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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
Functions/493156: can you please help me with this function,On a trip Alex avrages 300 miles/day.The distance d he covers is a function of the number of days n.
1 solutions
Answer 335297 by stanbon(57203)   on 2011-09-07 18:09:23 (Show Source):
You can put this solution on YOUR website!On a trip Alex avrages 300 miles/day.The distance d he covers is a function of the number of days n.
---------
distance = 300*# of days
================
Cheers,
Stan H.
================
|
Probability-and-statistics/492999: A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting
• an even number ten or less given the card is a not a heart.
• a five given the card is a face card.
• an Ace, given that the card is red.
I am having trouble figuring out the process of coming up with the answers to these questions. could someone please show me how to work these problems out?
1 solutions
Answer 335267 by stanbon(57203) on 2011-09-07 16:39:50 (Show Source):
You can put this solution on YOUR website!
A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting
• an even number ten or less given the card is a not a heart.
Ans = P(even <= 10 AND not heart)/P(not heart)
= (3*4/52)/(3/4)
----
= (3/13)/(3/4)
----
= 4/13
----------------
• a five given the card is a face card.
Ans = P(5 and a face card)/P(face card) = (0/52)/(12/52) = 0
----------------
• an Ace, given that the card is red.
Ans = P(ace and red)/P(red) = (2/52)/(26/52) = 1/13
======================================================
Cheers,
Stan H.
|
Probability-and-statistics/492974: The U.S. Department of Transportation requires tire manufacturers to provide tire performance information on the sidewall of the tire so that a prospective customer can be better informed when making a purchasing decision. One very important measure of tire performance is the tread wear index, which indicates the tire's resistance to tread wear compared with a tire graded with a base of 100. This means that a tire with a grade of 200 should last twice as long, on average, as a tire graded with a base of 100. Suppose that a consumer organization wants to estimate the actual tread wear index of a brand name of tires graded 200 that are produced by a certain manufacturer. A random sample of 18 of these tires produced a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4. Assuming that the population of tread wear indices is normally distributed, compute a 95% confidence interval estimate for the population mean tread wear index for tires produced by this manufacturer under this brand name. Place your answer, rounded to 2 decimal places
1 solutions
Answer 335262 by stanbon(57203) on 2011-09-07 16:28:58 (Show Source):
You can put this solution on YOUR website! This means that a tire with a grade of 200 should last twice as long, on average, as a tire graded with a base of 100.
--------------------
Suppose that a consumer organization wants to estimate the actual tread wear index of a brand name of tires graded 200 that are produced by a certain manufacturer.
--------------------------------
A random sample of 18 of these tires produced a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4.
--------------------------------
Assuming that the population of tread wear indices is normally distributed, compute a 95% confidence interval estimate for the population mean tread wear index for tires produced by this manufacturer under this brand name. Place your answer, rounded to 2 decimal places
---
p-hat = 195.3
ME = 1.96 = 9.8863
===============
95% CI: 195.3 - 9.8863 < u < 195.3 + 0.9963
185.41 < u < 205.19
===============
Cheers,
Stan H.
|
expressions/492882: evaluate functions in equation form:
problem is f(x)=3x(squared) minus 4x plus 1
where f(a-2)
meaning plug in (a-2) where x is in the problem
1 solutions
Answer 335204 by stanbon(57203) on 2011-09-07 12:54:19 (Show Source):
You can put this solution on YOUR website!evaluate functions in equation form:
problem is f(x)=3x(squared) minus 4x plus 1
where f(a-2)
---
f(a-2) = 3(a-2)^2 - (a-2) + 1
----
f(a-2) = 3[a^2-4a+4] - a + 3
---
f(a-2) = 3x^2 -13a + 15
===========================
Cheers,
Stan H.
===================
|
Miscellaneous_Word_Problems/492875: the honda civic GX is the only car offered to consumers in the united states that runs on natural gas and uses no gasoline. it gets 36 miles per gallon of natural gas on the highway and is the cleanest burning automobile engine in the country. although it is listed at $25,189, it is offered at a discount (including rebate on federal taxes) of 18%. find the sale price.
1 solutions
Answer 335203 by stanbon(57203) on 2011-09-07 12:51:18 (Show Source):
You can put this solution on YOUR website!although it is listed at $25,189, it is offered at a discount (including rebate on federal taxes) of 18%. find the sale price.
------------
Let the sale price be "x":
x = 25189- 0.25(25189)
---
x = 0.75*25189
----
x = $18,891.75
====================
Cheers,
stan H.
|
Linear-equations/492864: 4. Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 200 boxes. But when you raise your price to $4 you only sell 120 boxes.
a. Write an equation for the number of boxes you sell as a function of the price you charge.
b. Denote "B" for number of boxes, and "P" for the price you charge.
c. Assume the function is linear..
1 solutions
Answer 335201 by stanbon(57203) on 2011-09-07 12:45:05 (Show Source):
You can put this solution on YOUR website!Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 200 boxes. But when you raise your price to $4 you only sell 120 boxes.
----
You have two points: (3,200) and (4,120)
----
a. Write an equation for the number of boxes you sell as a function of the price you charge.
slope = (200-120)/(3-4) = -80
------
Form: # of boxes = mp + b
Solve for 200 = -80*3 + b
b = 440
------
Equation:
# of boxes = -80(charge) + 440
===================================================
b. Denote "B" for number of boxes, and "P" for the price you charge.
-------
c. Assume the function is linear..
B = -80*P + 440
=====================
Cheers,
Stan H.
==============
|
Numbers_Word_Problems/492783: One number is greater than thrice the other number by 2. If 4 times the smaller
number exceeds the greater by 5, find the numbers
1 solutions
Answer 335187 by stanbon(57203) on 2011-09-07 09:43:29 (Show Source):
You can put this solution on YOUR website!One number is greater than thrice the other number by 2. If 4 times the smaller
number exceeds the greater by 5, find the numbers
-----------------------
Equation:
x = 3*y + 2
4y = x + 5
----
3y + 2 = 4y - 5
y = 7
--
x = 3y+2 = 23
------------
Cheers,
Stan H.
|
Probability-and-statistics/492776: Suppose 75% of chemotherapy patients suffer nausea. We randomly select two such patients (assume these two patients are independent).
i) Find the probability that both suffer nausea
ii) Find the probability that at least one suffers nausea
1 solutions
Answer 335186 by stanbon(57203) on 2011-09-07 09:37:23 (Show Source):
You can put this solution on YOUR website!Suppose 75% of chemotherapy patients suffer nausea. We randomly select two such patients (assume these two patients are independent).
----
i) Find the probability that both suffer nausea:::(3/4)^2 = 9/16
-----
ii) Find the probability that at least one suffers nausea:::
Ans = 1- (1/4)^2
= 1-1/16
= 15/16
=============
Cheers,
Stan H.
=============
|
Mixture_Word_Problems/492778: How much salt must be added to 80 pounds of a 5% salt solution to make a 24% salt solution?
1 solutions
Answer 335185 by stanbon(57203) on 2011-09-07 09:29:40 (Show Source):
You can put this solution on YOUR website!How much salt must be added to 80 pounds of a 5% salt solution to make a 24% salt solution?
-----------
Equation:
salt + salt = salt
0.05*80 + x = 0.24(80+x)
---
Multiply thru by 100 to get:
5*80 + 100x = 24*80 + 24x
---
76x = 19*80
x = 20 lbs (amt of salt needed)
==========
Cheers,
Stan H.
|
Permutations/492769: Suppose that there is a large group of people, consisting of exactly 2N women and 2N men. The group is split in half at random. What is the probability that each half contains exactly N women and N men?
And the second part asks for a given N, set up Stirling's Formula so you can calculate the approx value for a given N.
I am having trouble thinking how to set up this problem. I know as N gets bigger, the possible combinations increase....I'm thinking 2^n.
I also know that the order does not matter, but with each selection you are taking removing someone from the pool of 4N people.
1 solutions
Answer 335183 by stanbon(57203) on 2011-09-07 09:04:17 (Show Source):
You can put this solution on YOUR website!Suppose that there is a large group of people, consisting of exactly 2N women and 2N men. The group is split in half at random. What is the probability that each half contains exactly N women and N men?
----
I don't like the answer I gave you.
----
Question: If the 4N people are split in half
how many split-pairs could there be.
---
We would have to have 2N in each half
--
How many ways can we get a group of 2N people
from a group of 4N people?
That should be (4N)C(2N) = (4N)!/[(4N-2N)!*(2N)!]
= [(4N)(4N-1)...(2N+1)]/[1*2*...(2N)]
---------
Only one of those sets has N women and N men.
----
The probability of there being N women and N men in
each of the halfs would be (1*2*...(2N))/[(4N)(4N-1)...(2N+1)]
------------------
As far as Stirling is concerned I don't know
anything about that.
================
Please post the problem again. Maybe someone else who
sees it can give you more help.
====================================
Cheers,
Stan H.
==============
|
Angles/492770: what is the measurement of the compliment of an angle that measures 80 degrees?
1 solutions
Answer 335182 by stanbon(57203) on 2011-09-07 08:59:28 (Show Source):
You can put this solution on YOUR website!what is the measurement of the complement of an angle that measures 80 degrees?
--------------
The complement of "x" is "90-x".
---
Complement of 80 degrees is 90-80 = 10 degrees
====================
cheers,
Stan H.
|
test/492766: I don't really know how to type this problem but I need help with this inequality | 4t-3 | is less than or equal to 7
1 solutions
Answer 335181 by stanbon(57203) on 2011-09-07 08:52:28 (Show Source):
You can put this solution on YOUR website!| 4t-3 | is less than or equal to 7
----
|4t-3| = 4t-3 if t >= 3/4
|4t-3| = 3-4t if t < 3/4
-------------------------------
Solve if t >= 3/4
4t-3 <= 7
4t <= 10
t <= 10/4
--
Solutions where (3/4)<= t <=(10/4)
========================================
Solve if t < 3/4
3-4t <= 7
4t >= -4
t >=-1
---
Combining those you get -1 <= t <= 10/4
====================================
Cheers,
Stan H.
============
|
Mixture_Word_Problems/492762: 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.
1 solutions
Answer 335179 by stanbon(57203) on 2011-09-07 08:46:54 (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.
---
Equations:
f = 2r
3(r-12) = (f-12)
---
substitute for "f" and solve for "r":
3r - 36 = 2r-12
r = 24 Robert's age now
----
f = 2r
father = 48 yrs old now
==========================
Cheers,
stan H.
==================
|
logarithm/492747: These problems have me stumped, any help would be greatly appreciated!
1. solve for x: (x-3)/2 - 3|2x-1|=-5/3
2. solve for x: log(base 3)(x+3)-log(base3)(x-1)=2
1 solutions
Answer 335177 by stanbon(57203) on 2011-09-07 08:41:36 (Show Source):
You can put this solution on YOUR website!1. solve for x: (x-3)/2 - 3|2x-1|=-5/3
----
|2x-1| = 2x-1 if x >= 1/2
|2x-1| is 1-2x if x < 1/2
-----
Consider x< 1/2 to get:
(x-3)/2 -3(1-2x) = -5/3
x-3 - 6(1-2x) = -10/3
x-3-6+12x = -10/3
13x = -10/3+9 = 17/3
x = 17/39
But 17/39 is not less than 1/2 so no solution in the interval x < 1/2
------------------------
Consider x >= 1/2
(x-3)/2 - 3(2x-1) = -5/3
---
Multiply thru by 6:
3(x-3) - 18(2x-1) = -10
3x-9 -36x+18 = -10
-33x = -19
x = 19/33 which is > 1/2
---
That is the solution.
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2. solve for x: log(base 3)(x+3)-log(base3)(x-1)=2
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log3[x+3)/(x-1)] = 2
---
(x+3)/(x-1) = 9
---
x+3 = 9x-9
8x = 12
x = 3/2
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Cheers,
Stan H.
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Travel_Word_Problems/492757: A car is traveling at 77 miles per hour. What is its speed in m/s?
1 solutions
Answer 335176 by stanbon(57203) on 2011-09-07 08:29:58 (Show Source):
You can put this solution on YOUR website!A car is traveling at 77 miles per hour. What is its speed in m/s?
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77(miles)/hour)(1 hr/3600 sec) = (77*1)/(1*3600)(miles/sec)
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= 0.0214 miles/sec
=========================
Cheers,
Stan H.
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Mixture_Word_Problems/492752: i am trying to get the equation for a mixture problem.
You have 7 ounces of 30% glucose solution. How much 30% glucose solution and how much water needs to be used to make 7 ounces of 20% solution?
my equation i tried is
.30(7) + x = .20(7-x)
is this the right equation to start the problem?
Thank you for the help
1 solutions
Answer 335174 by stanbon(57203) on 2011-09-07 08:24:48 (Show Source):
You can put this solution on YOUR website!You have 7 ounces of 30% glucose solution. How much 30% glucose solution and how much water needs to be used to make 7 ounces of 20% solution?
----------------
Equation:
sugar + sugar = sugar
0.30*7 + 0*x = 0.20(7+x)
----
Multiply thru by 100 to get:
30*7 + 0 = 20*7 + 20x
20x = 10*7
x = 3.5 ounces (amt. of water that should be added)
=================================================
Proof that this is the correct answer:
0.3*7 = 2.1 oz of sugar
0.2(7+3.5) = 0.2(10.5) = 2.1 oz of sugar
=====================
Cheers,
Stan H.
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Divisibility_and_Prime_Numbers/492753: which of the number2,3,4,5,6,9 and10 will divide 1380 or 3510
1 solutions
Answer 335173 by stanbon(57203) on 2011-09-07 08:19:59 (Show Source):
You can put this solution on YOUR website!which of the numbers 2,3,4,5,6,9 and 10 will divide 1380 or 3510
---
Both are divisible by 2,5 and 10
----
3510 is divisible by 9 because the digits add up to a multiple of 9
; so 3510 must also be divisible by 3
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1380 is divisible by 4
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I'll leave the rest to you.
========
Cheers,
Stan H.
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Probability-and-statistics/492609: Ebony has 4 male and 7 female kittens. She picks up 2 kittens to give to a friend. Find the probability of each selection.
P(2 male)
P (2 female)
P (1 of each)
1 solutions
Answer 335172 by stanbon(57203) on 2011-09-07 07:43:42 (Show Source):
You can put this solution on YOUR website!Ebony has 4 male and 7 female kittens. She picks up 2 kittens to give to a friend. Find the probability of each selection.
P(2 male) = 4C2/11C2 = 6/55
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P (2 female) = 7C2/11C2 = 21/55
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P (1 of each) = 1 - [6/55 + 21/55] = 1 - [27/55] = 28/55
============================
Cheers,
Stan H.
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Probability-and-statistics/492305: By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 3.92 seconds.
Answer each of the following (show all work):
(A) How many measurements should be made in order to be 90% certain that the maximum error of estimation will not exceed 2.0 seconds?
(B) What sample size is required for a maximum error of 1.5 seconds?
1 solutions
Answer 335171 by stanbon(57203) on 2011-09-07 07:37:27 (Show Source):
You can put this solution on YOUR website!By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 3.92 seconds.
Answer each of the following (show all work):
(A) How many measurements should be made in order to be 90% certain that the maximum error of estimation will not exceed 2.0 seconds?
---
n = [z*s/E]^2
--
n = [1.645*3.92/2]^2
---
n = 11 when rounded up
============================
(B) What sample size is required for a maximum error of 1.5 seconds?
n = [1.645*3.92/1.5]^2
n = 19 when rounded up
=============================
Cheers,
Stan H.
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Quadratic_Equations/492734: make m the subject of the formula W=(F/M+g/n)^-1
please explain to me how do you do it dont just give me the answer.
1 solutions
Answer 335170 by stanbon(57203) on 2011-09-07 07:29:40 (Show Source):
You can put this solution on YOUR website! make m the subject of the formula W=(F/M+g/n)^-1
----
Invert both sides to get:
(F/M+g/n) = 1/W
----
Subtract g/n from both sides:
F/M = (1/W)-(g/n)
---
Simplify the right side:
F/M = (n-gW)/(nW)
---
Invert both sides:
M/F = (nW)/(n-gW)
---
Multiply both sides by "F":
M = (FnW)/(n-gW)
======================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/492723: hi . the question that i have given to you is wrong . here is the new .
please help to solve this because i need it tomorrow . tank you :)
1 solutions
Answer 335169 by stanbon(57203) on 2011-09-07 07:18:02 (Show Source):
You can put this solution on YOUR website![4/w] + [3w/(w^2-4)] - [(2w+1)/(w^2-4w+4)]
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lcd = w(w+2)(w-2)^2
----
Rewrite each fraction with the lcd as its denominator:
-----
= [4(w+2)(w-2)^2/lcd] + [3w*w(w-2)/lcd] - [(2w+1)w(w+2)/lcd]
----
Combine the numerators over the lcd:
----
= [4(w+2)(w-2)^2 + 3w*w(w-2) - (2w+1)w(w+2)] / lcd
----
I'll leave the rest to you.
Cheers,
Stan H.
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Linear-equations/492724: Tell whether if the equation is Linear or not. If so, write the equation in standard form and give the values of A,B, and C.
The equation is 2x - y/3 = -4
1 solutions
Answer 335168 by stanbon(57203) on 2011-09-07 07:10:06 (Show Source):
You can put this solution on YOUR website!Tell whether if the equation is Linear or not. If so, write the equation in standard form and give the values of A,B, and C.
The equation is 2x - y/3 = -4
---
2x - (1/3)y = -4
Multiply thru by 3 to get:
----
6x - y = -12
That is the standard form:
A = 6
B = -1
C = -12
============
Cheers,
Stan H.
============
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Rectangles/492730: find the perimeter of a rectangular object which has a width of x+4 and a height of x
1 solutions
Answer 335167 by stanbon(57203) on 2011-09-07 07:01:53 (Show Source):
You can put this solution on YOUR website!find the perimeter of a rectangular object which has a width of x+4 and a height of x
---
Perimeter = 2(length + height)
P = 2(x + x+4)
P = 2(2x+4)
P = 4x+8
=========
Cheers,
Stan H.
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Probability-and-statistics/492579: A magazine article cited the numbers on household income in Berea, KY as given by the U.S. Census Bureau. Was a sample or the population used?
Will someone help me please? I don't understand.
1 solutions
Answer 335102 by stanbon(57203) on 2011-09-06 22:33:53 (Show Source):
You can put this solution on YOUR website! A magazine article cited the numbers on household income in Berea, KY as given by the U.S. Census Bureau. Was a sample or the population used?
-----
Although the Census attempts to collect data from every individual family
unit it does not succeed in doing it. Still a Census is considered as having
provided parameters of a population.
---
Congress refuses to authorize random sampling because the Founding
Fathers did not state that in the Constitution. Oh Well!
=============================================================
Cheers,
Stan H.
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Probability-and-statistics/492307: A 90% confidence interval estimate for a population mean was computed to be (49.3, 67.9). Determine the mean of the sample, which was used to determine the interval estimate (show all work).
1 solutions
Answer 335100 by stanbon(57203) on 2011-09-06 22:26:37 (Show Source):
You can put this solution on YOUR website!A 90% confidence interval estimate for a population mean was computed to be (49.3, 67.9). Determine the mean of the sample, which was used to determine the interval estimate
---------------------
The sample mean is the average of the confidence interval limits:
x-bar = (67.9+49.3)/2 = 58.6
=====================================
Cheers,
Stan H.
================
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Probability-and-statistics/492576: A certain type of home security system is triggered in 96% of burglaries. If 6 homes equipped with such a system experience a burglary, find the probability that at least 4 alarms are triggered. Round your answer to four decimal places.
1 solutions
Answer 335095 by stanbon(57203) on 2011-09-06 21:54:50 (Show Source):
You can put this solution on YOUR website!A certain type of home security system is triggered in 96% of burglaries. If 6 homes equipped with such a system experience a burglary, find the probability that at least 4 alarms are triggered. Round your answer to four decimal places.
---
Binomial Problem with n = 6 and p = 0.96
---
P(4<= x <=6) = 1 = P(0<= x <=3) = 1 - binomcdf(6,0.96,3) = 0.9988
===========================================
Cheers,
Stan H.
============================
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Probability-and-statistics/492540: if you roll two number cubes. about how many times can you expect the product of the numbers to be a multiple of 5?
1 solutions
Answer 335091 by stanbon(57203) on 2011-09-06 21:48:00 (Show Source):
You can put this solution on YOUR website! if you roll two number cubes. about how many times can you expect the product of the numbers to be a multiple of 5?
--------
Multiples of 5 when you roll 2 dice: 1/4;2/3;3/2;4/1;4/6;5/5;6/4
---
Ans: 7 of 36 outcomes are multiples of 5
=========================================
Cheers,
Stan H.
================
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Probability-and-statistics/492311: A confidence interval estimate for the population mean is given to be (45.37, 53.91). If the standard deviation is 12.604 and the sample size is 58, answer each of the following (show all work):
(A) Determine the maximum error of the estimate, E.
(B) Determine the confidence level used for the given confidence interval.
1 solutions
Answer 335084 by stanbon(57203) on 2011-09-06 21:13:31 (Show Source):
You can put this solution on YOUR website!A confidence interval estimate for the population mean is given to be (45.37, 53.91). If the standard deviation is 12.604 and the sample size is 58, answer each of the following (show all work):
(A) Determine the maximum error of the estimate, E.
The width of the confidence interval is ALWAYS 2E
2E = (53.9-45.37)
2E = 8.53
E = 4.265
---------------------
(B) Determine the confidence level used for the given confidence interval.
ME = z*s/sqrt(n)
---
4.265 = z*12.604/sqrt(58)
12.604*z = 4.265*sqrt(58)
z = 2.5771
---
Find the right tail for z = 2.5771
normalcdf(2.5771,100) = 0.005
---
The confidence level = 2*0.005 = 1%
=======================================
Cheers,
Stan H.
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Probability-and-statistics/492507: joanne has a roll of ribbon 6 feet long. She needs pieces that are 3/4 feet long . If she cuts the whole, how many pieces can she made ?
1 solutions
Answer 335082 by stanbon(57203) on 2011-09-06 21:02:56 (Show Source):
You can put this solution on YOUR website!joanne has a roll of ribbon 6 feet long. She needs pieces that are 3/4 feet long . If she cuts the whole, how many pieces can she made ?
---
Ans = 6/(3/4) = 6*(4/3) = 2*4 = 8 pieces
=============
Cheers,
Stan H.
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