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Recent problems solved by 'stanbon'
stanbon answered: 57911 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 , 57900..57929, >>Next
Probability-and-statistics/742137: in a certain firm 6 persons(4 females and 2 males)two are eligible for promotion to two higher positions.list all the possible outcomes.
1 solutions
Answer 452277 by stanbon(57984)   on 2013-04-26 08:09:07 (Show Source):
You can put this solution on YOUR website! in a certain firm 6 persons(4 females and 2 males)two are eligible for promotion to two higher positions.list all the possible outcomes.
------
# with 2 females: 4C2 = 6
# of 2 males: 2C2 = 1
# with one female and one male: 4*2 = 8
===========================================
Cheers,
Stan H.
|
logarithm/742138: Write the given equation in logarithmic form. 7^2=2401
1 solutions
Answer 452276 by stanbon(57984) on 2013-04-26 08:06:45 (Show Source):
You can put this solution on YOUR website!Write the given equation in logarithmic form. 7^2=2401
Comment: Please note that 7^2 is not 2401.
------
base = 7
exponent = log = 2
result = 2401
--------
Log Form:
log7(2401) = 2
|
Polynomials-and-rational-expressions/742143: Find the remaining zeros of the following polynomial given that P(i)=0.
P(x) = x^4 -8x^3 +14x^2 -8x +13
I know that -i is the conjugate so (x+i)(x-i) = (x^2+1). I am stuck with how to break down the polynomial. Sythetic division leaves a remainer. I also know I need to get this into quadradic from so I can use the formula.
1 solutions
Answer 452275 by stanbon(57984) on 2013-04-26 08:04:05 (Show Source):
You can put this solution on YOUR website! Find the remaining zeros of the following polynomial given that P(i)=0.
P(x) = x^4 -8x^3 +14x^2 -8x +13
I know that -i is the conjugate so (x+i)(x-i) = (x^2+1). I am stuck with how to break down the polynomial.
------
The problem is that "i" is not a root of P(x). You can see that
if you substitute "i" for "x".
------------
Cheers,
Stan H.
==============
|
Polynomials-and-rational-expressions/742139: Work problem:
Normally, it takes Jeffery 1 hour 45 minutes (105 min or 7/4 hour) to mow and trim an average lawn. When Lupe worked with him, an average lawn only took an hour. How long would it take Lupe to mow and trim an average yard on her own?
1 solutions
Answer 452274 by stanbon(57984) on 2013-04-26 07:55:43 (Show Source):
You can put this solution on YOUR website!Normally, it takes Jeffery 1 hour 45 minutes (105 min or 7/4 hour) to mow and trim an average lawn. When Lupe worked with him, an average lawn only took an hour. How long would it take Lupe to mow and trim an average yard on her own?
-----
Jeff time = 7/4 hr/job ; rate = (4/7) job/hr
------------------
Together time = 1 hr/job ; rate = 1 job/hr
---------------------
Lupe time = x hr/job ; rate = 1/x job/hr
-----------------
Equation:
rate + rate = together rate
4/7 + 1/x = 1
----
4x + 7 = 7x
3x = 7
x = 7/3 hrs (Lepe's time alone)
===================================
Cheers,
Stan H.
====================
|
Quadratic-relations-and-conic-sections/742140: Write the standard form of the equation Parabola with vertex at (-2,4) and focus at (3,4)
1 solutions
Answer 452272 by stanbon(57984) on 2013-04-26 07:47:01 (Show Source):
You can put this solution on YOUR website!Write the standard form of the equation Parabola with vertex at (-2,4) and focus at (3,4)
----
Plot those 2 points and you will see that the parabola opens
to the right.
----
Form: (y-k)^2 = 4p(x-h)
---
p = 3--2 = 5; so 4p = 20
---
h = -2 and k = 4
-----
Equation:
(y-4)^2 = 20(x+2)
=====================
Cheers,
Stan H.
======================
|
Radicals/742042: Rationalize each denominator
___________
1 solutions
Answer 452255 by stanbon(57984) on 2013-04-25 22:40:55 (Show Source):
You can put this solution on YOUR website!{3sqrt( 2 )-sqrt(7)} / {4sqrt( 2 )+2sqrt(5)}
============
Multiply numerator and denominator by (4sqrt(2)-2sqrt(5)) to get:
============
(3sqrt(2)-sqrt(7))(4sqrt(2)-2sqrt(5)) / (16*2-4*5)
----------------------
= (12*2 - 6sqrt(10) - 4sqrt(14) +2sqrt(35)) /12
=====================================
Cheers,
Stan H.
==================
|
�t�e�s�t/742040: Solve this by substitution.
2x-3y=8
x+y=11
enter answer like (_,_) please thanks
1 solutions
Answer 452253 by stanbon(57984) on 2013-04-25 22:28:29 (Show Source):
You can put this solution on YOUR website!Solve this by substitution.
2x-3y=8
x+y=11
===========
y = 11-x
-------
Substitute for "y" and solve for "x":
2x - 3*(11-x) = 8
2x -33 + 3x = 8
5x = 41
----
x = 41/5
======================================
Solve for "y":
y = 11-(41/5)
y = (5/5)-(41/5) = -36/5
===============================
Cheers,
Stan H.
====================
|
Mixture_Word_Problems/742036: a chemist wants to obtain 80 liters of a solution that is 12% hydrochloric acid. how many liters of 10% and 20% hydrochloric acid solutions should he mix to do so?
1 solutions
Answer 452252 by stanbon(57984) on 2013-04-25 22:23:18 (Show Source):
You can put this solution on YOUR website!a chemist wants to obtain 80 liters of a solution that is 12% hydrochloric acid. how many liters of 10% and 20% hydrochloric acid solutions should he mix to do so?
------------
Equation:
acid + acid = acid
0.10x + 0.20(80-x) = 0.12*80
--------
10x + 20*80 - 20x = 12*80
-10x = -8*80
x = 64 liters (amt. of 10% solution needed)
----
80-64 = 16 liters (amt. of 20% solution needed)
=========================
Cheers,
Stan H.
|
Probability-and-statistics/741966: A report states that 40% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 4% with 95% confidence?
1 solutions
Answer 452220 by stanbon(57984) on 2013-04-25 19:47:47 (Show Source):
You can put this solution on YOUR website!A report states that 40% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 4% with 95% confidence?
---------------------
n = [z/E]^2*p*q
-------
n = [1.96/0.04]^2*0.4*0.6 = 577 when rounded up
============================
Cheers,
Stan H.
================================
|
Probability-and-statistics/741969: A political strategist believes that at least 58% of voters in a certain state support his candidate. He then commissions a poll of 500 voters and 60% of them support his candidate. At α = .05, test the claim.
a) State the hypotheses and identify the claim
b) Find the critical values
c) Compute the test values
d) Make the decision
e) Summarize the results
1 solutions
Answer 452219 by stanbon(57984) on 2013-04-25 19:44:06 (Show Source):
You can put this solution on YOUR website!A political strategist believes that at least 58% of voters in a certain state support his candidate. He then commissions a poll of 500 voters and 60% of them support his candidate. At α = .05, test the claim.
a) State the hypotheses and identify the claim
Ho: p >= 0.58 (clsim)
Ha: p < 0.58
------------------------
b) Find the critical values
z = -1.645
---------------------------------------
c) Compute the test values
z(0.6) = (0.6-0.58)/sqrt(0.58*0.42/500) = 0.9061
---------
d) Make the decision
Since the test statistic is not in the reject interval,
fail to reject Ho.
----------------------
e) Summarize the results
The test results do not support the claim at the 5% significance level.
==================================
Cheers,
Stan H.
==================================
|
Probability-and-statistics/741964: An economics professor randomly selected 25 millionaires in the United States. The average age of these millionaires was 54.8 years with a sample standard deviation of 7.9 years. What is the 99% confidence interval for the mean age, µ, of all United States millionaires?
1 solutions
Answer 452217 by stanbon(57984) on 2013-04-25 19:37:22 (Show Source):
You can put this solution on YOUR website!An economics professor randomly selected 25 millionaires in the United States. The average age of these millionaires was 54.8 years with a sample standard deviation of 7.9 years. What is the 99% confidence interval for the mean age, µ, of all United States millionaires?
--------------
x-bar = 54.8
ME = 2.5758*7.9/sqrt(25) = 4.070
-------
99% CI: 54.8-4.070 < u < 54.8+4.070
============================
Cheers,
Stan H.
|
Circles/741956: Evaluate the six circular function values of θ for the given unit circle.
The image shows a circle with an acute angle of θ.
(Sorry, for the explanation. Been having trouble with the Unit Circles and Circular Functions lesson.
1 solutions
Answer 452215 by stanbon(57984) on 2013-04-25 19:29:58 (Show Source):
You can put this solution on YOUR website!Evaluate the six circular function values of θ for the given unit circle.
The image shows a circle with an acute angle of θ.
-------
Since r = 1,
sin = y/r = y
cos = x/r = x
tan = y/x
-------------
csc = r/y = 1/y
sec = r/x = 1/x
cot = x/y
===========================
Cheers,
Stan H.
===========================
|
Travel_Word_Problems/741947: If a plane can travel 500 miles per hour with the wind and 420 miles per hour against the wind, what is the speed of the plane in still air?
1 solutions
Answer 452211 by stanbon(57984) on 2013-04-25 19:19:58 (Show Source):
You can put this solution on YOUR website!If a plane can travel 500 miles per hour with the wind and 420 miles per hour against the wind, what is the speed of the plane in still air?
-----------
Equations:
p + w = 500 mph
p - w = 420 mph
-----
Add and solve for "p":
2p = 920
plane speed = 460 mph
-----
Solve for "w":
p + w = 500
460 + w = 500
wind speed = 40 mph
===============================
Cheers,
Stan H.
|
Mixture_Word_Problems/741937: Any help would be greatly appreciated.... thank you
Together, Paul and Quincy weigh 364 pounds, Quincy and Ramon weigh 354 pounds, and Paul and Ramon weigh 352 pounds. How much does each weigh individually?
1 solutions
Answer 452209 by stanbon(57984) on 2013-04-25 19:05:56 (Show Source):
You can put this solution on YOUR website!Together, Paul and Quincy weigh 364 pounds, Quincy and Ramon weigh 354 pounds, and Paul and Ramon weigh 352 pounds. How much does each weigh individually?
-----
Equations:
p + q = 364
r + q = 354
p + r = 352
-------
Rearrange:
p = 364-q
r = 354-q
----------
Substitute for "p" and "r" and solve for "q":
364-q + 354-q = 352
718 - 2q = 352
2q = 718-352
2q = 366
Quincy = 183 lbs
----
Solve for "p" and for "r":
p = 364 - 183 = 181 lbs
r = 354 - 183 = 171 lbs
=============================
Cheers,
Stan H.
|
test/741938: A punch mix made with tea and lemonade is made with 7 parts ice tea.what is the ratio of lemonade to total parts of punch?
1 solutions
Answer 452206 by stanbon(57984) on 2013-04-25 18:52:18 (Show Source):
You can put this solution on YOUR website!A punch mix made with tea and lemonade is made with 7 parts ice tea.what is the ratio of lemonade to total parts of punch?
----------------------
insufficient information
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Linear-systems/741874: The instructions say:
Draw the graph of the following linear function.
The function is:
g: x--> x-3
I am not even sure where to start. If you can please help me, that would be much appreciated! (:
~Jesse
1 solutions
Answer 452197 by stanbon(57984) on 2013-04-25 18:38:32 (Show Source):
You can put this solution on YOUR website!Draw the graph of the following linear function.
The function is:
g: x-3
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Two points:
(0,-3),(2,-1)
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Plot the two points and draw a line thru them:
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Cheers,
Stan H.
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Numbers_Word_Problems/741610: I need help figuring out how to solve this problem. If you could provide a formula and answer that would be great! Thanks in advance.
A number is divided by 4. The result is divided by 3, for a final result of 2. What was the origional number?
1 solutions
Answer 452084 by stanbon(57984) on 2013-04-24 23:00:13 (Show Source):
You can put this solution on YOUR website!A number is divided by 4. The result is divided by 3, for a final result of 2. What was the origional number?
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Equation:
(x/4)/3 = 2
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(x/4) = 6
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x = 24
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Cheers,
Stan H.
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Trigonometry-basics/741613: I'm having issues with this one question.
2 cos 4x+ radical 3=0
I managed to get through some of it but got stuck at:
cos 4x=(-radical3/2) or cos 4x=(-radical3 over 2)
If I can get some really quick help it would be greatly appreciated!
1 solutions
Answer 452083 by stanbon(57984) on 2013-04-24 22:55:37 (Show Source):
You can put this solution on YOUR website!2 cos 4x+ radical 3=0
----
2*cos(4x) = sqrt(3)
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cos(4x) = [sqrt(3)]/2
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4x = 60 degrees or 4x = -60 degrees
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x = 15 degrees or x = -15 degrees
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Cheers,
Stan H.
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Age_Word_Problems/741602: James is as twice as old as his son. in 20 years their combined ages will be 115 years. how old is his son?
1 solutions
Answer 452078 by stanbon(57984) on 2013-04-24 22:28:36 (Show Source):
You can put this solution on YOUR website!James is as twice as old as his son. in 20 years their combined ages will be 115 years. how old is his son?
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Equations:
j = 2*s
j+20 + s+20 = 115
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Substitute for "j" and solve for "s":
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2s+20 + s+20 = 115
3s + 40 = 115
3s = 75
son's age = 25
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James's age = 3s = 75
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Cheers,
Stan H.
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Linear-equations/741599: Pedro decides to draw a line through the points (1,2) and (4,7). Create an equation for Pedro's line of best fit that models y in terms of x
1 solutions
Answer 452077 by stanbon(57984) on 2013-04-24 22:21:22 (Show Source):
You can put this solution on YOUR website!Pedro decides to draw a line through the points (1,2) and (4,7). Create an equation for
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slope = (7-2)/(4-1) = 5/3
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Form: y = mx + b
Solve for "b":
2 = (5/3)1 + b
----
b = 1/3
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Equation:
y = (5/3)x + (1/3)
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Cheers,
Stan H.
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test/741597: 6x^2+6y^2=162
Parabola, circle, ellipse, or hyperbola
1 solutions
Answer 452076 by stanbon(57984) on 2013-04-24 22:16:48 (Show Source):
You can put this solution on YOUR website!6x^2+6y^2=162
Parabola, circle, ellipse, or hyperbola
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Since the coefficients of x^2 and y^2 are equal
the answer is "circle"
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x^2 + y^2 = 27
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Center at (0,0)
radius = sqrt(27) = 3sqrt(3)
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Cheers,
Stan H.
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Linear-equations/741593: elimination:-8x+2y=-18
-x +6y=15
1 solutions
Answer 452074 by stanbon(57984) on 2013-04-24 22:07:57 (Show Source):
You can put this solution on YOUR website!elimination:
-8x+2y=-18
-x +6y=15
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-24x + 6y = -54
-x + 6y = 15
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Subtract:
23x = 69
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x = 3
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Solve for "y":
-x + 6y = 15
-3 + 6y = 15
6y = 18
y = 3
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Cheers,
Stan H.
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Geometry_Word_Problems/741585: Jeremy helps Madeline build a rectangular pen with a perimeter of 86 feet. Twice the pen's width is one more than three times its length. What is the width of the pen?
1 solutions
Answer 452069 by stanbon(57984) on 2013-04-24 21:56:53 (Show Source):
You can put this solution on YOUR website!Jeremy helps Madeline build a rectangular pen with a perimeter of 86 feet. Twice the pen's width is one more than three times its length. What is the width of the pen?
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Perim = 2(width + length)
Perim = 2*width + 2*length
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2W = 3L + 1
--------
86 = 3L+1 + 2L
----
86 = 5L + 1
5L = 85
Length = 17 feet
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Solve for "W":
2W = 3L + 1
2W = 51+1
Width = 26 feet
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Cheers,
Stan H.
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Numeric_Fractions/741570: Please help me solve m+n over m-n / 3m+3n over m^-n^
I hope I wrote that okay... Thank you!
1 solutions
Answer 452063 by stanbon(57984) on 2013-04-24 21:51:14 (Show Source):
You can put this solution on YOUR website!solve m+n over m-n / 3m+3n over m^-n^
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[(m+n)/(m-n)]/[(3(m+n)/(m-n)]
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= [(m+n)/(m-n)]
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Cancel factors common to numerator and denominator to get:
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= 1/3
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Cheers,
Stan H.
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