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Recent problems solved by 'stanbon'
stanbon answered: 57889 problems
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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 , 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, >>NextInequalities/668664: mike wants to rent a car for his vacation . The rental costs $125 a week plus $0.15 a mile. How far to the nearest mile can Mike travel if he wants to spend at most $200.
1 solutions
Answer 415742 by stanbon(57962)   on 2012-10-18 19:55:18 (Show Source):
You can put this solution on YOUR website!mike wants to rent a car for his vacation . The rental costs $125 a week plus $0.15 a mile. How far to the nearest mile can Mike travel if he wants to spend at most $200.
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Equation:
200 = 125 + 0.15x
0.15x = 75
x = 500 miles
==============
Cheers,
Stan H.
|
Mixture_Word_Problems/668647: How many liters (L) of a 20% solution must be mixed with 40 L of a 80% solution to get a 50% solution?
My teacher wants us to make 2 equations. We solve them by plugging them into the calculator. I just need to know how to get 2 equations out of this. Thank you so much!
1 solutions
Answer 415736 by stanbon(57962) on 2012-10-18 19:46:43 (Show Source):
You can put this solution on YOUR website!How many liters (L) of a 20% solution must be mixed with 40 L of a 80% solution to get a 50% solution?
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Quantity Equation: x + 40 = y
Ingrediant Eq::: 0.20x + 0.80*40 = 0.50y
----------------------------------------------
Rearrange and multiply the 1st equation by 20
Rearrange and multiply the 2nd equation by 100
----------------------------------------------
20x - 20y = -800
20x - 50y = -3200
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Cheers,
Stan H.
|
Problems-with-consecutive-odd-even-integers/668638: my son has to list all the two-digit numbers that have a tens digit from 7,6 and a ones digit from 4,9. i dnt understand it can u please help me?
1 solutions
Answer 415728 by stanbon(57962) on 2012-10-18 19:23:11 (Show Source):
You can put this solution on YOUR website!my son has to list all the two-digit numbers that have a tens digit from 7,6 and a ones digit from 4,9. i dnt understand it can u please help me?
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74 ; 79
64 ; 69
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Thanks for helping your son.
Cheers,
Stan H.
=========================
|
Travel_Word_Problems/668614: The fast freight made the trip in 10 hours while the slow freight took 12 hours for the same trip. How long was the trip if the fast freight was 10kph faster than the slow freight?
1 solutions
Answer 415725 by stanbon(57962) on 2012-10-18 19:15:58 (Show Source):
You can put this solution on YOUR website!The fast freight made the trip in 10 hours while the slow freight took 12 hours for the same trip. How long was the trip if the fast freight was 10kph faster than the slow freight?
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Fast freight DATA:
time = 10 hrs ; distance = x km ; rate = d/t = x/10 kmh
----
Slow freight DATA:
time = 12 hrs ; distance = x km ; rate = d/t = x/12 kmh
---------
Equation:
rate - rate = 10 kmh
--------
x/10 - x/12 = 10
----
12x - 10x = 1200
2x = 1200
x = 600 km (distance)
========================
Cheers,
Stan H.
|
Geometric_formulas/668627: Write an equation in slope-intercept form of the line through points S(3,-4) and T(8,3)
m=y1-y2/x1-x2=-4-3/3-8=-7/-5=7/5
y-(-4)=7/5(x-3)
y+4=7/5(x+3)
This is as far as I could go. Please help
1 solutions
Answer 415714 by stanbon(57962) on 2012-10-18 18:54:10 (Show Source):
You can put this solution on YOUR website!Write an equation in slope-intercept form of the line through points S(3,-4) and T(8,3)
m=(-4-3)/(3-8) = (-7/-5) = (7/5)
y-(-4)=7/5(x-3)
y+4=7/5(x+3)
------
y = (7/5)x + (21/5) - (20/5)
----
y = (7/5)x + (1/5)
=========================
An easier way to find the equation:
m=(-4-3)/(3-8) = (-7/-5) = (7/5)
Form: y = mx + b
You are told y = -4 when x = 3, and m = (7/5)
Solve for "b":
-4 = (7/5)(-3) + b
----
-20/5 = (-21/5) + b
-----
b = 1/5
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Ans: y = (7/5)x + (1/5)
============================
Cheers,
Stan H.
==============
|
Travel_Word_Problems/668525: A light private plane can fly 120 mph in still air. Flying against the wind, the plane can fly 320 miles in the same time it requires to fly 640 miles with the wind. Find the rate of the wind.
If w represents the rate of the wind, which expression represents the time it takes the plane to travel the 640 miles with the wind?
1 solutions
Answer 415649 by stanbon(57962) on 2012-10-18 16:12:15 (Show Source):
You can put this solution on YOUR website!A light private plane can fly 120 mph in still air.
Flying against the wind, the plane can fly 320 miles in the same time it requires to fly 640 miles with the wind.
Find the rate of the wind.
If w represents the rate of the wind, which expression represents the time it takes the plane to travel the 640 miles with the wind?
--------------
Against the wind DATA:
distance = 320 miles ; rate = 120-w ; time = 320/(120-w) hrs
------------
With the wind DATA:
distance = 640 miles ; rate = 120+w ; time = 640/(120+w) hrs
---------
Equation:
time = time
320/(120-w) = 640/(120+w)
----
Divide both sides by 320:
1/(120-w) = 2/(120+w)
----
120+w = 2(120-w)
120+w = 240-2w
3w = 120
w = 40 mph (speed of the wind)
===================================
Cheers,
Stan H.
-------------------
|
Probability-and-statistics/668364: The manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is higher than Php 3,000. An auditor randomly samples 150 accounts and finds that the average owed is Php 4,170 with a standard deviation of P1,182.50. using the 0.05 level of significance, can the auditor conclude that there is evidence that the average monthly balance is really higher than Php 3,000?
1 solutions
Answer 415635 by stanbon(57962) on 2012-10-18 15:47:17 (Show Source):
You can put this solution on YOUR website!The manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is higher than Php 3,000. An auditor randomly samples 150 accounts and finds that the average owed is Php 4,170 with a standard deviation of P1,182.50. using the 0.05 level of significance, can the auditor conclude that there is evidence that the average monthly balance is really higher than Php 3,000?
------
Ho: u <= 3000
Ha: u > 3000 (?)
----
x-bar = 4170
test stat: z = (4170-3000)/[182.5/sqrt(150)] = 78.52
-----
Note: That means the sample count is 78.52 standard deviations above the mean.
-----
Since the critical values for 95% tests is +-1.96, that test stat is
definitely in the critical region.
----
Conclusion: Reject Ho. Results support the claim.
===================
Cheers,
Stan H.
===================
|
Probability-and-statistics/668363: Laboratory tests of bacterial counts are often used for declaring a water source "polluted". Suppose that the distribution of bacterial counts in a sample taken from a certain lake is normally distributed with a variance of 9,000,000. Suppose 25 water samples were taken over the course of july 2004 and yielded a mean count of 12,000. Construct an 80% confidence interval estimate of the unknown mean bacterial count in this lake at this time.
1 solutions
Answer 415582 by stanbon(57962) on 2012-10-18 14:22:14 (Show Source):
You can put this solution on YOUR website! Laboratory tests of bacterial counts are often used for declaring a water source "polluted".
-------
Suppose that the distribution of bacterial counts in a sample taken from a certain lake is normally distributed with a variance of 9,000,000.
-------
Suppose 25 water samples were taken over the course of july 2004 and yielded a mean count of 12,000.
-------
Construct an 80% confidence interval estimate of the unknown mean bacterial count in this lake at this time.
------
x-bar = 12,000
ME = 1.2816 * [sqrt[9000000/25] = 768.93
------
80% CI: 12,000 -768.93 < u < 12000 +768.93
============================================
Cheers,
Stan H.
===============
|
Probability-and-statistics/668477: say there are 5 male undergraduates, 2 female undergrduates, 2 male graduates, and 2 female graduates. find the probability of selecting an undergraduate or a female? i thought it was (7+4)/11 but thats just one ...
1 solutions
Answer 415580 by stanbon(57962) on 2012-10-18 14:10:34 (Show Source):
You can put this solution on YOUR website!say there are 5 male undergraduates, 2 female undergrduates, 2 male graduates, and 2 female graduates. find the probability of selecting an undergraduate or a female? i thought it was (7+4)/11 but thats just one ...
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P(undergrad OR female) = P(undergrad) + P(female) - P(undergrad AND female)
-----
= [7 + 4 - 2]/11 = 9/11
=============================
Cheers,
Stan H.
|
Probability-and-statistics/668443: Due to increasing crime rates over the past few years, the Spokane PD wants to implement a new hot spots policing policy. In order to determine which neighborhoods should receive extra patrols, the Chief wants to know which neighborhood has the highest mean number of calls for service per day over the past year. Unfortunately, two neighborhoods have a mean of 18 calls per day. Neighborhood A has an s of 12.23 and Neighborhood B has an s of 7.42. Using a 95% confidence level, calculate confidence intervals for both neighborhoods and then discuss which neighborhood you believe needs the extra patrols and why.
Confused on how to solve without knowing the N. I believe I am thinking about it too much
1 solutions
Answer 415579 by stanbon(57962) on 2012-10-18 14:05:52 (Show Source):
You can put this solution on YOUR website!the Chief wants to know which neighborhood has the highest mean number of calls for service per day over the past year. Unfortunately, two neighborhoods have a mean of 18 calls per day. Neighborhood A has an s of 12.23 and Neighborhood B has an s of 7.42. Using a 95% confidence level, calculate confidence intervals for both neighborhoods and then discuss which neighborhood you believe needs the extra patrols and why.
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A-CI:
18-1.96[12.23/sqrt(n)] < u < 18+1.96[12.23/sqrt(n)]
-----
B-CI:
18-1.96[7.42/sqrt(n)] < u < 18+1.96[7.42/sqrt(n)]
-----
Because 12.23 is larger than 7.42 the A-CI will have a greater
range than the B-CI. The true mean may reach a higher level
for neighborhood A than for neighborhood B. A should be assigned
extra patrols.
----
Cheers,
Stan H.
-----------
|
Probability-and-statistics/668447: Assume a system has 5 subsystems. As long as 3 of the subsystems are operational, the system is working. Also assume that each subsystem has a probability of survival equals to 0.9 for 1000 hours of operation without any failure.
What is the probability that the system will survive a 1000 hours of operation without a loss of more than 2 subsystems.
1 solutions
Answer 415576 by stanbon(57962) on 2012-10-18 13:53:04 (Show Source):
You can put this solution on YOUR website!Assume a system has 5 subsystems. As long as 3 of the subsystems are operational, the system is working. Also assume that each subsystem has a probability of survival equals to 0.9 for 1000 hours of operation without any failure.
What is the probability that the system will survive a 1000 hours of operation without a loss of more than 2 subsystems.
----
Binomial Problem with n = 5, p(fail) = 0.1, p(not fail) = 0.9
----------------------
Comment: That condition means you could have zero, one, or two subsystems fail.
P(0<= x <=2) = binomcdf(5,0.1,2) = 0.9914
==================
Cheers,
Stan H.
|
Probability-and-statistics/668466: Terry rolls a number cube labeled 1 through 6 two times . What is the probability that the number cube will land on 5 for the first roll and 3 for the second roll ?
1 solutions
Answer 415575 by stanbon(57962) on 2012-10-18 13:44:07 (Show Source):
You can put this solution on YOUR website!Terry rolls a number cube labeled 1 through 6 two times . What is the probability that the number cube will land on 5 for the first roll and 3 for the second roll ?
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The events are independent.
P(5 and 3) = P(5)*P(3) = 1/6 * 1/6 = 1/36
=============
Cheers,
Stan H.
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logarithm/668465: cuanto vale x para log(x+3)=log 2 - log (x-2)
1 solutions
Answer 415573 by stanbon(57962) on 2012-10-18 13:29:07 (Show Source):
You can put this solution on YOUR website!log(x+3)=log 2 - log (x-2)
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log[(x+3) = log[2/(x-2)]
-------
x+3 = 2/(x-2)
(x-2)(x+3) = 2
----
x^2 + x -8 = 0
---
x = [-1 +-sqrt(1-4*-8)]/2
----
x = [-1 +- sqrt(33)]/2
---
x = (-1/2) + sqrt(33)/2
----
Cheers,
Stan H.
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test/668412: Determine whether y varies directly with x. If so find the constant of variation k. -6y=-5x
1 solutions
Answer 415540 by stanbon(57962) on 2012-10-18 11:54:43 (Show Source):
You can put this solution on YOUR website!Determine whether y varies directly with x. If so find the constant of variation k.
-6y=-5x
y = 5x
----
As x increases, y increases so y and x vary diriectly.
------
The constant of variation is "5".
Cheers,
Stan H.
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Money_Word_Problems/668430: if the reserve rate is 9%and a bank recieves a deposit of 8000 how much of the 8000 is the bank free to lend
1 solutions
Answer 415537 by stanbon(57962) on 2012-10-18 11:51:51 (Show Source):
You can put this solution on YOUR website!if the reserve rate is 9%and a bank recieves a deposit of 8000 how much of the 8000 is the bank free to lend
----
The bank can lend 91% of the money.
0.91*8000 = $7280
------------------------
Cheers,
Stan H.
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Equations/668426: Please show how to solve and check the following: 6x + 18 = -2x -62
1 solutions
Answer 415533 by stanbon(57962) on 2012-10-18 11:47:08 (Show Source):
You can put this solution on YOUR website!Please show how to solve and check the following:
6x + 18 = -2x -62
------
Add 2x to both sides:
Subtract 18 from both sides:
-------
8x = -80
Divide both sides by 8 to get:
x = 10
-------------
Cheers,
Stan H.
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Money_Word_Problems/668425: You have already invested $550 in a stock with an annual return of 11%. How much more should be invested at 15% so that the return on the total investment is 12%?
1 solutions
Answer 415530 by stanbon(57962) on 2012-10-18 11:44:58 (Show Source):
You can put this solution on YOUR website!You have already invested $550 in a stock with an annual return of 11%. How much more should be invested at 15% so that the return on the total investment is 12%?
------
Equation:
interest + interest = interest
0.11*550 + 0.15x = 0.12(550+x)
---------
11*550 + 15x = 12*550 + 12x
3x = 550
x = 183.33 (amt. to be invested at 15%)
====================
Cheers,
stan H.
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Linear-equations/668406: write the equation of the line with slope 4/5 containing the point (3,7)
1 solutions
Answer 415513 by stanbon(57962) on 2012-10-18 10:39:54 (Show Source):
You can put this solution on YOUR website!write the equation of the line with slope 4/5 containing the point (3,7)
-----
Form: y = mx + b
----
You are told that y = 7 when x = 3 and you know m = 4/5
Solve for "b":
-------
7 = (4/5)3 + b
-----
7 = 12/5 + b
-----
35/5 = 12/5 + b
b = 23/5
--------
Equation:
y = (4/5)x + (23/5)
========================
Cheers,
Stan H.
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Permutations/668404: please help me!
Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if Maria is to sit in the aisle seat?
thanks!
1 solutions
Answer 415512 by stanbon(57962) on 2012-10-18 10:36:58 (Show Source):
You can put this solution on YOUR website!Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if Maria is to sit in the aisle seat?
----------------
Ans: 7! = 5040 ways
=====================
Cheers,
Stan H.
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Functions/668394: State the domain and range of f(x)=2^x. Here is what I did.....The domain of f(x)=2^x would be the x values. This would include all values that you can input as x in order to make this problem work. The domain of a function is usually all real numbers. The range of f(x)=2^x would be the y values. This would include all values that would be the output for the y value. An example of this would be if you used 2 as x then the function would read f(x)=2^2. The y would equal 4 which would be included in the range of this function. To find the domain and range of the inverse you would follow the proper steps to get the inverse of the function which would be x=2^y. The domain would be the x values and the range would be the y values. If you put 4 as x which would be your input for the domain you would get 2 for the y which would be the range.
I understand that the domain is all real numbers, but I still have to be able to state the entire range of the function. Thanks!
1 solutions
Answer 415510 by stanbon(57962) on 2012-10-18 10:31:18 (Show Source):
You can put this solution on YOUR website!State the domain and range of f(x)=2^x. Here is what I did.....The domain of f(x)=2^x would be the x values. This would include all values that you can input as x in order to make this problem work. The domain of a function is usually all real numbers. The range of f(x)=2^x would be the y values. This would include all values that would be the output for the y value. An example of this would be if you used 2 as x then the function would read f(x)=2^2. The y would equal 4 which would be included in the range of this function. To find the domain and range of the inverse you would follow the proper steps to get the inverse of the function which would be x=2^y. The domain would be the x values and the range would be the y values. If you put 4 as x which would be your input for the domain you would get 2^4 = 16 for the y which would be the range.
I understand that the domain is all real numbers, but I still have to be able to state the entire range of the function. Thanks!
---------
y = 2^x
----
Domain: All Real Numbers
Range: 2^x can never be 0 or negative
So, Range is All Real Numbers greater than zero.
-------------------
Cheers,
Stan H.
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Complex_Numbers/668244: We are suppose to solve the quadratic equations in the complex number system using the quadratic formula.
3x^2-2x+7=0
1 solutions
Answer 415417 by stanbon(57962) on 2012-10-17 22:13:20 (Show Source):
You can put this solution on YOUR website!3x^2-2x+7=0
-----
a = 3 ; b = -2 ; c = 7
------
x = [-b +-sqrt(b^2-4ac)]/(2a)
----
x = [2 +- sqrt(4-4*3*7)]/(6)
---
x = [2 +- sqrt(80)]/6
-----
x = [2 +- 4sqrt(5)]/6
----
x = (1/3) +- (2/3)sqrt(5)
=============================
Cheers,
Stan H.
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Permutations/668255: There are 20 students in the class. How many different seating charts can you make?
1 solutions
Answer 415415 by stanbon(57962) on 2012-10-17 22:08:23 (Show Source):
You can put this solution on YOUR website!There are 20 students in the class. How many different seating charts can you make?
----
Each student either does or does not occupy a given chair.
There are 20 chairs.
-----
# of possible seating charts = 2^20 = 1,048,576
============
Cheers,
Stan H.
============
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Proportions/668256: Brandon goes to the store and finds an item that is normaly $30 is on sale for $24. the sale is the same as what percentage off the original price of that item?
1 solutions
Answer 415414 by stanbon(57962) on 2012-10-17 22:05:07 (Show Source):
You can put this solution on YOUR website!Brandon goes to the store and finds an item that is normaly $30 is on sale for $24. the sale is the same as what percentage off the original price of that item?
-----
Amount of decrease in price: 30-24 = $6
----
Percent of decrease in price: 6/30 = 1/5 = 20%
====================================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/668250: Jacob can complete a plant installation in 5 hours using a planting tool. Aiden can complete the same plant installation in 20 hours using conventional tools. How long would it take the two men together to complete the plant installation if they are working together, each working with his tools?
1 solutions
Answer 415412 by stanbon(57962) on 2012-10-17 22:02:35 (Show Source):
You can put this solution on YOUR website!Jacob can complete a plant installation in 5 hours using a planting tool. Aiden can complete the same plant installation in 20 hours using conventional tools. How long would it take the two men together to complete the plant installation if they are working together, each working with his tools?
------
Jacob's rate: 1/5 job/hr
Alden's rate: 1/20 job/hr
-----
Together rate: 1/x job/hr
Equation:
rate + rate = together rate
-----
1/5 + 1/20 = 1/x
4x + x = 20
5x = 20
x = 4 hrs (time for them to do the job together)
==============
Cheers,
Stan H.
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Expressions-with-variables/668248: Could you help me? I'm having trouble with these types of problems:
3(2d-7)=(2+4d)2 Solve for d
this is what i have done:
3(2d-7)=(2+4d)2 Use the distributive property. Distribute the 3 and 2
6d-7=4+8d Use the addition and subtraction property of equality
-6d -6d
-7=4+2d
-4 -4
-11=2d Use the division property of equality
/2 /2
-5.5= d But when i plug -5.5 in for d, it just doesn't work
1 solutions
Answer 415406 by stanbon(57962) on 2012-10-17 21:56:03 (Show Source):
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Mixture_Word_Problems/668245: Why is it impossible to mix candy worth $4 per lb. and candy worth $5 per lb. to obtain a final mixture worth $6 per lb.?
1 solutions
Answer 415404 by stanbon(57962) on 2012-10-17 21:53:02 (Show Source):
You can put this solution on YOUR website!Why is it impossible to mix candy worth $4 per lb. and candy worth $5 per lb. to obtain a final mixture worth $6 per lb.?
----
The value of the $4 candy plus the value of the $5 candy
can never equal the value of $6 candy
---
4x + 5*(k-x) = 6*k has no solution:
4x + 5k-5x = 6k
-x = k
x = -k
But x is the amount of $4 candy; its weight cannot be -k
===============
Cheers,
Stan H.
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test/668246: The sum of a number and three is less than nineteen less the number
1 solutions
Answer 415401 by stanbon(57962) on 2012-10-17 21:47:44 (Show Source):
You can put this solution on YOUR website!The sum of a number and three is less than nineteen less the number
-----
Let the number be "x":
Equation:
x + 3 < 19-x
----
2x < 16
x < 8
----------------
cheers,
Stan H.
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