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Recent problems solved by 'stanbon'
stanbon answered: 57182 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209, >>NextLinear_Algebra/166495: State the number of positive real zeros, negative real zeros, and imaginary zeros for g(x)=9x^3-7x^2+10x-4.
I must show my work. This is from a worksheet and I'm not sure how to do it.
Thanks
1 solutions
Answer 122721 by stanbon(57250)   on 2008-11-08 14:44:31 (Show Source):
You can put this solution on YOUR website!State the number of positive real zeros, negative real zeros, and imaginary zeros for
g(x)=9x^3-7x^2+10x-4.
g(-x) = -9x^2 - 7x^2 - 10x -4
-------------------------------------
Using DesCartes Rule of Signs:
# of changes of sign in g(x) = 3; so 1 or 3 positive Real roots
------------------------------
# of changes of sign in g(-x) = 0; so 0 negative Real Roots
------------------------------
# of imaginary zeroes is 0 or two because g(x) is a cubic
================================
Comment: graphing g(x) is find it has one positive Real Root.
So it must have 2 imaginary roots.
=================================
Cheers,
Stan H.
|
Rate-of-work-word-problems/166515: Barry can do a certain job in 3 hours, whereas Sanchez 5 hours to do the same job. How long would it take them to do the job working together?
1 solutions
Answer 122720 by stanbon(57250) on 2008-11-08 14:03:15 (Show Source):
You can put this solution on YOUR website!Barry can do a certain job in 3 hours, whereas Sanchez 5 hours to do the same job. How long would it take them to do the job working together?
--------------------------
Barry DATA:
time = 3 hrs/job ; rate = 1/3 job/hr.
---------------------------
Sanchez DATA:
time = 5 hr/job ; rate= 1/5 job/hr
---------------------------
Together DATA:
time = x hr/job ; rate = 1/x job/hr.
---------------
EQUATION:
rate + rate = together rate
1/3 + 1/5 = 1/x
5x + 3x = 15
8x = 15
x = 15/8 hrs. (time to do the job together)
Comment: 15/8 hrs. = 1 hr. and 52 minutes and 50 seconds
=============================================
Cheers,
Stan H.
=====================
|
Percentage-and-ratio-word-problems/166516: A sum of $2730 is to be divided between two people in the ratio 7 to 6. How much does each person receive?
1 solutions
Answer 122716 by stanbon(57250) on 2008-11-08 13:52:51 (Show Source):
You can put this solution on YOUR website!A sum of $2730 is to be divided between two people in the ratio 7 to 6. How much does each person receive?
---------------------
7 to 6 is the same as 7x to 6x.
---------------------
EQUATION:
7x + 6x = 2730
13x = 2730
x = 210
--------
6x = 1260
7x = 1470
================
Cheers,
Stan H.
|
Complex_Numbers/166517: Complex Fraction
(2/14x)/(4/7xy)
1 solutions
Answer 122714 by stanbon(57250) on 2008-11-08 13:48:28 (Show Source):
You can put this solution on YOUR website!(2/14x)/(4/7xy)
------------------
Invert the denominator and change to multiplication to get:
= [1/7x] * [7xy/4]
Cancel factors common to a numerator and a denominator to get:
= [1/1] * [y/4[
= y/4
==============
Cheers,
Stan H.
|
test/166491: please help me solve
1) 6x^2+24x=2x^2-36
2) 3x^2-17x+20=0
for this one i got (x-6)(3x-5)
is this correct
3) x^2-36=0
1 solutions
Answer 122698 by stanbon(57250) on 2008-11-08 11:21:33 (Show Source):
You can put this solution on YOUR website!1) 6x^2+24x=2x^2-36
4x^2 +24x + 36 = 0
x^2 + 6x + 9 = 0
(x+3)^2 = 0
x = -3 with multiplicity 2
===================================
2) 3x^2-17x+20=0
3x^2 - 12x - -5x + 20 = 0
3x(x-4)-5(x-4) = 0
(x-4)(3x-5) = 0
x = 4 or x = 5/3
=====================
3) x^2-36=0
(x-6)(x+6) = 0
x = 6 or x = -6
======================
Cheers,
Stan H.
|
Linear_Algebra/166496: I am lost on how to do to problems
1. f(x)=3x and g(x)=4x-3, find f[g(5)] and g[f(5)].
2. find the inverse of f(x)=7x-2.
Can you please help. I must show my work. These are from a worksheet. We have no textbook to use.
Thanks
1 solutions
Answer 122694 by stanbon(57250) on 2008-11-08 11:08:34 (Show Source):
You can put this solution on YOUR website!1. f(x)=3x and g(x)=4x-3, find f[g(5)] and g[f(5)].
----
f[g(5)] = f[4*5-3] = f[17] = 3*17 = 51
-------------------------------------------
2. find the inverse of f(x)=7x-2.
1st: Interchage x and y to get:
x = 7y-2
2nd: Solve for y to get the inverse:
y = (1/7)x + (2/7)
======================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/166482: This question is from textbook Introductory Algebra
An open wooden box is a cube with side x cm. The box, including its bottom, is made of wood that is 1 cm thick. Find a polynomial for the interior volume of the cube.
1 solutions
Answer 122682 by stanbon(57250) on 2008-11-08 07:30:30 (Show Source):
You can put this solution on YOUR website!An open wooden box is a cube with side x cm. The box, including its bottom, is made of wood that is 1 cm thick. Find a polynomial for the interior volume of the cube.
--------------------
Draw the picture
----
Interior dimensions:
height = x-1
width = x-2
length = x-2
----------------
Volume = (x-1)(x-2)^2 cm^3
===============================
Cheers,
Stan H.
|
Distributive-associative-commutative-properties/166456: Name the Property.
a: 6+1*2=1*2+6
b: (7x)*y=7(xy)
c: 0+a=a
d: 2(x+3)=2x+2*3
e: 1/2(8*5)=(1/2*8)*5
f: 1*(-2/3)=-2/3
1 solutions
Answer 122665 by stanbon(57250) on 2008-11-07 21:52:54 (Show Source):
You can put this solution on YOUR website!Name the Property.
a: 6+1*2=1*2+6
Ans: commutative
-----------------------
b: (7x)*y=7(xy)
Ans: associative
-----------------------
c: 0+a=a
Ans: additive identity
------------------------
d: 2(x+3)=2x+2*3
Ans: distributive
------------------------
e: 1/2(8*5)=(1/2*8)*5
Ans: associative
-----------------------
f: 1*(-2/3)=-2/3
Ans: multiplicative identity
==================================
Cheers,
Stan H.
|
Exponential-and-logarithmic-functions/166450: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = 2x^3 - x^2 - 12x + 6
1 solutions
Answer 122664 by stanbon(57250) on 2008-11-07 21:49:52 (Show Source):
You can put this solution on YOUR website!Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = 2x^3 - x^2 - 12x + 6
------------------
I graphed it and found that x= 0.5 is a zero.
Use synthetic division to find the other zeroes:
0.5).....2....-1....-12....6
........2.....0.....-12..|..0
----------------------------------
Quotient: 2x^2-12
Remainder: 0
----------------------
Find the zeroes of the quotient:
2x^2-12 = 0
x^2 = 6
x = sqrt(6) or x = -sqrt(6)
=================================
The zeroes are x = 0.5, or sqrt(6) or -sqrt(6)
==================================
Cheers,
Stan H.
|
Percentage-and-ratio-word-problems/166454: You are an American exchange student planning to study in Florence,Italy, during the winter term. In preparation for your trip, you consult the Italian school's Web site to find out what the temperature is likely to be. However, the daily weather is given in the Celsius scale. Use the table to find a way to convert temperatures from the Celsius to the Fahrenheit scale.
(WATER) (FAHRENHEIT SCALE) (CELSIUS SCALE)
Freeze 32-degrees 0-degrees
Boils 212-degrees 100-degrees
1 solutions
Answer 122663 by stanbon(57250) on 2008-11-07 21:32:34 (Show Source):
You can put this solution on YOUR website!Use the table to find a way to convert temperatures from the Celsius to the Fahrenheit scale.
(WATER) (FAHRENHEIT SCALE) (CELSIUS SCALE)
Freeze 32-degrees 0-degrees
Boils 212-degrees 100-degrees
-----------------------
You have two points: (32,0) and (212,100)
slope = [100-0]/[212-32] = 100/180 = 5/9
------------
intercept: 0 = (5/9)32 + b
b = -160/9
----------------
EQUATION:
C(x) = (5/9)x - (160/9)
===========================
Chers,
Stan H.
|
Inverses/166441: Here is my worksheet problem: The function f(x)=|x+3|+9 is NOT a one-to-one function. The points (19,31) and (__,__) prove that f is not a one-to-one function. What is the missing set of points? Thanks for your help! Linda
1 solutions
Answer 122662 by stanbon(57250) on 2008-11-07 21:19:52 (Show Source):
You can put this solution on YOUR website!The function f(x)=|x+3|+9 is NOT a one-to-one function. The points (19,31) and (__,__) prove that f is not a one-to-one function. What is the missing set of points?
-------------------
Solve y = |19+3}+9
y = 31
----------
Solve 31 = |x+3|+9
22 = |x+3|
x+3 = 22 or x+3 = -22
x = 19 or x = -25
-----------------------
So two of the solution pairs are (19,31) and (-25,31)
This shows that f is not one-to-one.
===================================
Cheers,
Stan H.
|
Inequalities/166446: This question is from textbook Beginning Algebra
I caanot for the life of me figure out how to solve this problem. We are asked to collect the variable terms on the left side of the inequality.
0.2(3-x)+0.1>0.1(x-2)
1 solutions
Answer 122661 by stanbon(57250) on 2008-11-07 21:09:45 (Show Source):
You can put this solution on YOUR website!collect the variable terms on the left side of the inequality.
0.2(3-x)+0.1>0.1(x-2)
--------------------------
Multiply both sides of the inequality by 10 to get:
2(3-x) + 1 > 1(x-2)
6-2x + 1 > x-2
-3x+7 > -3
-3x > -10
=============
Cheers,
Stan H.
|
percentage/166304: I need Your Help in drawing a pie chart ?
please help and tell me how to make a pie chart.
I Shall be very thankful to you because i am taking a exam of maths tomorrow.
1 solutions
Answer 122579 by stanbon(57250) on 2008-11-07 06:57:44 (Show Source):
You can put this solution on YOUR website!I need Your Help in drawing a pie chart ?
please help and tell me how to make a pie chart.
-------------------
Let's say you have:
A: 12 items
B: 17 items
C: 25 items
---------------
1st: Add the items to get 54
----------
2nd: Convert each item count to percentage:
12/54 = 22%
17/54 = 31%
25/54 = 46%
----------------
3rd: Draw a circle and estimate the percentages as pieces of pie
that fill the circle.
===============================
Cheers,
Stan H.
|
Probability-and-statistics/166309: Find the expected value of the random variable in the experiment.
Three cards are drawn from a deck without replacement. THe number of aces is counted.
The choices are a) .2308 b) 1 c).2174 d)1.0134
1 solutions
Answer 122578 by stanbon(57250) on 2008-11-07 06:49:25 (Show Source):
You can put this solution on YOUR website!Find the expected value of the random variable in the experiment.
Three cards are drawn from a deck without replacement. THe number of aces is counted.
The choices are a) .2308 b) 1 c).2174 d)1.0134
----------------
The results are 0,1,2, or 3 aces
P(0 aces) = 48C3/52C3
P(1 ace) = 3[4/52][48/51][47/50]
P(2 aces) = 3[4/52][3/51][48/50]
P(3 aces) = 3[4/52][3/51][2/50][48/49]
---------------------
To get the expected value, multiply each "result" value by its probability
and then add the 4 results.
================================
Cheers,
Stan H.
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Probability-and-statistics/166316: a die is rolled twice. Write the indicated event in set notation. The sum of the rolls is 13.
1 solutions
Answer 122576 by stanbon(57250) on 2008-11-07 06:37:51 (Show Source):
You can put this solution on YOUR website!a die is rolled twice. Write the indicated event in set notation. The sum of the rolls is 13.
----------------------
You cannot get a sum of 13 so the set notation is the null set.
==============
Cheers,
Stan H.
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Probability-and-statistics/166311: Find the percent of the total area under the standard normal curve between the given z-scores. Z=-0.55 and Z=0.55
the choices are
a)-0.4176
b)-0.9000
c)0.4176
d)0.9000
1 solutions
Answer 122575 by stanbon(57250) on 2008-11-07 06:35:47 (Show Source):
You can put this solution on YOUR website!Find the percent of the total area under the standard normal curve between the given z-scores. Z=-0.55 and Z=0.55
the choices are
a)-0.4176
b)-0.9000
c)0.4176
---------------
Use your calculator or your z-chart to find -0.55 < z < 0.55 = 0.4176
=================
Cheers,
Stan H.
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Probability-and-statistics/166312: At one high school, students can run the 100-yard dash in an average of 15.2 seconds with a standard deviation of .9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are: greater than 16.1 seconds.
1 solutions
Answer 122574 by stanbon(57250) on 2008-11-07 06:32:44 (Show Source):
You can put this solution on YOUR website!At one high school, students can run the 100-yard dash in an average of 15.2 seconds with a standard deviation of .9 seconds. The times are very closely approximated by a normal curve. Find the percent of times that are: greater than 16.1 seconds.
--------------------
z(16.1) = (16.1-15.2)/0.9 = 1
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P(x>16.1)= P(z>1) = 0.1587.. = 15.87%
=================
Cheers,
Stan H.
|
Complex_Numbers/166314: If a complex equation is graphed on a plane and the solution point is on the r or i line (such as 0+8i) is it considered real or imaginary?
1 solutions
Answer 122573 by stanbon(57250) on 2008-11-07 06:27:17 (Show Source):
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Probability-and-statistics/166315: the odds in favor of Trudy beating her friend in a round of golf are 1:9. Find the probability that Trudy will lose.
1 solutions
Answer 122572 by stanbon(57250) on 2008-11-07 06:25:35 (Show Source):
You can put this solution on YOUR website!the odds in favor of Trudy beating her friend in a round of golf are 1:9. Find the probability that Trudy will lose.
-----------
Formula: "odds FOR event A" = P(A)/P(not A)
--------
Your Problem:
1:9 = P(A)/P(not A)
P(A) = (1/9)*P(not A)
----------
But P(A) + P(not A) = 1
So, P(not A) = 1 - P(A)
And P(not A) = 1 - [(1/9)P(not A)]
(10/9)P(not A) = 1
P(not A) = 9/10
=======================
That was a bit long-winded. Here's a shorter version.
Since odds FOR = 1:9
P(A) = 1/(1+9) = 1/10
So P(A') = 9/10
====================
Cheers,
Stan H.
|
absolute-value/166317: Find the possible value or values of r in the quadratic equation r2-7r-8=0
1 solutions
Answer 122571 by stanbon(57250) on 2008-11-07 06:14:37 (Show Source):
You can put this solution on YOUR website!Find the possible value or values of r in the quadratic equation r2-7r-8=0
---
Factor to get:
(r-8)(r+1) = 0
Since the product is zero, one of these factors must be zero:
So, r=8 or r=-1
===================
Cheers,
Stan H.
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Money_Word_Problems/166320: A certain number of boys bought a bicycle for P2000.00. One boy later withdrew and sold his share to the other boys for P420.00. The share of each boy of this additional cost turned out to be P190.00 less than what each boy originaly contributed. How many boys were here originaly?
1 solutions
Answer 122570 by stanbon(57250) on 2008-11-07 06:11:03 (Show Source):
You can put this solution on YOUR website!A certain number of boys bought a bicycle for P2000.00. One boy later withdrew and sold his share to the other boys for P420.00. The share of each boy of this additional cost turned out to be P190.00 less than what each boy originaly contributed. How many boys were here originaly?
-----------------
Let original number of boys be "x".
Average cost to each was 2000/x.
----------------
x-1 of the boys received back 420 so their total cost was 2000-420 = 1580
Their average cost was therefore 1580/(x-1).
------------
EQUATION:
original average - adjusted average = 190
2000/x - 1580/(x-1) = 190
---------
Solve for x to get the original number in the group.
=============
Cheers,
Stan H.
|
Signed-numbers/166295: For which integers a,b,c does a-b-c=a-(b-c)? justify your answer
Justify your answer.
Please help, I do not understand this question.
thank you so much
1 solutions
Answer 122557 by stanbon(57250) on 2008-11-06 21:14:19 (Show Source):
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Miscellaneous_Word_Problems/166261: X is Xavier’s age, Y is Yvette’s age, and Z is Zevon’s age. Yvette is twice as old as Xavier. If Zevon’s age is increased by 10 he will be as old as Yvette. Write an equation that shows Zevon’s age (Z) only in terms of Xavier’s age (X).
I am having difficulty figuring this out so far I came up with Z = 2X + 10. Can someone please help. Thank you
1 solutions
Answer 122531 by stanbon(57250) on 2008-11-06 19:51:56 (Show Source):
You can put this solution on YOUR website!X is Xavier’s age, Y is Yvette’s age, and Z is Zevon’s age. Yvette is twice as old as Xavier. If Zevon’s age is increased by 10 he will be as old as Yvette. Write an equation that shows Zevon’s age (Z) only in terms of Xavier’s age (X).
----------------
Y = 2X
Z+10 = Y
---------
Z = Y-10
Substitute to get:
Z = 2x - 10
====================
Cheers,
Stan H.
|
Linear-equations/166259: The national cost C in billions of dollars for dental services can be modeled by the linear equation
C = 2.85n + 30.52,
where n is the number of years since 1990
(Health Care Financing Administration, www.hcfa.gov).
a) Find and interpret the C-intercept for the line.
b) Find and interpret the n-intercept for the line.
c) Graph the line for n ranging from 0 through 20.
If I am not mistaken, are the steps solving for C, and then solving for N ? I am still a bit unclear on how to complete the problem
1 solutions
Answer 122529 by stanbon(57250) on 2008-11-06 19:46:37 (Show Source):
You can put this solution on YOUR website!The national cost C in billions of dollars for dental services can be modeled by the linear equation
C = 2.85n + 30.52,
where n is the number of years since 1990
(Health Care Financing Administration, www.hcfa.gov).
a) Find and interpret the C-intercept for the line.
Let n = 0; C(0) = 30.52 (cost of dental service in 1990)
---------------------------------------------------------------
b) Find and interpret the n-intercept for the line.
Let C=0: then n = -30.52/2.85 = -10.78..
Theoretically the dental cost was zero 11 years before 1990
---------------------------------------------------------------------
c) Graph the line for n ranging from 0 through 20.
================================================
Cheers,
Stan H.
If I am not mistaken, are the steps solving for C, and then solving for N ? I am still a bit unclear on how to complete the problem
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Age_Word_Problems/166257: Please held me solve this problem:
Mark is 11 years older that his sister. In 8 years he will be twice as old as she will be then. How old are they now?
1 solutions
Answer 122528 by stanbon(57250) on 2008-11-06 19:38:12 (Show Source):
You can put this solution on YOUR website!Please held me solve this problem:
Mark is 11 years older that his sister. In 8 years he will be twice as old as she will be then. How old are they now?
------------------
Ages NOW:
Sister's age is "x"
Mark's age is "x+11"
------------------------
Ages in 8 years:
Sister will be "x+8"
Mark will be "x+19"
------------------------
EQUATION:
x+19 = 2(x+8)
x+19 = 2x+16
x = 3
---------
Sister is NOW 3 years old
Mark is NOW 14 years old
===========================
Cheers,
Stan H.
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Human-and-algebraic-language/166248: This question is from textbook College Algebra
The highway has a 6% grade on descent, which means it's slope is - 6/100. Driving on this road, you notice from elevation signs that you have descended a distance of 1000 ft. What is the change in your horizontal distance?
1 solutions
Answer 122524 by stanbon(57250) on 2008-11-06 19:24:45 (Show Source):
You can put this solution on YOUR website!The highway has a 6% grade on descent, which means it's slope is - 6/100. Driving on this road, you notice from elevation signs that you have descended a distance of 1000 ft. What is the change in your horizontal distance?
------------------
slope = vertical change/horizontal change
----------------------------
Use a proportion:
1000/x = 6/100
x = 100000/6 = 16,666.67 ft (horizontal distance)
=====================================================
Cheers,
Stan H.
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Quadratic_Equations/166253: An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is the horizontal distance the football travels in yards and f(x) is the vertical distance the football travels. The bottom of the uprights is 3.5 yards above the ground.
The opposing team tries to block the kick by jumping with their arms and hands up in the air. If their highest reach is 3.5 yards and they are 2 yards away, will they block the kick? Why or Why not?
1 solutions
Answer 122521 by stanbon(57250) on 2008-11-06 19:17:58 (Show Source):
You can put this solution on YOUR website!An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is the horizontal distance the football travels in yards and f(x) is the vertical distance the football travels. The bottom of the uprights is 3.5 yards above the ground.
------------------------------------------------
f(x)= -.0625x²+2.7x
-------
Height of the ball when it reached the goal post:
f(41) = 5.6375 is the vertical height
-------------------------------------------
The opposing team tries to block the kick by jumping with their arms and hands up in the air. If their highest reach is 3.5 yards and they are 2 yards away, will they block the kick? Why or Why not?
f(2) = 5.15 is the vertical height.
========================================
Cheers,
Stan H.
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Percentage-and-ratio-word-problems/166254: The population of Detroit, Michigan, declined 14.6% from 1980 to 1990. The 1980 population was 1,203,369. What is the 1990 population?
1 solutions
Answer 122519 by stanbon(57250) on 2008-11-06 19:08:22 (Show Source):
You can put this solution on YOUR website!The population of Detroit, Michigan, declined 14.6% from 1980 to 1990. The 1980 population was 1,203,369. What is the 1990 population?
----------------
# = (1-0.146)*1203369 = 1,027,677
====================
Cheers,
Stan H.
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