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Recent problems solved by 'stanbon'
stanbon answered: 57311 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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49050..49079 , 49080..49109 , 49110..49139 , 49140..49169 , 49170..49199 , 49200..49229 , 49230..49259 , 49260..49289 , 49290..49319 , 49320..49349 , 49350..49379 , 49380..49409 , 49410..49439 , 49440..49469 , 49470..49499 , 49500..49529 , 49530..49559 , 49560..49589 , 49590..49619 , 49620..49649 , 49650..49679 , 49680..49709 , 49710..49739 , 49740..49769 , 49770..49799 , 49800..49829 , 49830..49859 , 49860..49889 , 49890..49919 , 49920..49949 , 49950..49979 , 49980..50009 , 50010..50039 , 50040..50069 , 50070..50099 , 50100..50129 , 50130..50159 , 50160..50189 , 50190..50219 , 50220..50249 , 50250..50279 , 50280..50309 , 50310..50339 , 50340..50369 , 50370..50399 , 50400..50429 , 50430..50459 , 50460..50489 , 50490..50519 , 50520..50549 , 50550..50579 , 50580..50609 , 50610..50639 , 50640..50669 , 50670..50699 , 50700..50729 , 50730..50759 , 50760..50789 , 50790..50819 , 50820..50849 , 50850..50879 , 50880..50909 , 50910..50939 , 50940..50969 , 50970..50999 , 51000..51029 , 51030..51059 , 51060..51089 , 51090..51119 , 51120..51149 , 51150..51179 , 51180..51209 , 51210..51239 , 51240..51269 , 51270..51299 , 51300..51329 , 51330..51359 , 51360..51389 , 51390..51419 , 51420..51449 , 51450..51479 , 51480..51509 , 51510..51539 , 51540..51569 , 51570..51599 , 51600..51629 , 51630..51659 , 51660..51689 , 51690..51719 , 51720..51749 , 51750..51779 , 51780..51809 , 51810..51839 , 51840..51869 , 51870..51899 , 51900..51929 , 51930..51959 , 51960..51989 , 51990..52019 , 52020..52049 , 52050..52079 , 52080..52109 , 52110..52139 , 52140..52169 , 52170..52199 , 52200..52229 , 52230..52259 , 52260..52289 , 52290..52319 , 52320..52349 , 52350..52379 , 52380..52409 , 52410..52439 , 52440..52469 , 52470..52499 , 52500..52529 , 52530..52559 , 52560..52589 , 52590..52619 , 52620..52649 , 52650..52679 , 52680..52709 , 52710..52739 , 52740..52769 , 52770..52799 , 52800..52829 , 52830..52859 , 52860..52889 , 52890..52919 , 52920..52949 , 52950..52979 , 52980..53009 , 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 , 57240..57269 , 57270..57299 , 57300..57329, >>NextNumbers_Word_Problems/233319: I am an odd number. The sum of my digits is 10. I am less than forty. What numbers can i be?
1 solutions
Answer 172222 by stanbon(57384)   on 2009-10-30 18:39:36 (Show Source):
You can put this solution on YOUR website!I am an odd number. The sum of my digits is 10. I am less than forty. What numbers can I be?
--------------
If less than forty it is a 2-digit number.
---
Let the number be 10t+u where t is the tens digit and u is the units digit.
---------------------------------
Equations:
10t+u < 40
t+u = 10
----------------
u = 10-t
----
Substitute into 10t+u<40 and solve for "t":
10t+10-t < 40
9t < 30
t < 30/9 = 3 1/3
----
t is 1,2,or 3
-------------------
If t is 1, u = 9 giving you the number 19
If t is 2, u = 8 giving you the number 28
If t is 3, u = 7 giviing you the number 37
===============================================
Cheers,
Stan H.
|
test/233313: The number S of ant species in Kyle Canyon, Nevasa, can be modeled by the function S=-0.000013 + 0.042E - 21 where E is the elevation (in meters). Predict the elevation(s) at which you would expect to find 10 species of ants.
1 solutions
Answer 172207 by stanbon(57384) on 2009-10-30 17:04:53 (Show Source):
You can put this solution on YOUR website!The number S of ant species in Kyle Canyon, Nevasa, can be modeled by the function S=-0.000013 E^2 + 0.042E - 21 where E is the elevation (in meters). Predict the elevation(s) at which you would expect to find 10 species of ants.
---------------------
-0.000013 E^2 + 0.042E - 21 = 10
---------------
-0.000013 E^2 + 0.042E - 31 = 0
---
Solve for E using the quadratic formula
and accepting only the positive solution.
===========================================
Cheers,
Stan H.
|
Travel_Word_Problems/233275: In a walk a thin to raise money for charity Elisa walked a certain distance at 5mph and then jogged twice that distance at 8 mph. her total time walking and jogging was 2 hours and 15 minutes. how far did she get?
1 solutions
Answer 172186 by stanbon(57384) on 2009-10-30 14:47:38 (Show Source):
You can put this solution on YOUR website!Elisa walked a certain distance at 5mph and then jogged twice that distance at 8 mph.
Her total time walking and jogging was 2 hours and 15 minutes.
How far did she get?
---
Walking DATA:
rate = 5 mph ; distance = x miles ; time = d/r = x/5 hrs.
------------------------------------------
Jogging DATA:
rate = 8 mph ; distance = 2x miles ; time = (2x)/8 hrs.
-------------------------------------------
Equations:
time + time = 2.25 hrs
x/5 + (2x)/8 = 9/4 hrs
Multiply thru by 20 to get:
4x + 5x = 5*9
x = 5 miles
---
Total distance: x + 2x = 5+10 = 15 miles
===========================================
Cheers,
Stan H.
|
real-numbers/233277: Mark every set that 1/2 is a member of.
Whole Numbers
Integers
Rational Numbers
Real Numbers
1 solutions
Answer 172185 by stanbon(57384) on 2009-10-30 14:38:26 (Show Source):
You can put this solution on YOUR website! Mark every set that 1/2 is a member of.
Whole Numbers---no
Integers--------no
Rational Numbers--yes
Real Numbers------yes
=======================
Cheers,
Stan H.
|
Finance/233276: There are 36 coins in a purse, all nickels and quarters. There are 8 more quarters than nickels. The total amount is $6.20. How many nickels and quarters are there?
1 solutions
Answer 172183 by stanbon(57384) on 2009-10-30 14:35:33 (Show Source):
You can put this solution on YOUR website!There are 36 coins in a purse, all nickels and quarters. There are 8 more quarters than nickels. The total amount is $6.20. How many nickels and quarters are there?
---------------------
Equations:
Quantity Equation: n + q = 36
Value Equation::::5n +25q = 620 cents
============================================
Multiply thru the Quantity Equation by 5 to get:
5n + 5q = 5*36
---
Subtract that from the Value equation to get:
20q = 620-5*36
20q = 440
q = 22 (number of quarters)
----
Substitute into n+q=36 to solve for "n":
n = 36-22 = 14 (number of nickels)
=====================================
Cheers,
Stan H.
|
Equations/233168: what is the equation for "y varies linearly with x"
and "y in inversely proportional to x"?
1 solutions
Answer 172173 by stanbon(57384) on 2009-10-30 12:26:36 (Show Source):
You can put this solution on YOUR website!what is the equation for "y varies linearly with x"
and "y in inversely proportional to x"?
----------------
linearly: y = kx
---
inversely: y = k/x
======================
k is the constant of proportionality and
it is different for each application.
K has to be found in order to solve most
proportion problems.
=============================
Cheers,
Stan H.
|
Functions/233239: Write the quotient
(2x^3+x^2-x+4)/(2x-5)
1 solutions
Answer 172171 by stanbon(57384) on 2009-10-30 12:21:22 (Show Source):
You can put this solution on YOUR website!Write the quotient
(2x^3+x^2-x+4)/(2x-5)
----------
Use synthetic division:
5/2)....2....1....-1....4
.........2....6....14..|..39
-----------------------------------
Quotient: 2x^2 + 6x + 14
Remainder: 39
=======================
Cheers,
Stan H.
|
Equations/233238: please help me :
given that for all values x:
3x²+12x+5= p(x+q)²+r
a) find the values of p,q and r
1 solutions
Answer 172169 by stanbon(57384) on 2009-10-30 12:18:35 (Show Source):
You can put this solution on YOUR website!given that for all values x:
3x²+12x+5= p(x+q)²+r
a) find the values of p,q and r
----------------------
If it is true for all values of x the left side must be identical
to the right side.
----------------------
3x^2 + 12x + 5 = px^2 + 2pqx + pq^2+r
---
Equate the coefficients of corresponding terms.
p must equal 3
---
12 must equal 2pq
---
5 must equal pq^2+r
--------------------------
Solve for p,q,r
p = 3
2pq = 12; so 2*3q=12; so q = 2
-------------------
pq^2+r = 5 ;so 3*2^2+r = 5 ; so r = -7
==========================================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/233222: Can someone please help me work through these problems?
a) Consider the following rational expression.Build the rational expression
above into an equivalent expression with the denominator xy^5.
7/y
b) Consider the following rational expression.Build the rational expression
above into an equivalent expression with the denominator 18(x - 1).
(x+9)/(9 x - 9)
Thank you,
Alan
1 solutions
Answer 172168 by stanbon(57384) on 2009-10-30 12:12:55 (Show Source):
You can put this solution on YOUR website!a) Consider the following rational expression.Build the rational expression
above into an equivalent expression with the denominator xy^5.
7/y
---
Set up the equation:
(7/y) = k/(xy^5)
Solve for k
k = (7xy^5/y) = 7xy^4
---
Therefore: 7/y = [7xy^4]/[xy^5]
=====================================
b) Consider the following rational expression.Build the rational expression
above into an equivalent expression with the denominator 18(x - 1).
(x+9)/(9 x - 9)
---
Do the same as above.
(x+9)/(9x-9) = k/[18(x-1)]
Solve for "k"
k = [18(x-1)(x+9)]/(9(x-1)] = 2(x+9)
----------------
Therefore (x+9)/(9x-9) = [2(x+9)]/[18(x-1)]
==============================================
Cheers,
Stan H.
|
Probability-and-statistics/233172: A researcher claims that the average age of people who buy theatre tickets is 40. A sample of 30 is selected and their ages are recorded as shown below. The standard deviation is 5. At α = 0.05 is there enough evidence to reject the researcher’s claim? Show all work.
45
38
40
45
35
37
45
43
45
48
44
38
45
44
41
45
50
45
37
39
45
46
35
41
39
41
38
39
39
55
I really need help with this question. I tried all the avenue to solve this problem. Thanks for all your help and support.
1 solutions
Answer 172165 by stanbon(57384) on 2009-10-30 12:05:35 (Show Source):
You can put this solution on YOUR website!What avenues have you tried?
---
Ho: u = 40
Ha: u is not 40
-----------------
Now add up all the numbers and divide by 30 to get the sample mean.
Now run a Ttest to get the test statistic and/or the p-value.
If the p-value is <5%, reject Ho.
--------------------------------------
Let me know if this is what you need.
Cheers,
Stan H.
|
Probability-and-statistics/233173: I submitted this question already and there was no solution to this problem.
Consider the sample data below. 34
21
23
52
34
38
36
49
36
34
20
50
44
36
43
27
45
40
52
39
31
54
20
30
34
50
40
25
26
27
26
21
43
Suppose we wish to test the following hypotheses for the data:
Ho:u < 40
Ho: u > 40
Given the mean and the standard deviation of the data as above:
(A) Compute the appropriate test statistic for testing (show all work).
(B) Determine the critical value for α = 0.05.
(C) Test Ho using the traditional/classical method.
(D) State the decision based on the results of the test.
(E) Had you used the p-value method of hypothesis testing, what would the p-value have been?
1 solutions
Answer 172162 by stanbon(57384) on 2009-10-30 11:51:29 (Show Source):
You can put this solution on YOUR website!Suppose we wish to test the following hypotheses for the data:
Ho:u <= 40
Ho: u > 40
------------------------------------------------
Given the mean and the standard deviation of the data as above:
sample mean = 36 ; sample std = 10.3923
------------------------------------------------
(A) Compute the appropriate test statistic for testing (show all work).
ts = z(36) = (36-40)/[10.3923/sqrt(30)] = -2.108..
=====================
(B) Determine the critical value for alpha = 0.05.
For one-tail test with alpha=5% and df=29: cv = -1.699..
=====================
(C) Test Ho using the traditional/classical method.
Reject Ho because the test statistic is in the rejection
interval (-inf,-1.699..)
=======================
(D) State the decision based on the results of the test.
u < 40
=======================
(E) Had you used the p-value method of hypothesis testing, what would the p-value have been?
p-value is P(t < -2.108, with df=29) = tcdp(-100,-2.108,29) = 0.0219..
===========================================================================
Cheers,
Stan H.
|
Expressions-with-variables/233225: How many of the possible 5-card hands from a standard 52-card deck would consist of the following cards?
a) 4 clubs and 1 non-club
b) 2 face cards and 3 non-face cards
c) 2 red cards, 2 clubs and a spade
1 solutions
Answer 172150 by stanbon(57384) on 2009-10-30 10:49:49 (Show Source):
You can put this solution on YOUR website! How many of the possible 5-card hands from a standard 52-card deck would consist of the following cards?
a) 4 clubs and 1 non-club
Pick 4 clubs: 13C4 = 715 ways
Pick a non-club: 39
# of possible hands: 715*39 = 27885
-----------------------------------------
b) 2 face cards and 3 non-face cards
Pick 2 face cards: 66
Pick 3 non-face cards: 40C3 = 9880
# of possible hands: = 66*9880 = 652080
-----------------------------------------
c) 2 red cards, 2 clubs and a spade
Pick 2 red card: 26C2 = 325
Pick 2 clubs: 13C2 = 78
Pick a spade: 13
# of possible hands: 325*78*13 = 329550
=========================================
Cheers,
Stan H.
|
Functions/233228: State the domain for the following experssion
(x+5)/(x^2-36)
1 solutions
Answer 172147 by stanbon(57384) on 2009-10-30 10:40:26 (Show Source):
You can put this solution on YOUR website!State the domain for the following experssion
(x+5)/(x^2-36)
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Undefined if x^2-36 = 0
x^2 = 36
x = 6 or x = -6
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Domain is All Real Numbers except x=6 or x=-6
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Cheers,
Stan H.
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Equations/233220: solve by the elimation method. 0.3x-0.2y=4
0.4x+5y=1 What is the solution set I came up with (220/23, - 130/23) am I right or close to it
1 solutions
Answer 172143 by stanbon(57384) on 2009-10-30 10:21:38 (Show Source):
You can put this solution on YOUR website! solve by the elimation method. 0.3x-0.2y=4
0.4x+5y=1 What is the solution set I came up with (220/23, - 130/23) am I right or close to it
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Multiply thru both equations by 10 to get:
3x-2y=40
4x+50y=10
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Multiply thru the 1st equation by 25:
75x-50y=1000
4x +50y = 10
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Add and solve for "x":
79x = 1010
x = 1010/79
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Then substitute into 3x-2y=50 to solve for "y".
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Cheers,
Stan H.
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Equations/233218: Solve using the elimination method: 5x+5y=-7
7x-2y=11 what is the solution set, I came up with (-5,7) am I close
1 solutions
Answer 172138 by stanbon(57384) on 2009-10-30 10:05:12 (Show Source):
You can put this solution on YOUR website!Solve using the elimination method: 5x+5y=-7
7x-2y=11 what is the solution set, I came up with (-5,7) am I close
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5x+5y = -7
7x-2y = 11
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Multiply thru 1st equation by 2 ; Multiply thru 2nd eq. by 5:
10x + 10y = -14
35x - 10y = 55
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Add to get:
45x = 41
x = 41/45
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Subtitute to solve for "y":
5(41/45) + 5y = -7
9*41 + 45*5y = -7*45
369+225y = -315
y = -76/25
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Cheers,
Stan H.
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Probability-and-statistics/233177: Sam bought 1 of 250 tickets selling for $2 in a game with a grand prize of $400. Was $2 a fair price to pay for a ticket to play this game?
1 solutions
Answer 172135 by stanbon(57384) on 2009-10-30 09:42:47 (Show Source):
You can put this solution on YOUR website!Sam bought 1 of 250 tickets selling for $2 in a game with a grand prize of $400. Was $2 a fair price to pay for a ticket to play this game?
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Random Variable Values: -2 and 398
Probability Values : 249/250 and 1/250
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Expected Winnings: (249/250)(-2)+(1/250)398 = -0.4 or -40 cents
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You can expect to lose 40 cents each time you play.
You can decide whether that is fair.
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Cheers,
Stan H.
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Expressions-with-variables/233134: I'm having a very hard time with solving equations with unknowns on both sides. Can you please explain in the simplest form possible. Example: 5a-9=1+3a
1 solutions
Answer 172106 by stanbon(57384) on 2009-10-29 22:45:45 (Show Source):
You can put this solution on YOUR website!5a-9=1+3a
Subtract 3a from both sides to get:
2a-9 = 1
Add 9 to both sides to get:
2a = 10
Divide both sides by 2 to get:
a = 5
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Cheers,
Stan H.
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absolute-value/233120: how do you find a equation for a line passing through (3,7) when y varies directly with x
1 solutions
Answer 172105 by stanbon(57384) on 2009-10-29 22:42:29 (Show Source):
You can put this solution on YOUR website!how do you find a equation for a line passing through (3,7) when y varies directly with x
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y = kx
Find "k":
7 = k*3
k = (7/3)
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Equation:
y = (7/3)x
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Cheers,
Stan H.
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Quadratic_Equations/233127: a basketball player has a vertical leap of about 36in.If the equation d=48t^2 describes his hang timet is a function of his verticalleap d,what is his hang time?
1 solutions
Answer 172104 by stanbon(57384) on 2009-10-29 22:29:36 (Show Source):
You can put this solution on YOUR website!a basketball player has a vertical leap of about 36in.If the equation d=48t^2 describes his hang timet is a function of his verticalleap d,what is his hang time?
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36 = 48t^2
t^2 = 3/4
t = (1/2)sqrt(3) seconds
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Cheers,
Stan H.
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Numbers_Word_Problems/233126: Find 2 consecutive #'s such that when you square the smaller number,the result is 8 less than the product of the 2 #'s?
1 solutions
Answer 172103 by stanbon(57384) on 2009-10-29 22:26:59 (Show Source):
You can put this solution on YOUR website!Find 2 consecutive #'s such that when you square the smaller number,the result is 8 less than the product of the 2 #'s?
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smaller: x
larger: x+1
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Equation:
x^2 = x(x+1)-8
x^2 = x^2+x-8
x = 8 (smaller number)
x+1 = 9 (larger number)
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Cheers,
Stan H.
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Geometry_Word_Problems/233123: A charter company will provide a plane for a fare of $200 each for 80 or fewer passengers. For each passenger in excess of 80, the fare is decreased by $2.00 per person for everyone. What number of passengers would produce the greatest revenue for the company.
1 solutions
Answer 172102 by stanbon(57384) on 2009-10-29 22:23:22 (Show Source):
You can put this solution on YOUR website!A charter company will provide a plane for a fare of $200 each for 80 or fewer passengers.
For each passenger in excess of 80, the fare is decreased by $2.00 per person for everyone.
What number of passengers would produce the greatest revenue for the company.
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Equation:
Revenue(x) = (80+x)(200-2x)
R(x) = -2x^2 + 40x + 16000
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Maximum Revenue occurs when x = -b/2a = -40/(-4) = 10
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80+10 = 90 would be the number of passengers needed to maximize Revenue.
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Cheers,
Stan H.
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Quadratic_Equations/233121: How would I solve the equation using the quadratic formula? The equation is x^2+10x+22=0
I end up with -10±2√14/2. Can I factor something here?
-Mike
1 solutions
Answer 172101 by stanbon(57384) on 2009-10-29 22:16:47 (Show Source):
You can put this solution on YOUR website!How would I solve the equation using the quadratic formula? The equation is x^2+10x+22=0
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x = [-10 +- sqrt(100 - 4*22)]/2
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x = [-10 +- sqrt(12)]/2
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x = [-10 +- 2sqrt(3)]/2
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x = [-5 +- sqrt(3)]
x = -5+sqrt(3) or x = -5-sqrt(3)
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Cheers,
Stan H.
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Rational-functions/233108: what is the simplified form of (2b-3c)^3? and is (X^2)-7x+5 consider prime ,becuse it can't be factored. Just checking my anwers.
1 solutions
Answer 172100 by stanbon(57384) on 2009-10-29 22:05:50 (Show Source):
You can put this solution on YOUR website!what is the simplified form of (2b-3c)^3?
Hardly simplified, but here is the expanded form.
(2b)^3 -3(2b)^2(3c)+3(2b)(3c)^2-(3c)^3
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8c^3 - 36b^2c + 54bc^2 - 37c^3
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Is (X^2)-7x+5 consider prime ,because it can't be factored. Just checking my anwers.
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It is considered to be prime in the Real Number system.
It is not prime in the Complex Number systerm.
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Cheers,
Stan H.
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Angles/233104: if the measure of an angle exceeds four times the measure of its complement by 25, what is the measure of the angle
1 solutions
Answer 172099 by stanbon(57384) on 2009-10-29 21:59:30 (Show Source):
You can put this solution on YOUR website!if the measure of an angle exceeds four times the measure of its complement by 25, what is the measure of the angle
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Let the angle be "x".
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Its complement is 90-x
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Equation:
x = 4(90-x)+25
x = 360-4x+25
5x = 385
x = 77
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Cheers,
Stan H.
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Quadratic_Equations/233100: determine whether the following equations have solutions that are two different rational solutions:two different irrational solutions:exactly one rational solution or two different imaginary solutions.
3 + 8z^2= -7z
1 solutions
Answer 172097 by stanbon(57384) on 2009-10-29 21:54:38 (Show Source):
You can put this solution on YOUR website!determine whether the following equations have solutions that are two different rational solutions:two different irrational solutions:exactly one rational solution or two different imaginary solutions.
3 + 8z^2= -7z
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Rearrange:
8z^2+7z+3 = 0
a=8 ; b=7 ; c=3
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Discriminant = b^2-4ac = 49 -4*8*3 < 0
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Since the discriminant is < 0
the quadrated has two different imaginary solutions.
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Cheers,
Stan H.
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Quadratic_Equations/233098: solve.
f(x) = (x+3)^2 find x so that f(x) = 10
1 solutions
Answer 172095 by stanbon(57384) on 2009-10-29 21:50:30 (Show Source):
You can put this solution on YOUR website!solve.
f(x) = (x+3)^2 find x so that f(x) = 10
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(x+3)^2 = 10
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(x+3)^2-10 = 0
Factor the difference of squares:
[x+3+sqrt(10)][x+3-sqrt(10)] = 0
x = -3-sqrt(10)) or x = -3+sqrt(10)
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Cheers,
Stan H.
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Volume/233094: The volume of a circular cone is V=1/3(pi)r^2h, where r is the radius and h is the height.
If V=235cm^3 and r=10 cm, what is the value of h?
Answer in units of cm.
1 solutions
Answer 172094 by stanbon(57384) on 2009-10-29 21:46:33 (Show Source):
You can put this solution on YOUR website!The volume of a circular cone is V=1/3(pi)r^2h, where r is the radius and h is the height.
If V=235cm^3 and r=10 cm, what is the value of h?
Answer in units of cm.
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235 = (1/3)(pi)(10)^2* h
h = (3*235)/(100pi)
h = 22.148 cm
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Cheers,
Stan H.
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Mixture_Word_Problems/233091: I have 10% of homemade salsa that is 25% jalapenos. I buy some store salsa that is 4% and mix the two salsa together. how much store salsa do i need in order to have a mixture that is 10% jalapenos?
1 solutions
Answer 172093 by stanbon(57384) on 2009-10-29 21:40:16 (Show Source):
You can put this solution on YOUR website!I have 10% of homemade salsa that is 25% jalapenos. I buy some store salsa that is 4% and mix the two salsa together. how much store salsa do i need in order to have a mixture that is 10% jalapenos?
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Equation:
jalapeno + jalapeno = jalapeno
0.25*10 + 0.04x = 0.10(10+x)
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Multiply thru by 100 to get:
25*10 + 4x = 10*10+10x
6x = 15*10
x = 25 (amount of 4% salsa needed in the mixture)
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Cheers,
Stan H.
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