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Recent problems solved by 'stanbon'
stanbon answered: 57146 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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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, >>NextProbability-and-statistics/68870: At Juan's dinner you have a choiceof 8 appetizers followed by 7 entrees and a pick of 4 desserts. How many ways can you choose 1 appetizer, 1 entree and 1 dessert?
1 solutions
Answer 49020 by stanbon(57214)   on 2007-01-31 21:30:19 (Show Source):
You can put this solution on YOUR website!At Juan's dinner you have a choiceof 8 appetizers followed by 7 entrees and a pick of 4 desserts. How many ways can you choose 1 appetizer, 1 entree and 1 dessert?
------------------
8*7*4= 224 ways
Cheers,
Stan H.
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Probability-and-statistics/68872: If a license plate consists of 3 letters followed by 2 numbers, how many license plates can be created without duplication? (allow all letters of the alphabet and all 10 digits to be used)
1 solutions
Answer 49016 by stanbon(57214) on 2007-01-31 21:26:01 (Show Source):
You can put this solution on YOUR website!If a license plate consists of 3 letters followed by 2 numbers, how many license plates can be created without duplication? (allow all letters of the alphabet and all 10 digits to be used)
--------------------------
Number = 26*25*24*10*9=140400
Cheers,
Stan H.
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Expressions-with-variables/68859: The value of a certain 2 digit number is 5 times the sum of its digits. If the digits are reversed,the resulting number 9 more than the original number . Find the original number. T is supposed to represent the tens, and U is supposed to represent the unit. Help. Need to write out this equation and solve it. Spent 3 hours already!!
1 solutions
Answer 49009 by stanbon(57214) on 2007-01-31 21:00:05 (Show Source):
You can put this solution on YOUR website!The value of a certain 2 digit number is 5 times the sum of its digits. If the digits are reversed,the resulting number 9 more than the original number . Find the original number. T is supposed to represent the tens, and U is supposed to represent the unit.
---------
Value = 10T+U (Just like 32 = 10(3)+2)
5 times sum of its digits = 5(T+U)
If digits are reversed Value = 10U+T
----------------
EQUATIONS:
1st: 10T+U=5(T+U)
2nd: 10U+T = 10T+U+9
---------------
Rewrite the equations:
1st becomes: 5T-4U=0
2nd becomes: 9T-9U+9=0
2nd again: T-U=-1
-----------------
Rewriting the two equations:
1st: 5T-4U=0
2nd:T-U=-1
Solve 2nd for T to get:
3rd: T=U-1
Substitute into 1st to get:
5(U-1)-4U=0
U=1
Substitute that into 3rd to get:
T=1-1=0
---------
The two digit number is 01
When you reverse it you get 10 which is 9 more than the original.
---------
Cheers,
Stan H.
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Expressions-with-variables/68863: This question is from textbook Introductory Algebra
The problem reads as follows......
SOFTWARE SALES Three software applications are priced as shown on the table. ( I'll give the table at the end of the problem) Spreedsheet and database programs sold in equal numbers, but 15 more word processing applications were sold than the other two combined. if the three applications generated sales of $72,000, how many spreedsheets were sold? ..........Table is as follows.............
Software Price
Spreedsheet $150
Database $195
Word Processing $210
I tried to work the problem for about an hour. This is what I tried.
150X (spreedsheet)+ 195X (database)+ 2X + 15 = 72,000
347x ( I get this by combining like terms)
347x + 15 = 72,000
- 15 -15
347x = 71985
X = 207.4495.....( I got this answer by dividing both sides by 347. Trying to solve for X)
I don't know what to do from here or if what I've even done is even close to being right. The answer in the back of the book says the answer is 90, so i tried to plug it in and still NO LUCK!!!!!!! Please Help!!!!!!!!!!!!!!
Thanks Rachel
1 solutions
Answer 49004 by stanbon(57214) on 2007-01-31 20:40:57 (Show Source):
You can put this solution on YOUR website!SOFTWARE SALES Three software applications are priced as shown on the table. ( I'll give the table at the end of the problem) Spreedsheet and database programs sold in equal numbers, but 15 more word processing applications were sold than the other two combined. if the three applications generated sales of $72,000, how many spreedsheets were sold? ..........Table is as follows.............
Software Price
Spreedsheet $150
Database $195
Word Processing $210
I tried to work the problem for about an hour. This is what I tried.
150X (spreedsheet)+ 195X (database)+ 210(2X + 15)= 72,000
150x + 195x + 420x + 3150 = 72,000
765x = 68850
x=90
----------
You forgot to multiply the number of word processors by $210.
Cheers,
Stan H.
|
Probability-and-statistics/68849: You roll a dice. What is the probability the sum of the first roll is 7 and the sum of the second roll is 10?
1 solutions
Answer 49002 by stanbon(57214) on 2007-01-31 20:30:56 (Show Source):
You can put this solution on YOUR website!You roll a dice. What is the probability the sum of the first roll is 7 and the sum of the second roll is 10?
-----------------
To get a 7: 1,6;2,5;3,4;4,3;5,2;6,1
Prob(sum = 7) = 6/36 = 1/6
------------------
To get a 10: 4,6; 5,5; 6,4
Prob (sum = 10)= 3/36 = 1/12
--------------------
Prob(sum is 7 and sum is 10)= 1/6 * 1/12 = 1/72
--------------
Cheers,
Stan H.
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Probability-and-statistics/68850: You roll two dice. What is the probability the sum of the first is 5 and the sum on the second roll is 8?
1 solutions
Answer 49001 by stanbon(57214) on 2007-01-31 20:23:30 (Show Source):
You can put this solution on YOUR website!You roll two dice. What is the probability the sum of the first is 5 and the sum on the second roll is 8?
---------
The roll results are independent because you are reusing the same pair
of dice.
To get a 5: 1,4;2,3;3,2;4,1
P(sum = 5) = 4/36=1/9
To get an 8: 2,6;3,5;4,4;5,3;6,2
P(sum=8)=5/36
------------
P(sum is 5 and sum is 8)= 1/9*5/36 = 5/324
--------
Cheers,
Stan H.
|
Probability-and-statistics/68857: A jar contains 5 green marbles and 3 orange marbles. you randomly choose a marble from a jar. Without replacing the marble, you choose a second marble. What is the probability that both marbles are orange?
1 solutions
Answer 49000 by stanbon(57214) on 2007-01-31 20:17:14 (Show Source):
You can put this solution on YOUR website!A jar contains 5 green marbles and 3 orange marbles. you randomly choose a marble from a jar. Without replacing the marble, you choose a second marble. What is the probability that both marbles are orange?
---------------
If you have studied conditional probability you know.
P(A and B) = P(A)*P(B|A)
You want:
P(orange and orange) = P(orange)*P(orange|orange}
P(orange)=3/8
P(orange|orange)=2/7 because if you have already removed
an orange there are only 2 left; and or course there are only 7 marbles left.
Answer: P(orange and orange)= (3/8)(2/7)=3/28
Cheers,
Stan H.
|
Linear-equations/68845: Find the slope of any line parrallel to the line through points (15,1)
and (4,2)
Please help me on this.
1 solutions
Answer 48987 by stanbon(57214) on 2007-01-31 19:22:35 (Show Source):
You can put this solution on YOUR website!Find the slope of any line parrallel to the line through points (15,1)
and (4,2)
---------
The slope is [1-2]/[15-4]= -1/11
The slope of any line parallel to the line thru these points
will have a slope of -1/11.
Cheers,
Stan H.
|
Probability-and-statistics/68843: A jar contains 5 green marbles and 3 orange marbles. You randomly choose a marble from the jar. After replacing the marble, you choose a second marble. What is the probability that both marbles are orange?
1 solutions
Answer 48985 by stanbon(57214) on 2007-01-31 19:20:17 (Show Source):
You can put this solution on YOUR website!A jar contains 5 green marbles and 3 orange marbles. You randomly choose a marble from the jar. After replacing the marble, you choose a second marble. What is the probability that both marbles are orange?
---------------
Because you replaced the marble after selecting the first, the
results of the two selections are independent.
P(orange and orange) = 3/8 *3/8= 9/64
---------
Cheers,
Stan H.
|
Sequences-and-series/68835: I cant figure this out. Please help.
Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27
to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space.
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.
Answer:
Show work in this space.
c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments.
Answer:
Show work in this space.
d) What observation can make about the successive partial sums of this series? In particular, what whole number does it appear that the sum will always be smaller than?
1 solutions
Answer 48981 by stanbon(57214) on 2007-01-31 19:13:24 (Show Source):
You can put this solution on YOUR website!Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27
to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space.
To find "r", divide any term by the one before it.
r=1/3
---------------------
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.
Answer:
Show work in this space.
S(10)=[(1/3)^11 - 1]/[(1/3)-1]
= 1.49999...
-------------------
c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments.
Answer:
Show work in this space.
S(12) = [(1/3)^13 - 1]/[(1/3)-1]
=1.499999...
--------------------
d) What observation can make about the successive partial sums of this series? In particular, what whole number does it appear that the sum will always be smaller than?
Smaller than 2
----------------
Cheers,
Stan H.
Stan H.
|
Sequences-and-series/68836: Please help. I tried to figure this problem out, but I couldnt.
CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Crane came out and gratefully thanked the traveling salesman for saving his daughters life. Mr. Crane insisted on giving the man an award for his heroism.
So, the salesman said, If you insist, I do not want much. Get your checkerboard and place one grain of wheat on the first square. Then place two grains of wheat on the next square. Then place four grains on the third square. Continue this until all 64 squares are covered with grains of wheat. As he had just harvested his wheat, Mr. Crane did not consider this much of an award, but he soon realized he made a miscalculation on the amount of wheat involved.
a) How much wheat would Mr. Crane have to put on the 24th square?
Answer:
Show work in this space.
b) How much total grain would the traveling salesman receive if the checkerboard only had 24 squares?
Answer:
Show work in this space.
c) Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman? Please provide the answer in either scientific notation, or calculate and show all 20 digits.
Answer:
1 solutions
Answer 48979 by stanbon(57214) on 2007-01-31 19:05:41 (Show Source):
You can put this solution on YOUR website!a) How much wheat would Mr. Crane have to put on the 24th square?
Answer: @^24 grains. (Use your calculator to get this answer.)
Show work in this space.
---------------------
b) How much total grain would the traveling salesman receive if the checkerboard only had 24 squares?
Answer:
Show work in this space.
S(24)= 1+2+2^2+2^3+...+2^24
This is a geometri series. r=2, n=24
S(24)=[ r^(n+1)-1]/[r-1]
=[2^25-1]/[1]
=33,554,431 grains
------------------
c) Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman? Please provide the answer in either scientific notation, or calculate and show all 20 digits.
S(64) = [2^(65)-1]/[2-1]
=3.689348815 X 10^19 grains
-------------
Cheers,
Stan H.
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Money_Word_Problems/68795: Claire bought three bars of soap and five sponges for $2.31. Steve bought five bars of soap and three sponges for $3.05. Find the cost of each item.
MUST Show Work!
1 solutions
Answer 48970 by stanbon(57214) on 2007-01-31 16:58:41 (Show Source):
You can put this solution on YOUR website!Claire bought three bars of soap and five sponges for $2.31. Steve bought five bars of soap and three sponges for $3.05. Find the cost of each item.
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1st: 3b+5s=2.31
2nd: 5b+3s=3.05
Multiply 1st by 5 to get:
3rd: 15b+25s=11.55
Multiply 2nd by 3 to get:
4th: 15b+9s=9.15
Subtract 4th from 3rd to get:
16s=2.4
s=0.15 or 15 cents (cost of bar of soap)
Substitute into 1st to solve for b:
3b+5(0.15)=2.31
3b+0.75=2.31
3b=1.56
b=0.52 or 52 cents (cost of a sponge)
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Cheers,
Stan H.
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Percentage-and-ratio-word-problems/68788: a chemist wants to make a 10% solution of fertilizer. How much water and how much of a 30% solution should the chemist mix to get 30 L of a 10% solution?
1 solutions
Answer 48969 by stanbon(57214) on 2007-01-31 16:50:17 (Show Source):
You can put this solution on YOUR website!a chemist wants to make a 10% solution of fertilizer. How much water and how much of a 30% solution should the chemist mix to get 30 L of a 10% solution?
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Let amount of 30% solution be "x" L ; amt. of active ingredient=0.30x L
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Amt. of 0% solution is "30-x" L; amt. of active ingredient = 0(30-x)=0 L
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Amt of mixture is 30 L ; amt of active ingredient = 0.10(30)= 3 L
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EQUATION:
active + active = active
0.30x + 0 = 3
x=10 L (He should add 10 L of 30% solution)
30-x=20L (He should add 20 L of water)
Cheers,
stan H.
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Circles/68730: I need to know: How would i convert (x^2+y^2+2x-10=0) into (x-h)^2+(y-k)^2=r^2 format? I needed to find the radius and the center of the equation.
1 solutions
Answer 48957 by stanbon(57214) on 2007-01-31 11:22:37 (Show Source):
You can put this solution on YOUR website!convert (x^2+y^2+2x-10=0) into (x-h)^2+(y-k)^2=r^2 format
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You need to "complete the square" on the x terms and separately
on the y terms, as follows:
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(x^2+2x+1) + (y^2) = 10+1
(x+1)^2 + (y-0)^2 = [sqrt(11)]^2
Center is at (-1,0)
Radius is sqrt(11)
Cheers,
Stan H.
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Exponential-and-logarithmic-functions/68752: I have two more Chapter quiz that I require assistance with in re-working the following questions:
The amount A in an account after t years of an initial principle P invested at an annual rate r compounded continuously is given by A=Pert where r is expressed as a decimal. What is the amount in the account if $500 is invested for 10 years at the annual rate of 5% compounded continuously?
The amount of a radioactive tracer remaining after t days is given by A=A0
e -0.18t, where A0 is the starting amount at the beginning of the time period. How much should be acquired now to have 40 grams remaining after 3 days?
Find the number log5(1/5).
Solve loga(8x+5)=loga(4x+29)
The amount A in an account after t years from an initial principle P invested at an annual rate r compounded continuously is given by A =Pert where r is expressed as a decimal. Solve this formula for t in terms of A, P, and r.
The decibel level of sound is given by D=10 log(I/10to the -12 power), where I is the sound intensity measured in watts per square meter. Find the decibel level of a whisper at an intensity of 5.4 x 10 to the power of -10 watts per square meter.
Respectfully,
John
1 solutions
Answer 48955 by stanbon(57214) on 2007-01-31 11:16:34 (Show Source):
You can put this solution on YOUR website!The amount A in an account after t years of an initial principle P invested at an annual rate r compounded continuously is given by A=Pe^(rt) where r is expressed as a decimal. What is the amount in the account if $500 is invested for 10 years at the annual rate of 5% compounded continuously?
A(10)=500e^(0.05(10)
A(10)=500e^0.5
A(10)=$824.36
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The amount of a radioactive tracer remaining after t days is given by
A(t)=A(o)e^(-0.18t), where Ao is the starting amount at the beginning of the time period. How much should be acquired now to have 40 grams remaining after 3 days?
40=Aoe^(-0.18(3))
40=Aoe^(-0.54)
Ao=40/(e^(-0.54))
Ao=40[e^(0.54))
Ao=40*1.716006862
Ao=68.64 grams at the beginning
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Find the number log5(1/5).
log(base 5) 5^(-1) = -1
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Solve loga(8x+5)=loga(4x+29)
If the logs are equal the anti-logs are equal:
8x+5 = 4x+29
4x=24
x=6
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The amount A in an account after t years from an initial principle P invested at an annual rate r compounded continuously is given by A =Pe^(rt) where r is expressed as a decimal. Solve this formula for t in terms of A, P, and r.
For t:
e^(rt)=A/P
Take the natural log to get:
rt= ln(A/P)
t= [ln(A/P)]/r
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For P: P=A/[e^(rt)]
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For r: r=[ln(A/P)]/t
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The decibel level of sound is given by D=10 log(I/10to the -12 power), where I is the sound intensity measured in watts per square meter. Find the decibel level of a whisper at an intensity of 5.4 x 10 to the power of -10 watts per square meter.
D=10log[(5.4 x 10^(-10))/(10^-12)
D=10log(5.4 x 10^2)
D=10log(500.4)
D=10*2.69931
D=26.99 db's
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Cheers,
Stan H.
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Percentage-and-ratio-word-problems/68751: The following represents the way a new company ships its goods.
Second day air freight - 40%
Truck - 45%
Next Day Air Freight - 15%
If the company shipped a total of 550 items last month, how many were shipped using second-day air freight?
1 solutions
Answer 48950 by stanbon(57214) on 2007-01-31 10:34:24 (Show Source):
You can put this solution on YOUR website!The following represents the way a new company ships its goods.
Second day air freight - 40%
Truck - 45%
Next Day Air Freight - 15%
If the company shipped a total of 550 items last month, how many were shipped using second-day air freight?
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40%(550)=0.40(550)=220
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/68750: A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to produce, and the wreaths take 2 hours. The labor available is limited to 80 hours per week, and the total production capacity is 60 items per week. Write a system of inequalities representing this situation, where x is the number of bouquets and y is the number of wreaths. Then graph the system of inequalities.
Thanks for any help you can provide.
1 solutions
Answer 48948 by stanbon(57214) on 2007-01-31 10:22:51 (Show Source):
You can put this solution on YOUR website!A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to produce, and the wreaths take 2 hours. The labor available is limited to 80 hours per week, and the total production capacity is 60 items per week. Write a system of inequalities representing this situation, where x is the number of bouquets and y is the number of wreaths. Then graph the system of inequalities
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Number of bouquets is "x"; Number of wreaths is "y".
1x+2y<=80
x+y<=60
x>=0
y>=0
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Shade the half-plane below y=(-1/2)x+40, below y=-x+60, to the
right of x=0, and above y=0.
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Cheers,
Stan H.
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Expressions-with-variables/68749: Solve the system by substitution.
3x y = 7
x + y = 9
Help!! I am pulling my hair out! :0) I need help with substitution, I am not understanding. Can someone please help me. Thanks.
1 solutions
Answer 48946 by stanbon(57214) on 2007-01-31 10:12:06 (Show Source):
You can put this solution on YOUR website!Solve the system by substitution.
3x y = 7
x + y = 9
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Solve either equation for y:
y=3x+7
Substitute that into the OTHER equation to get:
x+(3x+7)=-9
4x=-16
x=-4
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Substitute that into EITHER of the equations to solve for "x":
x+-4=-9
x=-5
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Answer: (-4,-5)
You could check this in the other quation:
3x y = 7
3(-4)-(-5)=-7
12+5=7
7=7
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Cheers,
Stan H.
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Graphs/68748: The revenue for a sandwich shop is directly proportional to its advertising budget. When the owner spent $2000. If the revenue is now $180,000, how much is the owner spending on advertising?
1 solutions
Answer 48945 by stanbon(57214) on 2007-01-31 10:06:33 (Show Source):
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Expressions-with-variables/68747: Solve the system by substitution.
x + y = 12
y = 2x
This problem has me a bit confused and need some help. Thanks.
1 solutions
Answer 48944 by stanbon(57214) on 2007-01-31 10:04:40 (Show Source):
You can put this solution on YOUR website!x + y = 12
y = 2x
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You are told that y=2x so substitute "2x" in place of "y"
in the 1st equation:
You get: x+2x=12
3x=12
x=4
Now you know what "x" is.
Substitute that value of x into the statement "y=2x"
You get y=2(4)=8
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So the solution for the system of equations is (4,8)
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Cheers,
Stan H.
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Graphs/68743: Graph the inequality.
2x + 3y > 6
I have been having the hardest time with this problem and cannot seem to figure it out. I need some help, Thanks.
1 solutions
Answer 48943 by stanbon(57214) on 2007-01-31 10:01:25 (Show Source):
You can put this solution on YOUR website!Graph the inequality.
2x + 3y > 6
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You may be having trouble if you are trying to
graph the INequality. What you need to do
is graph the EQUALity and then decide where
the INequality would lie.
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So, graph 2x+3y=6 as a dashed or dotted line.
You need two points:
If x=0, y=2, giving you point (0,2)
If y=0, x=3, giving you point (3,0)
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Plot those two points and draw a dashed or dotted line through them.
That is the "boundary" of the INequality.
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Now you have to figure out on which side of the boundary your INequality
lies.
So pick a test point: for example (0,0)
Test it in your INequality statement:
2x + 3y > 6
2(0) + 3(0) >6
0>6
This is not true; so the side of the dashed line that
contains (0,0) is not the side you want.
Shade the other side of the dashed line.
THAT IS THE GRAPH OF THE INEQUALITY.
Cheers,
Stan H.
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