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Recent problems solved by 'stanbon'
stanbon answered: 57351 problems
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2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359, >>NextExpressions-with-variables/74599: Someone Pleeze help explain this to me
Find the domain of f(x) = 7+(square root sign) 3x +21 and express it using interval notation.
I am so lost
Thanx for anyones help
1 solutions
Answer 53580 by stanbon(57424)   on 2007-03-15 20:52:39 (Show Source):
You can put this solution on YOUR website!Find the domain of f(x) = 7+(square root sign) 3x +21 and express it using interval notation.
--------------
y = 7 + sqrt(3x+21)
That 3x+21 must not be negative; it must be greater than or equal to zero
so that y can be a Real numberl
----------
So, 3x+21>=0
3x>=-21
x>=-7
--------------
So, Domain is all Real numbers x>=-7
==========
Cheers,
Stan H.
|
Functions/74600: what are the domains of these expressions? How do I find these domains?
1). the sqrt of 2-x
2). x-3 over x+2
3). 3x^2 +2x -8
1 solutions
Answer 53579 by stanbon(57424) on 2007-03-15 20:48:48 (Show Source):
You can put this solution on YOUR website!Find Domain of the following:
Domains are unrestricted unless certain x-values result in
non-Real numbers or produce denominators of zero.
1). the sqrt of (2-x
To avoid non-Real number results 2-x >=0; x<=2
So, Domain is all Real numbers x<=2
--------------
2). x-3 over x+2
To keep the denominator a non-zero value, x must not be -2
So, Domain is all Real numbers except x=-2
--------------
3). 3x^2 +2x -8
X can take on any value.
So, Domain is all Real numbers.
==============
Cheers,
Stan H.
|
Linear-equations/74603: what point lies in the solution set for the following system:
4x+y<1
8y-3x>24
1 solutions
Answer 53578 by stanbon(57424) on 2007-03-15 20:40:50 (Show Source):
You can put this solution on YOUR website!4x+y<1
8y-3x>24
--------------
Rewrite as:
4x+y=1
-3x+8y=4
------------
Multiply 1st equation by 8 to get:
32x+8y=8
-3x+8y=4
---------
Subtract to get:
35x=4
x=4/35
--------
Substitute to solve for "y"
4(4/35)+y=1
y = 35/35-16/35 = 19/35
-----------
The lines cross at (4/35,19/35)
Sketch the line y=-4x+1 the point you want must be below it (less y value)
such as (4/35,0)
=========
Cheers,
Stan H.
|
Probability-and-statistics/13026: Alexia has spread her collection of 20 rectangular stamps on a circular table. the table is 4ft in diameter, and each of the stamps is 2 in.x 1 1/2 in. Unfortunatley, a drop of ink from Alexia's pen flies off and lands randomly somewhere on the table. what is the probability that the tink will land on one of her stamps?
1 solutions
Answer 53577 by stanbon(57424) on 2007-03-15 20:13:24 (Show Source):
You can put this solution on YOUR website!Alexia has spread her collection of 20 rectangular stamps on a circular table. the table is 4ft in diameter, and each of the stamps is 2 in.x 1 1/2 in. Unfortunatley, a drop of ink from Alexia's pen flies off and lands randomly somewhere on the table. what is the probability that the tink will land on one of her stamps?
-----------
Area of one stamp = 2*(3/2)= 3 sq in
Area of 20 stamps = 20*3 sq in = 60 sq in
--------------
Area of circle = (pi)(24 in)^2
------------
Prob (ink lands on stamp) = 60/[24^2 * pi] = 0.033...
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/74598: anybody good at parabolas?
on my "Y" axis from 1 through 5 the top of the parbola (known as V(-3,4)) is at 4 where it begins its downward peak.
on the "X" axis the right leg comes through -1 curves through the "Y" axis of 4 and the left leg goes back down through -5 on the "x" axis.
Question: Determine the standard equation of the parabola.
I know you people are whizzes and I would really be impressed. I have missed every question concering parabolas.
Thank you
1 solutions
Answer 53576 by stanbon(57424) on 2007-03-15 20:05:52 (Show Source):
You can put this solution on YOUR website!on my "Y" axis from 1 through 5 the top of the parbola (known as V(-3,4)) is at 4 where it begins its downward peak.
on the "X" axis the right leg comes through -1 curves through the "Y" axis of 4 and the left leg goes back down through -5 on the "x" axis.
Question: Determine the standard equation of the parabola.
----------------------------
The V point is the vertex.
The vertex form of this parabola that opens downward is (x-h)^2 = 4p(y-k)
where (h,k) is the vertex.
So, (x+3)^2=4p(y-4)
When x=-5, y=0 so substitute and solve for "p".
(-5+3)^2 = 4p(0-4)
4=4p(-4)
p=-1/4
EQUATION:
on my "Y" axis from 1 through 5 the top of the parbola (known as V(-3,4)) is at 4 where it begins its downward peak.
on the "X" axis the right leg comes through -1 curves through the "Y" axis of 4 and the left leg goes back down through -5 on the "x" axis.
Question: Determine the standard equation of the parabola.
(x+3)^2=4(-1/4)(y-4)
(x+3)^2 = -y+4
y=-(x+3)^2+4
In standard form:
y=-x^2-6x-5
=============
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/74577: Determine whether each of the following is a trinomial square.
1. x^2-14x + 49
2. x^2-10x - 25
3. 36x^2-24x+16
4. 16x^2-40xy+25y^2
5. 9x^2 - 36x + 24
Can someone please help? Thank you!!
1 solutions
Answer 53574 by stanbon(57424) on 2007-03-15 19:50:52 (Show Source):
You can put this solution on YOUR website!Determine whether each of the following is a trinomial square.
Conditions: 1st and 3rd terms are perfect squares
2nd term is + or - twice the product of the square roots of 1st and 3rd
1. x^2-14x + 49 -------yes
2. x^2-10x - 25 -------yes
3. 36x^2-24x+16 -------no; middle term is not 2(6x)(4)=48x
4. 16x^2-40xy+25y^2 -----yes
5. 9x^2 - 36x + 24 ------no; 24 is not a perfect square
---------------
Cheers,
Stan H.
|
Trigonometry-basics/74591: Use the formula a(sub1) + a(sub1)r + a(sub1)r^2 + ...+ a(sub1)r^n-1 = a(sub1) 1-r^n/1-r for the nth partial sum of a geometric sequence to find the sume 1 + 2/3 + 4/9 + 8/27 + ... + 64/729.
1 solutions
Answer 53571 by stanbon(57424) on 2007-03-15 19:33:29 (Show Source):
You can put this solution on YOUR website!find the sum 1 + 2/3 + 4/9 + 8/27 + ... + 64/729.
The last term is (2/3)^6 and it is the 7th terms because the
series begins with (2/3)^0.
----------
The sum is S(7) = [(2/3)^8 -1]/[(2/3)-1) = 2.8829....
=========
Cheers,
Stan H.
|
Trigonometry-basics/74592: Five fair coins are tossed. Find the probability of obtaining 4 heads and
1 tail.
1 solutions
Answer 53565 by stanbon(57424) on 2007-03-15 19:09:09 (Show Source):
You can put this solution on YOUR website!Five fair coins are tossed. Find the probability of obtaining 4 heads and
1 tail.
---------------
The result for each coin is independent of the result for each other coin.
----------
P(H)=1/2 ; P(T)=1/2
The result you are looking for can be
THHHH
HTHHH
HHTHH
HHHTH
HHHHT
---------
These are "mutually exclusive" events and each has probability (1/32)^5=1/32
Because these events are mutually exclusive you add the probabilities to get:
P(4 heads and a tail) = 5(1/2)^5 =5/32
==============
Cheers,
Stan H.
|
Mixture_Word_Problems/74584: If you mix 140mL of a 60% acid solution with 200 mL of a 30% solution you get a 40 mL of a _______% solution.
1 solutions
Answer 53562 by stanbon(57424) on 2007-03-15 18:59:06 (Show Source):
You can put this solution on YOUR website!If you mix 140mL of a 60% acid solution with 200 mL of a 30% solution you get a 40 mL of a _______% solution.
-----------------------
60% solution DATA:
Amt = 140 ml ; Amt of acid = 0.6*140 = 84 ml
--------------------
30% solution DATA:
Amt = 200 ml ; Amt of acid = 0.3*200 = 60 ml
-------------------
x% solution DATA:
Amt ; 40 ml ; Amt of acid = 40x ml
--------------------------
EQUATION:
acid + acid = acid
84 +60 = 40x
144 = 40x
x= a percentage greater than 100%
COMMENT: Something is not stated right in your posting.
Maybe 40 ml should be 400 ml !!!!!!!
===============
Cheers,
Stan H.
|
Graphs/74585: Please help me understand this
If points A,B, and C lie on a coordinate line and points A and B have coordinates 15 and 7 respectively, then which of the possible coodinates for point C satisfy(ies) d(A,C) < d(B,C)
Thanks to anyone who takes the time to teach me this
1 solutions
Answer 53553 by stanbon(57424) on 2007-03-15 18:36:13 (Show Source):
You can put this solution on YOUR website!If "c" is the coordinate of C, then the
coordinate value is between eleven and fifteen.
Any of these coordinates will result in
the distance from A to C is less than the
distance from B to C.
-----------
Cheers,
Stan H.
|
Probability-and-statistics/74581: Given a normal distribution with µ = 100 and σ = 10, if you select a sample of n = 25, what is the probability that X bar is
a. less than 95?
b. Between 95 amd 97.5?
c. Above 102.2?
d. There is a 65% chance that X bar is above what value?
1 solutions
Answer 53552 by stanbon(57424) on 2007-03-15 18:18:48 (Show Source):
You can put this solution on YOUR website!Given a normal distribution with µ = 100 and sigma = 10, if you select a sample of n = 25, what is the probability that X bar is
a. less than 95?
z(95) = (95-100)/10/sqrt25) = -5/2 = -2.5
P(xbar<95)=P(z<-2.5)=0.006
-------------
b. Between 95 amd 97.5
z(95)=-2.5 ; z(97.5) = (97.5-100)/10/5=-2.5/2=-1.25
P(95
--------------
c. Above 102.2?
z(102.2)=(102.2-100)/2=1.1
P(xbar>102.2)=P(z>1.1)=0.135666...
---------------
d. There is a 65% chance that X bar is above what value?
The corresponding z-value is z=-0.38532...
Converting to raw score: -0.38532 = (xbar-100)/2;
xbar=2*(-0.38532)+100
xbar=99.23
-------------
======================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/74570: Hi. Im studing for a test and im having some problems. I was wondering if anyone can help me. I would really appreciate it. I have 4 questions.
1) Translate into algebraic expression.
The Difference between five times the input and seve.
2) six times the input, added to 8
3) Solve the problem
Write a symbolic rule that represents the relationship in which the output variable t is 5 more than 3.5 times the input variable r. What is the input corresponding to an output value of 26?
4) Write a symbolic rule that represents the relationship in which the output variable t is 7 more than 2.5 times the input variable r. What is the corrisponding to an input value of 8?
1 solutions
Answer 53542 by stanbon(57424) on 2007-03-15 16:29:58 (Show Source):
You can put this solution on YOUR website!1) Translate into algebraic expression.
The Difference between five times the input and seven.
Let the input be "x":
5x-7
-------------
2) six times the input, added to 8
6x+8
-----------------
3) Solve the problem
Write a symbolic rule that represents the relationship in which the output variable t is 5 more than 3.5 times the input variable r.
t=3.5r+5
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What is the input corresponding to an output value of 26?
t=3.5*26 +5
t = 91+5 = 96
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4) Write a symbolic rule that represents the relationship in which the output variable t is 7 more than 2.5 times the input variable r.
t = 2.5r+7
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What is the corrisponding to an input value of 8?
t = 2.5*8+7
t = 27
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Cheers,
Stan H.
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Rational-functions/74573: I don't know if this is in the correct area but, I will try anyways.
I don't understand how to get Rational Zeros from this equation at all.
The equation is 2x^3+4x^2-22x-24.
1 solutions
Answer 53540 by stanbon(57424) on 2007-03-15 16:13:01 (Show Source):
You can put this solution on YOUR website!2x^3+4x^2-22x-24=0
x^3+2x^2-11x-12 = 0
Notice that f(-1)=0 so x=-1 is a zero.
Use synthetic division to find the quotient after dividing by (x+1):
-1....1....2....-11....-12
.......1....1.....-12..|..0
So, x^2+x-12 is the other factor after dividing:
It factors into (x+4)(x-3)
Therefore x=-4, and x=3 are also zeroes.
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Cheers,
Stan H.
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Probability-and-statistics/74534: use this data.
subject actually told the truth and polygraph indicated truth 65
subject actually told the truth and polygraph indicated lie 15
subject actually told a lie and polygraph indicated truth 3
subject actually told a lie and polygraph indicated lie 17
Q1. If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told a lie.
Q2.If 1 of the 100 subjects is randomly selected, find the probability of getting someone for whom the polygraph test indicted that a lie was being told.
Q3.If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told a lie or had the polygraph test indicated that a lie was being told.
Q4.If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told the truth or had the polygraph test indicate that the truth was being told.
Q5. If 2 diffrent subjects are randomly selected, find the probability that they both told the truth.
Q6.If 2 different subjects are randomly selected, find the probability that they both had the polygraph test indicate that a lie was being told.
Q7.If 1 subject is randomly selected, find the probability that he or she told the truth, given that the polygraph test indicated that a lie was being told.
Q8. If 1 subject is randomly selected, find the probability that he or she has a polygraph test indication that a lie was being told, given that the subject actually told the truth.
Thank you i look forward to your answers.
1 solutions
Answer 53539 by stanbon(57424) on 2007-03-15 16:00:36 (Show Source):
You can put this solution on YOUR website!subject actually told the truth and polygraph indicated truth 65
subject actually told the truth and polygraph indicated lie 15
subject actually told a lie and polygraph indicated truth 3
subject actually told a lie and polygraph indicated lie 17
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Draw a "Contingency Table" with
two rows: Poly said true;and Poly said lied
two columns: Acutually told truth; Actually Lied
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Q1. If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told a lie.
(3+17)/100 = 1/5
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Q2.If 1 of the 100 subjects is randomly selected, find the probability of getting someone for whom the polygraph test indicted that a lie was being told.
(15+17)/100 = 32/100
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Q3.If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told a lie or had the polygraph test indicated that a lie was being told.
(20+3-17)/100 = 35/100
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Q4.If 1 of the 100 subjects is randomly selected, find the probability of getting someone who told the truth or had the polygraph test indicate that the truth was being told.
(80+68-65)/100 = 83/100
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Q5. If 2 different subjects are randomly selected, find the probability that they both told the truth.
80C2/100C2 = 0.638...
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Q6.If 2 different subjects are randomly selected, find the probability that they both had the polygraph test indicate that a lie was being told.
32C2/100C2 = 0.100...
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Q7.If 1 subject is randomly selected, find the probability that he or she told the truth, given that the polygraph test indicated that a lie was being told.
P(told truth|poly said lied) = 15/32
To get this " look only at the "poly said lied" row which has a total of 32
Then find the intersecting box for "told the truth" = 15
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Q8. If 1 subject is randomly selected, find the probability that he or she has a polygraph test indication that a lie was being told, given that the subject actually told the truth.
P(Poly said lied | person told truth)
Look at column for "told the truth" = 80
Find intersecting box "Poly said lied" = 15
P(...) = 15/80
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Cheers,
Stan H.
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Travel_Word_Problems/74550: The base of a ladder is 12 feet away from the wall. The top of the ladder is 13 feet from the floor. Find the length of the ladder to the nearest thousandth.
I need some help with this. Thanks.
1 solutions
Answer 53536 by stanbon(57424) on 2007-03-15 13:15:44 (Show Source):
You can put this solution on YOUR website!The base of a ladder is 12 feet away from the wall. The top of the ladder is 13 feet from the floor. Find the length of the ladder to the nearest thousandth.
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Draw the picture of the rt. triangle formed by the wall, floor, and ladder.
Use Pythagoras to find the length of the ladder.
ladder^2 = 12^2 + 13^2
ladder^2 = 144 + 169=313
ladder = 17.693 ft.
Cheers,
Stan H.
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Probability-and-statistics/13912: This is my problem: Three boys and two girls want to be on the softball team. If the coach chooses two of them at random, what is the probability that:
one boy and one girl will be chosen?
two boys will be chosen?
two girls will be chosen?
I already submitted it to my teacher and got it wrong...help! Thank you!
1 solutions
Answer 53534 by stanbon(57424) on 2007-03-15 13:08:14 (Show Source):
You can put this solution on YOUR website!Three boys and two girls want to be on the softball team. If the coach chooses two of them at random, what is the probability that:
two boys will be chosen?
Choose 2 boys in 3C2=3 ways
Choose 2 of any gender = 5C2=10
Therefore P(2 boys) = 3/10
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two girls will be chosen?
Choose two girls in 2C2=1 way
Choose 2 of any gender = 10
Therefore P(2 girls) = 1/10
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one boy and one girl will be chosen?
P(one boy and one girl)= 1-[prob(2 boys)+2(girls)] = 1-((3/10)+(1/10))=6/10
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Cheers,
Stan H.
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Quadratic-relations-and-conic-sections/74533: This question is from textbook Algebra 2
Hi! I just submitted this problem, but I think I figured it out! Can someone tell me if this is correct?
Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0).
The length of the major axis would be 12 units. 2a=12. a=6.
The length of the minor axis is 8 units. 2b=8. b=4.
The equation for an ellipse is y^2/a^2 + x^2/b^2=1.
So the answer would be y^2/36 + x^2/16=1.
Can someone please tell me if I did this right?
1 solutions
Answer 53498 by stanbon(57424) on 2007-03-15 09:04:59 (Show Source):
You can put this solution on YOUR website!Write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0).
The length of the major axis would be 12 units. 2a=12. a=6.
The length of the minor axis is 8 units. 2b=8. b=4.
The equation for an ellipse is y^2/a^2 + x^2/b^2=1.
So the answer would be y^2/36 + x^2/16=1.
Can someone please tell me if I did this right?
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Your equation would cause the center to be at (0,0)
If you plot the end points of the major and the minor axis you will
see that the center is at (1,0).
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Can you adjust your equation for that?
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Cheers,
Stan H.
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Mixture_Word_Problems/74505: A tank holds 80 liters of a chemical solution. Currently the solution has a strength of 30%. How much of this solution must be drained and replaced with a 70% solution to get a strength of 40%?
1 solutions
Answer 53475 by stanbon(57424) on 2007-03-14 23:12:54 (Show Source):
You can put this solution on YOUR website!A tank holds 80 liters of a chemical solution. Currently the solution has a strength of 30%. How much of this solution must be drained and replaced with a 70% solution to get a strength of 40%?
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30% solution DATA:
Amt = 80 L ; amt of active ingredient = 0.3*80 = 24 L
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70% solution DATA:
Amt = x L ; amt of active ingredient = 0.7x L
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40% remainder DATA:
Amt = (80) L ; Amt of active ingredient = 0.4(80) = 32 L
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EQUATION:
active - active = active
24 + 0.7x = 32
0.7x = 8
x= 11.43 L
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Cheers,
Stan H.
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Probability-and-statistics/14613: It has been estimated that eighty percent of people with coronoary disease have chest pain syptom and twenty-five percent of people without the disease have chest pain symptoms. A person visits a doctor with chest pain symptom, what are the probabilities of the following events?
a) the person has coronary heart disease
b)the person does not have coronary disease.
I have just started my module on probability, I know this maybe pretty basic stuff, but would appreciate any help that will make it easier for me to understand the subject,thanks in advance.
1 solutions
Answer 53470 by stanbon(57424) on 2007-03-14 22:47:52 (Show Source):
You can put this solution on YOUR website!It has been estimated that eighty percent of people with coronoary disease have chest pain syptom and twenty-five percent of people without the disease have chest pain symptoms. A person visits a doctor with chest pain symptom, what are the probabilities of the following events?
a) the person has coronary heart disease
Looks like a Bayes Problem:
Let "D" mean "has coronary disease"; Let "p" means "has pain".
P(D|P) = P(D and P)/[P(P and D) + P(P and not D)
= 0.80/(0.80 + 0.25) = 0.8/1.05 = 0.762
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b)the person does not have coronary disease.
Also, looks like a Bayes Problem.
P(not D |Pain) = P(not D and Pain)/[P(not D and Pain) + P(not D and not Pain)
=0.25/[0.25+0.20) = 0.556
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Cheers,
Stan H.
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Probability-and-statistics/14625: First of all, thaks for helping in advance...
Here's the problem
Suppose there are 10 items on a true-false test. The person taking the test does not read the questions; he just answers each question randomly. What is the probability of his guessing all answers correctly?
I ended up with 1/512...but I started this a while ago and now I've forgotten how I got to that. Any help would be great.
Thanks,
Liz
1 solutions
Answer 53415 by stanbon(57424) on 2007-03-14 07:22:56 (Show Source):
You can put this solution on YOUR website!The probability of getting one answer right is 1/2
The probability of getting two right is 1/2 *1/2 = 1/2^2=1/4
You multiply because the events are independent; what you do
on one problem does not effect what you do on the next.
The prob of get all 10 right is (1/2)^10 = 1/1024
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Cheers,
Stan H.
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