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Recent problems solved by 'stanbon'
stanbon answered: 57222 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>NextGraphs/196112: Hello.
I'm having a hard time getting this answer correct on homework
Solve the equation for a.
(a + 4)/b = (a - 4)/b + (b + 4)/a
a =
thanks!
1 solutions
Answer 147012 by stanbon(57290)   on 2009-05-12 19:13:04 (Show Source):
You can put this solution on YOUR website!Solve the equation for a.
(a + 4)/b = (a - 4)/b + (b + 4)/a
----------------------
Multiply thru by ab to get:
a(a+4) = a(a-4) + b(b+4)
a^2 + 4a = a^2 - 4a + b^2 + 4b
Subtract a^2 from both sides
Add 4a to both sides
8a = b^2+4b
a = (b^2+4b)/8
===================================
Cheers,
Stan H.
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Age_Word_Problems/196107: Lee is 7 years older than phil. 11 years ago Lee was twice as old as phil was then. find their ages now
1 solutions
Answer 147010 by stanbon(57290) on 2009-05-12 18:47:43 (Show Source):
You can put this solution on YOUR website!Lee is 7 years older than phil. 11 years ago Lee was twice as old as phil was then. find their ages now
-----------------
NOW DATA:
Let Phil be "x" yrs. old
Then Lee is "x+7" yrs. old
---------------------------------
11 years ago DATA:
Phil was "x-11" yrs. old
Lee was x+7-11 = "x-4" old
---------------------------------
Equation (based on 11 yrs. ago DATA:
x-4 = 2(x-11)
x-4 = 2x-22
x = 18 (Phil's age NOW)
x+7 = 25 (Lee's age NOW)
===============================
Cheers,
Stan H.
|
Probability-and-statistics/195842: ANOVA: Degrees of freedom and the F statistic
Cris Turlock owns and manages a small business in San Francisco, California. The business provides breakfast and brunch food, via carts parked along sidewalks, to people in the business district of the city.
Being an experienced businessperson, Cris provides incentives for the four salespeople operating the food carts. This year, she plans to offer monetary bonuses to her salespeople based on their individual mean daily sales. Below is a chart giving a summary of the information that Cris has to work with. (In the chart, a "sample" is a collection of daily sales figures, in dollars, from this past year for a particular salesperson.)
Groups Samples size Sample Mean Sample Variance
Salesperson 1 128 207.4 1868.4
Salesperson 2 149 207.6 2067.6
Salesperson 3 107 200.7 2594.9
Salesperson 4 51 193.6 2683.9
Cris' first step is to decide if there are any significant differences in the mean daily sales of her salespeople. (If there are no significant differences, she'll split the bonus equally among the four of them.) To make this decision, Cris will do a one-way, independent-samples ANOVA test of equality of the population means, which uses the statistic
F= Variation between the samples/Variation within the samples
For these samples, . F=1.75
Give the p-value corresponding to this value of the F statistic. Round your ansewer to at least three decimal places? ____ hide problem
1 solutions
Answer 147009 by stanbon(57290) on 2009-05-12 18:25:12 (Show Source):
You can put this solution on YOUR website!Cris' first step is to decide if there are any significant differences in the mean daily sales of her salespeople. (If there are no significant differences, she'll split the bonus equally among the four of them.) To make this decision, Cris will do a one-way, independent-samples ANOVA test of equality of the population means, which uses the statistic
F= Variation between the samples/Variation within the samples
For these samples, . F=1.75
Give the p-value corresponding to this value of the F statistic. Round your ansewer to at least three decimal places? ____ hide problem
Degrees of numerator freedom: c-1 = 4-1 = 3
Degrees of denominator freedom: n-c = 435-3 = 432
n = 128+149+107+51 = 435
F(3,432) = ?
---
I don't have an F-chart that details the the area to the right of 1.75
for the degrees of freedom listed above.
=============================================
Cheers,
Stan H.
Salesperson 1 128 207.4 1868.4
Salesperson 2 149 207.6 2067.6
Salesperson 3 107 200.7 2594.9
Salesperson 4 51 193.6 2683.9
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Probability-and-statistics/195845: Solve the problem.
The weights of the fish in a certain lake are normally distributed with a mean of 12 lb and a standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean weight will be between 9.6 and 15.6 lb?
a. 0.4032
b. 0.0968
c. 0.6730
d. 0.3270
1 solutions
Answer 146999 by stanbon(57290) on 2009-05-12 16:33:56 (Show Source):
You can put this solution on YOUR website!The weights of the fish in a certain lake are normally distributed with a mean of 12 lb and a standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean weight will be between 9.6 and 15.6 lb?
----------------
normalcdf(9.6,15.6,12,(12/sqrt(16)) = 0.6730
Cheers,
Stan H.
a. 0.4032
b. 0.0968
c. 0.6730
d. 0.3270
|
logarithm/196085: My worksheet is about logarithm. The problem is a word problem. " A lab assistant tested an antibiotic that causes a rate of decline. How long should it take for the population of 8000 bacteria to shrink to 500?"
1 solutions
Answer 146998 by stanbon(57290) on 2009-05-12 16:29:17 (Show Source):
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Probability-and-statistics/195853: Ok scores on an IQ test are normally distributed. The mean is 100 adn the standard deviation is 15. If 6000 people took the test, how many of them scored between 85 and 180?
1 solutions
Answer 146997 by stanbon(57290) on 2009-05-12 16:27:04 (Show Source):
You can put this solution on YOUR website!scores on an IQ test are normally distributed. The mean is 100 adn the standard deviation is 15. If 6000 people took the test, how many of them scored between 85 and 180?
---------------
Find the percentage of normaly distributed population, with mean
100 and sd = 15, with scores between 85 and 180
------------------
normalcdf(85,180,100,15) = 0.8413
-------------------------
Find that percent of 6000
x = 0.8413*6000 = 5048
==================================
Cheers,
Stan H.
|
Rational-functions/196008: I am stuck can you help me. Thank-you
1. Write a quadrtic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2+bx+c=0
Solution:10. only solution
The equation is _=0.
2.Write a quadratic equation in the variable x having given numbers as solutions. Type the equation in standard form, ax^2+bx+c=0
-sqrt7.8sqrt7
The equation is_=0.
1 solutions
Answer 146959 by stanbon(57290) on 2009-05-12 10:46:26 (Show Source):
You can put this solution on YOUR website!1. Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2+bx+c=0
Solution:10. only solution
If 10 is the only solution it must have multiplicity two.
Since 10 is a solution, (x-10) is a factor.
The equation is (x-10)^2 = 0
x^2 - 20x + 100 = 0
------------------------------------------------------
2.Write a quadratic equation in the variable x having given numbers as solutions. Type the equation in standard form, ax^2+bx+c=0
-sqrt7.8sqrt7
(x+sqrt(7))(x-8sqrt(7)) = 0
The equation is x^2 - 7sqrt(7)x - 56 = 0
================================================
Cheers,
Stan H.
|
Expressions-with-variables/195869: Use the discriminant to determine the number and type of solutions for the following equation.
24x2 + 13x = 0
1 solutions
Answer 146905 by stanbon(57290) on 2009-05-11 20:21:09 (Show Source):
You can put this solution on YOUR website!Use the discriminant to determine the number and type of solutions for the following equation.
24x^2 + 13x = 0
---
a = 24 ; b = 13 ; c = 0
----
determinant = b^2 -4ac = 13^2 - 0 = 169
-----
Since determinant > 0 there are 2 unequal Real Number solutions.
Cheers,
Stan H.
|
Probability-and-statistics/195815: In a British study around 1950, a group of 649 men with lung cancer were surveryed. A control group of the same size was established from a set of men who did not have lung cancer. The groups were matched according to ethnicity, age, and socieconomic status. The statistics from the survey follow.
Smokers: 647 lung cancer cases, 622 control, total 1269
non smokers: lung cancer cases 2, control 27, total 29
A.) what is the proportion of smiling in the goupd that has lung cancer in the study?
B.) what is the proportion of smoking in the control group?
C.) if a person is chosen at random from each of the two groups(smokers and non smokers) what is the probability that each person chosen has cancer?
D.) do you think this data presents a strong associatin between lung cancer and smoking?
e.)Do you think that this evidence is conclusive that smoking causes lung cancer?(problem taken from curriculum framework).
1 solutions
Answer 146904 by stanbon(57290) on 2009-05-11 20:17:20 (Show Source):
You can put this solution on YOUR website!In a British study around 1950, a group of 649 men with lung cancer were surveryed. A control group of the same size was established from a set of men who did not have lung cancer. The groups were matched according to ethnicity, age, and socieconomic status. The statistics from the survey follow.
Smokers: 647 lung cancer cases, 622 control, total 1269
non smokers: lung cancer cases 2, control 27, total 29
A.) what is the proportion of smoking in the goup that has lung cancer in the study?
647/1269
---------------
B.) what is the proportion of smoking in the control group?
622/649
------------------
C.) if a person is chosen at random from each of the two groups(smokers and non smokers) what is the probability that each person chosen has cancer?
647/1269 + 2/29 = 0.5788
===============================
D.) do you think this data presents a strong associatin between lung cancer and smoking?
Maybe
============
Cheers,
Stan H.
e.)Do you think that this evidence is conclusive that smoking causes lung cancer?
|
Proofs/195915: This question is from textbook
Concerned about Friday absenteeism, management examined absenteeism rates for the last three Fridays in four assembly plants. Does this sample prove that there is a significant difference in treatment means? Absences
Month Plant 1 Plant 2 Plant 3 Plant 4
4-Mar 19 18 27 22
11-Mar 22 20 32 27
18-Mar 20 16 28 26
1 solutions
Answer 146898 by stanbon(57290) on 2009-05-11 19:34:58 (Show Source):
You can put this solution on YOUR website!Concerned about Friday absenteeism, management examined absenteeism rates for the last three Fridays in four assembly plants. Does this sample prove that there is a significant difference in treatment means? Absences
Month Plant 1 Plant 2 Plant 3 Plant 4
4-Mar 19 18 27 22
11-Mar 22 20 32 27
18-Mar 20 16 28 26
---------------------------------
Ho: The means are the same for the 4 Plants
H1: At least one of the means is different
-------------
I ran an ANOVA Test on the 4 columns of data and got the following:
Test statistic: F = 14.18..
p-value = 0.00144
Conclusion:
Since the p-value is less than 5%, reject Ho.
At least one of the means is different.
===============================================
Cheers,
Stan H.
|
logarithm/195908: How can you solve 6^x+2=3^x+1 with out the calculator? I think you really can't because I tried it with the calculator and x comes out to be -3.584... so then the exponent would be a negative number...so I can't use logs.
1 solutions
Answer 146895 by stanbon(57290) on 2009-05-11 19:19:15 (Show Source):
You can put this solution on YOUR website!6^(x+2) = 3^(x+1)
(x+2)log6 = (x+1)log3
---
[log(6)-log(3)]x = [log(3) - 2log(6)]
---
x = [log(3) - 2log(6)] / [log(6)-log(3)]
x = log(3/6^2) / log(2)
---
x = log(1/12)/log(2)
x = log(base 2) (1/12)
=================================
Cheers,
Stan H.
|
logarithm/195909: My worksheet is on Logarithmic Functions. My directions say to "solve". The problem is 6 to the power of 3x+5 = 1
1 solutions
Answer 146892 by stanbon(57290) on 2009-05-11 19:09:56 (Show Source):
You can put this solution on YOUR website!The problem is 6 to the power of 3x+5 = 1
--------------------------
6^(3x+5) = 1
6^(3x+5) = 6^0
3x+5 = 0
x = -5/3
===============
Cheers,
Stan H.
|
Linear-equations/195780: Ben is making wooden toys for the next srt and crafts sale. Each toy cost Ben $1.80 to make. If he sells the toys for $3.00 each, how many will he sell to make a profit of exactly $36.00?
1 solutions
Answer 146810 by stanbon(57290) on 2009-05-11 09:33:12 (Show Source):
You can put this solution on YOUR website!Ben is making wooden toys for the next art and crafts sale. Each toy costs Ben $1.80 to make. If he sells the toys for $3.00 each, how many will he sell to make a profit of exactly $36.00?
-----------------------
His profit on one toy = 3.00 - 180 = 1.20
-------------------------
Let x be the number of toys he needs to make to earn $3600.
1.20x = 36.00
x = 30 toys
===============
Cheers,
Stan H.
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Probability-and-statistics/195516: During the last hour a telemarketor dialed 25 numbers and reached 7 busy signals 3 answering machines and 15 people. Use this information to determine the empirical probability the the next call will be answered in person
1 solutions
Answer 146807 by stanbon(57290) on 2009-05-11 09:25:48 (Show Source):
You can put this solution on YOUR website!During the last hour a telemarketor dialed 25 numbers and reached 7 busy signals 3 answering machines and 15 people. Use this information to determine the empirical probability the the next call will be answered in person
-----------------
P(answered in person) = 3/25
===================================
Cheers,
Stan H.
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logarithm/195709: I can't show what the power is so i'll just say to the ___ power.
3 to the x+2 power = 5 to the x-1 power. I'm not sure how to do it when there are x's on both sides and they normally cancel out in previous problems.
1 solutions
Answer 146805 by stanbon(57290) on 2009-05-11 08:01:24 (Show Source):
You can put this solution on YOUR website!3 to the x+2 power = 5 to the x-1 power.
---
3^(x+2) = 5^(x-1)
---
(x+2)log(3) = (x-1)log(5)
---
[log(3) - log(5)]x = -[2log(3) + log(5)]
Do the arithmetic and divide to get:
x = 7.452..
Cheers,
Stan H.
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Miscellaneous_Word_Problems/195761: I have two problems from a computer textbook program used in homeschool. I dont' understand them,and I was wondering if you would please help.
Thanks.
If a set has 1024 subsets, how many elements does it have?
How many bicycle license tags can you make with 4 numberal spaces? Use 10 digits and no blank spaces.
1 solutions
Answer 146804 by stanbon(57290) on 2009-05-11 07:53:24 (Show Source):
You can put this solution on YOUR website!If a set has 1024 subsets, how many elements does it have?
---
A set with n elements has 2^n subsets because each of the n elements
is either in or out of a given subset.
---
So, if 2^n = 1024
n = 10
=================
How many bicycle license tags can you make with 4 numeral spaces?
Use 10 digits and no blank spaces.
---
10 ways to choose the 1st space
10 ways to choose the 2nd space
10 ways to choose the 3rd space
10 ways to choose the 4th space
----
Total = 10^4 = 10,000 license tags possible
=====================================
Cheers,
Stan H
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Human-and-algebraic-language/195773: Hi would you help me to figure the formula for T(x). I am having a hard time with word problems.
Before and after. Jessica traveled 2x +50 miles in the
morning and 3x - 10 miles in the afternoon. Write a
polynomial T(x) that represents the total distance that she
traveled. Find the T(20).
1 solutions
Answer 146802 by stanbon(57290) on 2009-05-11 07:45:13 (Show Source):
You can put this solution on YOUR website!Jessica traveled 2x +50 miles in the
morning and 3x - 10 miles in the afternoon. Write a
polynomial T(x) that represents the total distance that she
traveled. Find the T(20).
-----------------
Total Distance traveled = 2x+50 + 3x-10
T(x) = 5x + 40
----------------------
T(20) = 5*20 + 40
T(20) = 140 miles
========================
Cheers,
Stan H.
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Graphs/195766: One last problem I'm having trouble with requires that I dtermine the co-ordinates of the lowest (minimum point on the curve)
y(x) = -8x - 7 - x^2.
I also need to prove the point is minimum.
Any help please.
Thanks, -nick
1 solutions
Answer 146800 by stanbon(57290) on 2009-05-11 07:42:33 (Show Source):
You can put this solution on YOUR website! dtermine the co-ordinates of the lowest (minimum point on the curve)
y(x) = -8x - 7 - x^2.
---
x^2 + 8x = -y+7
Complete the square:
---
x^2 + 8x + 16 = -y + 23
(x+4)^2 = -y + 23
y = -(x+4)^2 + 23
--------------
The vertex occurs at (-4,23)
The vertex is not the minimum point, it is the maximum point.
Cheers,
Stan H.
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Triangles/195769: Find the length of the hypotenuse of a right angled triangle with one leg 7 cm longer than the other and the hypotenuse 2 cm longer than the longer leg. So the hypotenuse = x+9, one side = x and the other side = x+7. I'm not sure what to do next though.
1 solutions
Answer 146798 by stanbon(57290) on 2009-05-11 07:31:39 (Show Source):
You can put this solution on YOUR website!Find the length of the hypotenuse of a right angled triangle with one leg 7 cm longer than the other and the hypotenuse 2 cm longer than the longer leg. So the hypotenuse = x+9, one side = x and the other side = x+7. I'm not sure what to do next
--------------
Solve (x+9)^2 = x^2 + (x+7)^2 for "x".
===========================================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/195770: The crushing load of a square wooden post varies directly as the fourth power of it's thickness and indirectly as the square of it's length. A post 10 cm thick and 4m high is crushed by a load of 22.5 tons. What is the crushing load on a
Post 5 cm thick and 3 m long
1 solutions
Answer 146797 by stanbon(57290) on 2009-05-11 07:29:37 (Show Source):
You can put this solution on YOUR website!The crushing load of a square wooden post varies directly as the fourth power of it's thickness and indirectly as the square of it's length.
-]--
C = k[t^4/L^2
-----
Find "k" using the following information:
A post 10 cm thick and 4m high is crushed by a load of 22.5 tons.
---
Comment: You have thicknes in cetimeters and length in meters but
have not stated whether they need to be expressed in the same unit.
==============
Cheers,
Stan H.
What is the crushing load on a
Post 5 cm thick and 3 m long
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Quadratic-relations-and-conic-sections/195772: Please help me put this in standard form x^2 - 4x + y^2 + 8y - 16 = 0
1 solutions
Answer 146795 by stanbon(57290) on 2009-05-11 07:20:25 (Show Source):
You can put this solution on YOUR website!put this in standard form x^2 - 4x + y^2 + 8y - 16 = 0
------------
Complete the square on the x-terms and the y-terms separately:
---
x^2-4x + 4 + y^2 + 8y + 16 = 16 + 4 + 16
(x - 2)^2 + (y + 4)^2 = 36
---
[(x-2)^2)/36] + [(y+4)^2)/36] = 1
=======================================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/195728: suppose it takes 3 days for space vehicle to travel from earth to the moon. about how long would it take the same vehicle traveling at the same speed to reach venus?
closest distance from earth to:
moon 240,000 mi
venus 26,000,000mi
1 solutions
Answer 146781 by stanbon(57290) on 2009-05-10 22:12:45 (Show Source):
You can put this solution on YOUR website!suppose it takes 3 days for space vehicle to travel from earth to the moon. about how long would it take the same vehicle traveling at the same speed to reach venus?
closest distance from earth to:
moon 240,000 mi
venus 26,000,000mi
------------------------------
Let the time neede to get to venus be "x".
Equation:
x/26,000,000 = 3/240,000
x = (3/240,000)*26,000,000
x = 325 days
===================
Cheers,
Stan H.
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Trigonometry-basics/195734: This question is from textbook Algebra 2
find the reference angle of 25 pi / 4
1 solutions
Answer 146780 by stanbon(57290) on 2009-05-10 22:07:58 (Show Source):
You can put this solution on YOUR website!find the reference angle of 25 pi / 4
---------------------------
Note: (8/4)pi is once around the circle.
---------------------------
So, (25/4)pi is 3 times around the circle + (1/4)pi
So the reference angle is (1/4)pi
=======================================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/195733: Building a pool in the shape of an ellipse. The equation for the pool is x^2/324 + y^2/196 = 1 Find the longest distance and shortest distance across the pool.
I'm not sure where to start?
y^2=1-x^2/324 and then square both sides?
1 solutions
Answer 146779 by stanbon(57290) on 2009-05-10 22:03:50 (Show Source):
You can put this solution on YOUR website! Building a pool in the shape of an ellipse. The equation for the pool is x^2/324 + y^2/196 = 1 Find the longest distance and shortest distance across the pool.
------------------------
a = sqrt(324) = 18 is one-half the major axis
b = sqrt(196) = 14 is one-half the minor axis
---------------------------
longest distance = 2*18 = 36
---
shortest distance = 2*14 = 28
---
Cheers,
Stan H.
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