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Recent problems solved by 'stanbon'
stanbon answered: 57911 problems
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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 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899 , 57900..57929, >>NextEquations/117879: Complete the statement
35 gal = _____L
a) 1,330
b) 9.21
c) 140
d) 133
1 solutions
Answer 85858 by stanbon(57984)   on 2007-12-21 07:30:56 (Show Source):
You can put this solution on YOUR website!35 gal = _____L
a) 1,330
b) 9.21
c) 140
d) 133
---------------
1 gallon is 3.785 liters
Multiply both sides by 35 to get:
35 gal = 35*3.785 = 132.475 liters
==============
Cheers,
Stan H.
|
Money_Word_Problems/117864: This problem does not tell me how many tickets were for adults and how many for a child. How can I tell this?
solve and check your answer
Tickets for a play at the community theater cost $12 for an adult and $4 for a child. If 130 tickets were sold and the total receipts were $840, how many of each type of ticket were sold?
1 solutions
Answer 85842 by stanbon(57984) on 2007-12-20 23:09:13 (Show Source):
You can put this solution on YOUR website!Tickets for a play at the community theater cost $12 for an adult and $4 for a child. If 130 tickets were sold and the total receipts were $840, how many of each type of ticket were sold?
------------------
Let # of adult tickets be "a"; Let # of child tickets be "c".
--------------------
Value EQUATION: 12a + 4c = 840
Number EQUATION: a + c = 130
------------
Multiply the 2nd equation by 4 to get:
4a+4c = 520
-----------------
Substract that from the 1st equation:
8a = 320
a = 40 (# of adult tickets sold)
-------------
Substitute to solve for "c":
40 + c = 130
c = 90 (# of child tickets sold)
=====================
Cheers,
Stan H.
|
Graphs/117859: A long distance phone call costs $0.70 for the first minute and $0.39 for each additional minute or portion thereof. Write an inequality representing the number of minutes a person could talk without exceeding $4. Do not solve the inequality.
1 solutions
Answer 85839 by stanbon(57984) on 2007-12-20 22:47:03 (Show Source):
You can put this solution on YOUR website!A long distance phone call costs $0.70 for the first minute and $0.39 for each additional minute or portion thereof. Write an inequality representing the number of minutes a person could talk without exceeding $4.
-----------------
Let "x" be the number of minutes used.
----------------------------------
INEQUALITY:
0.70 + 0.39(x-1) <= 4
======================
Cheers,
Stan H.
|
Equations/117849: Hello out there,I need some help with some tough problems,the first one is,Find the LCM for x^2+3x+2 and x^2+5x+6.The next one is,Find the LCD for 3/w and 4/w^2.The third one is,Simplify:3/x+x+3/y.And the last one is,Simplify:4y/y+2+-y/y+2.Thanks to whoever can help.
1 solutions
Answer 85838 by stanbon(57984) on 2007-12-20 22:22:14 (Show Source):
You can put this solution on YOUR website!Hello out there,I need some help with some tough problems,
the first one is,Find the LCM for x^2+3x+2 and x^2+5x+6.
Ans: (x+2)(x+1)(x+3)
--------------------------------------
The next one is,Find the LCD for 3/w and 4/w^2.
Ans: w^2
---------------------------------------
The third one is,Simplify:(3/x) + (x+3)/y
(3y + x(x+2))/xy
===============
And the last one is,
Simplify:(4y)/(y+2) + (-y)/(y+2)
= [4y -y]/(y+2)
= 3y/(y+2)
====================
Cheers,
Stan H.
|
Expressions-with-variables/117847: i need help with a math problem i need it to be solved
the problem is (40-2x)(17-2x) i know that the answer is 222 but i don't know how that is possible
1 solutions
Answer 85834 by stanbon(57984) on 2007-12-20 21:27:56 (Show Source):
You can put this solution on YOUR website!(40-2x)(17-2x)
Use FOIL:
F: 40*17 = 680
O: -2x*40 = -80x
I: -2x*17 = -34x
L: -2x*-2x = 4x^2
------------------
Combine the terms to get:
4x^2-114x+680
==============
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/117841: This question is from textbook
i want to know how to set up a problem like this for setting up linear equations
three pens and two notebooks cost $8.25. Two pens and three notebooks cost $8.00. How much would two pens and two notebooks cost
1 solutions
Answer 85833 by stanbon(57984) on 2007-12-20 21:24:49 (Show Source):
You can put this solution on YOUR website!three pens and two notebooks cost $8.25. Two pens and three notebooks cost $8.00. How much would two pens and two notebooks cost
---------------
Let the cost of one pen be "p"; Let the cost of one notebook be "n".
---------------
EQUATIONS:
3p + 2n = 8.25
2p + 3n = 8.00
-------------------
Multiply thru 1st by 2; Multiply thru 2nd by 3.
----------------
6p + 4n = 16.50
6p + 9n = 24.00
---------------
Substract 1st from 2nd to solve for "n":
5n = 7.50
n = $1.50 (cost of one notebook)
----------
Substitute to solve for "p":
6p + 4(1.50) = 16.50
6p + 6.00 = 16.50
6p = 10.50
p = $1.75 (cost of one pen)
==============
Cheers,
Stan H.
|
logarithm/117795: This question is from textbook Fund of Alg and Trig
I am trying to review for a final and would like to get help with A &B:
a. y= (10^x-10^-x)/ (2)
b. y= (e^x +e^-x) / (2)
1 solutions
Answer 85793 by stanbon(57984) on 2007-12-20 16:20:28 (Show Source):
You can put this solution on YOUR website!a. y= (10^x-10^-x)/ (2)
Multiply both sides by 2 to get:
2y = (10^x -10^-x)
Multiply both sides by 10^x to get:
10^x(2y) = 10^2x-1
Rearrange:
[10^x]^2 - [10^x](2y) + 1 = 0
Use the Quadratic Formula:
10^x = [2y +- sqrt((2y)^2-4*1*1)]/2
Simplify:
10^x = [2y +- sqrt(4y^2-4)]/2
10^x = y +- sqrt(y^2-1)
------------
Solve for "x" : x = log[y +- sqrt(y^2-1)]
Solve for "y" : y = 10^x + sqrt(y^2-1)
------------
---------------
b. y= (e^x +e^-x) / (2)
2y = (e^x + 1/e^x)
Multiply thru by e^x to get:
(2y)e^x = e^2x + 1
Rearrange:
e^2x -(2y)^x + 1 = 0
Use Quadratic Formula:
e^x = [2y +- sqrt((2y)^2-4*1*!)]/2
e^x = [2y +- sqrt(4y^2-4)]/2
e^x = [y +- sqrt(y^2-1)]
Solve for x: x = ln[y +- sqr(y^2-1)]
Solve for y: y = e^x + sqrt(y^2-1)
=======================
Cheers,
Stan H.
|
Trigonometry-basics/117789: solve:
cos -1(small in the upper righthand corner)x + cos -1(small in the upper right hand corner) 2x= 60degrees
1 solutions
Answer 85790 by stanbon(57984) on 2007-12-20 16:15:49 (Show Source):
You can put this solution on YOUR website!solve:
cos -1(small in the upper righthand corner)x + cos -1(small in the upper right hand corner) 2x= 60degrees
----------
cos^-1(x) + cos^-1(2x) = 60 degrees
---------------
Take the cos of both sides to get:
x + 2x = cos(60)
x + 2x = 1/2
3x= 1/2
x = 1/6
--------------
Cheers,
Stan H.
|
Linear-equations/117792: Find the slope and the y-intercept of the line represented by each of the following equations.
2x-3y-6
1 solutions
Answer 85781 by stanbon(57984) on 2007-12-20 16:09:06 (Show Source):
You can put this solution on YOUR website!Find the slope and the y-intercept of the line represented by each of the following equations.
2x-3y=6
---------
Solve for y:
3y = 2x-6
y = (2/3)x-2
--------------
slope = (2/3)
Intercept = -2
==================
Cheers,
stan H.
|
Linear-equations/117791: Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 miles horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth.
1 solutions
Answer 85777 by stanbon(57984) on 2007-12-20 16:06:30 (Show Source):
You can put this solution on YOUR website!Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 miles horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth.
---------------
vertical change = 1800 ft
horizontal change = 3.25*5280 ft = 17160 ft.
--------------------
slope = vert/hor = 1800/17160 = 0.1049
=================
Cheers,
Stan H.
|
Linear-equations/117779: Write the equation of the L satisfying the given geometric conditions.
L has y-intercept (0,-3) and is parallel to the line with equation y=2/3x+1
1 solutions
Answer 85770 by stanbon(57984) on 2007-12-20 15:52:41 (Show Source):
You can put this solution on YOUR website!L has y-intercept (0,-3) and is parallel to the line with equation y=2/3x+1
------------
If it is parallel, it has slope = (2/3)
You have the slope and the intercept
so, y = (2/3)x-3 is the equation you want.
===============
Cheers,
Stan H.
|
Trigonometry-basics/117778: Write equivalent equations in the form of inverse functions for
a. x= y+ cos0(that 0 is suppose to have a line through it)
b. cosy= x(to the second power)
1 solutions
Answer 85768 by stanbon(57984) on 2007-12-20 15:49:22 (Show Source):
You can put this solution on YOUR website!Write equivalent equations in the form of inverse functions for
===============================
a. x= y+ cos0(that 0 is suppose to have a line through it)
cos(theta) = x-y
theta = cos^-1(x-y)
=======================
b. cosy= x(to the second power)
cos(y) = x^2
y = Cos^-1(x^2)
=================
Cheers,
Stan H.
|
Geometric_formulas/117737: I need your help once again. Thank you all in advance
Estimate the following product by rounding each factor to the nearest hundred.
312x371
1 solutions
Answer 85738 by stanbon(57984) on 2007-12-20 13:44:26 (Show Source):
You can put this solution on YOUR website!Estimate the following product by rounding each factor to the nearest hundred.
312x371
Rounding 312 you get 300
Rounding 371 you get 400
---------
Taking the product you get 120,000
==================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/117765: This question is from textbook
A plane traveled 864 miles to Kampala and back. The trip there was with the wind. It took 9 hours. The trip back was into the wind. The trip back took 16 hours. Find the speed of the plane in still air and the speed of the wind. show work.
1 solutions
Answer 85736 by stanbon(57984) on 2007-12-20 13:41:51 (Show Source):
You can put this solution on YOUR website!A plane traveled 864 miles to Kampala and back. The trip there was with the wind. It took 9 hours. The trip back was into the wind. The trip back took 16 hours. Find the speed of the plane in still air and the speed of the wind. show work.
-----------------
Let plane speed be "p"; Let wind speed be "w".
------------------
To Kampala DATA:
Distance = 864 miles ; Time = 9 hrs. Rate = 864/9 = 96 mph
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From Kampala DATA:
Distance = 864 miles ; time = 16 hrs ; Rate = 864/(16) = 54 mph
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EQUATIONS:
p+w = 96
p-w = 54
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2p = 150
p = 75 mph (speed of the plane in still air)
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75+w = 96
w = 21 mph (speed of the wind)
============
Cheers,
Stan H.
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Probability-and-statistics/117729: Please answer this question for me.
Assume the following summary statistics, which describe the speed of a computer processor, are available from a sample of Intel Pentium IV chips manufactured at the company’s Arizona chip plant (values are in Megahertz):
Modal Speed: 3200
Median Speed: 3400
Mean Speed: 3600
S.D. Speed: 100
A. According to these statistics, how are the data distributed (i.e. left skew, normal, right skew)?
B. According to Chebyshev’s Theorem, what minimum proportion of processors have speeds between 3400 and 3800?
C. Assume Intel uses the mean speed as the accepted speed of their processors for advertising purposes. Given how the data are distributed, do you believe this could be misleading to P.C. buyers or not?
1 solutions
Answer 85714 by stanbon(57984) on 2007-12-20 10:37:57 (Show Source):
You can put this solution on YOUR website!Modal Speed: 3200
Median Speed: 3400
Mean Speed: 3600
S.D. Speed: 100
A. According to these statistics, how are the data distributed (i.e. left skew, normal, right skew)?
If you place the data on a normal-like curve you will see it is skewed to the right.
B. According to Chebyshev’s Theorem, what minimum proportion of processors have speeds between 3400 and 3800?
Those numbers are 2 SD to the left and 2SD to the right of the mean.
Chebyshev says there is at least 95% of the data within 2 SD of the mean.
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C. Assume Intel uses the mean speed as the accepted speed of their processors for advertising purposes. Given how the data are distributed, do you believe this could be misleading to P.C. buyers or not?
I'll leave that to you.
===========================
Cheers,
Stan h.
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Probability-and-statistics/117745: I have to define the Law of Large Numbers in an assignment and I need to be able to cite a credible source for it. I also have to define it in my own words which I can do but I cannot find a credible source to use as a citation.
Can anyone steer me in the right direction? Thank you SO much!
1 solutions
Answer 85713 by stanbon(57984) on 2007-12-20 10:24:21 (Show Source):
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Matrices-and-determiminant/117744: please help!!! I just spent 2 hours trying to figure this out. I have multiplied the second equation by -1 to eliminate two variables but the answer seemed wrong. I tried again and multiplied the first equation by -3 to eliminate z but this answer also seemed wrong. here is the problem...
solve the linear system without using matrices or detemrinants
0.1x+0.2y+0.2z=0.2
0.3x+0.5y+0.1z+-0.1
0.2x-0.3y-0.5z=0.7
1 solutions
Answer 85712 by stanbon(57984) on 2007-12-20 10:21:01 (Show Source):
You can put this solution on YOUR website!0.1x+0.2y+0.2z=0.2
0.3x+0.5y+0.1z+-0.1
0.2x-0.3y-0.5z=0.7
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Multiply every thing by 10 to get rid of the decimals:
x +2y+2z=2
3x+5y+z=-1
2x-3y-5z=7
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Multiply 1st by 3 and subtract from 2nd
Then Multiply 1st be 2 and subtract form 3rd.
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x +2y+2z=2
0 -y -5z=-7
0 -7y-9z=3
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Divide thru 2nd by -1
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x +2y+2z=2
0 y +5z=+7
0 -7y-9z=3
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Multiply 2nd by 7 and add to 3rd:
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x +2y+2z=2
0 y +5z=+7
0 0 26z=52
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Divide thru 3rd by 26 to get:
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x +2y+2z=2
0 y +5z=+7
0 0 z =2
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Now that you know z=2 you can solve 2nd for y; then you
can solve 1st for x.
===================
Cheers,
Stan H.
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Probability-and-statistics/117730: Please answer this question for me.
A local bakery determines that the probability of a customer ordering a blueberry muffin is 50%. 5 customers come into the bakery.
A. What is the probability that 3 out of the 5 order a blueberry muffin?
B. Explain why this scenario would meet the criteria of a binomial distribution.
1 solutions
Answer 85710 by stanbon(57984) on 2007-12-20 10:09:35 (Show Source):
You can put this solution on YOUR website!Please answer this question for me.
A local bakery determines that the probability of a customer ordering a blueberry muffin is 50%. 5 customers come into the bakery.
A. What is the probability that 3 out of the 5 order a blueberry muffin?
P(x=3) = 5C3(0.5)^3(0.5)^2 = 10/32 = 5/16
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B. Explain why this scenario would meet the criteria of a binomial distribution.
n=5 independent trials
p= 1/2 on each trial
===============
Cheers,
Stan H.
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Probability-and-statistics/117731: Please answer this question for me.
A random sample of 100 students who took a statistics exam were asked their score on the exam. The mean score on the test was 50; the standard deviation was 10. The scores are normally distributed.
A) What percent of the students scored below 30?
B) What percent scored between 30 and 55?
1 solutions
Answer 85706 by stanbon(57984) on 2007-12-20 08:48:06 (Show Source):
You can put this solution on YOUR website!A random sample of 100 students who took a statistics exam were asked their score on the exam. The mean score on the test was 50; the standard deviation was 10. The scores are normally distributed.
A) What percent of the students scored below 30?
Find the z-score for 30:
z(30)=(30-50)/10 = -2
Find P(z<-2) on your z-chart
or use normalcdf(-10,-2) = 0.0228 on your
TI calculator.
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B) What percent scored between 30 and 55?
Find the z=score for 55:
z(55)=(55-50)/10 = 1/2
Find P(-2
or use normalcdf(-2,0.5)= 0.6687
no your TI calculator.
============
Cheers,
Stan H.
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Probability-and-statistics/117732: Please answer this question for me.
The following data is a random sample of 1st quiz scores from previous Research 342 classes.
9.5, 6.5, 4.25, 8.5, 7.5, 4.5, 4.25, 6, 7
X = 6.44 S = 1.89
A) Based on the above data, find a 95% confidence interval for the average score on the 1st quiz.
B) Describe what the confidence interval tells you
1 solutions
Answer 85705 by stanbon(57984) on 2007-12-20 08:40:35 (Show Source):
You can put this solution on YOUR website!The following data is a random sample of 1st quiz scores from previous Research 342 classes.
9.5, 6.5, 4.25, 8.5, 7.5, 4.5, 4.25, 6, 7
X = 6.44 S = 1.89
A) Based on the above data, find a 95% confidence interval for the average score on the 1st quiz.
Formula: E = z*(s/sqrt(n))
E=1.96(1.89/sqrt(8)) = 1.3097
C.I.: 6.44-1.3097 < mu < 6.44+1.3097
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B) Describe what the confidence interval tells you
With 95% confidence we can say that mu lies between
5.1303 and 7.7497
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Cheers,
Stan H.
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Equations/117734: I realy need help with this problem:
4x-2x+4=x+10
don't understand this at all
1 solutions
Answer 85704 by stanbon(57984) on 2007-12-20 08:30:26 (Show Source):
You can put this solution on YOUR website!4x-2x+4=x+10
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Combine the "like" terms on the left side:
2x+4 = x+10
Subtract x from both sides:
x+4 = 10
Subtract 4 from both sides:
x = 6
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Cheers,
Stan H.
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