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Recent problems solved by 'stanbon'
stanbon answered: 57269 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269, >>Nexttest/479965: I'm doing elmination and I don't get how to do it with this problem: x-y=5 and x+y=23 can you please explain how to do it step by step please
1 solutions
Answer 328797 by stanbon(57342)   on 2011-08-09 22:09:36 (Show Source):
You can put this solution on YOUR website!x-y=5
x+y=23
-------------
Add and solve for "x":
2x = 28
---
x = 14
----
Solve for "y":
x + y = 23
14 + y = 23
y = 9
------------------
Solution: (14,9)
========================
Cheers,
Stan H.
|
Sequences-and-series/479951: What are the four missing terms between 4 and 1/16 in the geometric sequence?
1 solutions
Answer 328794 by stanbon(57342) on 2011-08-09 21:47:08 (Show Source):
You can put this solution on YOUR website!What are the four missing terms between 4 and 1/16 in the geometric sequence?
---
a(1) = 4
a(6) = 1/16
----------------
a = 4
a(6) = 4*r^5 = 1/16
r^5 = 1/64
r = (1/64)^(1/5) = (2^(-6))^(1/5) = 2^(-6/5)
----
2nd term: 4*2^(-6/5)
3rd term: 4*2^(-12/5)
4th term: 4*2^(-18/5)
5th term: 4*2^(-24/5)
6th term: 4*2^(-30/5) = 4*2^(-6) = 2^(-4) = 1/16
=============================================
Cheers,
Stan H.
============================
|
Sequences-and-series/479949: What is the sum of the first fourteen terms of the geometric series 1/3 + 1/12 + 1/49
1 solutions
Answer 328788 by stanbon(57342) on 2011-08-09 21:35:02 (Show Source):
You can put this solution on YOUR website!What is the sum of the first fourteen terms of the geometric series 1/3 + 1/12 + 1/49
---
a = 1/3
---
r = (1/12)/(1/3) = 1/4
----
S(n) = a[1-r^n]/[1-r]
----
S(14) = (1/3)[1-(1/4)^14]/[1-(1/4] = (1/3)[1/(3/4)] = (1/3)(4/3) = 4/9
======================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/479948: on two occasions last month,Sam rented a car from the same place and same model.He paid 210 and drove 625 miles the first trip.Second trip he paid 133.50 and drove 370 miles.
After plotting these two points on a graph and drawing the line that goes through
them, answer the following:
What is the equation of the line in the slope intercept form of the equation?
In your own words, explain what question the slope of the line answers for Sam.
What does the y intercept tell Sam and how does it help him?
Write a one paragraph memo explaining to Sam the answers to his question and
how knowledge of algebra and graphing helped you to find the answers.
1 solutions
Answer 328786 by stanbon(57342) on 2011-08-09 21:28:36 (Show Source):
You can put this solution on YOUR website!on two occasions last month,Sam rented a car from the same place and same model.He paid 210 and drove 625 miles the first trip.Second trip he paid 133.50 and drove 370 miles.
After plotting these two points on a graph and drawing the line that goes through them, answer the following:
---
Using (625 mi ; 210 dollars) and (370 miles ; 133.50 dollars)
---
Slope = (210-133.5)/(625-370) = 0.3
----
Form: y = mx + b
210 = 0.3*625+b
b = 22.5
---
Cost = 0.3(miles) + 22.5
---------
What is the equation of the line in the slope intercept form of the equation?
------
In your own words, explain what question the slope of the line answers for Sam.
For each mile he drives the cost rises 30 cents.
-----------------------------
What does the y intercept tell Sam and how does it help him?
The initial cost of renting the car was $22.50
===================
I'll leave the discussion paragraph to you.
=======================
Cheers,
Stan H.
================
|
test/479946: Give two examples of continous variable
1 solutions
Answer 328785 by stanbon(57342) on 2011-08-09 21:20:48 (Show Source):
You can put this solution on YOUR website!height and weight
---
Neither one is really mesurable as they
can always be measured with a greater
degree of accuracy if better measuring
instruments are available.
----
So, our weight and our height is just
an estimate.
-----------
Cheers,
Stan H.
===========
|
Probability-and-statistics/479929: suppose that at another plant Coca-Cola is filling bottles with the more traditional 20 ounce of fluid. A lab randomly samples 150 bottles and tests the bottles for fill volume
1 solutions
Answer 328776 by stanbon(57342) on 2011-08-09 20:26:55 (Show Source):
|
Linear-systems/479930: find the system of these equations -2x=2+1y and -6x-y=-2
1 solutions
Answer 328774 by stanbon(57342) on 2011-08-09 20:25:26 (Show Source):
You can put this solution on YOUR website!2x=2+1y and -6x-y=-2
---
Rearrange:
2x - y = 2
-6x- y = -2
----
Subtract and solve for "x":
8x = 4
x = 1/2
----
Solve for "y"
2x - y = 2
2(1/2) - y = 2
1 - y = 2
y = -1
===================
Cheers,
Stan H.
========================
|
Triangles/479920: A slide 4.7 m long makes an angle of 25 degrees with the ground. How far above the ground is the top of the slide?
1 solutions
Answer 328769 by stanbon(57342) on 2011-08-09 20:03:14 (Show Source):
You can put this solution on YOUR website!A slide 4.7 m long makes an angle of 25 degrees with the ground. How far above the ground is the top of the slide?
-----------------
Draw the picture.
4.7 is the hypotenuse
The angle at the ground is 25 degrees.
----
Let the side opposite the ground angle be "y":
----
Equation:
Solve sin(25) = y/4.7
y = 4.7*sin(25) = 1.9863 meters
==================================
Cheers,
Stan H.
==========
|
Travel_Word_Problems/479921: The elevatorin Washington Monument takes 75 seconds to travel 500 feet to the top floor. What is the spee of the elevator in miles per hour?
1 solutions
Answer 328767 by stanbon(57342) on 2011-08-09 19:57:18 (Show Source):
You can put this solution on YOUR website!The elevator in Washington Monument takes 75 seconds to travel 500 feet to the top floor. What is the speed of the elevator in miles per hour?
--------------------
(500/75)(ft/sec)[3600 sec/1hr)(1mi/5280ft)
------
= [500*1*3600*1)/(75*1*1*5280)(miles/hour)
---
= 4.55 mph
==================
Cheers,
Stan H.
==================
|
Percentage-and-ratio-word-problems/479749: hi there i am stuck on a homework question about ratio's becasue it has a fraction.... the question is...Write the ratio of lenght to width if a picture frame has length of 10 1/2 and a width and 8 3/4
1 solutions
Answer 328681 by stanbon(57342) on 2011-08-09 13:43:54 (Show Source):
You can put this solution on YOUR website!hi there i am stuck on a homework question about ratio's becaue it has a fraction.... the question is...Write the ratio of length to width if a picture frame has length of 10 1/2 and a width and 8 3/4
------------------
(10 1/2): (8 3/4)
---
= (21/2): (35/4
---
= (42/4): 35/4
----
= 42:35
---
= 7:5
==============
Cheers,
Stan H.
|
Points-lines-and-rays/479748: If the volume of a cube is 216 cubic meters, what is the length (in meters) of each side?
1 solutions
Answer 328679 by stanbon(57342) on 2011-08-09 13:34:42 (Show Source):
You can put this solution on YOUR website!If the volume of a cube is 216 cubic meters, what is the length (in meters) of each side?
----
Volume = (side)^3
216 = s^3
side = 216^(1/3)
side = 6 meters
====================
Cheers,
Stan H.
====================
|
Equations/479737: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
5x – 4y = 10.5
20x – 16y = 42
1 solutions
Answer 328675 by stanbon(57342) on 2011-08-09 13:22:39 (Show Source):
You can put this solution on YOUR website!Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
5x – 4y = 10.5
20x – 16y = 42
----
If you multiply thru the 1st equation by 4
you will see the two equations are the same.
----
Infinite number of solutions of the form (x , (4/5)x + (10.5/5))where
x is any Real Numbers
==============================
Cheers,
Stan H.
============
|
Linear_Equations_And_Systems_Word_Problems/479731: Select the set of equations that represents the following situation: Mary invested one amount at 5% simple interest, and a second amount at 4% interest, earning $21.32 in one year. If she had switched the amounts, she would have earned $25.84. What were the two amounts?
A)0.05x + 0.04y = 25.84; 0.05x + 0.04y = 21.32
B)5x + 4y = 21.32; 5y + 4x = 25.84
C)0.05x + 0.04y = 21.32; 0.05y + 0.04x = 25.84
D)5x + 4y = 25.84; 5x + 4y = 21.32
1 solutions
Answer 328674 by stanbon(57342) on 2011-08-09 13:18:16 (Show Source):
You can put this solution on YOUR website!13:11:42): Select the set of equations that represents the following situation: Mary invested one amount at 5% simple interest, and a second amount at 4% interest, earning $21.32 in one year. If she had switched the amounts, she would have earned $25.84. What were the two amounts?
A)0.05x + 0.04y = 25.84; 0.05x + 0.04y = 21.32
B)5x + 4y = 21.32; 5y + 4x = 25.84
C)0.05x + 0.04y = 21.32; 0.05y + 0.04x = 25.84
D)5x + 4y = 25.84; 5x + 4y = 21.32
---
Ans: C
===========
Cheers,
Stan H.
===========
|
logarithm/479709: Respected Sir/Madam ,
Please help me to solve my problem . I Will be very grateful for your help. My question is :
The value of 16 log(64/60) +12 log (50/48)+7 log (81/80) +log 2
As the Answer given is : 1
So please Sir/Madam provide me the steps for this question..
Thank you,
1 solutions
Answer 328665 by stanbon(57342) on 2011-08-09 12:24:30 (Show Source):
|
logarithm/479706: Respected Sir/Madam ,
Please help me to solve my problem . I Will be very grateful for your help. My question is :
The value of 16 log(64/60) +12 log (50/48)+7 log (81/80) +log 2
As the Answer given is :
So please Sir/Madam provide me the steps for this question..
Thank you,
1 solutions
Answer 328662 by stanbon(57342) on 2011-08-09 12:23:33 (Show Source):
You can put this solution on YOUR website!16 log(64/60) +12 log (50/48)+7 log (81/80) +log 2
---
Do some simplifying:
---
= 16*log(16/15) + 12*log(25/24) + 7*log(81/80) + log(2)
-----
= log[(16/15)^16*(25/24)^12*(81/80)^7*2]
---
= log[10]
---
= 1
===========
cheers,
Stan H.
|
Complex_Numbers/479700: Simply this: {{sqrt(2) + sqrt(6)}/{sqrt(2 + sqrt(3)}}
I multiplied numerator and denominator by {sqrt(2 - sqrt(3)} and was pleased to see the denominator go away, but I was still left with a radical inside a radical. (I already know that the answer is 2, but how do I get there?)
1 solutions
Answer 328661 by stanbon(57342) on 2011-08-09 12:18:02 (Show Source):
You can put this solution on YOUR website!Simply this: {{sqrt(2) + sqrt(6)}/{sqrt(2) + sqrt(3)}}
---
Multiply numerator and denominator by [sqrt(2)-sqrt(3)] to get:
---
{{sqrt(2) + sqrt(6)} /[2-3)
---
Simplify the numerator:
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[2-sqrt(6)+sqrt(12)-sqrt(18)]/(-1)
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= [2-sqrt(6)+2sqrt(3)-3sqrt(2)]/-1
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If the answer you have is 2 you probably made a mistake in
your post to this site.
Cheers,
Stan H.
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Probability-and-statistics/479349: How many green elements are required to make this a legitimate probability distribution if there are a total of 50 elements in this sample? ---
--x---- red---- blue--- orange--brown---green
P(x)--- 0.22--- 0.08----0.20----0.30
Thank you
1 solutions
Answer 328647 by stanbon(57342) on 2011-08-09 11:23:27 (Show Source):
You can put this solution on YOUR website!How many green elements are required to make this a legitimate probability distribution if there are a total of 50 elements in this sample? ---
--x---- red---- blue--- orange--brown---green
P(x)--- 0.22--- 0.08-----0.20----0.30-----?--
---------------------
? = 1 - [0.22 + 0.08 + 0.20 + 0.30]
? = 0.30
===
# of green = 0.3*50 = 15
===========================
Cheers,
Stan H.
============
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Probability-and-statistics/479372: Two and a half artists spend two and a half hours painting two and a half models on two and a half canvases. How many artists are needed to paint 24 models on 24 canvases in twenty hours?
1 solutions
Answer 328645 by stanbon(57342) on 2011-08-09 11:18:54 (Show Source):
You can put this solution on YOUR website!Two and a half artists spend two and a half hours painting two and a half models on two and a half canvases. How many artists are needed to paint 24 models on 24 canvases in twenty hours?
----
# of artists is directly related to # of models, directly related
to # of canvases and indirectly related to time.
---
a = k*m*c/t
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Solve for "k" using "Two and a half artists spend two and a half hours painting two and a half models on two and a half canvases".
----
(5/2) = [k*(5/2)*(5/2)]/(5/2)
(5/2) = k*(5/2)
k = 1
------
Equation:
a = mc/t
------------
How many artists are needed to paint 24 models on 24 canvases in twenty hours?
a = 24*24/20
a = 28.8 artists
====================
Cheers,
Stan H.
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Probability-and-statistics/479432: The water quality is acceptable if the mean amount of suspended solids is less than 49. Construct an α= .05 test to establish that the quality is acceptable.
X=47 S=9.4 degrees of freedom=13
(a)Specify H0 and H1.
(b)State the test statistic.
(c)What does the test conclude?
1 solutions
Answer 328639 by stanbon(57342) on 2011-08-09 11:09:13 (Show Source):
You can put this solution on YOUR website!The water quality is acceptable if the mean amount of suspended solids is less than 49. Construct an α= .05 test to establish that the quality is acceptable.
X=47 S=9.4 degrees of freedom=13
-------------------------------------
(a)Specify
H0: u >= 49
H1: u < 49 (?)
----------------------
(b)State the test statistic
t(47) = (47-49)/[9.4/sqrt(14)) = -2/[2.51] = -0.7961
----
p-value = P(t<-0.7961 when df = 13) = tcdf(-100,-0.7961,13) = 0.22
----
(c)What does the test conclude?
Since the p-value is greater than 5%, fail to reject Ho.
The test results indicate the water quality is not acceptable.
============================
Cheers,
Stan H.
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Probability-and-statistics/479441: The tiles E, T, F, U, N, X, and P of a word game are placed face down in the lid of the game. If two tiles are chosen at random, find each probability.
1) P(E ,then N) ,if replacement occurs
2) P(2 consonants) ,if replacement occurs
3) P(T ,then D) ,if replacement occurs
4) P(2 consonants) ,if no replacement occurs
5) P(select the same letter twice) ,if no replacement occurs
1 solutions
Answer 328633 by stanbon(57342) on 2011-08-09 10:52:29 (Show Source):
You can put this solution on YOUR website!The tiles E, T, F, U, N, X, and P of a word game are placed face down in the lid of the game. If two tiles are chosen at random, find each probability.
Vowels: E,U
Consonants: T,F,N,X,P
1) P(E ,then N) ,if replacement occurs:::::(1/7)^2
---------------
2) P(2 consonants) ,if replacement occurs:::(5/7)^2
---------------
3) P(T ,then D) ,if replacement occurs :::(1/7)^2
--------------------------------------
4) P(2 consonants) ,if no replacement occurs:::(5/7)(4/6) = 10/21
-----------------------------------------
5) P(select the same letter twice) ,if no replacement occurs:: 0 because
it cannot be done.
==============
Cheers,
Stan H.
==============
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Probability-and-statistics/479516: Find everything to the right of Z= -1.68
Find everything in between -1.68 and 2.42
1 solutions
Answer 328629 by stanbon(57342) on 2011-08-09 10:42:45 (Show Source):
You can put this solution on YOUR website!Find the area under the normal curve to the right of Z= -1.68
normalcdf(-1.68,100) = 0.9535
Find the area under the normal curve over the interval z= -1.68 and z = 2.42
normalcdf(-1.68,2.42) = 0.9458
=============
Cheers,
Stan H.
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Probability-and-statistics/479524: Let U = {5, 10, 15, 20, 25, 30, 35, 40}
A = {5, 10, 15, 20}
B = {25, 30, 35, 40}
C = {10, 20, 30, 40}.
Find A ⋂ B.
(Points : 1)
{5, 15, 30, 40}
Ø
{5, 10, 15, 20, 30, 40}
{10, 20}
1 solutions
Answer 328627 by stanbon(57342) on 2011-08-09 10:35:34 (Show Source):
You can put this solution on YOUR website!Let U = {5, 10, 15, 20, 25, 30, 35, 40}
A = {5, 10, 15, 20}
B = {25, 30, 35, 40}
C = {10, 20, 30, 40}.
Find A ⋂ B.
----
There are no elements common to A and B.
Ans: The empty set
-----------
cheers,
Stan H.
===============
(Points : 1)
{5, 15, 30, 40}
Ø
{5, 10, 15, 20, 30, 40}
{10, 20}
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