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Recent problems solved by 'stanbon'
stanbon answered: 57151 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>NextEquations/128271: Hi, Can I please have some help with this problem about functions? thank you!
An appliance dealer advertises a 15% discount on all his washing machines. In addition, the manufacturer offers a $80 rebate on the purchase of a washing machine. Let x represent the sticker price of the washing machine.
(a) Suppose only the 15% discount applies. Fund a function f that models the purchase price of the washer as a function of the sticker price x
f(x) =
(b) Suppose only the $80 rebate applies. Find a function g that models the purchase price of the washer as a function of the sticker price x.
g(x) =
(c) Find f º g.
(d) Find g º f.
1 solutions
Answer 93920 by stanbon(57219)   on 2008-02-21 19:34:49 (Show Source):
You can put this solution on YOUR website!An appliance dealer advertises a 15% discount on all his washing machines. In addition, the manufacturer offers a $80 rebate on the purchase of a washing machine. Let x represent the sticker price of the washing machine.
(a) Suppose only the 15% discount applies. Fund a function f that models the purchase price of the washer as a function of the sticker price x
f(x) = 0.85x
------------------------
(b) Suppose only the $80 rebate applies. Find a function g that models the purchase price of the washer as a function of the sticker price x.
g(x) = x - 80
-------------------
(c) Find f º g(x) = f[x-80] = 0.85(x-80) = 0.85x-0.68
------------------
(d) Find g º f(x) = g[0.85x] = 0.85x-80
-----------------------------------
Cheers,
Stan H.
|
Finance/128282: This question is from textbook Holt Pre-Algebra
Change 40 kilometers to meters per hour.
1 solutions
Answer 93919 by stanbon(57219) on 2008-02-21 19:26:10 (Show Source):
You can put this solution on YOUR website!Change 40 kilometers to meters per hour.
-----------------------------------
I assume you meant 40 kilometers per hour.
-----------------------------------
1 kilometer = 1000 meters
-----------------------
40 kilometersper hour = 40*1000 meters per our = 40,000 meters per hour
===============================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/128278: In a game,18 of a baseball team's 27 outs were fly balls. Fifty percent of the outs made by infielders and 100% of the outs made by outfielders were fly balls. How many outs were made by outfielders? How many outs were made by infielders? Hint: write one equation for the total number of outs and another equation for the number of fly ball outs.
1 solutions
Answer 93918 by stanbon(57219) on 2008-02-21 19:18:01 (Show Source):
You can put this solution on YOUR website!In a game,18 of a baseball team's 27 outs were fly balls. Fifty percent of the outs made by infielders and 100% of the outs made by outfielders were fly balls. How many outs were made by outfielders? How many outs were made by infielders? Hint: write one equation for the total number of outs and another equation for the number of fly ball outs.
----------------------------
Let I be the number of infielder outs; Let O be the number of outfielder outs.
EQUATIONS:
Total # of outs equation: I + O = 27
# of outs by fly-our : I +(1/2)O = 18
------------------------------------------------------
Subtract the 2nd equation from the 1st to get:
(1/2)O = 9
O = 18 (# of outs by outfielders)
I = 27-9 = 18 (# of outs by infielders)
====================================
Cheers,
Stan H.
|
Linear-equations/128277: A plane flying over Albuquerque at an elevation of 33,000ft begins its descent to land at Santa Fe 50 miles away. If the elevation of Santa Fe is 7000ft what should the slope of descent expressed as a percent? Id really appreciate it if someone could help me. Thanks
1 solutions
Answer 93913 by stanbon(57219) on 2008-02-21 18:56:51 (Show Source):
You can put this solution on YOUR website!A plane flying over Albuquerque at an elevation of 33,000ft begins its descent to land at Santa Fe 50 miles away. If the elevation of Santa Fe is 7000ft what should the slope of descent expressed as a percent?
--------------------------
1 mile = 5280 feet
slope = 33000/(50*5280) = 0.125 = 12.5%
=========================
Cheers,
Stan H.
|
Rational-functions/128268: This question is from textbook Algebra 2
How do i identify horizontal and vertical asymptotes of functions
1 solutions
Answer 93912 by stanbon(57219) on 2008-02-21 18:52:15 (Show Source):
You can put this solution on YOUR website!Vertical asymptotes occur where the denominator of a rational function are zero.
There is an exception to this, however. If a rational function has the same
factor in numberator and denominator there is a hole in the finction, not
a vertical asymptote.
----------------------
Horizontal asymptote occurs in a rational function where y = p/q,
where p and q are the coefficient of the highest power term that
occurs in the numerator OR the denominator.
-------------------------------------------
Example:
f(x) = [(x-3)(x+2)]/[(x+2)(2x+5)]
-------------
Hole: at x=-2 because there is a factor of (x+2) in numerator and denominator.
-------------
Vertical Asymptote: at x = -5/2 because (2x+5) is in the denominator.
----------------
Horizontal Asymptote: at y = 1/2 because the highest power term in numerator
and denominator is x^2; you have 1x^2/2x^2 = 1/2
--------------------------
Hope this helps.
Cheers,
Stan H.
|
Quadratic_Equations/128183: Please help me,I am totally confused with this.
What is the difference between 2x^2+4xy-3 and x^2-2xy-4
Please help me!
1 solutions
Answer 93864 by stanbon(57219) on 2008-02-21 12:41:32 (Show Source):
You can put this solution on YOUR website!What is the difference between 2x^2+4xy-3 and x^2-2xy-4
-------------------------------------------
(2x^2+4xy-3) - (x^2-2xy-4)
= 2x^2 + 4xy -3 -x^2 + 2xy + 4
Gather "like" terms to get:
= 2x^2-x^2 + 4xy+2xy -3+4
= x^2 + 6xy +1
==================
Cheers,
Stan H.
|
Numeric_Fractions/128188: How do I solve this: 3 over z = 9 over 5..............? (by "over" I mean 3 and 9 are numerators........z and 5 are denominators....
Solving for "z"...........Thank you
1 solutions
Answer 93863 by stanbon(57219) on 2008-02-21 12:37:54 (Show Source):
You can put this solution on YOUR website!solve this: 3 over z = 9 over 5
3/z = 9/5
Invert both sides to get:
z/3 = 5/9
Multiply both sides by 3 to get;
z = 5/3
===========
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/128190: find 2 positive numbers whoes squares have a sum of 113 and a difference of 15
1 solutions
Answer 93862 by stanbon(57219) on 2008-02-21 12:32:07 (Show Source):
You can put this solution on YOUR website!find 2 positive numbers whoes squares have a sum of 113 and a difference of 15
-----------
EQUATIONS:
x^2 + y^2 = 113
x^2 - y^2 = 15
----------------
Subtract the 2nd from the 1st to get:
2y^2 = 98
y^2 = 49
y = 7
---------
Substitute to solve for "x":
x^2 + 49 = 113
x^2 = 64
x = 8
===========
Cheers,
Stan H.
|
Triangles/128193: Two parallel guy wires are attached to a vertical pole 4.5m and 5.4m above the ground.They are secured on the level ground at points 1.2m apart.How long are the guy wires??
1 solutions
Answer 93858 by stanbon(57219) on 2008-02-21 12:18:34 (Show Source):
You can put this solution on YOUR website!Two parallel guy wires are attached to a vertical pole 4.5m and 5.4m above the ground.They are secured on the level ground at points 1.2m apart.How long are the guy wires??
---------------------
Draw and label the figure.
Let the missing part of the base be "x".
-----------------
EQUATION:
5.4/(x+1.2) = 4.5/x
5.4x = 4.5x+ 5.4
0.9x = 5.4
x = 6 meters
----------------
Now, use Pythagoras to determine the length of each wire.
==============
Cheers,
Stan H.
|
Probability-and-statistics/128028: This question is from textbook Fundamentals of Mathematics
Charlie's wallet contains a one-dollar bill, a five-dollar bill, a ten-dollar bill, and a twenty-dollar bill. If Charlie chooses one bill at random,find the probability that the value of the bill chosen is
a. even
b. odd
c. greater than one dollar
d. less than five dollars
e. less than twenty dollars
f. divisible by 3
1 solutions
Answer 93855 by stanbon(57219) on 2008-02-21 11:55:16 (Show Source):
You can put this solution on YOUR website!Charlie's wallet contains a one-dollar bill, a five-dollar bill, a ten-dollar bill, and a twenty-dollar bill. If Charlie chooses one bill at random,find the probability that the value of the bill chosen is
---------
Comment: I'm going to assum 1-dollar and 5-dollars bills are "odd".
---------------------------
a. P(even) = 2/4 = 1/2
b. P(odd) = 2/4 = 1/2
c. P(greater than one dollar) = 3/4
d. P(less than five dollars) = 1/4
e. P(less than twenty dollars) = 3/4
f. P(divisible by 3) = 0/4 = 0
=====================================
Cheers,
Stan H.
|
Probability-and-statistics/128036: This question is from textbook Fundamentals of Mathematics
Each individual letter of the word probability is typed on a separate identical slip of paper; all 11 pieces of paper are placed in a bowl and the pieces of paper are mixed. If one letter is chosen at random, find the probability that the letter chosen is
a. a t
b. a vowel
c. not a vowel
d. a b
e. a b or an i
f. neither a b nor an i
1 solutions
Answer 93837 by stanbon(57219) on 2008-02-21 09:50:11 (Show Source):
You can put this solution on YOUR website!Each individual letter of the word probability is typed on a separate identical slip of paper; all 11 pieces of paper are placed in a bowl and the pieces of paper are mixed. If one letter is chosen at random, find the probability that the letter chosen is
a. a t
P(t) = 1/11
-----------------
b. a vowel
P(vowel) = 4/11
-----------------
c. not a vowel
P(not vowel) = 7/11
----------------
d. a b
P(b) = 2/11
--------------
e. a b or an i
P(b or i) = 2/11 + 2/11 = 4/11
----------------
f. neither a b nor an i
P(not b and not i) = 7/11
=============================
Cheers,
Stan H.
|
Probability-and-statistics/128112: What z-score equation do we use on a continuous dataset? What is the equation that we should use on a proportion dataset?
1 solutions
Answer 93836 by stanbon(57219) on 2008-02-21 09:37:16 (Show Source):
You can put this solution on YOUR website!What z-score equation do we use on a continuous dataset? What is the equation that we should use on a proportion dataset?
-------------------------
z(x) = (x-mu)/sigma
------------------
OR
t(x) = (x-mu)/sigma
-------------------
If you do not have sigma you can substitute
The standard deviation of the sample.
============
Cheers,
Stan H.
|
Probability-and-statistics/128064: This question is from textbook Applie Statics in Business and Econmics
Can someone please help me with this one. Thanks so much!!!!
In a bumper test, three types of autos were deliberately crashed into a barrier at 5mp, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles?
Goliath= 1,600-760-880-1,950-1,220
Varmint= 1,290-1,400-1,390-1,850
Weasel=1,090-2,100-1,830-1,250-1,920
1 solutions
Answer 93835 by stanbon(57219) on 2008-02-21 09:31:38 (Show Source):
You can put this solution on YOUR website!In a bumper test, three types of autos were deliberately crashed into a barrier at 5mp, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles?
Goliath= 1,600-760-880-1,950-1,220
Varmint= 1,290-1,400-1,390-1,850-950
Weasel=1,090-2,100-1,830-1,250-1,920
-----------------
Ho: The means are the same
Ha: At least one of the means is different
----------
I ran an ANOVA Test using a TI calculator and got the following results.
p-value = 0.4188
Conclusion: Fail to reject Ho.
The test provides evidence you should not reject Ho.
=================
Cheers,
Stan H.
cheers,
Stan H.
|
Probability-and-statistics/128115: Problem One:
According to police records, from 1987 to 1995, the city of Davis, California experienced the following burglary rate (offenses per 1,000 residents for a given year):
(1) What is the mean burglary rate?
(2) What is the standard deviation of the burglary rate?
(3) What is the degree of freedom?
(4) What is the t-statistic @ 95% confidence?
(5) What is the standard error?
(6) What is the amount of error?
(7) What is the upper confidence bound per thousand offenses @ 95% confidence the mean annual burglary rate in Davis, California?
(8) What is the lower confidence bound per thousand offences @ 95% confidence the mean annual burglary rate in Davis, California?
1 solutions
Answer 93832 by stanbon(57219) on 2008-02-21 09:21:03 (Show Source):
You can put this solution on YOUR website!
Problem One:
According to police records, from 1987 to 1995, the city of Davis, California experienced the following burglary rate (offenses per 1,000 residents for a given year):
year: 1987 data 15.8
year: 1988 data 17.2
year: 1989 data 16.5
year: 1990 data 15.5
year 1991 data 17.1
year 1992 data 18.6
year 1993 data 21.4
year 1994 data 29.0
year 1995 data 19.3
(1) What is the mean burglary rate?
Add the numbers and divide by nine to get 18.9333
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(2) What is the standard deviation of the burglary rate?
I used a calculator to get: s = 4.2065
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(3) What is the degree of freedom?
9-1 = 8
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(4) What is the t-statistic @ 95% confidence?
t(18.9333) = (18.9333 - population mean)/[4.2065/(sqrt(9)]
Comment: You did not include the population mean in your posting.
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(5) What is the standard error?
E = 1.96= 2.7482
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(6) What is the amount of error?
Not sure how that differs from (5)
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(7) What is the upper confidence bound per thousand offenses @ 95% confidence the mean annual burglary rate in Davis, California?
18.9333+2.7482
(8) What is the lower confidence bound per thousand offences @ 95% confidence the mean annual burglary rate in Davis, California?
18.9333-2.7482
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Cheers,
Stan H.
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Probability-and-statistics/128116: Problem Two:
In designing a new dormitory, a progressive university wishes to determine where students prefer to study in order to provide appropriate space. A survey of 100 randomly selected undergraduate students shows that 33% prefer to study in their rooms.
(1) Construct a 95% confidence interval for the proportion of students who prefer to study in their rooms.
(2) If university has the option of making various sized rooms, what proportion of the rooms should be made larger to accommodate those who wish to study in their rooms?
1 solutions
Answer 93830 by stanbon(57219) on 2008-02-21 09:19:31 (Show Source):
You can put this solution on YOUR website!A survey of 100 randomly selected undergraduate students shows that 33% prefer to study in their rooms.
(1) Construct a 95% confidence interval for the proportion of students who prefer to study in their rooms.
E = z*sqrt(pq/n)
E = 1.96[sqrt(0.33)(0.67)/(100)] = 1.96*0.0470= 0.0922
C.I. = (0.33-0.0922,0.33+0.0922) etc.
=================
(2) If university has the option of making various sized rooms, what proportion of the rooms should be made larger to accommodate those who wish to study in their rooms?
To be 95% confident they should provide at least 42.22% of the students
with larger rooms.
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Cheers,
Stan H.
|
Numbers_Word_Problems/128152: One fifth of 12 more than a certain number equals one-forth of 2 more than the number. Find the number
1 solutions
Answer 93826 by stanbon(57219) on 2008-02-21 08:55:24 (Show Source):
You can put this solution on YOUR website!One fifth of 12 more than a certain number equals one-forth of 2 more than the number. Find the number
----------------------------
Let the number be "x".
EQUATION:
(1/5)(x+12) = (1/4)(x+2)
Multiply both sides by 20 to get rid of the fractions:
4(x+12) = 5(x+2)
4x+48 = 5x+10
x = 38
================
Cheers,
Stan H.
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Numbers_Word_Problems/128153: Find three consecutive even integers such that the sum of the first and third exceeds one-half the second by 15.
1 solutions
Answer 93825 by stanbon(57219) on 2008-02-21 08:51:12 (Show Source):
You can put this solution on YOUR website!Find three consecutive even integers such that the sum of the first and third exceeds one-half the second by 15.
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1st even: 2x
2nd even: 2x+2
3rd even: 2x+4
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EQUATION:
2x + (2x+4) = (1/2)(2x+2) + 15
4x+4 = x+1 + 15
3x = 12
x = 4
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1st even: 8
2nd even: 10
3rd even: 12
==================
Cheers,
Stan H.
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Equations/128149: 20 men finished 1/4 of the house in 7 days.but they have to finish it in 5 more days. how many men shall be added to the crew so that they can finish the house?
1 solutions
Answer 93824 by stanbon(57219) on 2008-02-21 08:45:41 (Show Source):
You can put this solution on YOUR website!20 men finished 1/4 of the house in 7 days.but they have to finish it in 5 more days. how many men shall be added to the crew so that they can finish the house?
----------------------------
# of men and # of houses completed are directly related
# of men and # of days required are inversely related
--------------
General Equation:
men = k[h/d]
Need to find "k"
---------------
Your problem:
20 = k[(1/4)/7]
k = 28*20 = 560
-----------------
Your Equation:
m = 560[h/d]
Substitute your given values of h= 3/4 of a house and d = 5 days
to get:
m = 560[(3/4)/5]
m = 140*3/5
m = 28*3
m = 84 (# of men to complete 3/4 th of the house in 5 days)
==============
Cheers,
Stan H.
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Circles/128117: Pls answer it imeediately because i need the answer as soon as possible, Thanks alot!...Q: A circular patch is to be placed over a 3" hole in a sheet of metal so that the patch extends 3/4" all around. The diameter of the patch will be???
1 solutions
Answer 93815 by stanbon(57219) on 2008-02-21 00:10:43 (Show Source):
You can put this solution on YOUR website!A circular patch is to be placed over a 3" hole in a sheet of metal so that the patch extends 3/4" all around. The diameter of the patch will be???
----------------
diameter = 3" + 2(3/4)"
= 3 + (3/2)
= 4 1/2 "
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Cheers,
Stan H.
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Equations/128119: Hi Can I have some help with the following function?
Consider the following.
f(x) = -10x^2 + 6, g(x) = 3x - 7
(a) Find the function f compose g.
1 solutions
Answer 93814 by stanbon(57219) on 2008-02-21 00:07:44 (Show Source):
You can put this solution on YOUR website!f(x) = -10x^2 + 6, g(x) = 3x - 7
(a) Find the function f compose g.
-------------------------------
fog(x) = f[g(x)]
=f[3x-7]
= -10(3x-7)^2+6
= -10(9x^2-42x+49)+6
= -90x^2 + 420x -484
===========================
Cheers,
Stan H.
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Points-lines-and-rays/128103: This question is from textbook Mathematics Structure and Method
Hello, would you please help me with this math problem:
M is the midpoint of line segment CD. Find the missing length.
CM=3x, CD=8x-14, x=?
Thank you very much
1 solutions
Answer 93807 by stanbon(57219) on 2008-02-20 22:47:44 (Show Source):
You can put this solution on YOUR website!M is the midpoint of line segment CD. Find the missing length.
CM=3x, CD= 8x-14, x=?
----------------------------
Draw the line segment CD.
Put M at the middle.
Do you see that CM + MD = CD ?
But M is the midpoint so CM = MD
Therefore 2(CM) = CD
----------------------
Substitute to get:
2(3x) = 8x-14
6x-8x = -14
-2x = -14
x = 7
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Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/128099: tyrels and dalia bought some pens and pencils. tyrel bought 4 pensand 5 pencils, which cost him $6.71. dalia bought 5 pens and 3 pencils, which cost her $7.12. Let A equal the price of a pen. let B equal the price of a pencil.
a. write an equation that relates the number of pens and pencils tyrel bought to the amount he paid for them.
b. write an equation that relates the number of pens and pencils dalia bought to the amount she paid for them.
c. solve the system you wrote for parts (a) and (b) to find the price of a pen and the price of a pencil.
1 solutions
Answer 93804 by stanbon(57219) on 2008-02-20 22:28:54 (Show Source):
You can put this solution on YOUR website!tyrel bought 4 pensand 5 pencils, which cost him $6.71. dalia bought 5 pens and 3 pencils, which cost her $7.12. Let A equal the price of a pen. let B equal the price of a pencil.
a. write an equation that relates the number of pens and pencils tyrel bought to the amount he paid for them.
EQUATION:
4A + 5B = 6.71
5A + 3B = 7.12
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Multiply the 1st equation by 5 and the 2nd equation by 4 to get:
20A + 25B = 5*6.71
20A + 12B = 4*7.12
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Subtract the 2nd equation from the 1st to get:
13B = 5.07
B = 39 cents (price of a pencil)
-------------------
Substitute to solve for A:
4A + 5(0.39) = 6.71
4A = 4.76
A = $1.19 (price of a pen)
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Cheers,
Stan H.
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Human-and-algebraic-language/128098: A baseball team played 20 games. They won 4 games more than they lost. How many Games did they win?
1 solutions
Answer 93802 by stanbon(57219) on 2008-02-20 22:06:27 (Show Source):
You can put this solution on YOUR website!A baseball team played 20 games. They won 4 games more than they lost. How many Games did they win?
--------------------
Let number of losses be "x" ; # of wins is "x+4"
---------------------
EQUATION:
x + x+4 = 20
2x+4 = 20
2x = 16
x = 8 (# of wins)
x+4 = 12 (# of losses)
=============================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/128084: A plane can travel 400 miles against the wind in the same time that it can travel 500 miles with the wind. If the speed of wind was 10 miles per hour. Find the speed fo the plane in still air.
1 solutions
Answer 93799 by stanbon(57219) on 2008-02-20 21:51:42 (Show Source):
You can put this solution on YOUR website!A plane can travel 400 miles against the wind in the same time that it can travel 500 miles with the wind. If the speed of wind was 10 miles per hour. Find the speed of the plane in still air.
---------------------------
Let the speeed of the plane in still air be "p":
With-the-wind DATA:
Distance = 500 miles; Rate = p+10 mph ; time = d/r = 500/(p+10) hrs.
---------------
Against-the-wind DATA:
Distance = 400 miles; Rate = p-10 mph ; time = d/r = 400/(p-10) hrs.
------------------
EQUATION:
time with = time against
500/(p+10) = 400/(p-10)
5/(p+10) = 4/(p-10)
Cross-multiply:
4p+50 = 5p-40
p = 90 mph (speed of the plane in still air)
===================
Cheers,
Stan H.
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Human-and-algebraic-language/128095: A local softball team hopes to win at least 3 games for every 2 lost during the season.If there are 15 games scheduled, how many games can the team win and still achieve its goal?
1 solutions
Answer 93798 by stanbon(57219) on 2008-02-20 21:34:48 (Show Source):
You can put this solution on YOUR website!A local softball team hopes to win at least 3 games for every 2 lost during the season.If there are 15 games scheduled, how many games can the team win and still achieve its goal?
----------------------
The team wants to win 3/5 th of its games
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EQUATION:
(3/5)(15) = 9
The team needs to win 9 of the 15 games
============================================
Cheers,
Stan H.
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