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Recent problems solved by 'stanbon'
stanbon answered: 57345 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 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359, >>NextProbability-and-statistics/129657: Evaluate:
a) P6,4
b) C7,2
c) P4,4
d) C9,0
1 solutions
Answer 94654 by stanbon(57418)   on 2008-02-28 15:55:33 (Show Source):
You can put this solution on YOUR website!P(n,r) = n!/(n-r)!]
C(n,r) = n!/[(n-r)!*r!]
---------
Evaluate:
a) P6,4 = 6!/2!=6*5*4*3 = 360
b) C7,2 = 7!/[5!*2!] = 7*6/1*2 = 21
c) P4,4 = 4!/(4-4)! = 4!/0!= 4! = 24
d) C9,0 = 9!/[9!*0!] = 1
=============
Cheers,
Stan H.
|
Quadratic_Equations/129645: The manager of an 80 unit apartment complex is trying to deceide what rent to charge. Experience has shown that at a rent of $200.00 all the units will be full but with one additional unit will remain vacant f0r each $20.00increase. Find the # of occupied unit if the total revenue is $20,020.
This is the problem I am trying to solve, however I am not clear on how or where to start it. If you could possibly show me the steps I would greatly appericate it. Thank you
1 solutions
--------------------------------------------------------------------------------
Answer 94355 by solver91311(860) on 2008-02-25 20:07:28:
You can put this solution on YOUR website!
Let x be the number of occupied units. Then 80 - x is the number of unoccupied units.
The rental fee is 200 plus 20 times the number of unoccupied units, so:
, which simplifies to:
This is the amount charged per apartment, and there are x occupied apartments, so the total revenue is:
and that is equal to $20,020.
So:
Divide by -20:
You can factor this (the prime factors of 1001 are 7, 11, and 13), or use the quadratic formula, whichever you prefer, but the roots come out to be and ,
So, if the rental fee is 200 + 20(3) = 260 (3 unoccupied units), then the total revenue is 77 * 260 = 20020.
But if the rental fee is 200 + 20(67) = 1540, then the total revenue is 13 * 1540, also = 20020.
The second root presumes that the relationship of rent to unoccupied units is linear across the entire range of possibilities, which I suspect is not the case in real life.
***************This the help that I received and I understand it up to here,however how do you compute this into a quadratic equation? That is what I don't understand. Thank you for your time........................................
1 solutions
Answer 94650 by stanbon(57418) on 2008-02-28 14:26:19 (Show Source):
You can put this solution on YOUR website!The manager of an 80 unit apartment complex is trying to deceide what rent to charge.
Experience has shown that at a rent of $200.00 all the units will be full but one additional unit will remain vacant f0r each $20.00 increase.
Find the # of occupied units if the total revenue is $20,020.
-------------------------
Let "x" be the number of $20 increases.
Price per unit will be (200+20x)
# of units occupied will be (80-x)
---------
EQUATION:
Revenue = price per unit * # of units occupied:
20,020 = (200+20x)(80-x)
-20x^2 +1600x-200x + 16000 = 20,020
-20x^2+1400x -4020 = 0
Divide thru by -20 to get:
x^2-70s+201=0
Factor to get:
(x-67)(x+3)=0
Positive answer:
x = 67 (The number of $20 raises)
====================
Cheers,
Stan H.
|
Probability-and-statistics/129644: Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more
should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10
or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding
a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of significance,
is the true mean greater than 10? (b) Use Excel to find the right-tail p-value.
1 solutions
Answer 94647 by stanbon(57418) on 2008-02-28 13:11:51 (Show Source):
You can put this solution on YOUR website!Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more
should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below.
The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages.
(a) At the .01 level of significance,is the true mean greater than 10?
Ho: mu = 10
Ha: mu > 10
--------------
t(14.44) = (14.44-10)/[4.45/sqrt(35)] = 4.44*sqrt(35)/4.45 = 5.9027...
----------------
p-value = P(5.9027
-------------------------
Since the p-value is far less than alpha=1%, hasten to reject
Ho. The test gives strong statistical evidence that the mean
is not 10.
You might conclude that the mean is greater than 10 since that
is the alternative hypothesis.
---------------
Cheers,
Stan H.
===============
Cheers,
Stan H.
(b) Use Excel to find the right-tail p-value.
|
Probability-and-statistics/129357: Given the digits 1, 3, 6, 9, find the probability that a four digit number formed by using each of them only once is divisible by 7.
1 solutions
Answer 94646 by stanbon(57418) on 2008-02-28 12:42:02 (Show Source):
You can put this solution on YOUR website!Given the digits 1, 3, 6, 9, find the probability that a four digit number formed by using each of them only once is divisible by 7.
-------------
That is a lot of numbers: 4^4 = 256
What criteria are you using for divisibility by 7?
Cheers,
Stan H.
|
Probability-and-statistics/129314: This question is from textbook Applie Statics in Business and Econmics
WOW! I am lost on how to do this. I have read the chapter and I have tried to get this. Please help!Thank you!!!
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, o otherwise), and Rank (1 if individual is an assistant professor, o otherwise).
Interpret the results.
Variable-------Coefficient---------t---------------------p
Intercept-------3,816,521-------negative29.4-----------.000
Year------------1,948------------29.8------------------.000
YearHire------negative826-------negative5.5------------.000
Race----------negative2,093-----negative4.3------------.000
Rank----------negative6,438-----negative22.3-----------.000
r2=.811--------------r2adj=.809-----------s=3,318
1 solutions
Answer 94645 by stanbon(57418) on 2008-02-28 12:32:13 (Show Source):
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Probability-and-statistics/129432: Problem 1:
Harold Hacker recently read in a national golf magazine that the average weekend golfer carries a handicap of 15 strokes and the standard deviation is 4 strokes. Harold manages a local men’s church league and just tallied the end-of-season totals. The 64 players in Harold’s league finished the year with an average handicap of 14 strokes.
a. Set up the null and alternative hypotheses to test if the average handicap in Harold’s league is not the same as the national average reported in the magazine.
b. Test your hypothesis using = 0.02.
c. Find the p value.
d. Based on Harold’s end-of-season data, what can you conclude?
Problem 2:
The players on last year’s football team at State College were able to bench press a mean of 312 lb. Coach Juarez made it clear to the players during spring training that the team’s average best lift had to improve. A special weight-training program was launched, and all the players participated. In an effort to measure the team’s progress, the coach recorded the heaviest lifts of the starting offensive and defensive lineups at the start of this season. Results are as follows:
346 412 332 285 396 461 321 275
246 315 298 347 430 419 406 311
319 385 377 365 385 400
a. State the appropriate null and alternative hypotheses.
b. Calculate the test statistic.
HINT sample mean=356.43 lb
Sample standard deviation = 56.05 lb
c. At = 0.01, should Coach Juarez reject the null hypothesis?
d. Assuming the starting lineup is a representative sample, what conclusion can the coach draw?
Problem 3:
a) 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
507
513
521
511
615
601
552
551
505
515
512
476
427 $492
514
536
511
528
678
611
653
596
516
534
543
498
437 $467
525
516
500
435
462
411
674
512
559
624
711
512
416
a) State the null hypothesis to test for equal population means.
b) Below are the results from EXCEL of ANOVA of the data at the 0.05 level of significance. Do the sample data indicate the at least one of the three population mean total returns is different from the others? Why? (Explain using “F” and “Fcrit” – a drawing is fine.)
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Column 1 14 7259 518.5 2555.962
Column 2 14 7647 546.2143 4340.335
Column 3 14 7324 523.1429 8389.209
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 6169 2 3084.5 0.605377 0.550917 3.2381
Within Groups 198711.6 39 5095.168
Total 204880.6 41
1 solutions
Answer 94644 by stanbon(57418) on 2008-02-28 12:29:05 (Show Source):
You can put this solution on YOUR website!Problem 1:
Harold Hacker recently read in a national golf magazine that the average weekend golfer carries a handicap of 15 strokes and the standard deviation is 4 strokes. Harold manages a local men’s church league and just tallied the end-of-season totals. The 64 players in Harold’s league finished the year with an average handicap of 14 strokes.
a. Set up the null and alternative hypotheses to test if the average handicap in Harold’s league is not the same as the national average reported in the magazine.
--------
Ho: mu = 15
Ha: mu is not 15
----------------
b. Test your hypothesis using = 0.02.
t(14) = (14-15)/[4/sqrt(64)] = -1*8/14 = -4/7 = -0.5714..
---------------
c. Find the p value.
p-value = P(-10
------------------
d. Based on Harold’s end-of-season data, what can you conclude?
The p-value is greater than 1% (half of 2% of this two-tailed test)
so we Fail to reject Ho.
Harold's results are statistically in keping with the published
national average.
================
Cheers,
StanH.
|
Rectangles/129625: translate to an algebraic equation then solve. the lenght of a rectangle is six units longer than the width. find the lenght and width if the perimeter of the rectangle is 60 units.
2) fin the circumference and area of a circle with the radius 3.5 feet. use 22/7 for pi.
3) the width of a rectangular playground is 18 meters less than the lenght. find the width when the perimeter of the rectangle is 84 meters.
once again thanks a lot this will help me get my ged
1 solutions
Answer 94642 by stanbon(57418) on 2008-02-28 11:22:36 (Show Source):
You can put this solution on YOUR website!translate to an algebraic equation then solve. the length of a rectangle is six units longer than the width. find the length and width if the perimeter of the rectangle is 60 units.
Let width = x units
Then length = x+6 units
Perimeter = 2(length + width)
2(x+(x+6)) = 60
2x+6 = 30
2x = 24
x = 12 units (width)
x+6 = 18 units (length)
-----------------------
2) find the circumference and area of a circle with the radius 3.5 feet. use 22/7 for pi.
Area = (pi)r^2
Area = (22/7)*3.5^2 = 22*3.5*3.5/7 = 22*3.5/2 = 11*3.5 = 38.5 sq ft
-----------------------
3) the width of a rectangular playground is 18 meters less than the lenght. find the width when the perimeter of the rectangle is 84 meters.
---------------
Let the length be "x meters; the width is "x-18" meters.
Perimeter = 2(length + width)
84 = 2(x + x-18)
2x-18 = 42
2x = 60
x = 30 meters (length)
x-18 = 12 meters (width)
================
Cheers,
Stan H.
|
Probability-and-statistics/129297: Michael is one of five contestants entered in three races to be run on a five-lane track. If in each race the runners are assigned to the lanes at random, what is the probability that Michael will be assigned to the inside lane at least once?
I know that the total number of possible outcomes is 5!, so I assume this to be the starting denominator.
1 solutions
Answer 94641 by stanbon(57418) on 2008-02-28 11:13:55 (Show Source):
You can put this solution on YOUR website!Michael is one of five contestants entered in three races to be run on a five-lane track. If in each race the runners are assigned to the lanes at random, what is the probability that Michael will be assigned to the inside lane at least once?
--------------
P(he is assigned to any particular lane) = 1/5 = p
There are three races so n=3
Since you want at least one succes use P(at least one) = 1- P(no successes)
---------------
P(he get assigned to the inside lane at least once ) = 1- P(he does not
get assigned to lane one in all three races) = 1- (4/5)^3 = 0.488
===================
Cheers,
Stan H.
|
Exponents-negative-and-fractional/129611: These are confusing???
120xy/10x^2y^7
2x(14x+12)/2^2
(8k^-7)^4
22a^7b^7/11a^3b^-7
1 solutions
Answer 94640 by stanbon(57418) on 2008-02-28 11:04:22 (Show Source):
You can put this solution on YOUR website!Comment: They are easier if you look at "like parts".
----------------
120xy/10x^2y^7
= (120/10)(x/x^2)(y/y^7)
= 12/(xy^6)
-------------------
2x(14x+12)/2^2
= [2x(2(7x+6))]/4
= [4x(7x+6)]/4
= [x(7x+6)]
==============
(8k^-7)^4 = 8k^-28 = 8/k^28
------------------
22a^7b^7/11a^3b^-7
=(22/11)(a^7/a^3)(b^7/b^-7)
= 2a^4b^14
=============
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/129619: I just can't seem to find a way to start this problem, we were told to use Systems to solve it and i just don't know were to start. here it goes
Scott received $5000 as a graduation gift from his aunt and uncle. he invested the money in stocks and bonds. This year he received a 3percent annual return on the bonds but the stocks lost 2percent of their original value. If his total annual income from the investments was $80, how much did he invest in each?
1 solutions
Answer 94629 by stanbon(57418) on 2008-02-28 09:40:24 (Show Source):
You can put this solution on YOUR website!Scott received $5000 as a graduation gift from his aunt and uncle. he invested the money in stocks and bonds. This year he received a 3percent annual return on the bonds but the stocks lost 2percent of their original value. If his total annual income from the investments was $80, how much did he invest in each?
----------------------
Let amt. invested at 3% be "x"; interest is 0.03x dollars
------------
Amt invested at 2% is "5000-x"; interest is 0.02(5000-x)=100-0.02x dollars
-------------
EQUATION:
gain - loss = 80 dollars
0.03x - (100-0.02x) = 80
0.05x = 180
x = $3600 (amount invested at 3%)
5000-x = $1400 (amount invested at 2%)
==================
Cheers,
Stan H.
|
Probability-and-statistics/129354: This question is from textbook fundamentals of maths
my mom is trying to help me with this problem, but we are not good at it. Can you continue to help us please? Here we go.
One thousand raffle tickets are sold for a firs prize $300. A second prize of $150. And a third prize of $50.00 dollars.What is a fair price to pay foe a raffle ticket? if Mary brought a raffle ticket for $1.00 dollar. What can you conclude about the cost of entering this raffle?. my mom says that i must do it this way.
1000 times $300.00 followed by $150.00 and so on. i know this is not right. Can you help us please?
1 solutions
Answer 94628 by stanbon(57418) on 2008-02-28 09:31:22 (Show Source):
You can put this solution on YOUR website!One thousand raffle tickets are sold for a first prize $300.
A second prize of $150.
And a third prize of $50.00 dollars.
---------------
Let your random variable be "x = gain"
Values of the random variable are:
300...................150................50.............-1.......
Corresponding probabilities are:
1/1000................1/1000.............1/1000.........999/1000
Expected "gain" value = (1/1000)(300+150+50)-(999/1000) = -499/1000= -49.9 cents
-------------------------
What is a fair price to pay for a raffle ticket?
About 50 cents
----------------
if Mary brought a raffle ticket for $1.00 dollar.
What can you conclude about the cost of entering this raffle?.
50 cents covers the cost of the prises; the rest benefits the orgainizer.
Mary can expect to lose 50 cents and every dollar she spends.
--------------------
Cheers,
Stan H.
|
Probability-and-statistics/129456: Suppose that you take all of the black cards out of a standard deck of 52 cards and thoroughly shuffle the remaining 26 red cards. From this deck of 26 red cards you will select 3 cards, one at a time, WITHOUT replacement, and record weather each card is picked is a face card (a jack, queen, or king), or not a face card.
a.) What is the probability that none of the 3 cards picked in this way is a face card?
b.) what is the probability that exactly one of the three cards picked is a face card?
1 solutions
Answer 94622 by stanbon(57418) on 2008-02-28 09:03:18 (Show Source):
You can put this solution on YOUR website!Suppose that you take all of the black cards out of a standard deck of 52 cards and thoroughly shuffle the remaining 26 red cards. From this deck of 26 red cards you will select 3 cards, one at a time, WITHOUT replacement, and record weather each card is picked is a face card (a jack, queen, or king), or not a face card.
-------------
There are 6 face-cards in the half-deck.
There are 20 non face-cards in the half-deck.
------------
a.) What is the probability that none of the 3 cards picked in this way is a face card?
P(3 non face) = 20C3/26C3 = 1140/2600=0.43846...
---------------
b.) what is the probability that exactly one of the three cards picked is a face card?
P(picking one face card) = 6/26= 3/13
P(picking one face in picking three) = 3C1(3/13)(10/13)^2 = 0.4096...
------------------
Cheers,
Stan H.
|
Probability-and-statistics/129473: Assume that a local bank knows from past experience that between 10am and 11am each day the mean arrival rate is 60 customers per hour. Determine the probability that exactly 2 customers will arrive in any given one-minute interval between 10am and 11am.
1 solutions
Answer 94621 by stanbon(57418) on 2008-02-28 08:53:39 (Show Source):
You can put this solution on YOUR website!Are you using Bernoulli trials on problems of this type?
Can you get it started and show where you get stuck with
the procedure?
Cheers,
Stan H.
|
Probability-and-statistics/129555: Two students, Katie and Carly, are playing a game that uses ten different numbered cards lying face down on a table. The faces of the cards are labeled with one of the numbers from 1 to 10(each card has a different number). If Katie and Carly each turn over a different card, what is the probability that the sum of the two cards is even?
1 solutions
Answer 94598 by stanbon(57418) on 2008-02-27 20:22:05 (Show Source):
You can put this solution on YOUR website!Two students, Katie and Carly, are playing a game that uses ten different numbered cards lying face down on a table. The faces of the cards are labeled with one of the numbers from 1 to 10(each card has a different number). If Katie and Carly each turn over a different card, what is the probability that the sum of the two cards is even?
----------------
Make a list of the possible outcomes:
1+1,1+2,1+3.................1+9
2+1,1+2,2+3,2+4.............2+9
3+1,etc
......
......
.......
9+1,1+2,9+3,................9+9
==================================
Count the number of even results.
Divide by 100
That fraction is the probability you are looking for.
-----------
Cheers,
Stan H.
|
Money_Word_Problems/129553: A group of friends went to dinner and received a bill totaling $288. The group decided to treat two people whose birthdays were that month and split the charges equally among the rest of the group. This resulted in each person having to pay $4.80 more than each would have paid had the bill been split equally among the entire group. How many people were in the dinner group?
1 solutions
Answer 94597 by stanbon(57418) on 2008-02-27 20:15:15 (Show Source):
You can put this solution on YOUR website!A group of friends went to dinner and received a bill totaling $288. The group decided to treat two people whose birthdays were that month and split the charges equally among the rest of the group. This resulted in each person having to pay $4.80 more than each would have paid had the bill been split equally among the entire group. How many people were in the dinner group?
---------------
Let the # in the group be "x".
If each paid his/her share the cost would be 288/x per person.
-------------
But two did not pay for their share so "x-2" shared the cost.
The new share was 288/(x-2) per person.
--------------
EQUATION:
New share - Old share = 4.80
288/(x-2) - 288/x = 4.80
Multiply thru by x(x-2) to get
288x - 288(x-2) = 4.8x(x-2)
576 = 4.8(x^2-2x)
x^2-2x-120 =0
(x-12)(x+10)=0
Positive answer:
x = 12 (original # of people in the group)
==============
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/129541: This question is from textbook
can you please help me?
2x^3+3x^2-2x-3
i have no idea where to start except that you need two sets of ()
1 solutions
Answer 94588 by stanbon(57418) on 2008-02-27 19:22:16 (Show Source):
You can put this solution on YOUR website!2x^3+3x^2-2x-3
--------------------
Frequently, when you have four terms and are asked to
factor, The procedure involves factoring the 1st two
terms and then the last two terms separaely.
--------------------
x^2(2x+3)-(2x+3)
= (2x+3)(x^2-1)
= (2x+3)(x-1)(x+1)
===========================
Cheers,
Stan H.
|
absolute-value/129429: could you please help me with this absolute value problem?Thank you in advance.
5-2 / 3x-4 /=-5 I didn't know how to make the straight lines on either side of the equation.Thank you for your time,and have a great day.
Joanie
1 solutions
Answer 94549 by stanbon(57418) on 2008-02-27 11:14:03 (Show Source):
You can put this solution on YOUR website!5-2 / 3x-4 /=-5
Subtract 5 from both sides to get:
-2|3x-4| = -10
Divide both sides by -2 to get:
|3x-4] = 5
3x-4= 5 or 3x-4=-5
3x=9 or 3x= -1
x = 3 or x = -1/3
=======================
Cheers,
Stan H.
|
Probability-and-statistics/129435: Suppose that it is known that 5% of the items produced by a particular machine are defective in some way, and that we will choose a random sample of exactly 20 parts made by this machine.
a.What is the expected number of defective items, out of the 20 we select?
b.What is the probability that exactly 1 of the 20 items is defective?
c. what is the probability that no more than 2 out of the 20 items selected are defective.
1 solutions
Answer 94548 by stanbon(57418) on 2008-02-27 11:10:26 (Show Source):
You can put this solution on YOUR website!Suppose that it is known that 5% of the items produced by a particular machine are defective in some way, and that we will choose a random sample of exactly 20 parts made by this machine.
a.What is the expected number of defective items, out of the 20 we select?
0.05*20 = 1
---------------------------
b.What is the probability that exactly 1 of the 20 items is defective?
P(x=1) = 20C1(0.05)(0.95)^19 = 0.377...
-----------------------------
c. what is the probability that no more than 2 out of the 20 items selected are defective.
P(0<=x<=2) = binomcdf(20,0.05,2)= 0.9245...
----------
Comment: The binomcdf is a function on a TI calculator.
For example binomcdf(20,0,05,2) = 20C0(0.05)^0+0.95^20 + 20C1(0.05)(0.95)^19
+ 20C2(0.05)^2(0.95)^18 = 0.9245...
===========================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/129431: I can not figure this out. Please help me, I just can not get word problems correct. Thanks so much for your help. I need this help by tomorrow please.
In 1991, the life expectancy of males in a certain country 68.9 years. In 1997 it was 71.7 years. Let E represent the life expectancy in year t and let t represent the number of years since 1991.
The linear function that fits the data is. E(t)= _t + _ ? Round answer to the nearest tenth.
Also, Use the function to predict the life expectancy of males in 2009.
1 solutions
Answer 94546 by stanbon(57418) on 2008-02-27 10:58:52 (Show Source):
You can put this solution on YOUR website!In 1991, the life expectancy of males in a certain country 68.9 years. In 1997 it was 71.7 years. Let E represent the life expectancy in year t and let t represent the number of years since 1991.
The linear function that fits the data is. E(t)= _t + _ ? Round answer to the nearest tenth.
Also, Use the function to predict the life expectancy of males in 2009.
-------------------
I'm sure you know how to find the equation of a line if you have two points.
Well, in this problem you are given two points: (0,68.9) and (6,71.7)
slope = (71.7-68.9) / (6-0) = 0.466667
Form is E(t) = slope(years since 1991) + b
Solve for "b"
68.9 = 0.466667*0 + b
b= 68.9
--------------
EQUATION:
E(t) = 0.466667t + 68.9
===========================
Use the function to predict the life expectancy of males in 2009.
E(2009-1991) = 0.46666667*18 + 68.9
E(18) = 77.3 yrs.
=====================
Cheers,
Stan H.
|
Radicals/129386: Could use any help available. Thanks
5i/3-i
1 solutions
Answer 94503 by stanbon(57418) on 2008-02-26 23:07:57 (Show Source):
You can put this solution on YOUR website!5i/3-i
---------
Multiply numerator and denominator by 3+i to get:
[5i(3+i)] / [(3-i)(3+i)]
= (-5+15i) / (10)
= [5(-1+3i)]/10
= (-1+3i)/2
= (-1/2) + (3/2)i
=============================
Cheers,
Stan H.
|
Rational-functions/129387: Find the quadratic model for the set of values.
(1,-2), (2,-2), (3,-4)
1 solutions
Answer 94502 by stanbon(57418) on 2008-02-26 23:03:29 (Show Source):
You can put this solution on YOUR website!Find the quadratic model for the set of values.
(1,-2), (2,-2), (3,-4)
----------------------------------
Substitute each of those x/y pairs into the
quadratic form y = ax^2+bx+c.
You will get three equations with variables a,b, and c.
Solve the system of equations.
Rewrite y = ax^2+bx+c with the values you find for a,b,and c.
Cheers,
Stan H.
Answer: y = -x^2+3x-4
=====================
|
Word_Problems_With_Coins/129380: A boy has a bag of quarters and dimes that equal 60 coins also total $7.00 how many quarters does he have
1 solutions
Answer 94501 by stanbon(57418) on 2008-02-26 22:55:39 (Show Source):
You can put this solution on YOUR website!A boy has a bag of quarters and dimes that equal 60 coins also total $7.00 how many quarters does he have
-------------------
Let # of quarters be "x" ; value is 25x cents
---------
# of dimes is "60-x" ; value is 10(60-x) = 600-10x cents
------------
EQUATION:
value + value = 700 cents
25x + 600-10x = 700
15x = 100
x = 20/3
-------
Comment: x cannot be 20/3; it must be a whole number if
if is the number of quarters. Please check your data.
=============
Cheers,
Stan H.
|
Rational-functions/129383: What is the midpoint of the line that connects the points (-3, 2) and (1, -2)?
1 solutions
Answer 94500 by stanbon(57418) on 2008-02-26 22:41:38 (Show Source):
You can put this solution on YOUR website!What is the midpoint of the line that connects the points (-3, 2) and (1, -2)?
-----------------
If (x,y) is the midpoint, x is the average of the x-coordinates
and y is the average of the y-coordinates.
------------------
x = (-3+1)/2 = -1
y = (2+-2)/2 = 0
-----------------------
Midpoint is (-1,0)
======================
Ceers,
Stan H.
|
Radicals/129384: Could use any help available. Thanks
(1-10i)-(3+2i)+(2+13i)
1 solutions
Answer 94499 by stanbon(57418) on 2008-02-26 22:36:46 (Show Source):
You can put this solution on YOUR website!(1-10i)-(3+2i)+(2+13i)
--------
1-10i-3-2i+2+13i
Combine the Real and the Imaginary part separately:
Real : 0
Imaginary: i
---------------
Answer: 0+i
=====================
Cheers,
Stan H.
|
Quadratic_Equations/129345: Write as a single log:
1/3 log(8c^6)+2 log (3a)-1/2 log 16 I think the answer is log(2c^2 + 9a^2-4)???
1 solutions
Answer 94490 by stanbon(57418) on 2008-02-26 20:54:24 (Show Source):
You can put this solution on YOUR website!Write as a single log:
1/3 log(8c^6)+2 log (3a)-1/2 log 16 I think the answer is log(2c^2 + 9a^2-4)???
-----------------------
log(2c^2) + log(9a^2) -log(4)
= log[18a^2c^2/4]
= log[(9/2)a^2c^2]
======================
Cheers,
Stan H.
|
Exponential-and-logarithmic-functions/129339: Using matrix calculations, solve the following problem. Show Your Work.
A total of $50,000 is invested in three funds paying 6%, 8%, and 10% simple interest. The yearly interest is $3,700. Twice as much money is invested at 6% as invested at 10%. How much is invested in each of the funds.
set up the 3 linear equations in 3 variables
put the coefficients into a matrix
solve the matrix using any method you like
provide the solutions for x, y, and z.
I have two equations already which are:
.06x+.08y+.10z=3,700
x+y+z=50,000
How and where do I get the last equation? I am not really sure what to do with this problem from here. Can someone please help me. I have been at this all day. Thank you
1 solutions
Answer 94483 by stanbon(57418) on 2008-02-26 20:47:26 (Show Source):
You can put this solution on YOUR website!Using matrix calculations, solve the following problem. Show Your Work.
A total of $50,000 is invested in three funds paying 6%, 8%, and 10% simple interest. The yearly interest is $3,700. Twice as much money is invested at 6% as invested at 10%. How much is invested in each of the funds.
set up the 3 linear equations in 3 variables
put the coefficients into a matrix
solve the matrix using any method you like
provide the solutions for x, y, and z
----------------------------
Quantity Equation: x + y + z = 50,000
Interest EQUATION:0.06x + 0.08y + 0.10z = 3700
Relation Equation: x + 0 - 2z = 0
--------------------------
Using the Matrix function of a TI calculator I got:
x = 30000
y = 5000
z = 15000
===================
Cheers,
Stan H.
|
test/129327: Lenox is planning to read 3 books in 5 weeks. The average number to read the same number books is 184. He wants to read the same number of pages everyday except on Friday, when he doesn't plan to read. How many pages should he read per day to finish the 3 books in 5 weeks?
1 solutions
Answer 94476 by stanbon(57418) on 2008-02-26 20:14:18 (Show Source):
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Probability-and-statistics/128586: A bag contains eight batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select two batteries at random, use the counting principle to determine how many points will be inthe sample space if the batteries are selected with replacement
Thank you for your help
1 solutions
Answer 94475 by stanbon(57418) on 2008-02-26 19:58:18 (Show Source):
You can put this solution on YOUR website!# of ways to select the 1st battery : eight
# of ways to select the 2nd battery : eight
-------------
Number of pairs in the sample space: 8*8 = 64
===============
Cheers,
Stan H.
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