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Ho: Ux=Uy=Uz
Ha: not all are equal
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compute the sum squares for between groups x,y,z
SSB=sum(ni*(Xi-Xbar)^2) where ni=sample size for group i, Xi=sample average for group i, and Xbar=overall average.
ni=25 for each group, Xx=5,Xy=4,Xz=6, Xbar=5
SSB=25*(0^2+(-1)^2+1^2)=50
degrees of freedom= k-1=3-1=2, k=number of groups
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Compute the sum squares for the error
SSE=sum((ni-1)*Si^2)=24*(2+1.5+2.5)=144
degrees of freedom= k(ni-1)=3(25-1)=3*24=72, k=number of groups
--
Compute Mean sum of squares for between groups and error
MSB=SSB/dof=50/2=25
MSE=SSE/dof=144/72=2
--
compute F statistic= MSB/MSE=25/2=12.5
--
determine the critical F value for alpha 0.05, num dof=2, denom dof=72
Fcritical= 3.12
--
Since Fstatistic > Fcritical then reject Ho and conclude
The universities differ in their average time socializing

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i've answered this problem already #394674

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loan P=7400
annual interest=0.109
term=3years
compounded monthly
Final =7400*(1-0.109/12)^(3*12)=5328.05

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A n B = {6,7}
--
not sure what you mean by C(AnB) is this CU(AnB) or Cn(AnB)? or something else like the complement

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the simplest way is to put them in standard form:
y=b+mx where b=y intercept and m=slope
--
if both lines have the same "m" (or slope) they are parallel

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let A =error found by test 1
let B=error found by test 2
let C=error found by test 3
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Given P(A)=0.2, P(B)=0.3, P(C)=0.5
therefore P(notA)=0.8, P(notB)=0.7, P(notC)=0.5
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Note: tests are independent P(notA & notB & notC)=P(notA)*P(notB)*P(notC)=0.8*0.7*0.5=0.28
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P(found by at least one test)= 1- P(not found by any test)=1-P(notA & notB & notC)=1-0.28=0.82

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In the following example what does the [ mean and why are { } used after the = sign and why is the I between the two x's. [a,oo)= {xIx > a} (there is a line under the greater than sign, I do not know what the symbol means)
My name is Dolly and my email is elkm@suddenlink.net
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in mathematics (and many other disciplines), there are short hand or short cuts for saying something.
a "[" means that the value is included, a ")" means the value is not included
"{}" is a way to say the set of numbers
the "I" is really not an I, but a short line to imply the meaning "such that"
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so [a,oo) means all values between a and infinity including a but since we do not know what infinity is it is left unincluded.
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{xIx > a} this means the set of x numbers, such that x is greater than a.
of course this statement is wrong since they are trying to define [a,oo) which includes "a". So the statement should look as [a,oo)= {xIx >= a}, its missing teh equal sign to show that it includes "a"

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use the binomial expansion = (Cn,n)*+(Cn,1)b+...(Cn,0)*
where Cnx= combinations= n!/[x!*(n-x)!] and comes from pascal triangle. Are you familiar with that?
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in your case
a=3
b=
n=3

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my mistake
I should have used combinations instead of permutations since order does not matter
small pizza: 8C3=336/6=56
medium pizza: 8C4=1680/24=70
large pizza: 8C5=6720/120=56
total pizzas= 56+70+56=182
==
ignore below
these answers do not make sense!
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for the small pizza there are 8P3=8*7*6=336 different types of small pizzas
for the medium pizza there are 8P4=8*7*6*5=1680
for the large pizza there are 8P5=8*7*6*5*4=6720
so there should be 336+1680+6720=8736 different pizzas

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let MB=prob with motherboards
let HD problems with hard drive
P(problems with MB or HD)=P(MB U HD)=P(MB)+P(HD)-P(MB n HD)=0.4+.3-.15=.7-.15=.55
--
This means that P(no MB or HD)= 1-0.55=0.45

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p(sandy wins/she goes first)=0.6
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reasoning
on her first try, she has 1/5 chance of getting the "3" tile and wins
if she does not get the "3" tile, then clause has 3/4 of not getting the "3" tile since there are only 4 tles left and the game can continue.
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On Sandy's second try, there are only 3 tiles left and for Sandy to get a second chance to win, she must of failed the first time 4/5 chance and Claude must of failed 3/4 chance and for Sandy to win in the second try she has 1/3 chance so Sandy can win on the second try with 4/5*3/4*1/3=1/5
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If Sandy does not win of the second, she gets a third try if she failed on the first and Claude failed oh his first and sandy failed on her second and cluade failed on his second and finally Sandy tries a 3rd time. This can happen by Sandy failing on first 4/5 chance, Claude failing first 3/4 chance, sandy failing on second 2/3 chance and claude failing on his second with 1/2 chance
or 4/5*3/4*2/3*1/2=1/5
after this there are no more tiles
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So sandy wins by going first if she wins on the first try, or second try or 3rd try = 1/5+1/5+1/5=3/5=0.6

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switch x and y and solve for y
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y=3x+5 then the inverse is found by switching variables x=3y'+5 and solving for y'
y'=(x-5)/3 this is the inverse

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3.Among employees of a certain firm, 70% know C/C++, 60% know Java, and 50% know both languages. What portion of programmers
a. does not know Java?
=1-0.6=0.4
b. does not know Java and C/C++?
know only C/C++=.7-.5=.2, know only java=.6-.5=0.1, know both=0.5
knows java or C/C++=.2+.5+.1=0.8
neither=1-.8=0.2
c. knows C/C++ but not Java?
.7-.5=0.2
d. knows Java but not C++?
.6-.5=0.1
e. If someone knows Java, what is the probability that he/she knows C/C++?
P(C/java)=P(both)/P(java)=0.5/.6=5/6
f. If someone knows C/C++, what is the probability that he/she knows Java?
P(java/C)=P(both)/P(C)=0.5/.7=5/7

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if the viruses are truly independent then
probability that the system gets damaged=
P(AUBUC)=P(A)+P(B)+P(C)-P(AnB)-P(anc)-P(bnc)+P(AnBnC)=
0.4+0.5+0.2-0.4*0.5-0.4*0.2-0.5*0.2+0.4*0.5*0.2=1.1-0.2-0.08-0.1+0.04
=0.76

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a system has no solution when the equations never meet or have no points of interception.
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a system has infinite solutions when the equations are one and the same, they just look different

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-3|x+5|=-9
==
first isolate the absolute expression
|x+5|=3 divide by -3
eliminate the absolute signs
x+5=3 or x+5=-3
solve for x
x=-2 or x=-8

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1)The hypothenuse of right triangle is 15cm. the sum of the legs is 21cm. Find the legs of triangle.
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Given: c=15, a+b=21
thus a=21-b
Pythagoream theorem: c^2=a^2+b^2




b=18/2=9 or b=24/2=12
Thus the legs of the triangle are a=21-b=21-9=12, b=9,c=15
===
2)A lidles box is constructed from a square piece of tin by cutting a 10cm square from each corner and bending up the sides for the box. if the volume of the box is 1200cm^3,find the dimensions to the nearest tenth of centimetre
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The base of the box will be square and measure x-2*(10)=x-20
The volume of the box: length*width*height= (x-20)*(x-20)*10=1200
therefore
(x-20)^2=120
x^2-40x+400=120
x^2-40x+280=0
use the quadratic formula
x=(40-21.9)/2=9.05 or x=(40+21.9)/2=30.95
since the base has dimensions x-20 and x-20, x has to be greater than 20
so x=9.05 cannot be one of the answers.
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Dimensions of the box length*width*height=30.95-20, 30.95-20,10
or 10.95,10.95,10

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Avg Cost/bike =
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This is a parabola with its "a" coefficient 0.1 being positive so the curve opens upward indicating that the vertex is a minimum. vertex is located at x=-b/(2a)= -(-0.4)/(2*0.1)=2, so the shop should build 200 bikes to minimize average cost
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Another way to do this is to take the first derivative of the avg cost function
this gives the instantenous slope and we want to find the extremas which occur when the instantenous slope=0 (also known as critical points)
0.2x-0.4=0
x=2 or 200 bikes since x is in hundreds of bikes.
to determine if this is a minimum or maximum extrema, take the second derivative
C"(x)=0.2 since this is positive at the critical point (and all points in this case) this means that it curves upward and the critical point is a minimum

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Find the x-intercepts and y-intercepts.

--
x intercepts occur when y=0


0=(x+6)*(x-8); x=-6 or x=8
(-6,0), (8,0)
--
Y intercepts occur when x=0
=48
(0,48)

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A piece of work can be done in 48 days by 40 men. After 15 days, 16 men were transferred. In how many days can the remaining men finish the work?
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40 men can do the job in 48 days, this means that 40 men can do 1/48 of the job each hour
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after 15 hours: 15/48 of the job is completed and 33/48=11/16 of the job incomplete
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16 men are transferred. That leaves 24 men to complete the job.
each man worked at a rate of 1/(48*40) (assuming they all work at the same rate).
So the remaining 24 men work at the rate of 24/(48*40)=1/80
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11/16 of the job needs to be done by a crew of 24 working at a rate of 1/80 per hour.
Job=rate *time or time =job/rate=(11/16)/1/80)=80*11/16=55hours

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It is known that
The sum of the interior angles of a "n" sided polygon is =(n-2)*180
--
assuming that all the interior angles are equal, then a single interior angle will measure (n-2)*180/n
==
Since you state that the interior angle is 90 then
(n-2)*180/n=90
180n-360=90n
90n=360
n=4

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d-distance to make up= 7.5 km
r=speed differential= 5kph
--
d=r*t or t=d/r
==
t=7.5/5=1.5 hours or 90 minutes

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The trains meet somewhere between station a and station b
--
let train 1 "from" station a
let train 2 "from" station b
let d1=distance train 1 travels after meeting train 2
let d2=distance train 2 travels after meeting train 1
let r1=rate of train 1
let r2=rate of train 2
let t=time when trains meet
distance =rate * time or d=r*t
==
from meeting point to station a: train 1 has travelled r1*t
and train 2 will travel 4 hours to get to station a or r2*4
so... r1*t = r2*4
--
likewise
r2*t=r1*9
--
solving for t: r2*4/r1=t and r1*9/r2=t
4*r2/r1=9*r1/r2
4r2^2=9*r1^2 (cross multiply)
2*r2=3*r1
2*r2/3=r1
--
we also know that the total distance is 300, so
d1+d2=300
4*r2+9*r1=300
4*r2+9*(2*r2/3)=300
4*r2+6r*2=300
10*r2=300
r2=30
r1=2*r2/3=20

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8. What do you need to know about the front upper plate and the front lower plate in order to show that any upper plate and any lower plate lie in parallel planes? Explain your reasoning.
==
I suppose you need to know that the distances in all places between the front upper plate and the front lower plate are always the same, this would insure that they lie in parallel plates.

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let t=time for smaller pipe to fill tank
let t-1 =time for larger pipe to fill tank
let c=tank capacity
==
Given
small pipe rate = 20 liters per minute
large pipe rate=25 liters per minute
==
use formula: tank capacity=rate * time
--
small pipe; tank capacity c=20*t
large pipe: tank capacity c=25*(t-1)
--
since tank capacity is the same for both pipes
20*t=25*(t-1)
20*t=25*t-25
25=5*t
5=t
--
answer: it takes the small pipe 5 minutes to fill the tank

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The answer depends on whether you are selecting with replacement of the selected numbers or without replacement of the selected numbers.
===
In order for the two numbers to sum to 3, the numbers selected must be 1 and 2.
--
Without replacement:
Probability of selecting 1 and 2=P(1,2)+P(2,1)=1/8*(1/7)+1/8*(1/7)=2/56=1/28
--
with replacement:
P(1,2)+P(2,1)=1/8*(1/8)+1/8*(1/8)=2/64=1/32

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car will catch up to the bike when
the distance for the car = distance for the bike
--
distance =rate * time
--
distance bike= head start distance + distance after car leaves
= 12mph*3 hours + 12mph*t = 36+12t
distance car=30mph * t
--
set distance bike=distance car
36+12t=30t
36=18t
36/18=2=t
--
answer: the car will catch the bike in 2 hours after the cars leaves.

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Surface area for cylinder: bottom+side+top
Bottom area=pi*r^2
Top area=pi*r^2
side area= 2*pi*r*h
--
if r=3in, h=5in then
surface area= bottom+top+side
=pi*(3)^2+pi*(3)^2+2*pi*(3)*(5)
=18*pi+30*pi=48*pi

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the greater of two consecutive odd integers is 7 greater than twice the lesser. Find the integers
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Let the two integers be X and (X+2)
--
Given: greater odd=7+2lesser
X+2=7+2X
2-7=2X-X
-5=X
--
answer:
Lesser: X=-5
Greater: X+2=-5+2=-3
--
verify
-3=7+2*(-5)

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In the sequence you provide each number changes by an "constant" value.
This is known as an arithmetic sequence
--
The change, or is the difference between any two values, so in this case =2
--
For an arithmetic sequence, the nth term =
and for an arithmetic series, its sum is defined as the average value times the number of terms or Sum=
==
in the sequence you provide, =3 and the last term
--
The sum = average value * n =

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20. What is the probability that exactly one card is a spade?
P(Spade followed by NonSpade + Nonspade followed by Spade)=
(13/52)*(39/51)+(39/52)*(13/51)
21. What is the probability that at least one card is a spade?
=1-P(both NonSpade) = 1-39/52*(38/51)
22. What is the probability that both cards are face cards?
P(face followed by face)=16/52*(15/51)
23. What is the probability that both cards are spade face cards?
=4/52*(3/51)
====
50. What is the probability of getting the first two questions correct?
P(CC)=1/2*1/2=1/4
52. What is the probability of getting all four questions correct given that the answers to the first two questions are correct?
P(four correct/first two correct)=P(last two correct)=1/2*(1/2)=1/4