and-statistics/454418: A teacher finds that the mean score of his class is 72 with a standard deviation of 8. Find the z-score corresponding to 50.
1 solutions
Answer 312030 by stanbon(57347) on 2011-05-26 13:19:35 (Show Source):
You can put this solution on YOUR website!A teacher finds that the mean score of his class is 72 with a standard deviation of 8. Find the z-score corresponding to 50.
--------------------
z(50) = (50-72)/8 = -22/8 = -2.75
=====================================
That means the data value, 50, is 2 3/4 standard
deviations below the mean of the data.
=====================================
Cheers,
Stan H.
|
Graphs/454417: Graph the system of inequalities. y is less than or equal to -5
x is less than or equal to 6. I will need the plot points because I have a really hard time understanding graphing.
1 solutions
Answer 312029 by stanbon(57347) on 2011-05-26 13:15:47 (Show Source):
You can put this solution on YOUR website!Graph the system of inequalities.
To graph an inequality, you must graphthe boundary
which is ALWAYS an equality.
=====
y is less than or equal to -5
Graph y = -5. using points (0,-5) and (2,-5)
Then shade the half-plane BELOW the boundary
because you want y to be LESS than -5.
-------------------------------------------
Note: The above can be shown on this site as follows:
---------------------------------
x is less than or equal to 6.
Graph x = 6 using points(6,0) and (6,5) as a vertical line.
Shade the half-plane to the LEFT of x = 6 because you
want x to be LESS than 6.
--------------
Note: This site cannot graph a vertical line because it
is not a function.
=====================
The solution for the system of inequalities is the intersection
of the two graphs.
------------------------
Cheers,
Stan H.
|
Probability-and-statistics/454322: The probability of an event occurring is 3/8. Find the odds against the event occurring
1 solutions
Answer 312018 by stanbon(57347) on 2011-05-26 12:17:45 (Show Source):
You can put this solution on YOUR website!The probability of an event occurring is 3/8.
Find the odds against the event occurring
---
Prob of event not occurring is 5/8.
----
Odds AGAINST event = P(not E)/P(E) = (5/8)/(3/8) = 5:3
============================================================
Cheers,
Stan H.
|
Rational-functions/454397: Please help me solve this equation I'm having problems in Algebra 2. I have 4 problems I need help with sir I was not sure if I could send all 4. eja
3x - 3
______________
3x + 18
1 solutions
Answer 312016 by stanbon(57347) on 2011-05-26 12:13:31 (Show Source):
You can put this solution on YOUR website! 3x - 3
______________
3x + 18
===================
Factor:
[3(x-1)]/[3(x+6)]
---
Cancle the common "3" factors:
---
= (x-1)/(x+6)
================
Cheers,
Stan H.
=======
|
Radicals/454398: i cant figure out how to solve this radical equation square root of 20-8x=x
1 solutions
Answer 312015 by stanbon(57347) on 2011-05-26 12:11:09 (Show Source):
You can put this solution on YOUR website!square root of 20-8x=x
---
If you meant sqrt(20-8x) = x
Square both sides to get: 20-8x = x^2
x^2+8x-20 = 0
(x+10)(x-2) = 0
Only solution:
x = 2 because sqrt(20-8x) must not be negative.
==========================
Cheers,
Stan H.
|
Money_Word_Problems/454395: you earn $85 on an investment that pays 7% for 18 months. How much did you invest ?
1 solutions
Answer 312014 by stanbon(57347) on 2011-05-26 12:08:12 (Show Source):
You can put this solution on YOUR website!you earn $85 on an investment that pays 7% for 18 months. How much did you invest ?
----
I = Prt
---
P = I/(rt)
----
P = 85/(0.07*1.5)
---
P = $809.52 (amount invested)
===============================
Cheers,
Stan H.
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Trigonometry-basics/454351: How do you solve;
sin(x)+sin(2x)=0
I understand that sin(2x)=2sin(x)cos(x), so here is what I have right now:
sin(x)+2sin(x)cos(x)=0
I don't understand how to factor it any further.
1 solutions
Answer 312013 by stanbon(57347) on 2011-05-26 12:05:04 (Show Source):
You can put this solution on YOUR website!sin(x)+2sin(x)cos(x)=0
I don't understand how to factor it any further.
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Factor out the common factor, sin(x):
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sin(x)[1+2cos(x)] = 0
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sin(x) = 0 or 1+2cos(x) = 0
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sin(x) = 0 or cos(x) = -1/2
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x = 0, or 180 or 240 or 300 degrees
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Cheers,
Stan H.
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Length-and-distance/454393: M(1,2) is the midpoint of line segment RS. If S has the coordinates (8,10), find the coordinates of R
1 solutions
Answer 312012 by stanbon(57347) on 2011-05-26 12:00:53 (Show Source):
You can put this solution on YOUR website!M(1,2) is the midpoint of line segment RS. If S has the coordinates (8,10), find the coordinates of R
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Let the coordinates of "R" be (x,y)
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(x+8)/2 = 1
(y+10)/2 = 2
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x+8 = 2
y+10 = 4
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x = -6
y = -6
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Ans: R(-6.-6)
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Cheers,
Stan H.
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Money_Word_Problems/454223: An installer can carpet a room in 3 hrs, an assistant needs 4.5 hours. If the assistant helps for one hour and then is called away, how long will it take the installer to finish
1 solutions
Answer 311932 by stanbon(57347) on 2011-05-25 22:44:20 (Show Source):
You can put this solution on YOUR website!An installer can carpet a room in 3 hrs, an assistant needs 4.5 hours. If the assistant helps for one hour and then is called away, how long will it take the installer to finish
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Installer rate = 1/3 job/hr
Assistant rate = 1/(9/2) = 2/9 job/hr
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Equations:
work + work = job done
1(2/9) + (1/3)x = 1
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(1/3)x = 7/9
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x = 7/3 = 2 1/3 hrs
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Cheers,
Stan H.
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Linear-systems/454226: how do I Find an equation of the line satisfying the conditions given. Express your answer in standard form. Parallel to 3x – y = -5 and passing through (-1, 0)
1 solutions
Answer 311931 by stanbon(57347) on 2011-05-25 22:08:46 (Show Source):
You can put this solution on YOUR website!how do I Find an equation of the line satisfying the conditions given. Express your answer in standard form.
Parallel to 3x – y = -5 and passing through (-1, 0)
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The given line can be written in slope-intercept form:
y = 3x+5
slope = 3
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Find equation of line with slope = 3 passing thru (-1,0)
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Form: y = mx + b
0 = 3*-1 + b
b = 3
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Equation:
y = 3x+3
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Cheers,
Stan H.
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test/454221: How many 4-digit numbers can you build with a 3, a 4, a 6, and an 8 that are over 6000?
1 solutions
Answer 311930 by stanbon(57347) on 2011-05-25 22:01:11 (Show Source):
You can put this solution on YOUR website!How many 4-digit numbers can you build with a 3, a 4, a 6, and an 8 that are over 6000?
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The thousands digit would have to be 6 or 8, i.e. 2 ways
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Each of the remaining 3 digits can be selected
in 4 ways, if repetition is allowed.
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That would give you 2*4^3 = 2*64 = 128 numbers
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If repetition is not allowed you get 2*3*2*1 = 12 numbers.
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Cheers,
Stan H.
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Probability-and-statistics/452639: Expand using Pascal's Triangle (x-4)^5
1 solutions
Answer 311903 by stanbon(57347) on 2011-05-25 19:38:09 (Show Source):
You can put this solution on YOUR website!Expand using Pascal's Triangle (x-4)^5
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= 5C5x^5 + 5C4x^4(-4) + 5C3x^3(-4)^2 + 5C2x^2(-4)^3 + 5C1x(-4)^4 + 5C0(-4)^5
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= x^5 -20x^4 + 10x^3(16) + 10x^2(-64) + 5x(256) + 1024
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= x^5 - 20x^4 + 160x^3 - 640x^2 + 1280x = 1024
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Cheers,
Stan H.
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Probability-and-statistics/454119: . In 2005, John G. Roberts was nominated by President Bush and confirmed by the Senate to be the 17th U.S. Supreme Court Chief Justice. During the nomination process, John G. Roberts's career as a lawyer and judge was the subject of many studies. For example, Kenneth Manning, associate professor of political science at the University of Massachusetts-Dartmouth presented a research paper titled “How Right Is He?” at the 2005 meeting of the American Political Science Association. In cases where Judge Roberts participated, the study categorized the cases into three types: criminal justice, civil rights, and economic activity. In each case, the study also labeled Judge Roberts's vote as either liberal or conservative. Forty-five cases that could not be clearly categorized for the study were not included. At the 0.01 significance level can we conclude Judge Roberts is more conservative in some types of cases?
Criminal Justice Civil Rights Economic Activity
Liberal 6 2 39
Conservative 38 11 49
1 solutions
Answer 311894 by stanbon(57347) on 2011-05-25 18:57:27 (Show Source):
You can put this solution on YOUR website!At the 0.01 significance level can we conclude Judge Roberts is more conservative in some types of cases?
Criminal Justice Civil Rights Economic Activity
Liberal 6 2 39
Conservative 38 11 49
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Ho: row and column factors are independent
Ha: they are dependent
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I ran a Chi-Sq on the 2 by 3 matrix of data and got the following:
Chi-Sq = 14.496...
p-value = 0.0007119
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Since the p-value is less than 1%, reject Ho.
Roberts opinion position tends to depend on the
type of case.
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Cheers,
Stan H.
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