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Recent problems solved by 'stanbon'
stanbon answered: 57894 problems
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2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899, >>NextProbability-and-statistics/128511: This question is from textbook fundamentals of maths
A bag contains five balls numbered 0 through 4. Two balls are chosen at random in succession. The first ball is replaced before the second is chosen.
a. How many outcomes are possible.
Thanks for helping. Could the answer be. 4 over 5
1 solutions
Answer 94044 by stanbon(57967)   on 2008-02-22 22:08:01 (Show Source):
You can put this solution on YOUR website!A bag contains five balls numbered 0 through 4. Two balls are chosen at random in succession. The first ball is replaced before the second is chosen.
a. How many outcomes are possible.
----------------------------
Since the 1st ball is replaced,
there are 5 ways to choose the 1st ball
there are 5 ways to choose the 2nd ball
--------------
The total # of outcome pairs is 5*5 = 25
=====================
Cheers,
Stan H.
|
Rational-functions/128515: Hello, I was wondering if anyone could help me with a polynomial function.
It says to find all the real zeros.
f(x)= 2x^4 -2x^2 -40
2(x^4 -x^2 -20) = 0
2(x^2 -5)(x^2 +4) = 0
1 solutions
Answer 94043 by stanbon(57967) on 2008-02-22 22:04:32 (Show Source):
You can put this solution on YOUR website!Hello, I was wondering if anyone could help me with a polynomial function.
It says to find all the real zeros.
f(x)= 2x^4 -2x^2 -40
2(x^4 -x^2 -20) = 0
Divide both sides by 2 to get:
(x^2 -5)(x^2 +4) = 0
Since the product is zero one of those factors must be zero:
x^2 = 5 or x^2 = -4
x = sqrt5 or x = -sqrt5
---------------
x^2 cannot be -4 if x is a Real Number.
================================
Cheers,
Stan H.
|
real-numbers/128449: How do you turn the irrational number 108 1/3 into a rational number?
1 solutions
Answer 94008 by stanbon(57967) on 2008-02-22 15:28:20 (Show Source):
You can put this solution on YOUR website!How do you turn the irrational number 108 1/3 into a rational number?
-------------
As it is written, 108 1/3 is NOT an irrational number, it is rational.
----------
You can change its form in a million different ways but it will be
rational no matter how you express it.
------------
For example you might write it as (3*108+1)/3 = 325/3
====================
Cheers,
Stan H.
|
Expressions-with-variables/128427: I need help in knowing how to do this problem when solving for x. (x+5)/(x-4)= 3/x+36/(x^2-4x) thank you
1 solutions
Answer 94003 by stanbon(57967) on 2008-02-22 14:17:53 (Show Source):
You can put this solution on YOUR website!(x+5)/(x-4)= (3/x)+(36/(x^2-4x))
The least common multiple of the denominators is x(x-4) or x^2-4x
=================
Multiply thru by the lcm to get:
(x+5)x = 3(x-4)+ 36
x^2+5x = 3x +24
x^2+2x-24 = 0
(x+6)(x-4) = 0
x = -6 or x = 4
---------------------
x=4 cannot be a solution as it would make the original denominator be zero.
--------------
Only solution: x = -6
=====================
Cheers,
Stan H.
|
Quadratic_Equations/128432: Write (81^(x+1)(1/9^(4-x) / 27(243^(x-2) as a single power.
1 solutions
Answer 94001 by stanbon(57967) on 2008-02-22 14:12:38 (Show Source):
You can put this solution on YOUR website!Write (81^(x+1)((1/9)^(4-x) / 27(243^(x-2) as a single power.
-------------------------------
(3^4(x+1)) * (3^-2(4-x)) / (3^3*(3^5(x-2)
---------------------------------
[3^(4x+4)][3^(-8+2x)]/[3^3(3^(5x-10)]
-------------------------------
= 3^(6x-4)/[3^(5x-7)]
= 3^(x+3)
=============
Cheers,
Stan H.
|
Quadratic_Equations/128430: Given 3x^2+(k+2)x=-3, determine the value(s) of k so that the equation has real and equal roots.
1 solutions
Answer 94000 by stanbon(57967) on 2008-02-22 14:07:44 (Show Source):
You can put this solution on YOUR website!Given 3x^2+(k+2)x=-3, determine the value(s) of k so that the equation has real and equal roots.
----------------
The discriminant must be zero.
b^2-4ac = (k+2)^2-4*3*3 = 0
(k+2)^2 = 36
k+2 = 6 or k+2 = -6
k = 4 or k = -8
==================
Cheers,
Stan H.
|
Graphs/128428: Biologists at the Long Beach aquarium would like to know if conditions at aquariums reduce the life span of dolphins. Dolphins live an average of 21 years in the wild with a standard deviation of 3 years. Furthermore, the lifespan of dolphins forms a normal distribution.
Because dolphins are exchanged with other aquariums and because some dolphins’ ages are unknown, the biologists were able to randomly select only 4 dolphins for the study. The four lived to the following ages: 17, 19, 20, 21. At a .05 significance level, can the biologists claim that dolphins living in captivity have a shorter life span than dolphins at sea?
Question 1: What is the null hypothesis?
Ho: mu = 21 yrs.
Q2: What is the alternate hypothesis?
Ha: mu < 21 yrs
Q3: Which is the correct hypothesis test (e.g., Z-, t-, or F-test)?
t
Q4: Is this a directional or nondirectional test?
If by directional you mean the same as "one-tail" the answer is directional.
Q5: What is the test statistic?
The sample mean is 19.25, so
t(19.25) = (19.25-21)/[3/sqrt(4)] = -1.1667
------------------------------
Q6: What is the p-value?
P(-10 < t < -1.1667) with df = 3 is 0.0960
------------------------------------
Q7: What is your conclusion?
Fail to reject Ho because the p-value is greater than alpha = 5%
------------------------------------
Q8: Is it possible that an error was committed? If so, which kind?
With such a small sample we may have failed to detect a real change
in the average life-span of dolphins. That is a Type II error of
failing to reject Ho when it fact it is false.
=========================
Cheers,
Stan H.
How does this problem work?
1 solutions
Answer 93998 by stanbon(57967) on 2008-02-22 14:00:44 (Show Source):
You can put this solution on YOUR website!I cant seem to completely solve this equation.
2x+y=3
7x+5y=21
------------------
It can be solved by graphing, substitution or elimination.
-------------------------
The 1st equation is "simple" so using substitution you
would get:
y = -2x+3
Substitute that into the 2nd equation to get:
7x + 5(-2x+3) = 21
Solve for "x":
7x -10x + 15 = 21
-3x = 6
x = -2
----------
Substitute that into y = -2x+3 to solve for "y":
y = -2(-2)+3
y = 7
==========
Final solution: x = -2, y=7
=============================
Cheers,
Stan H.
|
Probability-and-statistics/128355: Please kindly help me. I am stuck with this question and cannot move on. Thank you again for the help
Biologists at the Long Beach aquarium would like to know if conditions at aquariums reduce the life span of dolphins. Dolphins live an average of 21 years in the wild with a standard deviation of 3 years. Furthermore, the lifespan of dolphins forms a normal distribution.
Because dolphins are exchanged with other aquariums and because some dolphins’ ages are unknown, the biologists were able to randomly select only 4 dolphins for the study. The four lived to the following ages: 17, 19, 20, 21. At a .05 significance level, can the biologists claim that dolphins living in captivity have a shorter life span than dolphins at sea?
Question 1: What is the null hypothesis?
Q2: What is the alternate hypothesis?
Q3: Which is the correct hypothesis test (e.g., Z-, t-, or F-test)?
Q4: Is this a directional or nondirectional test?
Q5: What is the test statistic?
Q6: What is the p-value?
Q7: What is your conclusion?
Q8: Is it possible that an error was committed? If so, which kind?
1 solutions
Answer 93996 by stanbon(57967) on 2008-02-22 13:51:15 (Show Source):
You can put this solution on YOUR website!Biologists at the Long Beach aquarium would like to know if conditions at aquariums reduce the life span of dolphins. Dolphins live an average of 21 years in the wild with a standard deviation of 3 years. Furthermore, the lifespan of dolphins forms a normal distribution.
Because dolphins are exchanged with other aquariums and because some dolphins’ ages are unknown, the biologists were able to randomly select only 4 dolphins for the study. The four lived to the following ages: 17, 19, 20, 21. At a .05 significance level, can the biologists claim that dolphins living in captivity have a shorter life span than dolphins at sea?
Question 1: What is the null hypothesis?
Ho: mu = 21 yrs.
Q2: What is the alternate hypothesis?
Ha: mu < 21 yrs
Q3: Which is the correct hypothesis test (e.g., Z-, t-, or F-test)?
t
Q4: Is this a directional or nondirectional test?
If by directional you mean the same as "one-tail" the answer is directional.
Q5: What is the test statistic?
The sample mean is 19.25, so
t(19.25) = (19.25-21)/[3/sqrt(4)] = -1.1667
------------------------------
Q6: What is the p-value?
P(-10 < t < -1.1667) with df = 3 is 0.0960
------------------------------------
Q7: What is your conclusion?
Fail to reject Ho because the p-value is greater than alpha = 5%
------------------------------------
Q8: Is it possible that an error was committed? If so, which kind?
With such a small sample we may have failed to detect a real change
in the average life-span of dolphins. That is a Type II error of
failing to reject Ho when it fact it is false.
=========================
Cheers,
Stan H.
|
Graphs/128385: Dear Tutors,
I was just wondering if there are still people there helping with homework questions? The reason I asked is because I submitted a question yesterday,and never got a reply.I sure hope you do,because I need all the help I can get.We don't have to turn our homework in ,but if I don't do it I'm lost on the test.Thanks for all the help you have given me.
Sincerely,LH
1 solutions
Answer 93991 by stanbon(57967) on 2008-02-22 11:40:36 (Show Source):
You can put this solution on YOUR website!There are no guarantees on this site.
Sometimes problems arrive so fast they
drop out of sight on the list before
they get answered.
Sometimes the problems are poorly stated
so no one can tell exactly what the
question is.
Sometimes the link drops an important part
of the posted problem so it makes no
sense when read by a tutor.
There are many reasons why a given problem
might not be answered.
So what can you do?
1. Make sure your questions is complete in
its posted form
2. Add a plea to your posting if you truly
need an answer by a certain time.
3. Make your best effort to solve the problem
and point out in your post where you get stuck.
Cheers,
4. Don't shout (posting the same problem two
or more times in successive minutes) but do
repeat the question after a suitable time has
elapsed.
Cheers,
Stan H.
|
Probability-and-statistics/128371: Please help me. I need desperate help.
Biologists at the Long Beach aquarium would like to know if conditions at aquariums reduce the life span of dolphins. Dolphins live an average of 21 years in the wild with a standard deviation of 3 years. Furthermore, the lifespan of dolphins forms a normal distribution.
Because dolphins are exchanged with other aquariums and because some dolphins’ ages are unknown, the biologists were able to randomly select only 4 dolphins for the study. The four lived to the following ages: 17, 19, 20, 21. At a .05 significance level, can the biologists claim that dolphins living in captivity have a shorter life span than dolphins at sea?
Question 1: What is the null hypothesis?
Q2: What is the alternate hypothesis?
Q3: Which is the correct hypothesis test (e.g., Z-, t-, or F-test)?
Q4: Is this a directional or nondirectional test?
Q5: What is the test statistic?
Q6: What is the p-value?
Q7: What is your conclusion?
Q8: Is it possible that an error was committed? If so, which kind?
1 solutions
Answer 93990 by stanbon(57967) on 2008-02-22 11:26:47 (Show Source):
You can put this solution on YOUR website!Biologists at the Long Beach aquarium would like to know if conditions at aquariums reduce the life span of dolphins. Dolphins live an average of 21 years in the wild with a standard deviation of 3 years. Furthermore, the lifespan of dolphins forms a normal distribution.
Because dolphins are exchanged with other aquariums and because some dolphins’ ages are unknown, the biologists were able to randomly select only 4 dolphins for the study. The four lived to the following ages: 17, 19, 20, 21. At a .05 significance level, can the biologists claim that dolphins living in captivity have a shorter life span than dolphins at sea?
Question 1: What is the null hypothesis?
Ho: mu = 21 yrs.
Q2: What is the alternate hypothesis?
Ha: mu < 21 yrs
Q3: Which is the correct hypothesis test (e.g., Z-, t-, or F-test)?
t
Q4: Is this a directional or nondirectional test?
If by directional you mean the same as "one-tail" the answer is directional.
Q5: What is the test statistic?
The sample mean is 19.25, so
t(19.25) = (19.25-21)/[3/sqrt(4)] = -1.1667
------------------------------
Q6: What is the p-value?
P(-10 < t < -1.1667) with df = 3 is 0.0960
------------------------------------
Q7: What is your conclusion?
Fail to reject Ho because the p-value is greater than alpha = 5%
------------------------------------
Q8: Is it possible that an error was committed? If so, which kind?
With such a small sample we may have failed to detect a real change
in the average life-span of dolphins. That is a Type II error of
failing to reject Ho when it fact it is false.
=========================
Cheers,
Stan H.
|
Quadratic_Equations/128327: This question is from textbook algebra structure and method
I dont understand what we have to do for this problem.
Working alone, Anton can install a brick patio in 2 hours less than Bill. Together Anton and Bill can install the patio in 4 hours. To the nearest tenth of an hour, how long does it take Bill to install the patio working alone?
1 solutions
Answer 93954 by stanbon(57967) on 2008-02-21 23:27:44 (Show Source):
You can put this solution on YOUR website!Working alone, Anton can install a brick patio in 2 hours less than Bill. Together Anton and Bill can install the patio in 4 hours. To the nearest tenth of an hour, how long does it take Bill to install the patio working alone?
-----------------------------
Bill DATA:
Time = x hrs/job ; Rate = 1/x job/hr
-----------------------------------
Anto DATA:
Time = (x-2) hrs/job ; Rate = 1/(x-2) job/hr
---------------------------
Together DATA:
Time = 4 hrs/job ; Rate = 1/4 job/hr
=======================================
EQUATION:
rate + rate = together rate
1/x + 1/(x-2) = 1/4
Multiply thru by 4x(x-2) to get:
4(x-2) + 4x = x(x-2)
8x - 8 = x^2-2x
x^2-10x+8 = 0
x = [10 +- sqrt(100-4*8)]/2
x = [10 +- sqrt(68)]/2
Positive answer:
x = (10 + sqrt(68))/2
x = 9.1231 hrs (Time is takes Bill to do the job)
=====================
Cheers,
Stan H.
|
Rational-functions/128347: sq root(x^2+5)=x+3
Thank you
1 solutions
Answer 93953 by stanbon(57967) on 2008-02-21 23:15:52 (Show Source):
You can put this solution on YOUR website!sq root(x^2+5)=x+3
--------------------
Square both sides to get:
x^2+5 = x^2+6x+9
6x = -4
x = -2/3
---------------
Check:
Can x = -2/3 ?
sqrt((4/9)+5) = -2/3 + 3
sqrt(49/9) = 7/3
7/3 = 7/3
-------------
Final Ans: x = -2/3
========================
Cheers,
Stan H.
|
Linear-systems/128344: Solving a linear equation with several occurences of the veriable problem type 2
5x+7/3=1/3x-7/2. How can I solve this question
1 solutions
Answer 93952 by stanbon(57967) on 2008-02-21 23:11:40 (Show Source):
You can put this solution on YOUR website!5x+(7/3) = (1/3)x-(7/2)
Multiply thru by 6 to get:
---------------------------
30x + 14 = 2x - 21
28x = -35
x = -35/28
===============
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/128339: 2.A local landscape company had a 1-week sale.
On Monday,Mrs.Jones had $82 to spend.After purchasing 5 trees,she had just enough money left to purchase 1 shrub.Later in that same week,she purchased 2 trees.She had $37 with her,so she again had enough money left to purchase 1 shrub.Find the cost of a tree and the cost of a shrub.
1 solutions
Answer 93949 by stanbon(57967) on 2008-02-21 22:28:38 (Show Source):
You can put this solution on YOUR website!On Monday,Mrs.Jones had $82 to spend.After purchasing 5 trees,she had just enough money left to purchase 1 shrub.Later in that same week,she purchased 2 trees.She had $37 with her,so she again had enough money left to purchase 1 shrub.Find the cost of a tree and the cost of a shrub.
------------------------------------------
EQUATIONS:
5t+s = 82
2t+s = 37
------------
Subtract the 2nd equation from the 1st to get:
3t = 45
t = $15 (price of each tree)
-------
Substitute to solve for "s":
2*15 + s = 37
s = $7 (price of each shrub)
===================
Cheers,
Stan H.
|
Rational-functions/128335: x-12=sq root (16x)
1 solutions
Answer 93948 by stanbon(57967) on 2008-02-21 22:21:54 (Show Source):
You can put this solution on YOUR website!x-12=sq root (16x)
Square both sides to get:
x^2-24x+144 = 16x
x^2-40x+144 = 0
(x-36)(x-4) = 0
x = 36 or x = 4
-----------------
Checking:
Does x=36 ?
36-12 = sqrt(16*36)
24 = 4*6
-------------
Does x = 4 ?
4-12 = sqrt(16*4)
-8 = 4*2
Wrong
----------------
Only solution: x= 36
========================
cheers,
stan H.
|
Miscellaneous_Word_Problems/128330: Peter sold pumpkins from his farm. He sold Jumbo pumpkins for $9 each and sold Regular pumpkins for $4 each. Peter sold 80 pumpkins and collected $395. How many Jumbo pumpkins and Regular pumpkins did he sell?
1 solutions
Answer 93947 by stanbon(57967) on 2008-02-21 22:12:55 (Show Source):
You can put this solution on YOUR website!Peter sold pumpkins from his farm. He sold Jumbo pumpkins for $9 each and sold Regular pumpkins for $4 each. Peter sold 80 pumpkins and collected $395. How many Jumbo pumpkins and Regular pumpkins did he sell?
---------------------
Let # of jumbos be "x"; value = 9x dollars
--------------------
# of regulars is "80-x"; value = 4(80-x)= 320-4x dollars
----------------------
EQUATION:
value + value = 395 dollars
9x + 320-4x = 395
5x = 75
x = 15 (# of jumbos)
80-x = 65 (# of regulars)
==================
Cheers,
Stan H.
|
Graphs/128332: I need help with this homework problem
how do you solve the equation
y=3x+9:(0,),(, 24)(2,)
1 solutions
Answer 93944 by stanbon(57967) on 2008-02-21 22:03:01 (Show Source):
You can put this solution on YOUR website!how do you solve the equation
y=3x+9
(0,)
If x=0, y = 9
------------------
(, 24)
If y = 24, x = 5
--------------
(2,)
If x = 2, y = 15
====================
Cheers,
Stan H.
|
Probability-and-statistics/128024: This question is from textbook Fundamentals of Mathematics
Harry Hose keeps all of his socks in the top drawer of his bureau. In the drawer there are four blue socks, six black socks, seven brown socks (he lost one in the laundry), and four red socks. Harry reaches in a pulls a sock out at random. Find the probability that the sock chosen is
a. brown
b. blue
c. red
d. black
e. not brown
f. neither brown nor blue
1 solutions
Answer 93943 by stanbon(57967) on 2008-02-21 21:59:11 (Show Source):
You can put this solution on YOUR website!Harry Hose keeps all of his socks in the top drawer of his bureau. In the drawer there are four blue socks, six black socks, seven brown socks (he lost one in the laundry), and four red socks. Harry reaches in a pulls a sock out at random. Find the probability that the sock chosen is
a. P(brown) = 7/21 1/3
b. P(blue) = 4/21
c. P(red) = 4/21
d. P(black) = 6/21 = 2/7
e. P(not brown) = 2/3
f. P(neither brown nor blue) = 10/21
====================================
Cheers,
Stan H.
|
Quadratic_Equations/128294: At an airshow, a plane is in a power dive. The height of the plane, in metres above the ground , is recorded for the first six seconds.
Time(s): 1,2,3,4,5,6
Height(m): 214,180,150,124,102,84
a) Algebraically determine the quadratic function that models the path followed by the plane. Express the function in the form y=ax^2+bx+c.
b) Use the function to determine the minimum height of the plane.
1 solutions
Answer 93928 by stanbon(57967) on 2008-02-21 20:41:01 (Show Source):
You can put this solution on YOUR website!At an airshow, a plane is in a power dive. The height of the plane, in metres above the ground , is recorded for the first six seconds.
Time(s): 1,2,3,4,5,6
Height(m): 214,180,150,124,102,84
a) Algebraically determine the quadratic function that models the path followed by the plane. Express the function in the form y=ax^2+bx+c.
--------
Substitute three x/y pairs into the form to get three equations
with variables a,b, and c.
-------------------------------
f(1) = a + b + c = 214
f(2) =4a + 2b + c = 180
f(3) =9a + 3b + c = 150
----------------------------
I used the Matrix function of a TI calculator to find the following:
a = 2
b = -40
c = 252
------------
EQUATION:
y = 2x^2-40x+252
-------------------
b) Use the function to determine the minimum height of the plane.
minimum occurs at x = -b/2a = 40/4 = 10
f(10) = 52
-----------------
At 10 seconds the plane will be at 52 ft.
=======================
Cheers,
Stan H.
----------------------
|
expressions/128292: if T=a+(n-1)d find t when a=16 n=11 and d=6
find t when a=20 n=6 and d=-2
please help me im stuck!!!
1 solutions
Answer 93926 by stanbon(57967) on 2008-02-21 19:56:54 (Show Source):
You can put this solution on YOUR website!T=a+(n-1)d
find t when a=16 n=11 and d=6
t = 16 + (11-1)*6
t = 16 + 10*6
t = 16 + 60
t = 76
-------------------
find t when a=20 n=6 and d=-2
t = 20 + (6-1)*2
t = 20 + 5*2
t = 20 + 10
t = 30
=============
Cheers,
Stan H.
|
Equations/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(57967) 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(57967) 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(57967) 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(57967) 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(57967) 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(57967) 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(57967) 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.
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