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Recent problems solved by 'stanbon'
stanbon answered: 57883 problems
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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, >>NextMoney_Word_Problems/274104: if i want to buy a Wii for 300.00 and make 25.00 a day for babysitting at 3 days out of a week. How many weeks must I work in order to buy the Wii? 1 solutions
Answer 200098 by stanbon(57956) on 2010-02-25 10:34:43 (Show Source):
You can put this solution on YOUR website!if i want to buy a Wii for 300.00 and make 25.00 a day for babysitting at 3 days out of a week. How many weeks must I work in order to buy the Wii?
-------------------
Each week you make 3*25 = 75 dollars
-------
# of weeks = 300/75 = 4
================================
Cheers,
Stan H.
|
Probability-and-statistics/274080: I am working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. I need to determine the value of x from the following information:
a) 60% fo the values are greater than x
b) x is less than 17% of the values
c) 22% of the values are less than x
d) x is greater than 55% of the values. 1 solutions
Answer 200083 by stanbon(57956) on 2010-02-25 08:25:15 (Show Source):
You can put this solution on YOUR website!I am working with a data set that is normally distributed, with a mean of 200 and a standard deviation of 47. I need to determine the value of x from the following information:
----
Please draw a picture of the normal curve so you can see what
these problems are asking you to find.
Put 200 at the middle mark and note that sigma = 47.
--------
a) 60% of the values are greater than x
So you want a right tail that has 60% of the area in it.
1st: Find the z-value that marks off that region:
invNorm(0.4) = -0.2533
2nd: Find the corresponding "x" value using
x = z*sigma + u
x = -0.2533*47 + 200
x = 188.09
============================================
b) x is less than 17% of the values
Right-tail has 17% of the area
z value = invNorm(0.83) = 0.9542
x value = 0.9542*47+200 = 244.85
=============================================
c) 22% of the values are less than x
Left-tail of 22%
z-value = invNorm(0.22) = -0.7722
x-value = -0.7722*47+200 = 163.71
=============================================
d) x is greater than 55% of the values
Left-tail of 55%
z-value = invNorm(0.55) = 0.1257
x-value = 0.1257*47+200 = 205.91
=============================================
Cheers,
Stan H.
|
Probability-and-statistics/274006:
Exercise 7
Bob Nale is the owner of Nales Texaco GasTown. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a standard deviation of 3 gallons. From his records, he selects a random sample of 58 sales and finds the mean number of gallons sold is 8.51. (Round your answers to 2 decimal places.)
(a) The point estimate of the population mean is ?
(b) The 99 percent confidence interval for the population mean is and ? 1 solutions
Answer 200041 by stanbon(57956) on 2010-02-24 22:20:16 (Show Source):
You can put this solution on YOUR website!Bob Nale is the owner of Nales Texaco GasTown. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a standard deviation of 3 gallons. From his records, he selects a random sample of 58 sales and finds the mean number of gallons sold is 8.51. (Round your answers to 2 decimal places.)
---------------------------------------
(a) The point estimate of the population mean is ?
Ans: u = x-bar = 8.51 gallons
---------------------------------------
(b) The 99 percent confidence interval for the population mean is and ?
E = t*s/sqrt(n)
E = invT(0.995,df=56)*3/sqrt(57) = 2.6665*3/sqrt(57) = 1.0596
--------------------
99% CI: 8.51 - 1.0596 < u < 8.51 + 1.0596
--
99% CI: 7.45 < u < 9.5696
===============================
Cheers,
Stan H.
|
Rational-functions/274001: How would you solve this problem, (9x+5)/(2x-2)-(4x+3)(x-1)? I've done it at least 3 times and I can't get it right.
1 solutions
Answer 200038 by stanbon(57956) on 2010-02-24 22:07:21 (Show Source):
You can put this solution on YOUR website!(9x+5)/(2x-2)-(4x+3)/(x-1)?
------------------------------------
least common denominator: 2(x-1)
----
Rewrite each fraction with the lcd as its denominator:
-----
(9x+5)/lcd - (2(4x+3))/lcd
---------------------
Combine the numerators over the lcd:
[9x + 5 - 8x - 6]/lcd
---
(x-1)/[2(x-1)]
---
Cancel:
---
Ans: 1/2
==================
Cheers,
Stan H.
|
Travel_Word_Problems/274000: at noon a train leaves washington d.c. headed for charleston south carolina, a distance of 500 mi. the train travels at a speed of 60mph.at 1 pm a second train leaves charleston headed for washington dc traveling at 50mph . how long after the train leaves charleston will the 2 trains pass each other 1 solutions
Answer 200037 by stanbon(57956) on 2010-02-24 22:00:15 (Show Source):
You can put this solution on YOUR website!at noon a train leaves washington d.c. headed for charleston south carolina, a distance of 500 mi. the train travels at a speed of 60mph.
---------------------------------------
at 1 pm a second train leaves charleston headed for washington dc traveling at 50mph .
---------------------------------------
how long after the train leaves charleston will the 2 trains pass each other
---
Wash to Char train DATA:
rate = 60 mph: time = x hrs; distance = rt = 60x miles
-----------------
Char to Wash train DATA:
rate = 50 mph; time = x-1 hrs ; distance = rt = 50(x-1) miles
---------------------
Equation:
dist + dist = 500 miles
60x + 50x -50 = 500
110x = 550
x = 5 hrs
-----
x-1 = 4 hrs (time for the Char to Wash train
=======================
Cheers,
Stan H.
|
Permutations/273957: How many 5-cards hands having exactly 3 aces and 2 other cards can be dealt? 1 solutions
Answer 200020 by stanbon(57956) on 2010-02-24 20:54:22 (Show Source):
You can put this solution on YOUR website!How many 5-cards hands having exactly 3 aces and 2 other cards can be dealt?
-----------
Pick 3 aces: 4C3 = 4 ways
Pick 2 other cards: 48C2 = 48*47/1*2 = 1128 ways
----------------------------------
Ans: 4*1128 = 4512 ways
=========================
Cheers,
Stan H.
|
Travel_Word_Problems/273949: a ship traveling east at 25mph is 10 mi from a harbor when another ship leaves the harbor traveling east at 35mph. how long does it take the second ship to catch up to the first? 1 solutions
Answer 200018 by stanbon(57956) on 2010-02-24 20:47:14 (Show Source):
You can put this solution on YOUR website!a ship traveling east at 25mph is 10 mi from a harbor when another ship leaves the harbor traveling east at 35mph. how long does it take the second ship to catch up to the first?
-------------------------------------
1st ship DATA:
distance: x-10 mi ; rate = 25 mph ; time = d/r = (x-10)/25 hrs.
-----
2nd ship DATA:
distance = x miles ; rate = 35 mph ; time = d/r = x/35 hrs.
====================
Equation:
time = time
(x-10)/25 = x/35
35x - 350 = 25x
10x = 350
x = 35 miles
-----------------
time = x/35 = 35/35 = 1 hr
========================================
Cheers,
Stan H.
|
Travel_Word_Problems/273939: Two vehicles leave a gas station at the same time. One travels east at 60 miles per hour, the other travels west at 30 miles per hour. In how many hours will they be 150 miles apart? 1 solutions
Answer 200016 by stanbon(57956) on 2010-02-24 20:22:01 (Show Source):
You can put this solution on YOUR website!Two vehicles leave a gas station at the same time. One travels east at 60 miles per hour, the other travels west at 30 miles per hour. In how many hours will they be 150 miles apart?
-----------------------
The cars are separating at the rate of (60+30) = 90 mph
---
time = distance/rate
time = 150/90 = 15/9 = 5/3 = 1 2/3 hrs
time = 1 hr 40 minutes
================================
Cheers,
Stan H.
|
logarithm/273812: 2logsqrt(x+10)=log6-(1/2)log9
please show me the steps to solve this. 1 solutions
Answer 199982 by stanbon(57956) on 2010-02-24 16:30:00 (Show Source):
You can put this solution on YOUR website!2logsqrt(x+10)=log6-(1/2)log9
------
log[sqrt(x+10)]^2 = log[6] - log[9^(1/2)]
----
log(x+10) = log[6] - log[3]
---
log(x+10) = log[6/3]
---
log(x+10) = log[2]
---
x+10 = 2
x = -8
===============
Cheers,
Stan H.
|
logarithm/273810: How do you solve for x when log(base3)(2x-1)=2 1 solutions
Answer 199981 by stanbon(57956) on 2010-02-24 16:26:00 (Show Source):
You can put this solution on YOUR website!solve for x when log(base3)(2x-1)=2
-------------------------
The base is 3
The exponent is 2
The result is 2x-1
-------------------------
3^2 = 2x-1
2x-1 = 9
2x = 10
x = 5
===========================
Cheers,
Stan H.
|
Mixture_Word_Problems/273788: A cough medicine contains 25% alcohol. How much liquid should a pharmacists add to 120 milliliters of the cough medicine so that it contains only 20% alcohol? 1 solutions
Answer 199964 by stanbon(57956) on 2010-02-24 15:33:10 (Show Source):
You can put this solution on YOUR website!A cough medicine contains 25% alcohol. How much liquid should a pharmacists add to 120 milliliters of the cough medicine so that it contains only 20% alcohol?
--------------------------
Equation:
alcohol + alcohol = alcohol
0.25*120 + 0*x = 0.20(120+x)
Multiply thru by 100 to get:
25*120 + 0 = 20*120 + 20x
---
20x = 5*120
x = 25 milliliters ( amt. of "liquid" that must be added to the mixture)
================
Cheers,
Stan H.
|
Probability-and-statistics/273666: Dana has decided to apply to 7 colleges and wants to visit them over spring break. In how many ways can Dana choose the 4 colleges to visit? 1 solutions
Answer 199960 by stanbon(57956) on 2010-02-24 15:27:15 (Show Source):
You can put this solution on YOUR website!Dana has decided to apply to 7 colleges and wants to visit them over spring break. In how many ways can Dana choose the 4 colleges to visit?
-----------------------
Ans: 7C4 = 7*6*5/1*2*3 = 35
===============================
Cheers,
Stan H.
|
Probability-and-statistics/273723: A sample of 10 observations is selected from a normal population for which the population standard deviation is known to be 5. The sample mean is 19
(a) The standard error of the mean is
1 solutions
Answer 199959 by stanbon(57956) on 2010-02-24 15:23:21 (Show Source):
You can put this solution on YOUR website!A sample of 10 observations is selected from a normal population for which the population standard deviation is known to be 5. The sample mean is 19
(a) The standard error of the mean is
E = t*s/sqrt(n)
---
E = invT(0.97.5,df=9)*5/sqrt(10)
---
E = 3.5768
===========
Cheers,
stan H.
|
Probability-and-statistics/273759: I was wondering if this is right :)
4. When a pizza restaurant’s delivery process is operating effectively, pizzas are delivered in an average of
45 minutes with a standard deviation of 6 minutes. To monitor its delivery process, the restaurant randomly
selects five pizzas each night and records their delivery times. For the sake of the argument, assume that the
population of all delivery times on a given evening is normally distributed with a mean of µ = 45 minutes and a standard deviation of δ = 6 minutes.
z= X - mean/standard deviation = 5-45/6=-6.66
The area between z=0 and z=-6.66-= how do i find the area?? do I double 3?
1 solutions
Answer 199956 by stanbon(57956) on 2010-02-24 15:04:50 (Show Source):
You can put this solution on YOUR website!4. When a pizza restaurant’s delivery process is operating effectively, pizzas are delivered in an average of 45 minutes with a standard deviation of 6 minutes.
To monitor its delivery process, the restaurant randomly selects five pizzas each night and records their delivery times.
For the sake of the argument, assume that the population of all delivery times on a given evening is normally distributed with a mean of µ = 45 minutes and a standard deviation of δ = 6 minutes.
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Comment: You need to be given the mean delivery time for the t pizzas.
Then you need to find the t-value for that sample mean time using
t(x-bar) = (xbar-45)/[6/sqrt(5)]
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Comment: IF the alternate hypothis is "u is not equal to 45", the p-value
for your problem is 2*P(t > the t-value you obtained for x-bar)
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z= (X - mean)/standard deviation = 5-45/6=-6.66
Comment (5-45) is incorrect. 5 is the sample size; 45 is the expected
dilivery time. You need t(x-bar-45) where x-bar is the sample's mean
time.
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The area between z=0 and z=-6.66-= how do i find the area?? do I double
Comment: I'm not sure where you are going with with question. You don't
need the area (which is 0.5000). The doubling is associated with a p-score
for a two-tail test.
============================
Let me know if you need more help on this problem.
Cheers,
Stan H.
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Polynomials-and-rational-expressions/273690: JACK USUALLY MOWS HIS LAWN IN 6 HOURS. MARYILYN CAN MOW THE SAME YARD IN 5 HOURS. HOW MUCH TIME WOULD IT TAKE THEM TO MOW THE LAWN TOGETHER? 1 solutions
Answer 199909 by stanbon(57956) on 2010-02-24 11:31:18 (Show Source):
You can put this solution on YOUR website!JACK USUALLY MOWS HIS LAWN IN 6 HOURS. MARYILYN CAN MOW THE SAME YARD IN 5 HOURS. HOW MUCH TIME WOULD IT TAKE THEM TO MOW THE LAWN TOGETHER?
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Jack's rate: 1/6 job/hr
Marilyn rate: 1/5 job/hr
Together rate: 1/x job/hr
------------------------------
Equation:
rate + rate = together rate
1/6 + 1/5 = 1/x
Multiply thru by 30x
5x + 6x = 30
11x = 30
x = 30/11 = 2.73 hrs
0.73hr = 0.73(60 minutes) = 43.8 minutes
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Ans: 2 hr and 44 minutes
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Cheers,
Stan H.
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Equations/273700: I need help with the following problem, including the steps needed to get to the answer. Thanks so much!!
Find the value of c to make a perfect square. 1 solutions
Answer 199903 by stanbon(57956) on 2010-02-24 11:23:38 (Show Source):
You can put this solution on YOUR website!Find the value of c to make  a perfect square.
--------------------------------
g^2 - 18g + c
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= g^2 - 18g + (18/2)^2
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g^2 - 18g + 81 is a perfect square
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Ans: c = 81
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Cheers,
Stan H.
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Polynomials-and-rational-expressions/273699: I need help with the following problem please, including the steps to get to the answer if needed... thanks!!
Factor the polynomial . If the polynomial cannot be factored, write PRIME. 1 solutions
Answer 199900 by stanbon(57956) on 2010-02-24 11:18:45 (Show Source):
You can put this solution on YOUR website!Factor the polynomial s^2+25
----
It is PRIME in the Real Number System.
---
In the COMPLEX Number System it factors
as (s+5i)(s-5i) where i is the sqrt(-1).
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Cheers,
Stan H.
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Equations/273697: Can you please help with the following problem including the steps!! Thanks!!
to divide 7 over x+2 by x-2 over 14, you can multiply 7 over x+2 by: 1 solutions
Answer 199896 by stanbon(57956) on 2010-02-24 11:15:37 (Show Source):
You can put this solution on YOUR website!divide 7 over x+2 by x-2 over 14
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[7/(x+2)] / [(x-2)/14]
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Invert the denominator and multiply to get:
---
[7/(x+2)]
---
(7*14)/[(x+2)(x-2)]
---
98/(x^2-4)
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Cheers,
Stan H.
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Probability-and-statistics/273698: If the paired differences are normal in a test of mean differences, the distribution used for testing is the 1 solutions
Answer 199893 by stanbon(57956) on 2010-02-24 11:11:46 (Show Source):
You can put this solution on YOUR website!If the paired differences are normal in a test of mean differences, the distribution used for testing is the
-----------------------------------------
Ans: t-distribution
=====================
Cheers,
Stan H.
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Rational-functions/273696: Find each pair of functions, find f(g(x)) and g(f(x))
,
Thank you!!! 1 solutions
Answer 199892 by stanbon(57956) on 2010-02-24 11:08:33 (Show Source):
You can put this solution on YOUR website!
Find each pair of functions, find f(g(x)) and g(f(x))
 , 
------------------
f(g(x)) = f(4x+1) = (4x+1)^2 -2 = 16x^2+8x+1-2 = 16x^2+8x-1
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g(f(x)) = g(x^2-2) = 4(x^2-2)+1 = 4x^2-8+1 = 4x^2-7
===========================
Cheers,
Stan H.
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Rectangles/273644: Find the vertex of y+xsquared + 5 1 solutions
Answer 199882 by stanbon(57956) on 2010-02-24 10:03:13 (Show Source):
You can put this solution on YOUR website!Find the vertex of y+xsquared + 5
---
I'm going to assume you meant y = x^2+5
---
You have a quadratic with a = 1, b = 0, c = 5
---
The vertex occurs where x = -b/2a = -0/(2) = 0
--
The y-value when x = 0 is y = 0^2+5 = 5
---
So the vertex is (0,5)
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Cheers,
Stan H.
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decimal-numbers/273629: what is the answer to write each rule using words n x 12 and n divided by 6?
1 solutions
Answer 199877 by stanbon(57956) on 2010-02-24 09:49:50 (Show Source):
You can put this solution on YOUR website!what is the answer to
write each rule using words n x 12 and n divided by 6?
---
The sum of the product of n and 12 and the quotient of n and 6.
----
OR
The product of n and 12 added to the quotient of n and 6.
=============================================================
Cheers,
Stan H.
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Average/273631: The average of a list of positive numbers is 20 per cent of the sum of the
numbers. How many numbers are there in the list?
(A) 5 (B) 20 (C) 80 (D) 100 (E) Cannot be said. 1 solutions
Answer 199873 by stanbon(57956) on 2010-02-24 09:46:08 (Show Source):
You can put this solution on YOUR website!The average of a list of positive numbers is 20 per cent of the sum of the
numbers. How many numbers are there in the list?
------------
Let the sum be "x":
---
Average = sum/#
---
Average = 0.20x
sum/# = 0.20x
x/# = 0.20x
# = 1/0.20
# = 5
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Cheers,
Stan H.
(A) 5 (B) 20 (C) 80 (D) 100 (E) Cannot be said.
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Age_Word_Problems/273650: How many triangles can be formed by connecting any 3 vertices of a regular hexagon? 1 solutions
Answer 199871 by stanbon(57956) on 2010-02-24 09:39:08 (Show Source):
You can put this solution on YOUR website!How many triangles can be formed by connecting any 3 vertices of a regular hexagon?
There are 6 vertices on a hexagon
---
Any three non-collinear points determine a triangle.
--
# of triangles = 6C3 = 6*5*4/1*2*3 = 20
==============================
Cheers,
Stan H.
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Exponents/273659: I know how to do a problem with one exponent, but what happens if the problem has the exponent -15(30)? ex: 1-(1+5)^-15(30)
both exponents 1 solutions
Answer 199870 by stanbon(57956) on 2010-02-24 09:36:55 (Show Source):
You can put this solution on YOUR website!)what happens if the problem has the exponent -15(30)?
ex: 1-(1+5)^-15(30)
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1 - 6^(-450)
---
The negative means "invert:
---
1 - (1/6)^450
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Comment: (1/6)^450 is extremly small.
Any calculator would say it is zero
---
Answer: 1
==================
Cheers,
Stan H.
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absolute-value/273658: X-4
---------- > 0
X^2-3X-10 -
(IM TRYING TO SHOW THAT IT IS GREATER THAN OR EQUAL TO) 1 solutions
Answer 199867 by stanbon(57956) on 2010-02-24 09:31:38 (Show Source):
You can put this solution on YOUR website! X-4
---------- > 0
X^2-3X-10 -
--------------------------
Put it in factor form:
(x-4)/[(x-5)(x+2)] >=0
------------
Graph the EQUALITY to establish the boundary for the INEQUALITY:
Notice:
vertical asymptotes at x = 5 and at x = -2
horizontal asymptote is y = 0 because the degree of the
denominator is greater than the degree of the numerator.
---
y-intercept at -4/-10 = 2/5
x-intercept at x = 4
Now sketch the curve

----------------------------------------
Pick several check points to see where the INEQUALITY area is:
Test in (x-4)/[(x-5)(x+2)] > 0
---
(0,0)::::: -4/[(2)(-5)] > 0 ; true ; so that region is solution area
(-10,-10): -14/[(-15)(-8)>0 ; false; so that region is not a solution area
(10,10)::: 6/[(5)(12)] > 0 ; true; so that region is solution area
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Cheers,
Stan H.
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Permutations/273656: How many ways can a 6-person kickball team be chosen from 27 students?Is this a combination or permutation? 1 solutions
Answer 199861 by stanbon(57956) on 2010-02-24 09:16:30 (Show Source):
You can put this solution on YOUR website!How many ways can a 6-person kickball team be chosen from 27 students?Is this a combination or permutation?
---
Just picking the "team" is picking a group of people so
that is a combination.
---
If, after picking the ,you assign the players to positions
that would be a permutation.
---
# of teams 27C6
---
# of assigments to positions 6P6 = 6!
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Cheers,
Stan H.
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