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Recent problems solved by 'stanbon'
stanbon answered: 57264 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, >>NextNumbers_Word_Problems/423230: (20t^2+t)^2-22(20t^2+t)+21=0
what are the solutions of t?
1 solutions
Answer 295253 by stanbon(57337)   on 2011-03-16 22:08:52 (Show Source):
You can put this solution on YOUR website!(20t^2+t)^2-22(20t^2+t)+21=0
----
Let w = 20t^2+t
----
Substitute to get:
w^2 - 22w + 21 = 0
----
Factor:
(w-21)(w-1) = 0
w = 21 or w = 1
-----
Solve for "t":
If w = 21,
20t^2+t = 21
20t^2+t-21 = 0
(t-1)(20t+21) = 0
t = 1 or t = -21/20
------
If w = 1
20t^2+t= 1
20t^2+t-1 = 0
(5t-1)(4t+1) = 0
t = 1/5 of t = -1/4
=============================
Cheers,
Stan H.
|
Quadratic_Equations/423208: Hello, need an explanation on how to find the x intercepts, and the vertex of this equation y is less than or equal to -x^2+3x+2. I do not know how to factor yet, so if we could do it by guessing two points and checking by plugging them into the equation and finding some easy to graph points. Thanks soOoOoOo much!
1 solutions
Answer 295245 by stanbon(57337) on 2011-03-16 21:24:00 (Show Source):
You can put this solution on YOUR website!need an explanation on how to find the x intercepts, and the vertex of this equation y is less than or equal to -x^2+3x+2.
--------------
a = -1 ; b = 3 ; c = 2
----
Vertex occurs at x = -b/(2a) = -3/(-2) = 3/2
---
Vertex y-value: f(3/2) = -(3/2)^2+3(3/2)+2 = -9/4+(9/2)+2 = 17/4
----
Vertex:(3/2 , 17/4)
--------------------------
x-intercepts:
solve -x^2+3x+2 = 0
x = [-3 +- sqrt(9-4*-1*2)]/(-2)
= [-3 +- sqrt(17)]/(-2)
Those are the x-intercepts
================================
Cheers,
Stan H.
============
|
Probability-and-statistics/423183: Four managers, five engineers and one lawyer are in a meeting when a message arrives for one of them. of these people, three managers, two engineers and the lawyer are women. find the probability of each of the following events:
A) The message is for a man.
B) The message is not for a male engineer.
1 solutions
Answer 295240 by stanbon(57337) on 2011-03-16 21:14:21 (Show Source):
You can put this solution on YOUR website! Four managers, five engineers and one lawyer are in a meeting when a message arrives for one of them. of these people, three managers, two engineers and the lawyer are women. find the probability of each of the following events:
A) The message is for a man.
There are 4 men and 6 women
P(msg for man) = 4/10
--------
B) The message is not for a male engineer.
There are 3 male engineers.
P(msg not for male engineer) = 7/10
=========================================
cheers,
Stan H.
|
Probability-and-statistics/423194: Hello,
I think this is a probability problem... if it is not considered probability than i am sorry.
During boot camp, the drill sergeant measured the weight of the men in his unit. the average weight of the men was 142 pounds and the standard deviation was 14 pounds. the data is normally distributed. if there are 100 men in the unit, how many men would be expected to weigh less than 128 pounds?
The 100 men part of the problem threw me off. thanks for all of your help :)
1 solutions
Answer 295237 by stanbon(57337) on 2011-03-16 21:09:14 (Show Source):
You can put this solution on YOUR website!During boot camp, the drill sergeant measured the weight of the men in his unit. the average weight of the men was 142 pounds and the standard deviation was 14 pounds. the data is normally distributed. if there are 100 men in the unit, how many men would be expected to weigh less than 128 pounds?
--------------
Find z-value of 128.
z(128) = (128-142)/14 = -1
-----
P(x < 128) = P(z < -1) = 0.1587
=======
If there are 100 men in the unit, how many men would be expected to weigh less than 128 pounds?
---
Expected # of 100 men = 0.1587*100 = 158.7 = 159 men
====================================================
Cheers,
Stan H.
============
|
Numbers_Word_Problems/423184: One number is 4/3 times another and they have a differce of 10. What are the two numbers?
1 solutions
Answer 295234 by stanbon(57337) on 2011-03-16 20:53:45 (Show Source):
You can put this solution on YOUR website!One number is 4/3 times another and they have a differce of 10. What are the two numbers?
-------------------
Equations:
x = (4/3)y
x-y = 10
----
Substitute for "x" and solve for "y":
(4/3y)-y = 10
(1/3)y = 10
y = 30
----
Now solve for "x":
x = (4/3)y
x = (4/3)30
x = 40
========
Solution: (40,30)
====================
Cheers,
stan H.
|
Systems-of-equations/423173: Could someone please help me with 8th grade algebra? solve the linear system using substitution.
x=16-4y
3x+4y=8
1 solutions
Answer 295228 by stanbon(57337) on 2011-03-16 20:44:44 (Show Source):
You can put this solution on YOUR website!solve the linear system using substitution.
x=16-4y
3x+4y=8
-----
The 1st equation tells you x = 16-4y
---
Substitute that into the 2nd equation
and solve for "y":
3(16-4y)+4y = 8
48 - 12y + 4y = 8
-8y = -40
---
y = 5
---
Solve for "x"
x = 16-4y
x = 16-4*5
x = 16-20
x = -4
----------
Solution: (-4,5)
=======================
Cheers,
Stan H.
=============
|
Geometric_formulas/423151: The decay rate of a certain chemical is 9.5% per year. What is it's half life? Use the exponential decay model P(t)=P/subscript/0e^-kt where k is the decay rate and P/subscript/0 is the original amount of chemical..
1 solutions
Answer 295225 by stanbon(57337) on 2011-03-16 20:36:57 (Show Source):
You can put this solution on YOUR website! The decay rate of a certain chemical is 9.5% per year. What is it's half life? Use the exponential decay model P(t)=P/subscript/0e^-kt where k is the decay rate and P/subscript/0 is the original amount of chemical..
-------------------------
P(t) = Po*e^(-kt)
----
(0.5)Po = Po*e^(-0.095t)
----
e^(-0.095t)= 0.5
----
Take the natural log of both sides.
-0.095t = ln(0.5)
t = 7.296 years (half-life of the chemical)
=========================
Cheers,
Stan H.
|
Travel_Word_Problems/423139: Ellen and Kate raced on their bicycles to the library after school. They both left school at 3:00pm and bicycled along the same path. Ellen rode at a speed of 12mph and Kate rode at a speed of 9mph. Ellen got to the library 15mins before Kate. What time did Ellen get to the library?
1 solutions
Answer 295213 by stanbon(57337) on 2011-03-16 20:11:16 (Show Source):
You can put this solution on YOUR website!Ellen and Kate raced on their bicycles to the library after school.
They both left school at 3:00pm and bicycled along the same path.
Ellen rode at a speed of 12mph and Kate rode at a speed of 9mph.
Ellen got to the library 15mins before Kate.
What time did Ellen get to the library?
-----
Ellen data:
rate = 12 mph ; time = x hrs. ; distance = rt = 12x miles
----------------
Kate data:
rate = 9 mph ; time = (x+(1/4)) hrs ; distance = 9(x+(1/4)) = 9x+(9/4) miles
------------------------
Equation:
12x = 9x+(9/4)
3x = 9/4
x = 3/4 hr.
---
Ellen will arrive at the library at 3:45
=============================================
Cheers,
Stan H.
==================
|
Triangles/423137: How would I use the Pythagorean theorem to determine if given measures could be sides of a right triangle? (eg. 12,34,37)
1 solutions
Answer 295211 by stanbon(57337) on 2011-03-16 20:05:55 (Show Source):
You can put this solution on YOUR website! How would I use the Pythagorean theorem to determine if given measures could be sides of a right triangle? (eg. 12,34,37)
----
The hypotenuse would have to be the longest side.
Pythagoras:
hypotenuse^2 = leg1^2 + leg2^2
-----------------------------------
Check:
37^2 = 12^2 + 34^2
1369 = 144 + 1156
1369 = 1300
---
False; so the measures could not be the sides
of a right triangle.
===============
Cheers,
Stan H.
===============
|
Complex_Numbers/423089: find all seventh roots of 3+4i please try and give all steps...
1 solutions
Answer 295199 by stanbon(57337) on 2011-03-16 19:11:17 (Show Source):
You can put this solution on YOUR website!find all seventh roots of 3+4i please try and give all steps...
----
r = sqrt(3^2+4^2) = 5
theta = tan^-1(4/3) = 53.13 degrees
-----
(3+4i)^(1/7) = 5^(1/7)(cis(53.13+360n)/7)
---
To find the 7 roots let n = 0,1,2,3,...,6
Note: 360/7 = 51.43 degrees
and 53.13/7 = 7.59
---
So for n = 3 you get: 5^(1/7)cis(7.59+3(41.43))
etc.
-------------------------------------------
Cheers,
Stan H.
|
Probability-and-statistics/422983: Essay; show all work. A community 5K run will award $50 to the winner. 60 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent.
1 solutions
Answer 295196 by stanbon(57337) on 2011-03-16 18:59:53 (Show Source):
You can put this solution on YOUR website!Essay; show all work. A community 5K run will award $50 to the winner. 60 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent.
------------------------------------
Random-gain values: 50-20 = 30 ; -20
Probabilities: 1/60 ; 59/60
-----------
E(gain)= 30(1/60)-20(59/60) = 1/2 - (59/3)= (3-59)/6 = -$9.33
----
A fair price would be 20-9.33 = $10.67
---------------------------------------------
Cheers,
Stan H.
===========
|
Numbers_Word_Problems/423040: One number is 4 less than 11 times another. The sum of the two numbers is 92. Find the two numbers.
1 solutions
Answer 295175 by stanbon(57337) on 2011-03-16 18:03:16 (Show Source):
You can put this solution on YOUR website!One number is 4 less than 11 times another. The sum of the two numbers is 92. Find the two numbers.
---
Equatios:
x = 11y-4
x + y = 92
---
Substitute for "x" and solve for "y":
11y-4 + y = 92
12y = 96
y = 8
---
Solve for "x":
x = 11y-4
x = 11*8-4 = 84
------------------------
Cheers,
Stan H.
|
Probability-and-statistics/423038: the ratio of male students to female students in the drama club at Campbell High School is 3:4. If the number of male students in the club is 18, predict the number of females students?
1 solutions
Answer 295172 by stanbon(57337) on 2011-03-16 17:54:18 (Show Source):
You can put this solution on YOUR website!the ratio of male students to female students in the drama club at Campbell High School is 3:4. If the number of male students in the club is 18, predict the number of females students?
------
3:4 is the same as 3x:4x where 3x is # of male and 4x is # of female.
---
Equation:
3x = 18
x = 6
------------
4x = 24 (# of female students)
=================
Cheers,
Stan H.
==============
|
Functions/423036: What is the domain for f(x)= 1/x ? I need an explaination, thank you.
1 solutions
Answer 295169 by stanbon(57337) on 2011-03-16 17:48:50 (Show Source):
You can put this solution on YOUR website! What is the domain for f(x)= 1/x ? I need an explaination,
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The denominator cannot be zero; so x cannot be 0.
Domain: All Real Numbers except x = 0
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cheers,
Stan H.
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Probability-and-statistics/423007: Test the claim that the mean time between uses of a TV remote control by adults during commercials is not greater than 5.0 seconds. The standard deviation is known and equal 2.5 seconds.
The mean of a SRS sample of size n=650 was measured and found to be 5.25 seconds. Use significance level of 0.01.
1 solutions
Answer 295157 by stanbon(57337) on 2011-03-16 17:28:31 (Show Source):
You can put this solution on YOUR website!Test the claim that the mean time between uses of a TV remote control by adults during commercials is not greater than 5.0 seconds.
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Ho: u <= 5 seconds (claim)
Ha: u > 5 seconds
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The standard deviation is known and equal 2.5 seconds.
The mean of a SRS sample of size n=650 was measured and found to be 5.25 seconds. Use significance level of 0.01.
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t(5.25) = (5.25-5)/[2.5/sqrt(650)] = 2.5495
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p-value = P(t <= 2.5495 when df = 649) = 0.9945
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That p-value is enormous; since it's greater than 1%
fail to reject Ho.
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Cheers,
Stan H.
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Probability-and-statistics/422965: A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 83 and standard deviation σ = 22. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
(a) x is more than 60
(b) x is less than 110
(c) x is between 60 and 110
(d) x is greater than 140 (borderline diabetes starts at 140)
1 solutions
Answer 295152 by stanbon(57337) on 2011-03-16 17:13:09 (Show Source):
You can put this solution on YOUR website!A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood.
Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 83 and standard deviation σ = 22. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
(a) x is more than 60
z(60) = (60-83)/22 = -1.0455
P(x > 60) = P(z > -1.0455) = 0.8521
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(b) x is less than 110
z(110) = (110-83)/22 = 1.2273
P(x < 110) = P(z < 1.2273) = 0.8901
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(c) x is between 60 and 110
Find the 2 z-values; then find the area between them.
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(d) x is greater than 140 (borderline diabetes starts at 140)
Find the z-value; then find its right tail.
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Cheers,
Stan H.
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Word_Problems_With_Coins/422961: Hi,
Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x be the number of nickels and y represent the number of quarters. Then he solved the system by graphing. What is the solution?
A)(6,9)
B) (5,10)
Thanks for you help, been really appreciated
1 solutions
Answer 295124 by stanbon(57337) on 2011-03-16 15:46:10 (Show Source):
You can put this solution on YOUR website!Marcos had 15 coins in nickels and quarters.
n + q = 15
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He had 3 more quarters than nickels.
q = n + 3
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He wrote a system of equations to represent this situation, letting n be the number of nickels and q represent the number of quarters. Then he solved the system by graphing. What is the solution?
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Ans: A
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Cheers,
Stan H.
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A)(6,9)
B) (5,10)
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test/422924: Find any value (s) for which the rational expression is undefined.
3p/p2-6p+9
1 solutions
Answer 295121 by stanbon(57337) on 2011-03-16 15:40:17 (Show Source):
You can put this solution on YOUR website! Find any value (s) for which the rational expression is undefined.
3p/p2-6p+9
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undefined when p^2-6p+9 = 0
when (p-3)^2 = 0
when p = 3
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Cheers,
Stan H.
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Evaluation_Word_Problems/422934: If a board is 12 2/3 feet long is cut into 3 equal pieces. Whats it the length of each piece
1 solutions
Answer 295104 by stanbon(57337) on 2011-03-16 15:10:08 (Show Source):
You can put this solution on YOUR website!If a board is 12 2/3 feet long is cut into 3 equal pieces. Whats it the length of each piece?
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12 2/3 ft = 38/3 ft
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Let each piece be "x".
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Equation:
3x = 38/3 ft
x = 38/9 ft = 4 2/9 ft
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