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Recent problems solved by 'stanbon'
stanbon answered: 57214 problems
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43110..43139 , 43140..43169 , 43170..43199 , 43200..43229 , 43230..43259 , 43260..43289 , 43290..43319 , 43320..43349 , 43350..43379 , 43380..43409 , 43410..43439 , 43440..43469 , 43470..43499 , 43500..43529 , 43530..43559 , 43560..43589 , 43590..43619 , 43620..43649 , 43650..43679 , 43680..43709 , 43710..43739 , 43740..43769 , 43770..43799 , 43800..43829 , 43830..43859 , 43860..43889 , 43890..43919 , 43920..43949 , 43950..43979 , 43980..44009 , 44010..44039 , 44040..44069 , 44070..44099 , 44100..44129 , 44130..44159 , 44160..44189 , 44190..44219 , 44220..44249 , 44250..44279 , 44280..44309 , 44310..44339 , 44340..44369 , 44370..44399 , 44400..44429 , 44430..44459 , 44460..44489 , 44490..44519 , 44520..44549 , 44550..44579 , 44580..44609 , 44610..44639 , 44640..44669 , 44670..44699 , 44700..44729 , 44730..44759 , 44760..44789 , 44790..44819 , 44820..44849 , 44850..44879 , 44880..44909 , 44910..44939 , 44940..44969 , 44970..44999 , 45000..45029 , 45030..45059 , 45060..45089 , 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47070..47099 , 47100..47129 , 47130..47159 , 47160..47189 , 47190..47219 , 47220..47249 , 47250..47279 , 47280..47309 , 47310..47339 , 47340..47369 , 47370..47399 , 47400..47429 , 47430..47459 , 47460..47489 , 47490..47519 , 47520..47549 , 47550..47579 , 47580..47609 , 47610..47639 , 47640..47669 , 47670..47699 , 47700..47729 , 47730..47759 , 47760..47789 , 47790..47819 , 47820..47849 , 47850..47879 , 47880..47909 , 47910..47939 , 47940..47969 , 47970..47999 , 48000..48029 , 48030..48059 , 48060..48089 , 48090..48119 , 48120..48149 , 48150..48179 , 48180..48209 , 48210..48239 , 48240..48269 , 48270..48299 , 48300..48329 , 48330..48359 , 48360..48389 , 48390..48419 , 48420..48449 , 48450..48479 , 48480..48509 , 48510..48539 , 48540..48569 , 48570..48599 , 48600..48629 , 48630..48659 , 48660..48689 , 48690..48719 , 48720..48749 , 48750..48779 , 48780..48809 , 48810..48839 , 48840..48869 , 48870..48899 , 48900..48929 , 48930..48959 , 48960..48989 , 48990..49019 , 49020..49049 , 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53010..53039 , 53040..53069 , 53070..53099 , 53100..53129 , 53130..53159 , 53160..53189 , 53190..53219 , 53220..53249 , 53250..53279 , 53280..53309 , 53310..53339 , 53340..53369 , 53370..53399 , 53400..53429 , 53430..53459 , 53460..53489 , 53490..53519 , 53520..53549 , 53550..53579 , 53580..53609 , 53610..53639 , 53640..53669 , 53670..53699 , 53700..53729 , 53730..53759 , 53760..53789 , 53790..53819 , 53820..53849 , 53850..53879 , 53880..53909 , 53910..53939 , 53940..53969 , 53970..53999 , 54000..54029 , 54030..54059 , 54060..54089 , 54090..54119 , 54120..54149 , 54150..54179 , 54180..54209 , 54210..54239 , 54240..54269 , 54270..54299 , 54300..54329 , 54330..54359 , 54360..54389 , 54390..54419 , 54420..54449 , 54450..54479 , 54480..54509 , 54510..54539 , 54540..54569 , 54570..54599 , 54600..54629 , 54630..54659 , 54660..54689 , 54690..54719 , 54720..54749 , 54750..54779 , 54780..54809 , 54810..54839 , 54840..54869 , 54870..54899 , 54900..54929 , 54930..54959 , 54960..54989 , 54990..55019 , 55020..55049 , 55050..55079 , 55080..55109 , 55110..55139 , 55140..55169 , 55170..55199 , 55200..55229 , 55230..55259 , 55260..55289 , 55290..55319 , 55320..55349 , 55350..55379 , 55380..55409 , 55410..55439 , 55440..55469 , 55470..55499 , 55500..55529 , 55530..55559 , 55560..55589 , 55590..55619 , 55620..55649 , 55650..55679 , 55680..55709 , 55710..55739 , 55740..55769 , 55770..55799 , 55800..55829 , 55830..55859 , 55860..55889 , 55890..55919 , 55920..55949 , 55950..55979 , 55980..56009 , 56010..56039 , 56040..56069 , 56070..56099 , 56100..56129 , 56130..56159 , 56160..56189 , 56190..56219 , 56220..56249 , 56250..56279 , 56280..56309 , 56310..56339 , 56340..56369 , 56370..56399 , 56400..56429 , 56430..56459 , 56460..56489 , 56490..56519 , 56520..56549 , 56550..56579 , 56580..56609 , 56610..56639 , 56640..56669 , 56670..56699 , 56700..56729 , 56730..56759 , 56760..56789 , 56790..56819 , 56820..56849 , 56850..56879 , 56880..56909 , 56910..56939 , 56940..56969 , 56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>NextRate-of-work-word-problems/171680: Three painters can finish painting a wall in 10 minutes. The first painter can finish a wall in 20 minutes and the second one can do it in 30 minutes. How long would it take the third painter to do the job alone.
1 solutions
Answer 126805 by stanbon(57282)   on 2008-12-06 15:29:48 (Show Source):
You can put this solution on YOUR website!Three painters can finish painting a wall in 10 minutes. The first painter can finish a wall in 20 minutes and the second one can do it in 30 minutes. How long would it take the third painter to do the job alone.
------------------------
1st painter DATA
Time = 20 min/job ; rate = 1/20 job/min
-------------
2nd painter DATA:
Time = 30 min/job ; rate = 1/30 job/min
---------------
3rd painter DATA:
Time = x min/job ; rate = 1/x job/min
-----------------
Together DATA:
Time = 10 min/job ;rate = 1/10 job/min
-------------------
EQUATION:
rate + rate + rate = together rate
1/20 + 1/30 + 1/x = 1/10
Multiply thru by 60x to get:
3x + 2x + 60 = 6x
x = 60 minutes (time for the 3rd painter to do the job)
=======================
Cheers,
Stan H.
|
Travel_Word_Problems/171663: Judy averaged 42 miles per hour (mph) driving from Allentown to Harrisburg and 51 mph driving from Harrisburg to Pittsburgh. See the accompanying figure. Ifshe drove a total of 288 miles in 6 hours, then how long did it take her to drive from Harrisburg to Pittsburgh?
1 solutions
Answer 126795 by stanbon(57282) on 2008-12-06 13:48:18 (Show Source):
You can put this solution on YOUR website!Judy averaged 42 miles per hour (mph) driving from Allentown to Harrisburg and 51 mph driving from Harrisburg to Pittsburgh. See the accompanying figure. Ifshe drove a total of 288 miles in 6 hours, then how long did it take her to drive from Harrisburg to Pittsburgh?
-----------------------------
A to H DATA:
rate = 42 mph ; distance = x miles ; time = x/42 hrs.
-----------------------
H to P DATA:
rate = 51 mph ; distance = 288-x miles ; time = (288-x)/51 hrs
-----------------------
EQuATION:
time + time = 6 hrs
x/42 + (288-x)/51 = 6
51x + 42*288 - 42x = 6*42*51
9x = 42(6*51-288)
x = 42*18/9
x = 84 miles
----
H to P
distance: 288-x = 204
time = 204/51 = 4 hrs.
============================
Cheers,
Stan H.
|
absolute-value/171637: Please solve this inequasion for me!!! |x+2|/|x-3|≤2
1 solutions
Answer 126793 by stanbon(57282) on 2008-12-06 13:39:21 (Show Source):
You can put this solution on YOUR website! |x+2|/|x-3|≤2
------------------
1st: x cannot be 3
----------------------------------
2nd: Solve the EQUALITY:
(x+2)/x-3) = 2
x+2 = 2x-6
x = 8
-------
If -2 < x < 3,
(x+2)/[-(x-3)] = 2
x+2 = -2x+6
3x = 4
x = 1.3333333...
-------------
Plot those three values on a number line: 1.3333, 3, 8
------------------
Check test values in the 4 resulting intervals to see where the solutions are.
-------------
Check x = -10: |-10+2|/|-10-3| < = 2; true, so solutions in (-inf,1.3333]
Check x = 2 ; |2+2|/|2-3| = 4 < 2; false
Check x =5 ; |5+2|/|5-3| =7/2 < 2; false
Check x = 10 ; |10+2|/|10-3|=12/7 < 2; true, so solution in [8,+inf)
--------------
Ans: (-inf,1.333]U[8,+inf)
==============================
Cheers,
Stan H.
|
Triangles/171640: the hypotneuse of a right triangle is 2.9 inches long.the longer leg is 1.7 units longer than the shorter leg. what is the length of the side of the triangle?
1 solutions
Answer 126787 by stanbon(57282) on 2008-12-06 11:51:06 (Show Source):
You can put this solution on YOUR website! the hypotneuse of a right triangle is 2.9 inches long.the longer leg is 1.7 units longer than the shorter leg. what is the length of the side of the triangle?
-----------------
Let shorter leg be x inches long
then 2nd leg is "x+1.7" inches long.
----------------
EQUATION:
2.9^2 = x^2 + (x+1.7)^2
8.41 = x^2 + x^2 + 3.4x + 2.89
2x^2 + 3.4x - 5.52 = 0
x^2 + 1.7x - 2.76 = 0
x = [-1.7 +- sqrt(1.7^2 - 4*-2.76)]/2
x = [-1.7 +- sqrt(13.93)]/2
x = [-1.7 +- 3.7323]/2
Positive solution:
x = 1.01615000
Cheers,
Stan H.
================
|
Geometric_formulas/171644: The height h (in feet) of an object that is dropped from the height of s feet is given by the formula h = s - 16t 2 , where t is the time the object has been falling. A 5 foot tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from the 3 story. How long does she have to get out of the way? Round to the nearest tenth. (A story is 12 feet.)
1 solutions
Answer 126785 by stanbon(57282) on 2008-12-06 11:32:18 (Show Source):
You can put this solution on YOUR website!The height h (in feet) of an object that is dropped from the height of s feet is given by the formula h = s - 16t 2 , where t is the time the object has been falling. A 5 foot tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from the 3 story. How long does she have to get out of the way? Round to the nearest tenth. (A story is 12 feet.)
--------------------
h(t) = s - 16t^2
------------------
5 = 36 -16t^2
-16t^2 = -31
t^2 = 31/16
t = (sqrt(31))/4
t = 1.39.. seconds
========================
Cheers,
Stan H.
|
Probability-and-statistics/171641: This question is from textbook
Please double check my work
The Ph of a patients blood was measured periodically during one week, and the measured values were 7.37, 7.40, 7.45, 7.45, and 7.44. Find the standard deviation and variance for the data. Round the results to the nearest thousandth.
I added 7.37 + 7.40 + 7.45 + 7.45 + 7.44 = 37.11
then I divided 37.11/ 5 and came up with the answer of 7.4222
Did I do this right?
1 solutions
Answer 126783 by stanbon(57282) on 2008-12-06 11:25:06 (Show Source):
You can put this solution on YOUR website!
The Ph of a patients blood was measured periodically during one week, and the measured values were 7.37, 7.40, 7.45, 7.45, and 7.44. Find the standard deviation and variance for the data. Round the results to the nearest thousandth.
I added 7.37 + 7.40 + 7.45 + 7.45 + 7.44 = 37.11
then I divided 37.11/ 5 and came up with the answer of 7.4222
Did I do this right?
---------
That is the mean; you want the standard deviation (s) and the variance (s^2)
======================
Cheers,
Stan H.
|
Probability-and-statistics/171574: I NEED URGENT HELP WITH THESE TWO QUESTIONS. MY STEPS WERE CORRECT BUT CALCULATIONS ARE WRONG. I WANT TO REVIEW FOR MY FINALS. ALL TUTOR YOU ARE WELCOME TO ANSWER. PAID OR NOT. THANKS A BUNCH! I NEED EXPLAINED SOLUTIONS.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.
6) The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9 lb. Assuming that ! is known to be 121.2 lb, use a 0.10 significance level to test the claim that the population mean of all such employees
weights is less than 200 lb.
Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution.
7) A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-five job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 183 and 12, respectively. Use a 0.05 level of significance to test the claim that this sample comes from a population with a mean score greater than 160.
1 solutions
Answer 126765 by stanbon(57282) on 2008-12-06 08:29:03 (Show Source):
You can put this solution on YOUR website!6) The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9 lb. Assuming that ! is known to be 121.2 lb, use a 0.10 significance level to test the claim that the population mean of all such employees
weights is less than 200 lb.
Ho: mu >= 200
Ha: mu < 200
------
n= 54; s = 121.2, x-bar = 183.9, alpha = 0.10
------
If you use a z-test you get:
test statistic = -0.97516.. and p-value=0.164493...
Conclusion: Since p>10%, Fail to reject Ho.
-----
If you use a t-test you get:
test statistic = -0.976158... and p-value = 0.1667104
so you would still "Fail to Reject Ho".
================================================
Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution.
-----------------------------------
7) A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-five job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 183 and 12, respectively. Use a 0.05 level of significance to test the claim that this sample comes from a population with a mean score greater than 160.
Ho: u = 160
Ha: u > 160
--------------
n=25; sample mean = 183, s=12, alpha = 5%
------
z-test results: test statistic = 9.583333... p-value = 1.0000
since p is greater than 5%, Fail to reject Ho.
------
t-test results: test stat= 9.58333; p-value = 0.9999999
Conclusion: same as z-test
------
Comment: I have a feeling that your posted data for the 2nd
question is not accurate. Is that standard deviation really 12?
==============================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/171612: The formula I=PRT
23.If I owe $84.00 in interest after four years on a loan at 6% interest, how much did I originally borrow?
32. The difference in age between two churches is 154 years.
a. How old is the older church if the newer church is 226 years old.
is the answer 380?
b. If the newer church was built in the year 1650, what year was the older church built?
is the answer 1496?
44.About 71.5 % of the drivers involved in fatal motor vehicle accidents are male. In 1999, 30,400 male drivers were involved in fatal motor vehicle accidents. How many accidents were there in all?
Of last year's graduates from a local high school, 182 responded to a higher education survey. That was 28% of the graduating class. How many people graduated from that school last year?
1 solutions
Answer 126763 by stanbon(57282) on 2008-12-06 07:55:35 (Show Source):
You can put this solution on YOUR website!The formula I=PRT
23.If I owe $84.00 in interest after four years on a loan at 6% interest, how much did I originally borrow?
84 = P*0.06*4
84 = P*0.24
P = 84/0.24
P = $350.00
========================
32. The difference in age between two churches is 154 years.
a. How old is the older church if the newer church is 226 years old.
is the answer 380?
Ans: newer + 154 = older
226 + 154 = older
older = 380
You are correct
=========================
b. If the newer church was built in the year 1650, what year was the older church built?
is the answer 1496?
newer - 154 = older
1650 - 154 = older
older = 1496
You are correct
==========================
44.About 71.5 % of the drivers involved in fatal motor vehicle accidents are male. In 1999, 30,400 male drivers were involved in fatal motor vehicle accidents. How many accidents were there in all?
Let "x" be the total number of accidents.
Then 0.715x = 30,400
x = 30400/0.715
x = 42517.48
Rounding down you get 42517
=================================
Of last year's graduates from a local high school, 182 responded to a higher education survey. That was 28% of the graduating class. How many people graduated from that school last year?
0.28x = 182
x = 182/0.28
x = 650
==================================
Cheers,
Stan H.
|
Expressions-with-variables/171614: simplify the expression:write in lowest terms _3x+1_ * _x-2_
x-2 2x+3
this is in fraction form just slide the numbers over...I tried to make it like a fraction ???? I actually have a lot more that I don't understand if anyone is willing to help that would be great
1 solutions
Answer 126761 by stanbon(57282) on 2008-12-06 07:36:23 (Show Source):
You can put this solution on YOUR website!_3x+1_ * _x-2_
x-2 2x+3
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Cancel the x-2 factor which is common to numerator and denominator to get:
= (3x+1)/(2x+3)
That is about all you can do with this problem.
Cheers,
Stan H.
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Radicals/171619: This question is from textbook Introductory Algebra
Solve.
12/sqrt 5x + 6 = sqrt 2x + 5
1 solutions
Answer 126760 by stanbon(57282) on 2008-12-06 07:32:51 (Show Source):
You can put this solution on YOUR website!12/sqrt(5x + 6) = sqrt(2x + 5)
Multiply thru by sqrt(5x+6) to get:
12 = sqrt[2x+5)(5x+6)]
----
Square both sides to get:
144 = 10x^2 + 37x +30
10x^2 + 37x - 114 = 0
Use the quadratic formula to get:
x = [-37 +- sqrt(5929)]/20
x = [-37 +- 77]/20
x = 2 or x = -114/20
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2 is a solution; -114/20 is extraneous
=============================
Cheers,
Stan H.
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Numbers_Word_Problems/171591: In a list of numbers,the first is 2,the second is 7,and each subsequent number is the sum of all the preceding numbers.What is the fifth number in the list.
If the 100th number in the list is x,what is the 103rd number in the list?
The sum of two numbers is 19.If 5 times the smaller number is 3 less than twice the larger number,what are the numbers?
1 solutions
Answer 126750 by stanbon(57282) on 2008-12-05 22:52:40 (Show Source):
You can put this solution on YOUR website!In a list of numbers,the first is 2,the second is 7,and each subsequent number is the sum of all the preceding numbers.What is the fifth number in the list.
List the numbers: 2,7,9,16,25
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If the 100th number in the list is x,what is the 103rd number in the list?
Good question.
-----------------------------------------
The sum of two numbers is 19.5 If 5 times the smaller number is 3 less than twice the larger number,what are the numbers?
----------------
Equations:
x + y = 19
5x = 2y-3
---------------
Rearrange:
x + y = 19
5x-2y = -3
---------------
5x + 5y = 95
5x - 2y = -3
---------------
7y = 98
y = 14
Then x = 5
===============
Cheers,
Stan H.
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Linear-equations/171593: This is a work sheet from my daughter's teacher.
Graph the linear system and tell how many solutions it has. If there is exactly one solution, estimate the solution and check it algebratically.
1.)x+y=4
x-y=2
2.)y=3x
2y=6x
3.)y=1/2x+2
y=1/2x-2
Solve the system using any algebratic method.
4.)x+y=2
3x-2y=6
5.)y=3x
x+y=12
6.)5x-2y=30
x+2y=6
1 solutions
Answer 126749 by stanbon(57282) on 2008-12-05 22:44:45 (Show Source):
You can put this solution on YOUR website!It would be better if your daughter tries these herself.
She could then ask for help on only the ones she cannot
handle.
We learn one step at a time.
Cheers,
Stan H.
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Inequalities/171600: Hi Everybody! I've been out of school for 23 years and even when I was there I was never any good at this stuff. Any help would be Appreciated.
Here's the problem:
2[-7y-3(5-4y)+10]=10y-12
1 solutions
Answer 126748 by stanbon(57282) on 2008-12-05 22:42:18 (Show Source):
You can put this solution on YOUR website!2[-7y-3(5-4y)+10]=10y-12
Divide both sides by 2 to get:
[-7y-3(5-4y)+10] = 5y - 6
[-7y -15 + 12y + 10] = 5y -6
5y -5 = 5y -6
If you subtract 5y from both sides you get this contradiction:
-5 = -6
================
The equation is "inconsistent" and has no solution.
The thing that was inconsistent was all those "y's".
You thought they all meant the same number; they don't.
===================
Welcome back to the land of the learning.
------------------------
Cheers,
Stan H.
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Geometry_Word_Problems/171595: The measure of the second angle of a triangle is 30% more than that of the first angle. The measure of the third angle is 10% less than twice the first angle. Find the measures of all the angles.
I tried doing somethings but honestly i don't even know where to start.
1 solutions
Answer 126747 by stanbon(57282) on 2008-12-05 22:36:34 (Show Source):
You can put this solution on YOUR website!The measure of the second angle of a triangle is 30% more than that of the first angle. The measure of the third angle is 10% less than twice the first angle. Find the measures of all the angles.
--------------------------------
Let the measure of the 1st angle be "x" degrees.
Then the measure of the 2nd angle is 1.30x degrees
And the measure of the 3rd angle is 0.90(2x) degrees
----------------------------------
EQUATION:
x + 1.3x + 1.8x = 180
10x + 13x + 18x = 1800
41x = 1800
x = 43.90 degrees (measure of the 1st)
1.3x = 57.073 degrees (measure of the 2nd)
1.8x = 79.024 degrees (measure of the 3rd)
==============================================
Cheers,
Stan H.
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Equations/171597: Can not figure out the answers to combine like terms.
1.) -3+13w -7w-5
2.) 5x^4+3x^2- 6x^4+x
3.) 2- 5+3y+5y^2+4y
4.) 2d^3-4d+6
Please help! :) Thanks
1 solutions
Answer 126745 by stanbon(57282) on 2008-12-05 22:25:57 (Show Source):
You can put this solution on YOUR website!combine like terms.
1.) -3+13w -7w-5 = 6w-8
--------------------------------
2.) 5x^4+3x^2- 6x^4+x = -x^4+3x^2+x
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3.) 2- 5+3y+5y^2+4y = 5y^2+7y-3
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4.) 2d^3-4d+6 = 2d^3 - 4d + 6
-----------------------------------
Cheers,
Stan H.
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Finance/171599: KIM SPENT TWO FIFTHS OF HER SALARY ON A SHIRT AND A HAT. THE SHIRT COST THREE TIMES AS MUCH AS THE HAT. IF SHE HAS $36.00 LEFT, HOW MUCH DID THE HAT COST?
1 solutions
Answer 126744 by stanbon(57282) on 2008-12-05 22:22:35 (Show Source):
You can put this solution on YOUR website!KIM SPENT TWO FIFTHS OF HER SALARY ON A SHIRT AND A HAT. THE SHIRT COST THREE TIMES AS MUCH AS THE HAT. IF SHE HAS $36.00 LEFT, HOW MUCH DID THE HAT COST?
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Her salary = s + h + 36
----------------------------
s = 3h
s+h = (2/5)[s+h+36]
--------------------------
Substitute to solve for "h":
3h + h = (2/5)[3h + h + 36]
4h = (2/5)[4h + 36]
20h = 2[4h+36]
10h = 4h + 36
6h = 36
h = $6 (the hat cost)
============================
Cheers,
Stan H.
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Geometry_Word_Problems/171598: Latisha puts a fence around her back yard. She finds that she uses 15 more feet for each long side of the yard than she does for each width. If she used 70ft of fencing, how long is each side of her yard(answer with a length and a width).
1 solutions
Answer 126743 by stanbon(57282) on 2008-12-05 22:12:37 (Show Source):
You can put this solution on YOUR website!
Latisha puts a fence around her back yard. She finds that she uses 15 more feet for each long side of the yard than she does for each width. If she used 70ft of fencing, how long is each side of her yard(answer with a length and a width).
----------------
Let the width be "x",
then the length will be "x+15".
----------------
Perimeter: P = 2(L+W)
70 = 2(x + x+15)
2x+15 = 35
2x = 20
x = 10 ft. (width)
x+15 = 15 ft (length)
======================
Cheers,
Stan H.
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logarithm/171560: find x
7^x = 4^x+1
that you do this but i dont know how find x
log7^x=log4^x+1
xlog7=xlog4+1log4
x(log7-xlog4)=1log4
x= 1log4/log7-log4
1 solutions
Answer 126723 by stanbon(57282) on 2008-12-05 19:19:52 (Show Source):
You can put this solution on YOUR website!find x
7^x = 4^(x+1)
Take the log of both sides to get:
xlog(7) = (x+1)log(4)
xlog(7)-xlog(4) = log4
x(log(7/4)) = log4
x = [log(4)]/[log(7/4)]
x = 2.477225...
Cheers,
Stan H.
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Quadratic_Equations/171528: / means square root.
[] means absoulte value..
1.. simpliy -/-169
2..find [-1+i]
1 solutions
Answer 126720 by stanbon(57282) on 2008-12-05 19:15:38 (Show Source):
You can put this solution on YOUR website!/ means square root.
[] means absolute value..
1.. simpliy -/-169
-sqrt(-169) = -13i
------------------------------
2..find [-1+i]
|-1+i| = sqrt((-1)^2 + 1^2)
= sqrt(2)
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Cheers,
Stan H.
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Mixture_Word_Problems/171548: Trying to solve Algebra-1 Mixture problems. Some of the simple ones I understand, but I am stumped on this one:
Steven has 3 pounds of Brand 121 nuts that sell for $2.23 a pound. He also has Brand 330 nuts that sell for $1.75 per pound. If he wants a mixture of nuts that sell for $1.93 a pound, how many pounds of Brand 330 should he add?
In following the previous examples they have given me, I build a table such as:
........$$$........LBS.......TOTAL
121.....2.23........3.........6.69
330.....1.75........X.........1.75X
MIX.....1.93.......3+X......1.93(3+X)
The answer is suppose to be 5 pounds, but I don't understand how to take the data from the table and get 5 pounds.
HELP!
and thanks!
1 solutions
Answer 126719 by stanbon(57282) on 2008-12-05 19:10:52 (Show Source):
You can put this solution on YOUR website!Steven has 3 pounds of Brand 121 nuts that sell for $2.23 a pound. He also has Brand 330 nuts that sell for $1.75 per pound. If he wants a mixture of nuts that sell for $1.93 a pound, how many pounds of Brand 330 should he add?
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Value equation: 223*3 + 175x = 193(3+x)
669 + 175x = 579 + 193x
Subtract 579 from both sides;
Also, subtract 175x from both sides to get:
18x = 90
x = 5 lbs. (amt of Brand 330 nuts needed for the mixture)
======================
Cheers,
stan H.
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Square-cubic-other-roots/171503: okay so how do i simplify the square root of 128? i know it has something to do with prime numbers i was thinking product rule using 4, 2 and sixteen but i am not sure what to do after that or how to write it!
1 solutions
Answer 126645 by stanbon(57282) on 2008-12-05 13:48:00 (Show Source):
You can put this solution on YOUR website!how do i simplify the square root of 128
The prime number breakdown of 128 is
128 = 2*64
= 2*2*32*
= 2*2*2*16
= 2*2*2*2*8
---
---
= 2*^7
------------
So sqrt(128) = sqrt(2^7)
= sqrt(2*6)*sqrt(2)
= 2*^3*sqrt(2)
= 8sqrt(2)
-----------------
A shorter way to go is
sqrt(64*2) = sqrt(64)*sqrt(2)
= 8*sqrt(2)
================
Cheers,
Stan H.
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absolute-value/171505: X - 10%=180
THIS IS AN EXAMPLE. TOTAL PRICE MINUS 10% EQUALS 180.HOW DO YOU FIND OUT THE START NUMBER AND HOW MUCH THE 10% IS?
1 solutions
Answer 126642 by stanbon(57282) on 2008-12-05 13:41:41 (Show Source):
You can put this solution on YOUR website! X - 10%=180
THIS IS AN EXAMPLE. TOTAL PRICE MINUS 10% EQUALS 180.HOW DO YOU FIND OUT THE START NUMBER AND HOW MUCH THE 10% IS?
------------
If X is the total price and you are subtracting 10% of x
your equation should be
x - 0.10x = 180
0.90x = 180
x = 200
===========
Cheers,
Stan H.
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Miscellaneous_Word_Problems/171502: Given the group(Allen,Brenda,Chad,Dorothy,Eric,Fred,Gail) determine ther number of ways of chooding a president, vice president, secretary and treasurer
1 solutions
Answer 126640 by stanbon(57282) on 2008-12-05 13:37:27 (Show Source):
You can put this solution on YOUR website!Given the group(Allen,Brenda,Chad,Dorothy,Eric,Fred,Gail) determine ther number of ways of choosing a president, vice president, secretary and treasurer
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Order is implied by the offices listed, so the answer is a number of permutations. That answer is 7P4 = 6!/(6-4)! = 7*6*5*4*3 = 840
This is equivalent to 7 ways to choose the pres, 6 ways to choose the vp,
etc.
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If the offices do not imply order the answer is 7C4 = 35
This is equivalent of 35 ways to simply picking 4 people from the 7 available.
=========================
Cheers,
Stan H.
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