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Recent problems solved by 'stanbon'
stanbon answered: 57178 problems
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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, >>NextLinear-systems/139890: x-y=-5
x=3y=3 couldyou please help me understand how to solve this problem?
1 solutions
Answer 101970 by stanbon(57246)   on 2008-05-03 22:15:39 (Show Source):
You can put this solution on YOUR website!x - y =-5
x -3y = 3
----------------
Subtract the 2nd equation from the 1st to solve for "y":
4y = -8
y = -2
----------------
Substitute to solve for "x":
x --2 = -5
x + 2 = -5
x = -7
=================
Cheers,
Stan H.
|
Exponential-and-logarithmic-functions/139884: sample final questions:
write as a single logarithm expression: have no clue how to start:
(#1) -2logbase3(1/x)+1/3logbase3(squa rt OF x)
(#2) 2log2-3logx-1/2[log(x+3)log(x-2)]
express as sum & difference of logarithms, express powers as factors:
(#3) ln(x^3sqrtx^2+1 /x-3)
solve each equation:
(#4) log(7x+8)=2logx
THANK YOU AND GOD BLESS....THIS IS HELPING ME STUDY WITH THE CORRECT METHOD AND ANSWER.....I TRULY APPRECIATE ALL YOUR HELP AS ALWAYS!!!!
1 solutions
Answer 101969 by stanbon(57246) on 2008-05-03 22:12:03 (Show Source):
You can put this solution on YOUR website!(#1) -2logbase3(1/x)+1/3logbase3(squa rt OF x)
= -2log3 (x^-1) + (1/3)log3 x^(1/2)
= (-1)(-2)log3 x + (1/2)(1/3)log3 x
= 2log3 x + (1/6) log3 x
= (13/6)log3 x
-------------------------------------
(#2) 2log2-3logx-1/2[log(x+3)log(x-2)]
= 2log2 - logx -(1/2)[log(x+3)log(x-2)]
= log(4/x) -(1/2)log(x+3)*log(x-2)
---------------------------------------
express as sum & difference of logarithms, express powers as factors:
(#3) ln(x^3sqrt[(x^2+1)/(x-3)]
= 3lnx + (1/2)ln[(x^2+1)/(x-3)]
-----------------------------------------
solve each equation:
(#4) log(7x+8)=2logx
log(7x+8) = log x^2
7x+8 = x^2
x^2-7x-8 = 0
(x-8)(x+1) = 0
Potitive solution:
x = 8
=============
Cheers,
Stan H.
|
Probability-and-statistics/139855: This question is from textbook
in a bridge club, there are three more women than men. how many people are members of the club if the probability that a member chosen at random, is a woman is 3/5?
1 solutions
Answer 101967 by stanbon(57246) on 2008-05-03 21:51:40 (Show Source):
|
Probability-and-statistics/139876: Johnson’s Service Center has devised three potential options available to preferred customers who redeem coupons and buy at least 10 gallons of fuel when they stop in. Option A is a flat 3 cents off each gallon. Option B is a combination of 2 cents off plus another $1 discount on the regular price of a $5 deluxe car wash. Option C is a $2 discount on the same $5 deluxe car wash but no reduction in the fuel purchase. The owner, Harold Johnson, ran each option on three different two-week trial periods and tracked daily sales receipts from those customers who redeemed their coupons. Results are shown in the table below:
Option A Option B Option C
$453________492________467
507_________514________525
513_________536________516
521_________511________500
511_________528________435
615_________678________462
601_________611________411
552_________653________674
551_________596________512
505_________516________559
515_________534________624
512_________543________711
476_________498________512
427_________437________416
Harold elected to conduct a one-way ANOVA for his single-factor experiment.
What is the total sum of squares ?
a. 211,049.6
b. 204,880.6
c. 198,711.6
d. 173,512.1
What is the sum of squares error?
a. 204,880.6
b. 198,711.6
c. 211,049.6
d. 167,343.1
What are the values of the F statistic and the critical value at the 0.05 level of significance?
a. 5.325, 19.55
b. 1.653, 5,18
c. 0.937, 3.24
d. 0.605, 3.24
What conclusion can Harold make, based on the results of the ANOVA?
a. Receipts from option A are significantly greater than the receipts from either options B or C.
b. Receipts from option B are significantly greater than the receipts from either options A or C.
c. Receipts from option C are significantly greater than the receipts from either options A or B.
d. Receipts from all three options are the same
1 solutions
Answer 101953 by stanbon(57246) on 2008-05-03 19:03:17 (Show Source):
You can put this solution on YOUR website!What is the total sum of squares ?
a. 211,049.6
b. 204,880.6
c. 198,711.6
d. 173,512.1
------------------------
What is the sum of squares error?
a. 204,880.6
b. 198,711.6
c. 211,049.6
d. 167,343.1
Ans: 198,711.6
------------------------------
Ans: 204,880.6
What are the values of the F statistic and the critical value at the 0.05 level of significance?
a. 5.325, 19.55
b. 1.653, 5,18
c. 0.937, 3.24
d. 0.605, 3.24
-----
Test statistic: F = 0.605377...
p-value: 0.5509
Conclusion: Fail to Reject Ho.
What conclusion can Harold make, based on the results of the ANOVA?
a. Receipts from option A are significantly greater than the receipts from either options B or C.
b. Receipts from option B are significantly greater than the receipts from either options A or C.
c. Receipts from option C are significantly greater than the receipts from either options A or B.
d. Receipts from all three options are the same
-------------
Ans: d
=======================
Cheers,
Stan H.
|
Probability-and-statistics/139856: This question is from textbook
in a bridge club, there are three more women than men. how many people are members of the club if the probability that a member chosen at random, is a woman is 3/5?
1 solutions
Answer 101951 by stanbon(57246) on 2008-05-03 18:31:32 (Show Source):
You can put this solution on YOUR website!in a bridge club, there are three more women than men. how many people are members of the club if the probability that a member chosen at random, is a woman is 3/5?
-------------------------------
P(women) = (# of women)/(total number of people) = 3/5
P(men) = 2/5
Odds for women = (3//5)/(2/5) =3:2 which is the same as 3x/2x
where 3x is # of women and 2x is # of men.
EQUATION:
3x = 2x + 3
x = 3
3x = 9 = # of women
2x = 6 = # of men
-----------------
# in the club = 9+6 = 15
=============================
Cheers,
Stan H.
-----------------------
|
Exponential-and-logarithmic-functions/139875: These problems are froma a sample final, not a text book.
question #1 - 9^2x = 5^3x-4 solve equation
question #2 - log(base 5)e - use change of base formula
question #3 - log (base 2)(a^2 sqrt b^3)^4 write as summ/differ of log,express powers as factors
question #4 - ln(9-x^2) - find domain
I am studying my sample final...finals coming soon, these 4 problems are giving me trouble...ANY HELP WOULD BE GREATLY APPRECIATED!!!!
exponetial and logaarithmic problems are giving me major pproblems.
Thanks again for all your help!!!
1 solutions
Answer 101947 by stanbon(57246) on 2008-05-03 17:05:51 (Show Source):
You can put this solution on YOUR website!question #1 - 9^(2x) = 5^(3x-4) solve equation
Take the log of both sides:
2xlog9 = (3x-4)log5
xlog81 = 3xlog5 -4log5
xlog81 = xlog15^3 - log5^4
x(log81-log15^3) = log5^4
x = log5^4/(log81 -log15^3)
x = -1.7261
--------------------------
question #2 - log(base 5)e - use change of base formula
log5 e = lne/ln5 = 1/ln5 = 0.62133...
-------------------------------
question #3 - log (base 2)(a^2 sqrt b^3)^4 write as summ/differ of log,express powers as factors:
log (base 2)(a^2 sqrt b^3)^4 = log2 (a^8 b^2)= 8log2 a + 2log2 b
---------------------------------
question #4 - ln(9-x^2) - find domain
9-x^2 > 0
x^2 < 9
-3 < x < 3
--------------
Domain: All Real numbers except -3 < x < 3
=========================================
Cheers,
Stan H.
|
Probability-and-statistics/139745: There is no answer associated with the question below posted but is showing as answered in the que. Please help!
Question 139208: High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this
hazard for many hours. A Boeing 727 co-pilot collected 61 noise observations using a handheld
sound meter. Noise level is defined as “Low” (under 88 decibels), “Medium” (88 to 91 decibels),
or “High” (92 decibels or more). There are three flight phases (Climb, Cruise, Descent). Research
question: At α = .05, is the cockpit noise level independent of flight phase? (Data are from Capt. Robert E. Hartl, retired.) Noise
Noise Level Climb Cruise Descent Row Total
Low 6 2 6 14
Medium 18 3 8 29
High 1 3 14 18
Col Total 25 8 28 61
1 solutions
Answer 101932 by stanbon(57246) on 2008-05-03 12:51:25 (Show Source):
You can put this solution on YOUR website!High level of cockpit noise in an aircraft can damage hearing of pilots who are exposed to this hazard for many hours. A Beoing 727 co-pilot collected 61 noise observations using a handled sound meter. Noise level is defined as "low (under 88 decibles), Medium (88 to 91), high (92 or more). There are three flight phases (Climb,Cruise,Descent). At alph=.05, is the cockpit noise level independent of flight phase?
State hypothesis
Ho: noise and flight phase are independent
Ha: they are dependent
--------------------------
show degrees of freedom
(# of rows -1)(# of columns -1) = (2)(2) = 4
--------------------------
find critical value of chisquare
Chi-Sq critical values for 2-tail Chi-Sq. Test: 0.484 and 11.143
--------------------------
interpret p=value
p-value is 0.0044
Only 0.0044 of test results would show stronger evidence for rejecting Ho.
Since p-value is less than 5%, reject Ho.
-----------------------------------
Noise Level,Climb,Cruise,Descent,Row Total
Low,6,2,6,14
Medium,18,3,8,29
High,1,3,14,18
Col total,25,8,28,61
---------------------
Cheers,
Stan H.
|
Probability-and-statistics/139761: Find the probability that a dart will (a)hit in the baseball field (b) hit in one of the 4 smaller squares (c) will miss all five target squares, on a square dart board that has 60cm sides with a square baseball field (inside the square dart board)40cm on it's sides, and 4 smaller squares (inside square dart board, but outside of baseball field) each 10cm on a side as the targets.
1 solutions
Answer 101931 by stanbon(57246) on 2008-05-03 12:22:21 (Show Source):
You can put this solution on YOUR website!Find the probability that a dart will
(a)hit in the baseball field = 1600/3600 = 4/9
(b) hit in one of the 4 smaller squares = 400/3600 = 1/9
(c) will miss all five target squares: 4/9
-------------------------------------------
on a square dart board that has 60cm sides: area = 3600 sq cm.
-----------------------------------
square field (inside the dart board)40cm on it's sides: 40^2 = 1600 sq cm.
----------------------,
and 4 smaller squares (inside square dart board, but outside of baseball field) each 10cm on a side as the targets. 4*10^2 = 400 sq cm.
------------------------
Cheers,
Stan H.
|
Probability-and-statistics/139746: This question is from textbook
An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year (year in which the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if individual is black, 0 otherwise), and Rank (1 if individual is an assistant professor, 0 otherwise). Interpret these results.
Variable Coefficient t p
Intercept −3,816,521 −29.4 .000
Year 1,948 29.8 .000
YearHire −826 −5.5 .000
Race −2,093 −4.3 .000
Rank −6,438 −22.3 .000
R2 = 0.811 R2adj = 0.809 s = 3,318
1 solutions
Answer 101930 by stanbon(57246) on 2008-05-03 12:14:45 (Show Source):
You can put this solution on YOUR website!An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year (year in which the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if individual is black, 0 otherwise), and Rank (1 if individual is an assistant professor, 0 otherwise). Interpret these results.
---------
Variable Coefficient t p
Intercept −3,816,521 −29.4 .000
Year 1,948 29.8 .000
YearHire −826 −5.5 .000
Race −2,093 −4.3 .000
Rank −6,438 −22.3 .000
R2 = 0.811 R2adj = 0.809 s = 3,318
-------
Reg. Eq: Salary = -3816.541 + 1948(year variable) -826(year hire)
=2.093(race variable)-6.438(Rank variable)
-------------
The .0000 p-values means to reject the hypotheses that the coefficient is zero.
R2 = 0.811 means that 81.1 % of the variation between salary and
the independent variables is explained by the regression equation.
s = 3318 means the variance on the predicted salary is $3,318
======================
Cheers,
Stan H.
PS: This problem has been posted a number of times. What is the
source? what is the text used to cover this material?
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Probability-and-statistics/139765: The technique that is used to determine if more than two population means are equal by analyzing the variation in the data is known as
a. chi-square.
b. analysis of variance.
c. correlation analysis.
d. least squares regression.
1 solutions
Answer 101929 by stanbon(57246) on 2008-05-03 12:03:52 (Show Source):
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Probability-and-statistics/139767: Helen Smith just conducted a single-factor experiment and collected 30 observations. Her analysis of variance produced a sum of squares total (SST) that contained how many degrees of freedom?
a. 28
b. 29
c. 30
d. 31
1 solutions
Answer 101928 by stanbon(57246) on 2008-05-03 12:00:30 (Show Source):
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Probability-and-statistics/139794: This question is from textbook Applied statistics in business and economics
High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this
hazard for many hours. A Boeing 727 co-pilot collected 61 noise observations using a handheld
sound meter. Noise level is defined as “Low” (under 88 decibels), “Medium” (88 to 91 decibels),
or “High” (92 decibels or more). There are three flight phases (Climb, Cruise, Descent). Research
question: At α = .05, is the cockpit noise level independent of flight phase?
1 solutions
Answer 101912 by stanbon(57246) on 2008-05-03 09:00:54 (Show Source):
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Miscellaneous_Word_Problems/139839: This question is from textbook Algebra Structure and Method
I have been working on this math problem for awhile now and I got to the second step, but I don't know where to go from there. I was wondering if someone could help me?? I would deeply appreciate it!! Please and Thank you!!
Factoring by Grouping
Factor each expression as a difference of squares
Original Problem
x^2-2xy+y^2-4
Work that I did
x^2-2xy+y^2-4
(x)^2-(2+y)^2
1 solutions
Answer 101909 by stanbon(57246) on 2008-05-03 08:55:05 (Show Source):
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Probability-and-statistics/139808: Stan you answered this question but my instructor came back with another question. Here is the orginal question. The number of admissions for Carolinas Medical Center hospital emergency room over the course of a lunar cycle was 129 patients per 36 days per full moon as compared to 1,315 patients per 330 days per nonfull moon days
Perform a chi-square test on the data. Use the test to prove (or disprove) that hospital emergency room admissions are dependent (or independent) on (of) the full moon lunar phase.
Full moons were defined as three-day periods in the 29.531-day lunar cycle, with the middle day being described in the world almanac as the full moon.
: The number of admissions for Carolinas Medical Center hospital emergency room over the course of a lunar cycle was 129 patients per 36 days per full moon as compared to 1,315 patients per 330 days per nonfull moon days.
Here is the question my instrutor asked....How did you get the test statistics, I'm sure your classmates are curious of how the .0287 generated as well as the p-value of .5920. Help.
1 solutions
Answer 101908 by stanbon(57246) on 2008-05-03 08:50:55 (Show Source):
You can put this solution on YOUR website!Ho: full-moon and # of patients are independent
Ha: they are dependent
--------------------------
I set up 2 rows of DATA in a matrix on a TI caluculator:
full-moon.....129......36
no full-m....1315......330
----------------------------
I ran a Chi-Sq Test on the matrix and got:
test statistic: Chi-Sq = 0.87089...
p-value = 0.59209..
df = (2-1)(2-1)
------------------------------
You could do this by hand:
The data listed above is the "Observed" data.
You could generate the "Expected data"; that is the numbers you would
expect to see if the # of patients was independent of the full-moon.
That matrix would be:
full-moon.....131.64......33.365
no full-m.....1312.4......332.64
----------------
Then you would have to calculate the Chi-Sq statistic
using:
Chi-Sq = Sum[ (observed-expected)^2/expected] for each of the 4 entry
positions.
Then you would have to use your Chi-Sq chart to calculate the area
to the right of your test statistic to get the p-value.
---------------------------
I don't know how much evidence your instructor requires. The
calculator is handy as it does all the arithmetic. However,
you should try to understand what is behind the numbers the
calculator generates.
--------------------------
Cheers,
Stan H.
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Circles/139832: I am not sure how to word this queation but I'll give it a try. I actually have a diagram of a circle with a shaded region but I don't know how to show you that:( The shaded region is 1 solutions
Answer 101906 by stanbon(57246) on 2008-05-03 08:28:18 (Show Source):
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Circles/139831: Given P(a,b) and Q( 3a,5b), what is the distance from R(3a,2b) to the midpoint of PQ? I think it is sqrt a^2+16b^2 ??????????????
1 solutions
Answer 101905 by stanbon(57246) on 2008-05-03 08:27:01 (Show Source):
You can put this solution on YOUR website!Given P(a,b) and Q( 3a,5b), what is the distance from R(3a,2b) to the midpoint of PQ?
----------
The midpoint of PQ is [(a+3a)/2 , (5b+b)/2] or (2a,3b)
------------------
The distance from (3a,2b) to (2a,3b) is:
d = sqrt[(3a-2a)^2 + (2b-3b)^2] = sqrt[a^2+b^2]
======================
Cheers,
Stan H.
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Probability-and-statistics/139813: This question is from textbook Fundamentals of Algerbraic Modeling
A city is growing exponentially at a rate of 1.5% annually. Its population is currently 56,750 people. Predict the population in 10 years.
1 solutions
Answer 101904 by stanbon(57246) on 2008-05-03 08:20:25 (Show Source):
You can put this solution on YOUR website!A city is growing exponentially at a rate of 1.5% annually. Its population is currently 56,750 people. Predict the population in 10 years.
--------------------
A(t) = 56750(1.015)^t
A(10) = 56750(1.015)^10
A(10) = 56750(1.16054...)
A(10) = 65861 when rounded up
=================
Cheers,
Stan H.
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Probability-and-statistics/139772: I need help on this problem....thanks
2. For the ANOVA table below, answer each question.
A. How many treatments (groupings) are being compared?
B. How many total observations are in this analysis?
C. What is the hypothesis tested here?
Source DF Sum of Squares Mean Square F Ratio Prob>F
ID 2 49.38620 24.6931 1.4837 0.2415
Error 33 549.20797 16.6427
C. Total 35 598.59417
1 solutions
Answer 101889 by stanbon(57246) on 2008-05-02 20:09:41 (Show Source):
You can put this solution on YOUR website! For the ANOVA table below, answer each question.
A. How many treatments (groupings) are being compared?
Since DF = k-1 = 2, therefoe k= 3, there are three treatments
----------------------
B. How many total observations are in this analysis?
Since DF = 35, there are 36 observations
----------------------
C. What is the hypothesis tested here?
Ho: u1=u2=u3
============================
Cheers,
Stan H
===============================
--------------------------------
Source DF..Sum of Squares Mean Square F Ratio Prob>F
ID..... 2.. 49.38620...... 24.6931... 1.4837 0.2415
Error. 33.. 549.20797..... 16.6427
CTotal 35...598.59417
-----------------------------------
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Quadratic-relations-and-conic-sections/139710: Please help me with this problem. I have asked for hrlp before but could not find the answer to it. Thank you for your help. This problem is from a homework sheet.
Write the series in summation notation. Use the index i and let i begin at 1 in each summation.
3.) 9 + 14 + 19 + 24 + 29
1 solutions
Answer 101828 by stanbon(57246) on 2008-05-02 09:20:46 (Show Source):
You can put this solution on YOUR website!Write the series in summation notation. Use the index i and let i begin at 1 in each summation.
9 + 14 + 19 + 24 + 29
a(n) = 9 + 5(n-1)
a(n) = 9 + 5n-5
a(n) = 4+5n
-----------------
Summation Notation:
Sum from i=1 to n of (4+5n)
========================
Cheers,
Stan H.
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Quadratic-relations-and-conic-sections/139711: I need help with this problem. I do not know where to begin. Can someone please help me. Thank you. This is from a worksheet.
Write a formula for the nth term of the infinite sequence whose nth term is given.
7.) -4,-2,0,2,4...
1 solutions
Answer 101825 by stanbon(57246) on 2008-05-02 08:21:23 (Show Source):
You can put this solution on YOUR website!-4,-2,0,2,4...
----------------
a(1) = -4
d = -2--4 = 2
----------------
a(n) = a(1) + (n-1)d
a(n) = -4 + (n-1)*2
a(n) = -4 +2n-2
a(n) = -6 + 2n
===================
Cheers,
Stan H.
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Inequalities/139678: Tutor could you help me please: A homeowner wants to fence a rectangular garden using 120 ft of fencing. The side of the garage will be used as one side of the rectangle. Find the dimensions for which the area is a maximum.
thank you
1 solutions
Answer 101824 by stanbon(57246) on 2008-05-02 08:18:03 (Show Source):
You can put this solution on YOUR website!Tutor could you help me please: A homeowner wants to fence a rectangular garden using 120 ft of fencing. The side of the garage will be used as one side of the rectangle. Find the dimensions for which the area is a maximum.
------------------
Draw the picture.
You have three lengths of fence; two are equal so call them "x": one
is not equal but it can be called 120-2x because it is the rest of
the fence after you have used up the two x's.
-------------------
EQUATION:
Area of the rectangle = x*(120-2x) = 120x-2x^2
----------
That is a quadratic with a=-2 and b = 120
------------
The maximum occurs when x = -b/2a = -120/(2*-2) = 30
--------------
So the two equal sides are each 30 ft.
The other side is 120 - 2x = 120 - 2*30 = 60 ft.
------------------------
Cheers,
Stan H.
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test/139671: How many 3 letter and 3 number licenses plates can be made if you cant use the numbers 1,2,3 and you cant use the letters t,v,w,x,y and no number or letter can repeat in the plate.
1 solutions
Answer 101822 by stanbon(57246) on 2008-05-02 08:10:19 (Show Source):
You can put this solution on YOUR website!How many 3 letter and 3 number licenses plates can be made if you cant use the numbers 1,2,3 and you cant use the letters t,v,w,x,y and no number or letter can repeat in the plate.
------------------
There are 7 digits you can use.
# of ways to pick 3 of the 7 digits: 7C3
-----------------------------------
There are 21 letters you can use.
number of ways you can pick 3 of the 21 letters: 21C3
------------------------------------
# of ways to arrange the 7 objects you pick: 7!
-----------------------------------
Total # of license plates: 7C3 * 21C3 * 7! = 35*1330*5040 = 234,612,000
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Miscellaneous_Word_Problems/139696: In how many different ways can two black cards be drawn from a standard deck of cards? Assume that the order of the cards matters.
1 solutions
Answer 101820 by stanbon(57246) on 2008-05-02 08:01:01 (Show Source):
You can put this solution on YOUR website!In how many different ways can two black cards be drawn from a standard deck of cards? Assume that the order of the cards matters.
--------------------
# of ways to pick the two black cards from a deck of 52 = 26C2
# of ways to order the two cards picked = 2
============
Total # of ways = 26C2 * 2 = 26*25/1*2 *2 = 26*25 = 650
==============
Cheers,
Stan H.
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Quadratic_Equations/139635: HELP NO clue how to do this!
An eagle is circling a field at a height of 250 feet sees a snake below. The eagle dives at an initial speed of 110 feet per second. Determine the time the snake has to escape.
1 solutions
Answer 101807 by stanbon(57246) on 2008-05-01 22:10:12 (Show Source):
You can put this solution on YOUR website!An eagle is circling a field at a height of 250 feet sees a snake below. The eagle dives at an initial speed of 110 feet per second. Determine the time the snake has to escape.
-----------------------------
Let h(t) be height at time "t".
EQUATION:
h(t) = -16t^2-110t+ 250
When the eagle hits the snake its height is zero.
-16t^2-110t+250 = 0
-2(8t^2+55t-125) = 0
t = [-55 +- sqrt(55^2 - 4*8*-125)]/16
t = [-55 +- sqrt(7025)]/16
t = [-55 +- 83.82]
Positive answer:
t = (-55+83.83)/16
t = 1.8 seconds
=====================
Cheers,
Stan H.
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Quadratic_Equations/139645: Find the side of a square with an area of 625 ft.^2 by using a quadratic equation. I know that to find the area of a square you do length times width and all sides of a square are equal so I found the square root of 625, which was 25. But I am not sure on how to solve this problem using a quadratic equation. Thanks!!
1 solutions
Answer 101801 by stanbon(57246) on 2008-05-01 21:03:54 (Show Source):
You can put this solution on YOUR website!Let each side of the square be "x".
EQUATION:
Area = x^2 = 625
x^2 = 625
x^2-625 = 0
(x-25)(x+25)= 0
Positive answer:
x = 25
=============
Cheers,
Stan H.
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percentage/139642: A population grows at a rate of 8% per year forever. The population starts at 100. What is the size of the population at the end of year n? ( for any integer n)
1 solutions
Answer 101797 by stanbon(57246) on 2008-05-01 20:40:23 (Show Source):
You can put this solution on YOUR website!A population grows at a rate of 8% per year forever. The population starts at 100. What is the size of the population at the end of year n? ( for any integer n)
-----------------
size(n) = 100(1.08)^n
=========================================
Cheers,
Stan H.
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