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Recent problems solved by 'stanbon'
stanbon answered: 57239 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 , 57150..57179 , 57180..57209 , 57210..57239, >>Next
Linear-equations/267795: The cost for burning a 75 watt bulb is given by the function c(h), where h represents the number of hours that the bulb burns.
(a) How much does it cost to burn a 75 watt bulb for 3 hours per night for a 28 day month? Express your answer to the nearest cent.
$
(b) Graph the function c(h) = 0.0055h. (Do this on paper. Your instructor may ask you to turn in this graph.)
(c) Use the graph in part (b) to approximate the cost of burning a 75 watt bulb for 295 hours. (Express your answer to the nearest tenth of dollar.)
$
(d) Use c(h) = 0.0055h to find the exact cost, to the nearest cent, of burning a 75 watt bulb for 295 hours.
$
1 solutions
Answer 196454 by stanbon(57307) on 2010-02-09 20:32:46 (Show Source):
You can put this solution on YOUR website!The cost for burning a 75 watt bulb is given by the function c(h) = 0.0055h, where h represents the number of hours that the bulb burns.
----------------------------
(a) How much does it cost to burn a 75 watt bulb for 3 hours per night for a 28 day month? Express your answer to the nearest cent.
c(3*28) = 0.0055(3*28) = $0.462
----------------------------------
(b) Graph the function c(h) = 0.0055h. (Do this on paper. Your instructor may ask you to turn in this graph.)

------------------------------------------------
(c) Use the graph in part (b) to approximate the cost of burning a 75 watt bulb for 295 hours. (Express your answer to the nearest tenth of dollar.)
$
(d) Use c(h) = 0.0055h to find the exact cost, to the nearest cent, of burning a 75 watt bulb for 295 hours.
c(295) = 0.0055(295) = $1.62
===================================
Cheers,
Stan H.
$
|
Linear-equations/267835: Elevation 27600 feet at 7 am, person reached summit elevation 29028 at 1:25 pm.
Assuming the rate of ascent to be a linear function,
a)Find rate of ascent in feet per minute 1 solutions
Answer 196453 by stanbon(57307) on 2010-02-09 20:24:36 (Show Source):
You can put this solution on YOUR website!Elevation 27600 feet at 7 am, person reached summit elevation 29028 at 1:25 pm.
Assuming the rate of ascent to be a linear function,
a)Find rate of ascent in feet per minute
---------------------
rate = rise/time
rate = (29028-27600)/(6 hr 25 min)
rate = 1428/(6*60+45)
rate = 1428/405
rate = 3.526 ft/min
=========================
Cheers,
Stan H.
|
Probability-and-statistics/267816: If you roll 16 dice, what is the probability of getting at least one six? Express your answer as a decimal, with 5 digits after the decimal point.
1 solutions
Answer 196452 by stanbon(57307) on 2010-02-09 20:20:16 (Show Source):
You can put this solution on YOUR website!If you roll 16 dice, what is the probability of getting at least one six? Express your answer as a decimal, with 5 digits after the decimal point.
----------------------
P(at least one 6) = 1 - P(no 6)
= 1 - (5/6)^16
= 0.9459..
Cheers,
Stan H.
|
Numbers_Word_Problems/267831: Mrs. Donegan opened a book so the sum of the page numbers on the facing pages was 33. Show the pages of her open book...What are the consecutive page numbers? 1 solutions
Answer 196448 by stanbon(57307) on 2010-02-09 20:06:08 (Show Source):
You can put this solution on YOUR website!Mrs. Donegan opened a book so the sum of the page numbers on the facing pages was 33. Show the pages of her open book...What are the consecutive page numbers?
-------------
1st page: x
Next page: x+1
----------------------
Equatiion:
x + x+1 = 33
2x + 1 = 33
2x = 32
x = 16 (1st page)
x+1 = 16 (next page)
========================
cheers,
Stan H.
|
Graphs/267828: The length of a rectangle is 5cm less then 3 times as long as the width. The rectangle has a perimeter of 100. What is the length and width? 1 solutions
Answer 196447 by stanbon(57307) on 2010-02-09 20:03:56 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is 5cm less then 3 times as long as the width. The rectangle has a perimeter of 100. What is the length and width?
---------------------
Let width be "w".
Then length = 3w-5
------
Perimeter = 2(length + width)
100 = 2(3w-5+w)
50 = 4w-5
4w = 55
w = 55/4 = 13 + 3/4 cm
----
length = 3(55/4)-5 = 165/4 - 20/4 = 145/4 = 36 1/4 cm
=========================================================
Cheers,
Stan H.
=========================================================
|
Percentage-and-ratio-word-problems/267823: Hello. I have a problem here that I'm having trouble with. It's a word problem. It says:Sonya made a scale model of the new school in her town. She used a scale of 3/4in.=1ft. If the height of the school model is 48 inches, What is the actual height of the school?
I tried it and I divided 48 by 3/4 then multiplying by 12 because there's 12 in. in a foot. Am I right? And if I'm not can you tell me what I did wrong?
Thank You! 1 solutions
Answer 196445 by stanbon(57307) on 2010-02-09 19:56:41 (Show Source):
You can put this solution on YOUR website!Sonya made a scale model of the new school in her town. She used a scale of 3/4in.=1ft. If the height of the school model is 48 inches, What is the actual height of the school?
------------
Proportion:
x/48" = 1ft/(3/4)"
-----
Cross-multiply to get:
(3/4)x = 48
x = (4/3)*48
x = 4*16
x = 64 ft (height of the school)
====================================
Cheers,
Stan H.
I tried it and I divided 48 by 3/4 then multiplying by 12 because there's 12 in. in a foot. Am I right?
|
Numbers_Word_Problems/267817: Flo is pedalboating on the river. Going downstream their speed is 40 m/min. Coming back upstream their speed is only 26 m/min. How fast do they move through water? How fast is the current going? 1 solutions
Answer 196441 by stanbon(57307) on 2010-02-09 19:46:30 (Show Source):
You can put this solution on YOUR website!Flo is pedalboating on the river.
Going downstream their speed is 40 m/min.
Coming back upstream their speed is only 26 m/min.
-----------------------
Equations:
boat + current = 40 m/min
boat - current = 26 m/min
-------------------------------
2b = 66 m/min
boat speed = 33 m/min
---
Substitute and solve for current:
33 + current = 40
current = 7 m/min
---------------------------
Cheers,
Stan H.
===========================
How fast do they move through water?
How fast is the current going?
|
Probability-and-statistics/267744: The theoretical probability of undesirable side effects resulting from taking Xyclon is 1 in 12. If 120 people take Xyclon to relieve pain from stomach ulcers, theoretically how many will encounter undesirable side effects? 1 solutions
Answer 196435 by stanbon(57307) on 2010-02-09 19:33:38 (Show Source):
You can put this solution on YOUR website!The theoretical probability of undesirable side effects resulting from taking Xyclon is 1 in 12.
If 120 people take Xyclon to relieve pain from stomach ulcers, theoretically how many will encounter undesirable side effects?
Ans: (1/12)(120) = 10
==========================
Cheers,
Stan H.
|
Exponents/267789: (2x^3y/8x^-2y^2)^-2
^=raised to
please help with simplification 1 solutions
Answer 196432 by stanbon(57307) on 2010-02-09 19:26:10 (Show Source):
You can put this solution on YOUR website!(2x^3y/8x^-2y^2)^-2
------
The "negative" in the exponent tells you to invert.
The 2 in the exponent tells you to square each factor
----------------------------
1st simplify inside the parenthesis to get:
---
(x^5/4y)^-2
---
invert to get:
(4y/x^5)^2
---
Square to get:
(16y^2/x^10)
====================
Cheers,
Stan H.
|
Volume/267802: what is the height of a solid with a volume of 120 meters cubic and a base area of 30 meters square? 1 solutions
Answer 196428 by stanbon(57307) on 2010-02-09 19:21:48 (Show Source):
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Polynomials-and-rational-expressions/267799: Can you please do this problem step by step.
x/(x+1)^2 + 2/X+1 1 solutions
Answer 196426 by stanbon(57307) on 2010-02-09 19:20:30 (Show Source):
You can put this solution on YOUR website!x/(x+1)^2 + 2/X+1
--------------------
least common denominator: (x+1)^2
--------------
Rewrite each fraction with the lcd as its denominator:
x/(x+1)^2 becomes x/lcd
2/(x+1) becomes 2(x+1)/lcd
---
The problem is now:
x/lcd + 2(x+1)/lcd
----
Combine the numerators over the lcd:
(x+2(x+1))/lcd
---
(3x+2)/(x+1)^2
=====================
Cheers,
Stan H.
|
Probability-and-statistics/267798: suppose a factory contains two machines. there is a 19 % probability that the first machine will break down and a 22 % chance the second machine breaks down. the two machines are independent.
A. what is probability both machines break down
B. what is the probability AT LEAST one machine breaks down
C. What is probability that only one breaks down.
A. Pr (A and B) = .0418
B. ?
C. ? 1 solutions
Answer 196423 by stanbon(57307) on 2010-02-09 19:12:27 (Show Source):
You can put this solution on YOUR website!suppose a factory contains two machines. there is a 19 % probability that the first machine will break down and a 22 % chance the second machine breaks down. the two machines are independent.
A. probability both machines break down = (0.19)(0.22)
------------------------------------
B. probability AT LEAST one machine breaks down = 1-(p(neither breaks down)
= 1 - [0.81*0.78]
---------------------------------
C. probability that only one breaks down = 1 - P[both break down]-P[neither
breaks down] = 1 - (ans. to A)- 0.81*0.78
================================================
Cheers,
Stan H.
================================================
A. Pr (A and B) = .0418
B. ?
C. ?
|
Probability-and-statistics/267747: The odds in favor of Galloping George winning the horse race are 23:4. Determine the probability that Galloping George wins the horse race. 1 solutions
Answer 196420 by stanbon(57307) on 2010-02-09 19:04:16 (Show Source):
You can put this solution on YOUR website!The odds in favor of Galloping George winning the horse race are 23:4. Determine the probability that Galloping George wins the horse race.
-------------
If odds in favor of winning are a:b, P(winning) = a/(a+b)
--------------
Your problem:
P(GG winning) = 23/27
=============================
Cheers,
Stan H.
|
Rational-functions/267779: computer sale: you have a coupon for $200 off the price of a personal computer. When you arrive at the store, you find that the computers are on sale for 20% off. Let x represent the original price of the computer.
question 28) form the composition of the functions f and g that represents your cost if you use the discount first, then use the coupon.
well I know f(x)=x-$200
g(x)=x-20%
but I don't know how to solve this problem 1 solutions
Answer 196417 by stanbon(57307) on 2010-02-09 19:02:15 (Show Source):
You can put this solution on YOUR website!computer sale: you have a coupon for $200 off the price of a personal computer. When you arrive at the store, you find that the computers are on sale for 20% off. Let x represent the original price of the computer.
question 28) form the composition of the functions f and g that represents your cost if you use the discount first, then use the coupon.
-------------
f(x) = 0.80x
g(x) = x-200
-----
gof(x) = g[f(x)} = g[0.80x] = 0.80x-200
---------------------
Cheers,
Stan H.
================================
well I know f(x)=x-$200
g(x)=x-20%
|
Evaluation_Word_Problems/267753: A woodworking shop makes tables and chairs. To make a chair, 8 min is needed on the lathe and 8 min is needed on the sander. To make a table, 8 min is needed on the lathe and 20 min on the sander. The lathe operator works 6h/day and the sander operator works 7h/day. How many chairs and tables can they make in one day working at this capacity? 1 solutions
Answer 196405 by stanbon(57307) on 2010-02-09 18:15:56 (Show Source):
You can put this solution on YOUR website!A woodworking shop makes tables and chairs.
To make a chair, 8 min is needed on the lathe and 8 min is needed on the sander.
To make a table, 8 min is needed on the lathe and 20 min on the sander.
The lathe operator works 6h/day and the sander operator works 7h/day.
-----------------------------------
How many chairs and tables can they make in one day working at this capacity?
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Lathe Equation:: 8c + 8t = 6*60 minutes
Sander Equation: 8c +20t = 7*60 minutes
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Subtract 1st from 2nd to get:
12t = 60
t = 5 (# of tables that can be produced)
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Substitute into 8c+8t = 6*60 and solve "c":
8c + 8*5 = 6*60
8c = 320
c = 40 (# of chairs that can be produced)
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Cheers,
Stan H.
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Angles/267743: the largest angle in a triangle is 50 degrees more than the smallest angle. the sum of the measures of the smaller 2 angles is 10 degrees more than the largest angle. find the measure of each angle 1 solutions
Answer 196399 by stanbon(57307) on 2010-02-09 18:00:16 (Show Source):
You can put this solution on YOUR website!the largest angle in a triangle is 50 degrees more than the smallest angle. the sum of the measures of the smaller 2 angles is 10 degrees more than the largest angle. find the measure of each angle
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Let the smallest angle = x
Then largest = x+50
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x + 2nd = x+50+10
So 2nd = 60
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Equation:
x + 60 + x+50 = 180
2x + 110 = 180
2x = 70
x = 35 (smallest)
2nd = 60 degrees
x+50 = 85 degrees
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Cheers,
Stan H.
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Probability-and-statistics/267667: In 3 spins of an 8 spot spinner, what is the probability of getting exactly one number that is 5 or less than 7. 1 solutions
Answer 196395 by stanbon(57307) on 2010-02-09 17:50:55 (Show Source):
You can put this solution on YOUR website!In 3 spins of an 8 spot spinner, what is the probability of getting exactly one number that is 5 or less than 7.
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P(get 5 or 1-6) = P(get 5) + P(get 1-6) - P(5 AND 1-6)
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Note: P(5 AND 1-6) = P(get 5)
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So, P(get 5 or 1-6) = P(get 1-6) = 6/8 = 3/4
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Comment: I may not be reading your problem correctly
but that's what it says to me.
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Cheers,
Stan H.
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Probability-and-statistics/267725: A college has an enrollment of 5678 and 24 % of these will graduate and 1250 more students will enroll each year. How many students will there be in 6 years? How many in 15 years.
Thank you 1 solutions
Answer 196392 by stanbon(57307) on 2010-02-09 17:34:26 (Show Source):
You can put this solution on YOUR website!A college has an enrollment of 5678 and 24 % of these will graduate and 1250 more students will enroll each year. How many students will there be in 6 years? How many in 15 years.
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Equation:
N(x) = 5678(0.76)^x + 1250x
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N(6) = 5678(0.76)^6 + 1250*6 = 8594.15
Rounding down N(6) = 8594
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Cheers,
Stan H.
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Probability-and-statistics/267680: Please help with this probability question. Thank You!
A recent survey found that 40% of air traffic controllers found their job extremely stressful. Suppose 12 air traffic controllers are selected at random, what is the probability that 2 or more consider their job stressful?
Thank you very much! 1 solutions
Answer 196389 by stanbon(57307) on 2010-02-09 17:22:57 (Show Source):
You can put this solution on YOUR website!A recent survey found that 40% of air traffic controllers found their job extremely stressful. Suppose 12 air traffic controllers are selected at random, what is the probability that 2 or more consider their job stressful?
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It's a binomial problem:
n= 12 ; p = 0.4
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P(2<= x <=12) = 1 - P(0<= x <=1) = 1 - binomcdf(12,0.4,1) = 0.9804
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Cheers,
Stan H.
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Age_Word_Problems/267633: Robert is one-half as old as his father. Twelve years ago, Robert was one-third as old as his father was then. Find their present ages.
I only got as far as their age now is:
Robert = 1/2 x
Father = x
Twelve years ago:
Father = x-12
Robert = 1/3 (x -12) ??? 1 solutions
Answer 196345 by stanbon(57307) on 2010-02-09 14:34:27 (Show Source):
You can put this solution on YOUR website!Robert is one-half as old as his father. Twelve years ago, Robert was one-third as old as his father was then. Find their present ages.
I only got as far as their age now is:
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Let Father be 2x yrs old
Robert is then x yrs old
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Equation:
(x-12) = (1/3)(2x-12)
3x-36 = 2x-12
x = 24 (Robert's age now)
2x = 48 (Father's age now)
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Cheers,
Stan H.
Robert = (1/2) x
Father = x
Twelve years ago:
Father = x-12
Robert = 1/3 (x -12) ???
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Angles/267634: The ratio of an angle to its supplement is 3:7. Find the ratio of the angle to its complement. 1 solutions
Answer 196341 by stanbon(57307) on 2010-02-09 14:29:44 (Show Source):
You can put this solution on YOUR website!The ratio of an angle to its supplement is 3:7. Find the ratio of the angle to its complement.
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Equation:
x/(180-x) = 3/7
Cross-multiply and solve for "x":
7x = 3(180-x)
7x = 540-3x
10x = 540
x = 54 degrees (the angle)
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Complement = 90-54 = 26
Ratio of angle to complement: 54/26 = 27/13 = 27:13
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Cheers,
Stan H.
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Linear_Algebra/267616: f is a linear function.
1.)
If f(2) = 10 and f(10) = -2, find f(-10) and f(100)
I really have no idea what to do.Help?
Thank You! 1 solutions
Answer 196338 by stanbon(57307) on 2010-02-09 14:24:41 (Show Source):
You can put this solution on YOUR website!f is a linear function.
If f(2) = 10
f(10) = -2
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slope = (10--2)/(2-10) = 12/-8 = -3/2
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Form: y = mx + b
You know m = -3/2 and y = 10 when x = 2.
Solve for "b":
10 = (-3/2)2 + b
b = 13
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Equation:
f(x) = (-3/2)x + 13
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find f(-10) = (-3/2)(-10) + 13 = 28
and f(100) = (-3/2)(100) + 13 = -150 + 13 = -137
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Cheers,
Stan H.
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Quadratic_Equations/267626: . What is the equation for x = 2, 3? Can you also draw the graph 1 solutions
Answer 196337 by stanbon(57307) on 2010-02-09 14:15:51 (Show Source):
You can put this solution on YOUR website!What is the equation for x = 2, 3? Can you also draw the graph
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The graph of x=2 is the vertical line that passes thru
all points where x = 2.
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The graph of x=3 is the vertical line that passes thru
all points where x = 3.
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Cheers,
Stan H.
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Angles/267623: if the measure of an angle is 2x and the measure of its complement is x what is the value of x?
1 solutions
Answer 196336 by stanbon(57307) on 2010-02-09 14:13:21 (Show Source):
You can put this solution on YOUR website!if the measure of an angle is 2x and the measure of its complement is x what is the value of x?
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an angle and its complement add up to 90 degrees.
2x + x = 90
3x = 90
x = 30
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Cheers,
Stan H.
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Angles/267625: True or False
two angles are supplementary. if one angle has a measure twice the other angle what are the measures of the angles? -- supplementary means they add up to 180
1 solutions
Answer 196335 by stanbon(57307) on 2010-02-09 14:09:29 (Show Source):
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Probability-and-statistics/267588: A box contains 30 balls: 20 are red and 10 are blue. Five balls are selected at random, without replacement. What is the probability that four of them are red? What if the five balls are selected at random with replacement (i.e, a selected ball is put back in the box before the next selection is made)? 1 solutions
Answer 196334 by stanbon(57307) on 2010-02-09 14:07:30 (Show Source):
You can put this solution on YOUR website!A box contains 30 balls: 20 are red and 10 are blue.
Five balls are selected at random, without replacement.
What is the probability that four of them are red?
P(r = 4) = (20C4*10C1)/30C5 = 4845/27405 = 0.1768
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What if the five balls are selected at random with replacement (i.e, a selected ball is put back in the box before the next selection is made)?
P(r = 4) = 5C4(2/3)^4(1/3) = 0.3292
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Cheers,
Stan H.
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