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Recent problems solved by 'stanbon'
stanbon answered: 57288 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, >>NextQuadratic_Equations/121713: What is the correct mapping rule to show the transformation of y=2^x for the equation 1/4(y-5)=2^2x-3 ? Can someone please help, I've been stuck for a few days on this one.I'm guessing: (x,y)-(x+3),(4y+5), anyone know?
1 solutions
Answer 89352 by stanbon(57361)   on 2008-01-22 08:51:30 (Show Source):
You can put this solution on YOUR website!What is the correct mapping rule to show the transformation of y=2^x for the equation 1/4(y-5)=2^2x-3 ? Can someone please help, I've been stuck for a few days on this one.I'm guessing: (x,y)-(x+3),(4y+5), anyone know?
----------
Rearranging I get:
y = 4*(2^(2x-3)-3)+5
y = 4*2^(2x-3)+7
Not sure about this one, but:
It looks to me like y=2^x is moved (3/2)to the right, up 7, and "stretched"
by a factor of 4.
-----------------
Maybe (x,y)----(x-(3/2),4y+7)
----------------
What do you think?
=============
Cheers,
Stan H.
|
Mixture_Word_Problems/121715: Please help me solve this word problem: A pharmacist needs to strengthen a 15% alcohol solution so that it contains 32% alcohol. How much pure alcohol should be added to 100ml of the 15% solution?
1 solutions
Answer 89351 by stanbon(57361) on 2008-01-22 08:36:50 (Show Source):
You can put this solution on YOUR website!A pharmacist needs to strengthen a 15% alcohol solution so that it contains 32% alcohol. How much pure alcohol should be added to 100ml of the 15% solution?
---------------
15% solution DATA:
Amount = x ml ; Amt of active ingredient = 0.15x ml
-------------------------
Pure alcohol DATA:
Amt = 100-x ml : Amt of active is 100-x ml
--------------------------
32% solution DATA:
Amt = 100 ml ; Amt of active is 0.32*100 = 32 ml
------------------------
EQUATION:
active + active = active
0.15x + 100-x = 32
-0.85x = -68
x = 80 ml
-------------
Amt of pure alcohol needed for the solution = 100-x = 20 ml
=============
Cheers,
Stan H.
|
Quadratic_Equations/121714: Joey did an experiment in which he measured the temperature(T) of a cup of hot chocolate, in degrees celcius, with respect to time(t), in minutes. He found that the function T=33(0.28)^t/26 +24 described the relationship. What was the room temperature of the room in which it was placed to cool?
I think it is 24 degrees celcius, does anyone know this one ?
1 solutions
Answer 89350 by stanbon(57361) on 2008-01-22 08:30:42 (Show Source):
You can put this solution on YOUR website!Joey did an experiment in which he measured the temperature(T) of a cup of hot chocolate, in degrees celcius, with respect to time(t), in minutes. He found that the function T=33(0.28)^t/26 +24 described the relationship. What was the room temperature of the room in which it was placed to cool?
I think it is 24 degrees celcius, does anyone know this one ?
-------------------------
Find T(0) to get the starting temperature
find T(some very large number) to get the temperature after
the cup has cooled a very large time.
---------------
As t get's larger and larger (0.28)^t gets closer and closer to
zero.
So as t get's larger and larger T get's closer and closer to 24.
----------
I think you are right.
Cheers,
Stan H.
|
Linear_Algebra/121687: I have a question on a story problem...
Mary has a total of $4.75 in her bank. There are 39 coins in all: some are dimes are some are quarters. How many coins of each are there in her bank?
please
d+q=39
10d+25q=475
1 solutions
Answer 89334 by stanbon(57361) on 2008-01-21 22:59:23 (Show Source):
You can put this solution on YOUR website!Mary has a total of $4.75 in her bank. There are 39 coins in all: some are dimes are some are quarters. How many coins of each are there in her bank?
please
-------------------
d+q=39
10d+25q=475
------------
d=39-q
Substitute to solve for "q":
10(39-q)+25q=475
390-10q+25q=475
15q = 85
-------------
Comment: q does not become a whole number.
Check your statement of the problem.
------------
Cheers,
Stan H.
|
Linear_Algebra/121686: i have a wksht ???..can you still help me?
Solve the following system of equations:
4x-y=3
2x+3y=5
i got x=-7/9
y=-29/7
i dont think what i have is right
1 solutions
Answer 89332 by stanbon(57361) on 2008-01-21 22:52:01 (Show Source):
You can put this solution on YOUR website!4x-y=3
2x+3y=5
-----------
y = 4x-3
Substitute that into the 2nd equation to solve for "x":
2x+3(4x-3)=5
2x+12x-9=5
14x = 14
x = 1
----------
Substitute that into y = 4x-3 to solve for "y":
y = 4*1-3
y = 1
================
Solution: x=1; y=1
================
Cheers,
Stan H.
|
Equations/121667: May I have some help with the following inequality?
Solve the nonlinear inequality. Express the solution using interval notation.
x^2 + x > 90
1 solutions
Answer 89331 by stanbon(57361) on 2008-01-21 22:47:54 (Show Source):
You can put this solution on YOUR website!Solve the nonlinear inequality. Express the solution using interval notation.
x^2 + x > 90
------------------
x^2+x-90 >0
Factor:
(x+10)(x-9)>0
Draw a number line; plot the points x=-10 and x=9 on it.
Test each of the three resulting intervals to see where the
solution set may be.
-------------
Test x=-11 in the inequality: (-11+10)(-11-9)>0; true
Test x = 0 in the inequality: (0+10)(0-9)>0 ; false
Test x = 10 in the inequality: (10+10)(10-9); true
-----------------
Two intervals comprise the solution set:
(-inf,-10) and (9,+inf)
================================
Cheers,
Stan H.
|
Geometry_Word_Problems/121681: Hi, I would really like to know if these two equations are the same.
x^2 = 3x + 12 re-wrote as x^2 + 3x = 12
x^2+3x=12
x^2+ 3x+ (3/2)^2=12+(3/2)^2
(x+3/2)^2= √57/4
x+ 3/2= + √(57/4)=+ √((3^1*〖19〗^1)/2^2 )=+ √57/2
= x+ 3/2= - √(57/4)=- √((3^1*〖19〗^1)/2^2 )- √57/2
x+3/(2 )– 3/2=+√57/2-3/2
x+3/(2 )– 3/2=-√57/2-3/2
x=-3/2+ √57/2
x=-3/2- √57/2
x^2+3x=12
(-3/2+ √57/2)^2+3*(-3/2+ √57/2)=12
(-3/2- √57/2)^2+3*(-3/2- √57/2)=12
Thank you.
1 solutions
Answer 89329 by stanbon(57361) on 2008-01-21 22:35:20 (Show Source):
|
Age_Word_Problems/121670: The ages of two brothers are in the ratio two to three, but in eight years the ratio of their ages will be three to four. Find their present age?
1 solutions
Answer 89328 by stanbon(57361) on 2008-01-21 22:32:12 (Show Source):
You can put this solution on YOUR website!The ages of two brothers are in the ratio two to three, but in eight years the ratio of their ages will be three to four. Find their present age?
------------------
NOW DATA:
Let the two brothers ages be 2x and 3x.
-------------------
Eight yrs. from now DATA:
2x will be 2x+8
3x will be 3x+8
--------------------
Eight yrs from now EQUATION:
2x+8/3x+8 = 3/4
-------
Cross-multiply to get:
3(3x+8) = 4(2x+8)
9x+24 = 8x+32
x = 8
----------
2x = 16 (one of the brother's age)
3x = 24 (the other brother's age)
----------------------------------
Cheers,
Stan H.
|
Complex_Numbers/121649: use synthetic division to divide: (x^2-4x-2)/[x-(3+2i)]
1 solutions
Answer 89302 by stanbon(57361) on 2008-01-21 19:59:40 (Show Source):
You can put this solution on YOUR website!use synthetic division to divide: (x^2-4x-2)/[x-(3+2i)]
---------------------------------------
3+2i)....1......-4......-2
..........1.....-1+2i....|..(-9+6i)
Remainder: -9+6i
Quotient: x -1+2i
=======================
Cheers,
Stan H.
|
Functions/121639: find the domain of (h/g)(x), given that h(x)=5x/(3x-7) and g(x)=(x^4-1)/(5x-15). State your answer in interval notation.
1 solutions
Answer 89299 by stanbon(57361) on 2008-01-21 19:50:40 (Show Source):
You can put this solution on YOUR website!find the domain of (h/g)(x), given that h(x)=5x/(3x-7) and g(x)=(x^4-1)/(5x-15). State your answer in interval notation.
-----------------------------------------------
(h/g)(x) = [h(x)]/[g(x)] = [5x/(3x-7)]/[(x^4-1)/(5x-15)]
= [5x/(3x-7)] * [5(x-3)/(x-1)(x+1)(x^2+1)]
---------------
I have factored as far can be done; there are no
factors common to numerator and denominator so no
further simplifying is possible.
==================
Cheers,
Stan H.
|
Linear-equations/121625: A six-foot tall person walks around the earth. how much farther does the person's head travel than the person's feet?
1 solutions
Answer 89290 by stanbon(57361) on 2008-01-21 19:16:16 (Show Source):
You can put this solution on YOUR website!A six-foot tall person walks around the earth. how much farther does the person's head travel than the person's feet?
--------------
If you assume the radius of the earth is x-ft, the
circumference is 2(pi)x ft.
-----------
If you add the 6 ft to the radius you have a radius of x+6 ft.
The circumference of the the path of the head is 2(pi)(x+6) ft.
------------------------
The difference is [2pi(x+6)]-[2(pi)x] ft
2(pi)x+12pi - 2(pi)x
= 12(pi) ft or about 37.6991 ft.
=======================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/121615: how do i divide these two problems:
y^2-12y+20 /y-2
and 2x^2+7x+3 / 2x+1
i need the steps for these two problems by today january 21,2008 at 8:00pm
please its urgent
1 solutions
Answer 89283 by stanbon(57361) on 2008-01-21 18:28:21 (Show Source):
You can put this solution on YOUR website!y^2-12y+20 /y-2
Factor to get:
= [(y-2)(Y-10)]/(y-2
= y-10
=========================================
2x^2+7x+3 / 2x+1
Factor to get:
= [2x^2+6x+x+3]/(2x+1)
= [2x(x+3)+(x+3)]/(2x+1
= [(x+3)(2x+1)]/(2x+1)
----------------
Comment:
Are you sure that denominator is not 2x+1 ?
------------------
Well, you say it is 2x+1 so you can cancel the 2x+1 in numerator and denominator to get:
= x+3
=================
Cheers,
Stan H.
|
Geometry_Word_Problems/121608: In a triangle whose perimeter is 40 cm, the length of the longest side is four cm less than the sum of th lengths of the other sides. The length of the shortest side is four cm more than the difference between the lengths of the other sides. What is the length of the longest side?
1 solutions
Answer 89281 by stanbon(57361) on 2008-01-21 18:14:15 (Show Source):
You can put this solution on YOUR website!In a triangle whose perimeter is 40 cm,
the length of the longest side is four cm less than the sum of th lengths of the other sides.
The length of the shortest side is four cm more than the difference between the lengths of the other sides.
What is the length of the longest side?
------------------------------
Let the sides be x,y,z; x be the shortest, z be the longest.
-------------------------
x+y+z = 40 cm
z = (x+y)-4
x = 2(z-y)
----------------
Rearrange:
x+y+z = 40
x+y-z = 4
x+2y-2z=0
---------------
Using the Matrix function of a TI caluculator I get:
x = 8 (shortest)
y = 14
z = 18 (longest)
=================
Cheers,
Stan H.
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Quadratic-relations-and-conic-sections/121595: how do I graph 3y^2-x^2+12y+2x=5
1 solutions
Answer 89271 by stanbon(57361) on 2008-01-21 17:11:31 (Show Source):
You can put this solution on YOUR website!how do I graph 3y^2-x^2+12y+2x=5
---------------
You should convert the equation to a standard form
by completing the square on the y-terms and on the
x-terms separately:
------------
3(y^2+4y+4)-(x^2-2x+1) = -5+12-1
3(y+2)^2 - (x-1)^2 = 6
3(y+2)^2/6 - (x-1)^2/6 = 1
(y+2)^2/2 - (x-1)^2/6 = 1
-----------------------
The graph is a hyperbola with center at (1,-2)
The hyperbola opens up and down.
The y -intercept can be found by letting x=0 and
finding two values for "y".
================================
Cheers,
Stan H.
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Evaluation_Word_Problems/121594: This question is from textbook
2y+x=1
y-2x=8
But I really need help with it all.
1 solutions
Answer 89269 by stanbon(57361) on 2008-01-21 16:58:39 (Show Source):
You can put this solution on YOUR website!2y+x=1
y-2x=8
---------
Solve the 2nd equation for "y": y = 2x+8
Substitute into the 1st to solve for "x":
-----------
2(2x+8)+x=1
4x+16+x=1
5x=-15
x = -3
Substitute into y=2x+8 to solve for y:
y = 2*-3+8
y = 2
===============
Cheers,
Stan H.
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Exponents-negative-and-fractional/121369: Please help me understand how to do this. I am to simplify if possible and solve.
5 to the negative 7 th *5^9 =
1 solutions
Answer 89268 by stanbon(57361) on 2008-01-21 16:51:49 (Show Source):
You can put this solution on YOUR website!5 to the negative 7 th *5^9 =
---------------------------
The general rules:
a^x*a^y=a^(x+y)
-------
(a^x)/(a^y) = a^(x-y) = 1/(a^(y-x)
--------
Your Problem:
5^-7*5^9 = 5^(-7+9) = 5^2 = 25
OR
5^-7 * 5^9 = (5^9)/(5^7) = 5^(9-7)= 5^2 = 25
=======================
Cheers,
Stan H.
|
Equations/121590: Hi. May I have some help with this inequality?
Solve the linear inequality. Express the solution using interval notation.
-1 < 2x - 2 ≤ 5
1 solutions
Answer 89262 by stanbon(57361) on 2008-01-21 16:36:55 (Show Source):
You can put this solution on YOUR website!Solve the linear inequality. Express the solution using interval notation.
-1 < 2x - 2 ≤ 5
Add 2 along the line to get:
1 < 2x <= 7
Divide thru by 2 to get:
(1/2)< x <= (7/2)
--------------
Interval notation: (1/2 , 7/2]
=================================
Cheers,
Stan H.
|
Probability-and-statistics/121528: what is...
theoretical probability
experimental probability
fraction operations
probability with replacement
and punnett squares
1 solutions
Answer 89259 by stanbon(57361) on 2008-01-21 16:34:17 (Show Source):
You can put this solution on YOUR website!what is...
theoretical probability
The teoretical prob. of getting a 3 when you roll a die is 1/6;
but if you actually roll a die 1000 times and find that the 3
comes up half of the time, the experimental probability of
getting a three is 1/2.
experimental probability
----------------------------
fraction operations
Sounds like arithmetic to me.
------------------------------
probability with replacement
If you have a jar with 3 red and 2 blue marbles the probability
of selecting a red and then a blue depends on whether you
"replace" the 1st drawn marble.
With replacement the probability is (3/5)(2/5) = 6/25
without replacement the prob is (3/5)(2/4) = 6/20
--------
"With replacement" means you are conducting the same experiment
on each draw. Without replacement means the experiment is
changing on each draw.
----------
With replacement means the different draw results are independent.
Without replacement means the different draw results are dependent.
===============
and punnett squares
I have no idea.
================
Cheers,
Stan H.
|
Quadratic_Equations/121500: What type of function does the following table of values represent?
x- -21,-18,-15,-12,-9
y- 3,6,12,24,48
Is it arithmetic,quadratic, cubic, or exponential?
1 solutions
Answer 89175 by stanbon(57361) on 2008-01-21 10:51:25 (Show Source):
You can put this solution on YOUR website!Common differences do not give you a constant difference
so it is not arithmeti, quadratic, or cubic.
I tried fitting it into y = ab^x and got y = 384(2^(x/3)
by solving for a and b.
So it is exponential.
=======================
Cheers,
Stan H.
|
percentage/121517: 78 students took a test. 2 students failed the test. What percent of the students passed the test? What percent of the students failed the test?
1 solutions
Answer 89171 by stanbon(57361) on 2008-01-21 10:37:33 (Show Source):
You can put this solution on YOUR website!78 students took a test. 2 students failed the test. What percent of the students passed the test? What percent of the students failed the test?
-----------
# who failed = 2
% who failed = 2/78 = 2.56%
---------------
% who passed = 76/78 = 97.4%
======================
Cheers,
Stan H.
|
Quadratic_Equations/121508: Which function represents the data in the following table of values?
a) x- 0,1,2,3
y- 24,12,6,3
Is it (a)y=24(0.5)^1/x ,(b)y=24(2)^x ,(c) y=12(0.5)^x, or (d) y=24(0.5)^x
b) x-0,3,6,9
y-5,10,20,40
Is it (a) y=5(2)^x ,(b)y=5(3)^x ,(c) y=5(2)^x/3,or (d) y=5(3)^x/2
1 solutions
Answer 89167 by stanbon(57361) on 2008-01-21 10:09:16 (Show Source):
You can put this solution on YOUR website!a) x- 0,1,2,3
y- 24,12,6,3
Is it (a)y=24(0.5)^1/x ,(b)y=24(2)^x ,(c) y=12(0.5)^x, or (d) y=24(0.5)^x
--------
Notice that when x=0 answer "a" is undefined
answer b = 24 but when x=1 you get 48 instead of 12
answer c = 12
anser d = 24 and you 12 when x = 1; you get 6 when x =2 etc.
So, d is the answer
-------------------------
b) x-0,3,6,9
y-5,10,20,40
Is it (a) y=5(2)^x ,(b)y=5(3)^x ,(c) y=5(2)^x/3,or (d) y=5(3)^x/2
answer a, b, c and d give 5 when x = 0
answer a gives 10 when x=1; the others do not
So, a is the answer
=======================
Cheers,
Stan H.
|
Quadratic_Equations/121510: Given the quadratic equation x^2-15=2k(x-4), find k if there are two real and equal roots.
1 solutions
Answer 89165 by stanbon(57361) on 2008-01-21 10:00:40 (Show Source):
You can put this solution on YOUR website!Given the quadratic equation x^2-15=2k(x-4), find k if there are two real and equal roots.
-----------
The discriminant will be zero.
-------------
x^2-15=2kx-8k
x^2-2kx+8k-15=0
---------------
Discriminant: b^2-4ac
(2k)^2-4*1(8k-15) = 0
4k^2-32k+60 =0
k^2-8k+15 = 0
(k-3)(k-5)=0
k = 3 or k=5
================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/121516: The world's most populous countries are China and India. As of mid-2005, the combined population of these two countries was estimated at 2.4 billion. If there was about 4/5 as many people living in India as China, what was the population of each country, to the nearest tenth of a billion?
1 solutions
Answer 89163 by stanbon(57361) on 2008-01-21 09:51:40 (Show Source):
You can put this solution on YOUR website!The world's most populous countries are China and India. As of mid-2005, the combined population of these two countries was estimated at 2.4 billion. If there was about 4/5 as many people living in India as China, what was the population of each country, to the nearest tenth of a billion?
---------------
I + C = 2.4 billion
I= (4/5)C
----------
Substitute and solve for C
(4/5)C + C = 2.4 billion
1.8C = 2.4
C = 1 1/3 is appox 1.3 billion
-------------------
I = (4/5)(4/3) = 16/15 = 1.0667 is approx 1.1 billion
=======================
Cheers,
Stan H.
|
Graphs/121515: This question is from textbook algebra 1
Hi i need major help on how to solve an equation using the substitution method the equation is as follows {3x + y = 21,
10x +5y =65
1 solutions
Answer 89161 by stanbon(57361) on 2008-01-21 09:45:29 (Show Source):
You can put this solution on YOUR website!3x + y = 21,
10x +5y =65
---------------
Solve the 1st equation for "y": y = -3x+21
Substitute into the 2nd equation after dividing thru by 5
2x+y = 13
2x+(-3x+21)=13
-x=-8
x = 8
--------
Substitute into y = -3x+21 to solve for "y":
y = -3*8+21
y = -24+21
y = -3
============
Cheers,
Stan H.
|
Probability-and-statistics/121514: Please help this needs to be done by tonight January 21 and I'm lost
If you use Excel, submit a single Excel attachment with labeled tabs; please do not submit multiple Excel attachments. A PowerPoint attachment is OK, too. I’ll deduct a point for every extra attachment.
2 - Research at the University of Toledo indicates that 50 percent of the students change their major area of study after their first year in a program. A random sample of 100 students in the College of Business revealed that 48 had changed their major area of study after their first year of the program. Has there been a significant decrease in the proportion of students who change their major after the first year in this program? Test at the .05 level of significance.
1 solutions
Answer 89160 by stanbon(57361) on 2008-01-21 09:41:07 (Show Source):
You can put this solution on YOUR website!Research at the University of Toledo indicates that 50 percent of the students change their major area of study after their first year in a program. A random sample of 100 students in the College of Business revealed that 48 had changed their major area of study after their first year of the program. Has there been a significant decrease in the proportion of students who change their major after the first year in this program? Test at the .05 level of significance.
---------------------
Ho: p=0.5
Ha: p<0.5
-------------
alpha = 5% implies the critical value is -1.645
-------------
Test Statistic: z(48/100)= (0.48-0.50)/sqrt[0.5*0.5/100]=-0.02/sqrt(0.0025)
=-0.4
-----------
p-value = 35.5%
------------
Conclusion: Fail to reject Ho.
==================================
Cheers,
Stan H.
|
Functions/121447: This question is from textbook intro & intermediate algebra
ok i vaguely remember what the domain is ... which is x ...right? if im wrong here is the problem
what is the domain of x+3over 2x^2-13x+15?
1 solutions
Answer 89126 by stanbon(57361) on 2008-01-20 22:05:39 (Show Source):
You can put this solution on YOUR website!what is the domain of x+3over 2x^2-13x+15?
-------------------
The domain is the set of values "x" can have.
--------------------
Your Problem:
(x+3)/(2x^2-13x+15)
Factor so you can see what values x cannot take:
(x+3)/[(2x^2-10x-3x+15)]
(x+3)/[2x(x-5)-3(x-5)]
(x+3)/[(x-5)(2x-3)]
--------------------
The denominator cannot zero, so
x-5 cannot be zero; x cannot be 5
2x-3 cannot be zero; x cannot be 3/2
------------------------
Domain is all Real Numbers except x = 5, and x=3/2
=======================
Cheers,
Stan H.
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