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Recent problems solved by 'stanbon'
stanbon answered: 57880 problems
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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 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899, >>NextExpressions-with-variables/579412: how do you solve 8x-2y=12 7x+3y=15?
1 solutions
Answer 370978 by stanbon(57953)   on 2012-02-28 11:40:49 (Show Source):
You can put this solution on YOUR website!solve
8x-2y=12
7x+3y=15
-------------
Multiply thru 1st by 3 and 2nd by 2 to get:
24x - 6y = 36
14x + 6y = 30
----
Add and solve for "x":
38x = 66
x = 33/19
-----
Solve for "y":
8(33/19) - 2y = 12
264/19 - 2y = 12
---
132/19 - y = 6
y = (132/19)-(114/19)
y = 18/19
-----
Check the arithmetic.
Cheers,
Stan H.
|
Money_Word_Problems/579408: Tony deposits$6000 into an account that pays simple interest at a rate of 2% per year. How much interest will he be paid in the first 6 years?
1 solutions
Answer 370977 by stanbon(57953) on 2012-02-28 11:33:27 (Show Source):
You can put this solution on YOUR website! Tony deposits$6000 into an account that pays simple interest at a rate of 2% per year. How much interest will he be paid in the first 6 years?
--------------
i = prt
---
i = 6000*0.02*6
----
i = $720
=============
Cheers,
Stan H.
|
Mixture_Word_Problems/579410: Tracy and Max determined that the vacation they would like to take for their anniversary would cost $2250. If they put the money saved by making their own coffee into a vacation account, would there be enough money in eight months to take their vacation
1 solutions
Answer 370976 by stanbon(57953) on 2012-02-28 11:30:48 (Show Source):
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test/579394: Find the polynomial p(x) with given zeros 2,-4,5
1 solutions
Answer 370966 by stanbon(57953) on 2012-02-28 11:07:21 (Show Source):
You can put this solution on YOUR website!Find the polynomial p(x) with given zeros 2,-4,5
------
p(x) = (x-2)(x+4)(x-5)
---
p(x) = (x^2+2x-8)(x-5)
---
p(x) = x^3-2x^2-5x-5x^2-10x+40
----
p(x) = x^3-7x^2-15x+40
=================
cheers,
Stan H.
|
Linear-systems/579401: URGENT!!! PLEASE SOLVE! Solve the system of equations. Make sure to check your solution.
y = 1/3x + 10
x = 3y + 6
1 solutions
Answer 370964 by stanbon(57953) on 2012-02-28 11:03:06 (Show Source):
You can put this solution on YOUR website!y = (1/3)x + 10
x = 3y + 6
----
Rearrange:
y = (1/3)x + 10
y = (1/3)x - 2
----
Subtracting you would get:
0 = 8, which is a contradiction.
----
Conclusion: There is no solution.
The lines are parallel; notice that they have the same slope.
==========
Cheers,
Stan H.
|
Points-lines-and-rays/579399: Find a polynomial for the perimeter and area for a square with the height of D and the length of D+5
1 solutions
Answer 370963 by stanbon(57953) on 2012-02-28 10:59:30 (Show Source):
You can put this solution on YOUR website!Find a polynomial for the perimeter and area for a square with the height of D and the length of D+5
---
Note: That is not a square; it is a rectangle.
-------------------------------
Area = D(D+5) = D^2+5D
---
Perimeter = 2D + 2(D+5) = 4D+10
================================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/579392: 3n^4-33n^2+30 is the problem I have to factor. This is the way I did it.
3n^4-33n^2+30
3n^2-11n+10
(3n-5)(n-2)
3n^4-11n^2+10
(3n^2-5)(n^2-2)
3n^2*1n^2=3b^4
I don't know what I did wrong. My answer is suppose to be 3(n-1)(n+1)(n^2-10)
Can you please help me
1 solutions
Answer 370962 by stanbon(57953) on 2012-02-28 10:49:20 (Show Source):
You can put this solution on YOUR website!3n^4-33n^2+30
----
3n^4-30n^2-3n^2+30
-----
Factor:
3n^2(n^2-10)-3(n^2-10)
-----
Factor:
(n^2-10)(3n^2-3)
----
= (n-sqrt(10))(n+sqrt(10))(3(n^2-1))
-----
= (n-sqrt(10))(n+sqrt(10))(3(n^2-1))
----
= (n-sqrt(10))(n+sqrt(10))(3(n-1)(n+1)
----
Rearrange any way you wish.
Cheers,
Stan H.
=================
|
Probability-and-statistics/579324: 3. The probability that a bulb produced by a factory will fuse after certain period of time is 0.05. Find the probability that out of 5 such bulbs
a. None fuses
b. Not more than 2 fuse
c. More than 2 fuse
1 solutions
Answer 370957 by stanbon(57953) on 2012-02-28 09:18:16 (Show Source):
You can put this solution on YOUR website!The probability that a bulb produced by a factory will fuse after certain period of time is 0.05. Find the probability that out of 5 such bulbs
a. P(None fuses) = 0.95^5 = 0.7738
----------------------------------------------
b. P(Not more than 2 fuse) = binomcdf(5,0.05,2) = 0.9988
----------------------------------------------
c. P(More than 2 fuse) = 1-0.9988 = 0.0012
==============================================
Cheers,
Stan H.
================
|
Probability-and-statistics/579359: A batch of 20 used automobile alternators contains 4 defectives. If 3 alternators are selected at random, find the probability of the events (Using the Rule of combinations):
A= None of the defective appears
B= Exactly two defective appears
The answer for A is .491 the answer for B is .084 but I can not figure out for the life of me how they got these answers.
I've tried 3 of 20 which gave the 1140 total selections possible. Than if there is 4 defective and I want the probability of selecting none. I tried 0 of 4 which doesn't work 1 of 4 likewise doesn't work. I'm stuck. Please help I know this is probably going to be something so simple I am missing.
1 solutions
Answer 370956 by stanbon(57953) on 2012-02-28 09:13:38 (Show Source):
You can put this solution on YOUR website!A batch of 20 used automobile alternators contains 4 defectives and 16 good ones.
-------.
If 3 alternators are selected at random, find the probability of the events (Using the Rule of combinations):
A= None of the defective appears
P(no defectives) = P(3 good ones) = 16C3/20C3 = 0.4912
-------
B= Exactly two defective appears
P(x = 2) = 3C2(4/20)^2(16/20) = 3*(1/25)(4/5) = 12/125 = 0.0960
----
Note: The answer to "B" is not 0.084
=============
Cheers,
Stan H.
==================
|
Probability-and-statistics/579176: Party Time Co. will run a promotional raffle that offers a chance to win either a lifetime discount on Spring Festival Merchandises (which results in a $1,000 savings) or a 5-year limited discount on any party-goods (which results in a $400 savings).
a) Winning a lifetime discount has a 1-in-100 chance.
b) Winning a 5-year limited discount has a 1-in-20 chance.
Is this promotion worth it if the tickets cost $35?
1 solutions
Answer 370906 by stanbon(57953) on 2012-02-27 22:20:12 (Show Source):
You can put this solution on YOUR website!Party Time Co. will run a promotional raffle that offers a chance to win either a lifetime discount on Spring Festival Merchandises (which results in a $1,000 savings) or a 5-year limited discount on any party-goods (which results in a $400 savings).
a) Winning a lifetime discount has a 1-in-100 chance.
b) Winning a 5-year limited discount has a 1-in-20 chance.
Is this promotion worth it if the tickets cost $35?
-----
Random winning values:::::::::: 965::::::: 365 ::::::: -35
Corresponding probabilities:::: 1/100 :::::5/100::::: 94/100
---------------
Expected Value = (965 + 5*365 - 94*35)/100 = -1230/100 = -$12.30
----
The company will gain $12.50 on each ticket that is bought.
The ticket buyer can expect to lose $12.50 on each ticket bought.
================
Cheers,
Stan H.
|
Probability-and-statistics/579203: A local vendor claims that the average price of hair products is comparable to a large, well known online retail outlet. Being the skeptical person that you are, you randomly price 25 items at both stored and record the data below. At the .05 level of significance, is there evidence of a difference between the mean price of items at the local vendor's store and the online retailer?
1 solutions
Answer 370902 by stanbon(57953) on 2012-02-27 22:05:16 (Show Source):
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Probability-and-statistics/579213: Spoke Weaving Corporation has eight weaving machines of the same kind and of the same age. The probability is 0.08 that any weaving machine will break down at any time.
Find the probability that at any given time
none of the weaving machines will be broken down
1 solutions
Answer 370901 by stanbon(57953) on 2012-02-27 22:02:54 (Show Source):
You can put this solution on YOUR website!Spoke Weaving Corporation has eight weaving machines of the same kind and of the same age. The probability is 0.08 that any weaving machine will break down at any time.
Find the probability that at any given time
none of the weaving machines will be broken down
---
P(all 8 are working properly) = 0.92^8 = 0.5132
-----
Cheers,
Stan H.
|
Numeric_Fractions/579117: I am having a difficult time with the below math problem. Can you please help me solve this algebra problem.
g(x)= 10/x+7
1 solutions
Answer 370856 by stanbon(57953) on 2012-02-27 19:52:04 (Show Source):
You can put this solution on YOUR website!I am having a difficult time with the below math problem. Can you please help me solve this algebra problem.
g(x)= 10/(x+7)
----
It's an equation with 2 variables.
You cannot solve it unless you give "x" some value.
For that reason x is called the independent variable.
Once you know what x is you can solve for g(x).
---
If x = 3, y = 10/(3+7) = 1
If x = -2, y = 10/(-2+7) = 2
etc. to get more points
----
Plot (3,1) and (-2,2) and your other points and draw a graph thru them.
That is a picture of ALL of the solutions for the equation.
---
-----------------
Cheers,
Stan H.
|
Word_Problems_With_Coins/579103: 2 jars of dimes total $10.00, jar 1 has $3.00 more that 2, how many dimes are in each jar?
1 solutions
Answer 370853 by stanbon(57953) on 2012-02-27 19:43:58 (Show Source):
You can put this solution on YOUR website!2 jars of dimes total $10.00, jar 1 has $3.00 more that 2,
how many dimes are in each jar?
-----
Jar 2 has x dollars
Jar 1 has x+3 dollars
----
Equation:
x + x + 3 = 10
2x = 7
x = $3.50 (35 dimes in Jar #2)
----
x+3 = $6.50 (65 dimes in Jar #1)
==================================
Cheers,
Stan H.
================
|
Probability-and-statistics/579009: Suppose SPS professors have an average life normally distributed of 82 years, with a population standard deviation of 5 years.
a) What percent of SPS professors will make it past the age of 70?
b) What percent of SPS professors will not live more than 80 years?
c) Calculate the 95th percentile.
d) What proportion of SPS professors will live between 85 and 90 years?
1 solutions
Answer 370830 by stanbon(57953) on 2012-02-27 18:12:31 (Show Source):
You can put this solution on YOUR website!Suppose SPS professors have an average life normally distributed of 82 years, with a population standard deviation of 5 years.
a) What percent of SPS professors will make it past the age of 70?
z(70) = (70-82)/5 = -12/5
P(x > 70) = P(z > -12/5) = 0.9918
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b) What percent of SPS professors will not live more than 80 years?
z(80) = (80-82)/5 = -2/5
P(x <= 80) = P(z <= -2/5) = 0.3446
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c) Calculate the 95th percentile.
InvNorm(0.95) = 1.645
x = 1.645*5+82 = 90.225
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d) What proportion of SPS professors will live between 85 and 90 years?
Using a TI-84: P(85<= x <=90) = normalcdf(85,90,82,5) = 0.2195
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Cheers,
Stan H.
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Probability-and-statistics/579018: There are four people playing a game with a standard die. In the game, the person who rolls the lowest number wins. Ties are broken by continuing to roll until the tie is broken. One of the four people rolls a three. What is the probability that they will win?
1 solutions
Answer 370826 by stanbon(57953) on 2012-02-27 17:58:04 (Show Source):
You can put this solution on YOUR website!There are four people playing a game with a standard die. In the game, the person who rolls the lowest number wins. Ties are broken by continuing to roll until the tie is broken. One of the four people rolls a three. What is the probability that they will win?
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The only way they can lose is for someone to roll a 1 or a 2.
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The way they will win is for others to roll 4,5, or 6.
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P(they will win) = 3/6 = 1/2
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Cheers,
Stan H.
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Probability-and-statistics/578909: Assume drivers are independent.
a) If 5% of the drivers fail to stop at a red light, find the probability tahat at least 2 of the next 100 drivers fail to stop.
b) If on the average 3 drivers fail to stop at the red light during each rush hour, what is the probability that at least 2 drivers fail to stop at the red light during tonight’s rush hour?
1 solutions
Answer 370824 by stanbon(57953) on 2012-02-27 17:45:43 (Show Source):
You can put this solution on YOUR website!Assume drivers are independent.
a) If 5% of the drivers fail to stop at a red light, find the probability that at least 2 of the next 100 drivers fail to stop.
Binomial Problem with n = 100 and p(fail to stop) = 0.05
P(2<= x <=100) = 1- binomcdf(100,0.05,1) = 0.9629
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b) If on the average 3 drivers fail to stop at the red light during each rush hour, what is the probability that at least 2 drivers fail to stop at the red light during tonight’s rush hour?
That is a Poisson problem.
Cheers,
Stan H.
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Probability-and-statistics/578882: If a committee of 4 workers is to be chosen what is the probability that it must include at least 2 males?
*there are five males and 5 females
1 solutions
Answer 370823 by stanbon(57953) on 2012-02-27 17:35:06 (Show Source):
You can put this solution on YOUR website!If a committee of 4 workers is to be chosen what is the probability that it must include at least 2 males?
*there are five males and 5 females
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# of ways to succeed : 5C2+5C3+5C4 = 10+10+5 = 25
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# of random groups of 4: 10C4 = 210
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Ans: 25/210 = 5/42
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Cheers,
Stan H.
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Probability-and-statistics/578942: The probability that a hockey game will go into overtime is .3; Of the next 12 hockey games, what is the probability that more than 3 (P(x >3)) will go into overtime?
I think this is Poisson, but am not 100 percent sure. Would appreciate some guidance. Thank you.
1 solutions
Answer 370818 by stanbon(57953) on 2012-02-27 16:53:44 (Show Source):
You can put this solution on YOUR website!The probability that a hockey game will go into overtime is .3; Of the next 12 hockey games, what is the probability that more than 3 (P(x >3)) will go into overtime?
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Binomial Problem with n = 12 and p(overtime) = 0.3
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P(4<= x <=12) = 1 - P(0<= x <=3) = 1 - binomcdf(12,0.3,3)
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= 1 - 0.4925
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= 0.5075
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Cheers,
Stan H.
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Age_Word_Problems/578962: Can you please help me solve the following problem.
Tomorrow,the number of candles on Claire's birthday cake will be one less than three times two-fifths of the number five years ago.How old is Claire today?
1 solutions
Answer 370816 by stanbon(57953) on 2012-02-27 16:45:07 (Show Source):
You can put this solution on YOUR website!Tomorrow,the number of candles on Claire's birthday cake will be one less than three times two-fifths of the number five years ago.
How old is Claire today?
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Equation:
x = 3(2/5)(x-5)-1
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x+1 = (6/5)(x-5)
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5x+5 = 6x-30
x = 35 (Claire's age today)
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Cheers,
Stan H.
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Proportions/574059: solve each proportion
1. n/6= 25/30
2. 6.1/x= 2/3
3. 100/25= t/4
I need help ASAP!
Help!
1 solutions
Answer 370805 by stanbon(57953) on 2012-02-27 14:12:01 (Show Source):
You can put this solution on YOUR website!solve each proportion
1. n/6= 25/30
Multiply both sides by 6 to get:
n = 6(25/30)
n = (6/30)*25
n = (1/5)*25
n = 5
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2. 6.1/x= 2/3
Invert both sides:
x/6.1 = 3/2
Multiply both sides by 6.1 to get:
x = 6.1(3/2)
x = 18.3/2
x = 9.15
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3. 100/25= t/4
Multiply both sides by 4 to get:
t = 4(100/25)
t = 4*4
t = 16
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cheers,
Stan H.
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Proportions/578870: I'm doing proportions with fractions well at least that's what the lessons called and I need help understanding it
1 solutions
Answer 370804 by stanbon(57953) on 2012-02-27 14:05:49 (Show Source):
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Probability-and-statistics/578761: i would please like help with this question,
"if may of a particular year was picked at random, what is the probability that average high temperature for that may was exactly 70 degrees?"
thank you!
1 solutions
Answer 370788 by stanbon(57953) on 2012-02-27 12:41:03 (Show Source):
You can put this solution on YOUR website!i would please like help with this question,
"if may of a particular year was picked at random, what is the probability that average high temperature for that may was exactly 70 degrees?"
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Answer: Temperature is a continuous variable (as opposed to a discrete variable).
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In a continuous distribution the propability of any particular value is zero.
Your answer is zero.
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cheers,
Stan H.
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Probability-and-statistics/578817: Given: P(good)= 0.70 and P(defective)= 0.30
In a sample of five items, find P(exactly four are good)
1 solutions
Answer 370785 by stanbon(57953) on 2012-02-27 12:35:30 (Show Source):
You can put this solution on YOUR website!Given: P(good)= 0.70 and P(defective)= 0.30
In a sample of five items, find P(exactly four are good)
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P(x = 4) = 5C4*0.7^4*0.3 = binompdf(5,0.7,4) = 0.3601
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Cheers,
Stan H.
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Probability-and-statistics/578786: Assume that blood pressure readings are normally distributed with a mean of 117 and a standard deviation of 5. A researcher wishes to select people for a study but wants to exclude the top 10 percent. What would be the cutoff blood pressure to qualify for the study?
a)120.5
b)117.0
c)124.6
d)123.4
e)121.8
1 solutions
Answer 370784 by stanbon(57953) on 2012-02-27 12:32:42 (Show Source):
You can put this solution on YOUR website!Assume that blood pressure readings are normally distributed with a mean of 117 and a standard deviation of 5. A researcher wishes to select people for a study but wants to exclude the top 10 percent. What would be the cutoff blood pressure to qualify for the study?
Find the z-value with a left-tail of 0.90
invNorm(0.90) = 1.6449
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Find the corresponding bp value:
bp = z*s + u
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blood pressure = 1.6449*5+117 = 125.22
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Cheers,
Stan H.
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a)120.5
b)117.0
c)124.6
d)123.4
e)121.8
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Probability-and-statistics/578804: 3 red and 4 blue balls are in a basket. A member of PPTeam is drawing balls from the basket. What is the probablity of getting the 3 red balls simultaneously?
1 solutions
Answer 370783 by stanbon(57953) on 2012-02-27 12:27:21 (Show Source):
You can put this solution on YOUR website!3 red and 4 blue balls are in a basket. A member of PPTeam is drawing balls from the basket. What is the probablity of getting the 3 red balls simultaneously?
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# of ways to succeed: 3C3 = 1
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# of random triples: 7C3 = 35
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P(3 red) = 1/35
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Cheers,
Stan H.
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