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Recent problems solved by 'stanbon'
stanbon answered: 57911 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 , 57900..57929, >>Nextpercentage/88941: I know the answer, but I want to know the process of getting there. I would like to know step-by-step of how to get this answer. Here is the problem:
Use the Pie Charts to answer the question. (Since I can't copy and paste the pie charts, I will just list their percentages.
Pie Chart 1:
Total Expenditures:
-Taxes: 17%
-Research & Development: 10%
-Salaries: 38%
-Advertising: 35%
Pie Chart 2:
Expenditures on Advertising:
-Television: 43%
-Newspapers: 36%
-Fliers: 3%
-Radio: 18%
The first pie chart represents a company's expenditures, and the second pie chart shows a breakdown of the company's advertising expenditures. What percent of the company's expenditures is spent on radio advertising?
a) 6.3%
b) 11.7%
c) 18.0%
d) 35.0%
1 solutions
Answer 64642 by stanbon(57984)   on 2007-07-18 09:49:36 (Show Source):
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Age_Word_Problems/88942: Ruffy is 3/4 as old as Orlie.Four years ago,Ruffy was 1year more than 1/2 old as Orlie.How old is each
1 solutions
Answer 64641 by stanbon(57984) on 2007-07-18 09:43:48 (Show Source):
You can put this solution on YOUR website!Ruffy is 3/4 as old as Orlie.Four years ago,Ruffy was 1year more than 1/2 old as Orlie.How old is each
--------
NOW DATA:
Orlie's age = x yrs ; Ruffy's age = (3/4)x yrs
------------
4 yrs ago DATA:
Orlie's age was (x-4) yrs ; Ruffy's age was (3/4)x-4
--------------
EQUATION: (based on 4 yrs ago DATA)
Ruffy =(1/2)Orlie +1
(3/4)(x)-4 = (1/2)(x-4) + 1
Multiply thru by 4 to get rid of the denominators:
3x-16 = 2(x-4) + 4
3x-16 = 2x-4
x=12 (Orlie's age NOW)
(3/4)x = 9 (Ruffy's age NOW)
===========
Cheers,
Stan H.
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expressions/88936: These are on exponentials with logs; in case stan happens to see this, thanks alot for your help- I had to use my moms' last paycheck (she had to leave work to have surgery done on her anuerysms) to pay $400 for this class to make sure I have this Algebra II credit to graduate this upcoming year. You taking out time to do those 5 little problems were a BIG help and may god bless you.
2^x = 30
5^x - 1 = 3^x
3.5^3x + 1 = 65.4
16^x - 4 = 3^3 - x
7^x - 2 = 5^x
1 solutions
Answer 64640 by stanbon(57984) on 2007-07-18 09:30:18 (Show Source):
You can put this solution on YOUR website!2^x = 30
Take the log of both sides to get:
x(log2) = log30
x = [log30]/[log2]
x = 4.90689..
---------------------
5^(x - 1) = 3^x
Take the log of both sides
(x-1)log5 = xlog3
xlog5 -xlo3 = log5
x(log5 - log3) = log5
x(0.2218487..) = 0.6987000...
x = 5.15066...
---------------
3.5^(3x + 1) = 65.4
Take the log of both sides:
(3x+1)log3.5 = log65.4
(3log3.5)x = log65.4
x = 0.329266....
-----------
16^(x - 4) = 3^(3 - x )
Take the log of both sides
(x-4)log16 = (3-x)log3
Can you take it from here?
--------
7^(x - 2) = 5^x
Take the log of both sides
Can you take it from here?
=============
Cheers,
Stan H.
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Polynomials-and-rational-expressions/88928: Would someone please explain to me step by step how to figure out this problem. Thank you.
A triangle has sides 2x-5, 3x+1, and 4x+2. Find the polynomial that represents its perimeter.
1 solutions
Answer 64638 by stanbon(57984) on 2007-07-18 09:00:51 (Show Source):
You can put this solution on YOUR website!A triangle has sides 2x-5, 3x+1, and 4x+2. Find the polynomial that represents its perimeter.
---------
Add the sides to get the perimeter:
2x-5+3x+1+4x+2
=9x-2
==========
Cheers,
Stan H.
|
Quadratic_Equations/88933: Could someone help me with this one please. If you do not mind would you show me step by step how you came upon the answer? Thank you
Solve (x-5)^2=6
1 solutions
Answer 64637 by stanbon(57984) on 2007-07-18 08:58:31 (Show Source):
You can put this solution on YOUR website!Solve (x-5)^2=6Solve (x-5)^2=6
----------
Take the square root of both sides to get:
x-5 = sqrt6 or x-5 = -sqrt6
Add 5 to both sides to get:
x = 5+sqrt6 or x= 5-sqrt6
=============
Cheers,
stan H.
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Equations/88931: These are exponential equations ( not that I know what the actually are); can someone please solve these before I die of stupidness!!!!
9^2x = 27^x - 1
5^n-1 = 1/ 25
25^x = 5^(x^2 - 15)
2^x * 4^x+5 = 4^2x-1
sqrt(3)^2x+4 = 9^x-2
1 solutions
Answer 64636 by stanbon(57984) on 2007-07-18 08:56:06 (Show Source):
You can put this solution on YOUR website!9^2x = 27^(x - 1)
3^4x = 3^(3(x-1))
3^4x = 3^(3x-3)
Since the bases are the same the exponents must be equal:
4x = 3x-3
x = -3
-------------
5^n-1 = 1/ 25
5^(n-1) = 5^-2
n-1 = -2
n=-1
-----------
25^x = 5^(x^2 - 15)
5^2x = 5^(x^2-15)
2x = x^2-15
x^2-2x-15=0
(x-5)(x+3)=0
x=5 or x=-3
--------------
2^x * 4^x+5 = 4^2x-1
2^x * 2^(2x+10) = 2^(4x-2)
2^(3x+10) = 2^(4x-2)
3x+10 = 4x-2
x = 12
---------------
sqrt(3)^2x+4 = 9^x-2
3^[(1/2)(2x+4)] = 3^(3(x-2))
3^(x+2) = 3^(3x-6)
x+2 = 3x-6
2x=8
x=4
============
Be patient; it will come.
==============
Cheers,
Stan H.
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Age_Word_Problems/88929: seven years ago,mary was 6times as old as cora.in one year,she will be only twice as old as cora.find their present ages
1 solutions
Answer 64634 by stanbon(57984) on 2007-07-18 08:38:06 (Show Source):
You can put this solution on YOUR website!seven years ago,mary was 6 times as old as cora.in one year,she will be only twice as old as cora.find their present ages
--------------
7 years ago DATA:
Cora's age = x ; Mary's age = 6x
----------------
NOW DATA:
Cora's age = x+7 ; Mary's age = 6x+7
-----------------
One year from now DATA:
Cora's age = x+8 ; Mary's age = 6x+8
-------------------
EQUATION: (based on one year from now DATA)
6x+8 = 2(x+8)
6x+8 = 2x+16
4x = 8
x = 2
----------------
x+7 = 9 yrs old (Cora's age NOW)
6x+7 = 19 yrs old (Mary's age NOW)
========
Cheers,
Stan H.
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Miscellaneous_Word_Problems/88925: Bill sells is vintage 1974 Road Runner for $9500. He uses the money to invest in a 36 month CD that pays 4.12% interest compounded quartely. How much money will he receive when he cashes in his CD at the end of the 36 months?
1 solutions
Answer 64633 by stanbon(57984) on 2007-07-18 08:29:21 (Show Source):
You can put this solution on YOUR website!Bill sells is vintage 1974 Road Runner for $9500. He uses the money to invest in a 36 month CD that pays 4.12% interest compounded quartely. How much money will he receive when he cashes in his CD at the end of the 36 months?
-----------
A = P(1+r/n)^(nt)
Your Problem:
A is the future value
P is the pricipal or investment
r is the yearly interest rate
n is the number of compounding periods per year
t is the number of years
--------------------
A = 9500(1+0.0412/4)^(4*3)
A = 9500(1.1308)
A = $10743.06
==================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/88897: Simplify each expression
1. (y^-4y^5)^2
2. Brackets around the whole problem -3x^8x^-3 divided by 6x^-3x^4 then outside the brackets is a ^3
3. x^8nx^3n
4. x^2n divided by x^5n
1 solutions
Answer 64590 by stanbon(57984) on 2007-07-17 23:12:48 (Show Source):
You can put this solution on YOUR website!1. (y^-4y^5)^2 = [y^1]^2 = y^2
-------------------------
2. Brackets around the whole problem -3x^8x^-3 divided by 6x^-3x^4 then outside the brackets is a ^3
= [(-3x^5)/(6x)]^3
= [-x^4/2]^3
= [-x^12]]/8 = (-1/8)x^12
----------------
3. x^8nx^3n
= x^11n
------------------
4. x^2n divided by x^5n
= 1/x^3n
===============
Cheers,
Stan H.
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Polynomials-and-rational-expressions/88896: simplify each expression
1. 15(x^4y^3)^4 divided by 21(x^5y)^2
2. 8^0
3. 12 divided by (2x)^0
4. 1 divided by 5^-3
1 solutions
Answer 64588 by stanbon(57984) on 2007-07-17 23:03:38 (Show Source):
You can put this solution on YOUR website!simplify each expression
1. 15(x^4y^3)^4 divided by 21(x^5y)^2
= [15x^16y^12]/[21x^10y^2]
= (5/7)x^6y^10
----------------------------------------------------
2. 8^0 = 1
---------------------
3. 12 divided by (2x)^0
= 12/1 = 12
--------------------
4. 1 divided by 5^-3
= 1/5^-3 = 5^3 = 125
===============================
Cheers,
Stan H.
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percentage/88888: How many liters of an 11% alcohol solution should be mixed with 60 liters of a 5% alcohol solution to obtain a mixture that is 7% alcohol?
1 solutions
Answer 64586 by stanbon(57984) on 2007-07-17 22:57:09 (Show Source):
You can put this solution on YOUR website!How many liters of an 11% alcohol solution should be mixed with 60 liters of a 5% alcohol solution to obtain a mixture that is 7% alcohol?
---------
Amt of 5% solution = 60 L ; amt of active ingredient = 0.05*60 = 3 L
-------
Amt of 11% solution = x L ; amt of active ingredient = 0.11x L
---------------
Amt of 7% mixture = (60+x) L ; Amt of active ingre = 0.07(60+x) = 4.2+0.07x L
===================
EQUATION:
active + active = active
3 + 0.11x = 4.2+0.07x
0.04x = 1.2
x = 30 liters (amt of 11% solution that must be mixed)
==========
Cheers,
Stan H.
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Polynomials-and-rational-expressions/88865: word problem that I need help with
Keiven earned $165 interest for 1 year on an investment of $1500. At the same rate what amount of interest would be earned by an investment of $2500.00.
Thank a million
1 solutions
Answer 64580 by stanbon(57984) on 2007-07-17 22:03:25 (Show Source):
You can put this solution on YOUR website!Keiven earned $165 interest for 1 year on an investment of $1500. At the same rate what amount of interest would be earned by an investment of $2500.00.
-----------
Let x be the amt of interest on $2500
x/2500 = 165/1500
x = 2500(165/1500)
x = $275
=============
Cheers,
Stan H.
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Polynomials-and-rational-expressions/88868: I need some help please: the question reads simplify each expression. Be sure you write each answer without parentheses or negative/zero exponents
1. x8x3 (it reads x to the 8th power and x to the 3rd power)
2. y4y3y (y to the 4th power y to the 3rd power and y)
3.(x5)4 (x to the 5th power then 4th power on the outside parentheses)
4.(x4y3)3 (x to the 4th power y to the 3rd power inside parentheses the out side parentheses its 3rd power) hope this makes sence.
1 solutions
Answer 64578 by stanbon(57984) on 2007-07-17 21:59:14 (Show Source):
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Graphs/88885: I need help with the following problems. All of these problems ar inside of the curly brackets.. example { }
Solve by any convenient method :
4x + 12y = 24
2x + 6y = 12
Solve by any convenient method :
8x + 4y =7
x = 2-2y
Solve by Elimination :
2x -3y =-1
3x + y +15
Solve by Substitution :
3x + 8y = 7
x- 4y =9
1 solutions
Answer 64574 by stanbon(57984) on 2007-07-17 21:48:14 (Show Source):
You can put this solution on YOUR website!Solve by any convenient method :
4x + 12y = 24
2x + 6y = 12
--------------
Multiply the 2nd equation by 2 and you will see the two equations are the same.
So the solution for the system of equations is 2x+6y=12
or x+3y=6 or y=-(1/3)x+2
---------------------------------
Solve by any convenient method :
8x + 4y =7
x = 2-2y
------
Substitute x=2-2y into the 1st equation to solve for y:
8(2-2y)+4y=7
16-16y+4y=7
-12y = -9
y = 3/4
-----------------
Solve by Elimination :
2x -3y =-1
3x + y =15
-------------
Multiply the 2nd equation by 3 to get:
9x+3y=45
Add that to the 1st equation so you can solve for x:
11x=44
x=4
-------
Substitute that into 3x+y=15 to solve for y:
3*4+y=15
y = 3
------------------------
Solve by Substitution :
3x + 8y = 7
x- 4y =9
--
Solve the 2nd equation for x: x=4y+9
Substitute into the 1st equation so you can solve for y:
3(4y+9)+8y = 7
12y+27+8y = 7
20y = -20
y = -1
-------
Substitute that into x=4y+9 to solve for x:
x=4*-1+9
x=5
============
cheers,
Stan H.
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Rational-functions/88886: i have this 1 more question
for all x not equal to -4, wich of the following is equivalent to x^2 +12x+32/x+4
and the options are:
a)x+3
b)x+8
c)x+11
d)x+16
how do i solve it??
1 solutions
Answer 64572 by stanbon(57984) on 2007-07-17 21:38:37 (Show Source):
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Polynomials-and-rational-expressions/88873: Determine weather each of the following trinomials is a perfect square. If it is, factor the trinomial.
A)x^2-24x+48
B)16x^2+40xy+25y^2
C)a^2(b-c)-16b^2(b-c)
1 solutions
Answer 64571 by stanbon(57984) on 2007-07-17 21:36:38 (Show Source):
You can put this solution on YOUR website!Determine weather each of the following trinomials is a perfect square. If it is, factor the trinomial.
A)x^2-24x+48
This is not a perfect square as 48 is not equal to (24/2)^2
----------------
B)16x^2+40xy+25y^2
= (4x+5y)^2
-----------------
C)a^2(b-c)-16b^2(b-c)
= (b-c)(a-4b)(a+4b)
======================
Cheers,
Stan H.
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Probability-and-statistics/88827: A state lottery is designed so that a player chooses six numbers from 1-30 on one lottery ticket. What is the probability that a player with 1 lottery ticket will win? What is the probability of winning if 100 different tickets are purchased?
1 solutions
Answer 64555 by stanbon(57984) on 2007-07-17 19:06:48 (Show Source):
You can put this solution on YOUR website!A state lottery is designed so that a player chooses six numbers from 1-30 on one lottery ticket. What is the probability that a player with 1 lottery ticket will win? What is the probability of winning if 100 different tickets are purchased?
--------------------
Repetition is not allowed on lottery tickets, so there are
30C6 = 593,775 different 6-number sets.
Prob of winning with 1 ticket = 1/593,775
Prob of winning with 100 tickets = 100/593,775 = 1/5938
================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/88853: Could someone explain to me exactly how to work these problems. It is like another language to me.
Rewrite the middle term as the sum of two terms and the factor completely.
A)12w^2+19w+4
B)4z^3-18z^2-10z
1 solutions
Answer 64553 by stanbon(57984) on 2007-07-17 18:51:36 (Show Source):
You can put this solution on YOUR website!Rewrite the middle term as the sum of two terms and the factor completely.
A)12w^2+19w+4
Think of two numbers whose product is 4*12=48
and whose sum is 19
The numbers are 3 and 16
--------
Rewrite 19w as 3w+16w to get:
12w^2+3w+16w+4
Factor the 1st two and the last two terms separately:
3w(4w+1)+ 4(4w+1)
Factor again to get:
(4w+1)(3w+4)
Comment: This is called the AC Method of factoring trinomials.
---------------------
B)4z^3-18z^2-10z
z(4z^2-18z-10)
Think of two numbers whose product is -10*4=-40
and whose sum is -18
The numbers are -20 and +2
-------
Replace -18z by -20z+2z to get:
z(4z^2-20z+2z-10)
= z(4z(z-5)+2(z-5))
= z(z-5)(4z+2)
==============
Cheers,
Stan H.
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Geometry_Word_Problems/88854: Could you please assist with the following problem? A stone is projected vertically upward from a platform that is 20 ft high at a rate of 160 ft per second. When will the stone reach its maximum height? What will be the maximum height?
Thank you very much for any help you can provide.
1 solutions
Answer 64552 by stanbon(57984) on 2007-07-17 18:41:21 (Show Source):
You can put this solution on YOUR website!A stone is projected vertically upward from a platform that is 20 ft high at a rate of 160 ft per second. When will the stone reach its maximum height? What will be the maximum height?
----------------
s(t) = -16t^2+160t+20
maximum occurs at t=-b/2a or t=-160/-32 = 5 seconds
-----------------------
Height at that time is s(5) = -16(5^2)+160*5+20
Height after 5 seconds = 420 ft
====================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/88855: An object that is falling or vertically projected into the air has its height, in feet, above the ground given by s=-16t^2+vot=so Where s is the height, in fee, vo is the original velocity of the object in feet per second, t is the time the object is in motion, is seconds, and so is the height in feet, from which the object is dropped or projected. The figure shows that a ball is thrown straight up from a rooftop at an original velocity of 80 feet per second from a height of 96 feet. The ball misses the rooftop on its way down and eventually strikes the ground. Use the formula and the infromation to solve problem 89-91 I am solving even #90
s=-16t^2+80t+96
t=4
s= -16(4^2)+80(4)+96
s= -16(16)+320+96
s=-256+320+96
s= 160ft
CAN SOMEONE PLEASE HELP ME SOLVE THE SECOND PART OF THIS PROBLEM USING THE EQUATION s=-16t^2+80t+96 How many seconds the ball will take to reach the ground?
1 solutions
Answer 64551 by stanbon(57984) on 2007-07-17 18:34:35 (Show Source):
You can put this solution on YOUR website!An object that is falling or vertically projected into the air has its height, in feet, above the ground given by s=-16t^2+vot=so Where s is the height, in fee, vo is the original velocity of the object in feet per second, t is the time the object is in motion, is seconds, and so is the height in feet, from which the object is dropped or projected. The figure shows that a ball is thrown straight up from a rooftop at an original velocity of 80 feet per second from a height of 96 feet. The ball misses the rooftop on its way down and eventually strikes the ground. Use the formula and the infromation to solve problem 89-91 I am solving even #90
s=-16t^2+80t+96
t=4
s= -16(4^2)+80(4)+96
s= -16(16)+320+96
s=-256+320+96
s= 160ft
CAN SOMEONE PLEASE HELP ME SOLVE THE SECOND PART OF THIS PROBLEM USING THE EQUATION s=-16t^2+80t+96 How many seconds the ball will take to reach the ground?
-------------------
s = 0 when the ball hits the ground.
-16t^2+90t+96 = 0
-2(8t^2 - 45t - 48)=0
(8t^2 - 45t - 48)=0
t = [45 +-sqrt(45^2-4*8*-48)]/16
t = [45 +- 59.67411]/16
t = 6.54 seconds
=================
Cheers,
Stan H.
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Polynomials-and-rational-expressions/88851: I need some help. I am so confused on this one. I have read my book over and ovr and it is just not clicking on how to do this.
Find all positive values for k for which each of the following can be factored.
x^2+x-k
1 solutions
Answer 64549 by stanbon(57984) on 2007-07-17 18:13:46 (Show Source):
You can put this solution on YOUR website!Find all positive values for k for which each of the following can be factored.
x^2+x-k
--------------
Assuming you mean "factoring in the Real Number System" b^2-4ac must be
greater than or equal to zero".
--------
Your problem:
a = 1; b=1; c=k
EQUATION:
1^2-4*1*k>=0
1-4k>=0
-4k>=-1
x <- 1/4
-----------------
Conclusion: x^2+x-k is factorable in the Real Number System as long
as k<=1/4
================
Cheers,
Stan H>
|
Permutations/88733: find the value of the expression 10C8
--------
10C8 is the same as 10C2
10C2 = [10*9]/[1*2] = 45
============================
Cheers,
Stan H.
1 solutions
Answer 64480 by stanbon(57984) on 2007-07-16 22:50:24 (Show Source):
You can put this solution on YOUR website!find the value of the expression 10C8
--------
10C8 is the same as 10C2
10C2 = [10*9]/[1*2] = 45
============================
Cheers,
Stan H.
|
Permutations/88731: a club with 10 members is to pick a president, vice president, treasurer, and secretary. If each office is to be held by one person and no person can hold 2 offices, in how many ways can those offices be filled?
1 solutions
Answer 64476 by stanbon(57984) on 2007-07-16 22:41:55 (Show Source):
You can put this solution on YOUR website!a club with 10 members is to pick a president, vice president, treasurer, and secretary. If each office is to be held by one person and no person can hold 2 offices, in how many ways can those offices be filled?
-------------
10 ways to choose a president
9 ways to choose a vp
8 ways to choose a treasurer
7 ways to choose a secretary
----------------
Multiply to get the total number of ways to choose the officers.
-----------------
Anothe way to get it 10P4 = 5040
=====================
Cheers,
Stan H.
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Functions/88724: determine whether each relation is a function.. give the domain and range for each relation..
A.{(2,7)},(3,7),(5,7)}
B.{(1,10)(2,500),(13,pie)}
1 solutions
Answer 64475 by stanbon(57984) on 2007-07-16 22:31:21 (Show Source):
You can put this solution on YOUR website!
determine whether each relation is a function.. give the domain and range for each relation..
A.{(2,7)},(3,7),(5,7)}
Domain: {2,3,5}
Range: {7}
It is a function because each domain value has only one range value.
----------------------
B.{(1,10)(2,500),(13,pie)}
Domain: {1,2,13}
Range: {10,500,pi}
It is a function because each domain value has only one range value.
========================
Cheers,
Stan H.
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Permutations/88720: in how many ways can you make a four-letter password from A, B, C, D, E if you are not allowed to repete characters?
1 solutions
Answer 64474 by stanbon(57984) on 2007-07-16 22:15:03 (Show Source):
You can put this solution on YOUR website!in how many ways can you make a four-letter password from A, B, C, D, E if you are not allowed to repeat characters?
5 ways to select the 1st letter
4 ways to select the 2nd letter
3 ways to select the 3rd letter
2 ways to select the 4th letter
-------------
Total # of ways = 5*4*3*2 = 120 passwords
----------------------
Another way to get the answer 5P4 = 5!/(5-4)!
----------------------
Cheers,
Stan H.
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Polynomials-and-rational-expressions/88712: I have problem with word problems and need some help.
Science and medication:
Ariana took 2 hrs longer to drive 360 miles on the first day of a vaction trip than to drive 144 miles the second day. If his averade driving rate was the same both days what was the driving time each day?
1 solutions
Answer 64473 by stanbon(57984) on 2007-07-16 22:06:07 (Show Source):
You can put this solution on YOUR website!Ariana took 2 hrs longer to drive 360 miles on the first day of a vaction trip than to drive 144 miles the second day. If his average driving rate was the same both days what was the driving time each day?
------------
1st day DATA:
time = x+2 hrs; distance = 360 miles; rate = d/t = 360/(x+2) mph
-------------
2nd day DATA::
time = x hrs; distance = 144 miles; rate = d/t = 144/x mph
---------------
EQUATION:
rate = rate
360/(x+2) = 144/x
360x = 144x + 288
216x = 288
x = 1 1/3 hrs (time on 2nd day)
x+2 = 3 1/3 hrs (time on 1st day)
============
Cheers,
Stan H.
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