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Recent problems solved by 'stanbon'
stanbon answered: 57274 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, >>NextRational-functions/79352: I cant figure out how to enter the square root symbol into this program?
But the question reads:
2 sq. root of x + 3 sq. root of y divided by sq. root of x - 4 sq. root of y.
I am supposed to simplify this one. Please help me
1 solutions
Answer 56950 by stanbon(57347)   on 2007-04-23 22:57:39 (Show Source):
You can put this solution on YOUR website!2 sq. root of x + 3 sq. root of y divided by sq. root of x - 4 sq. root of y.
--------
[2sqrtx + 3sqrty] / [sqrtx - 4sqrty]
Multiply numerator and denominator by [sqrtx + 4sqrty] to get:
= [(2sqrtx+3sqrty)(sqrtx+4sqrty)]/[x-16y]
= [2x+12y+11sqrt(xy)]/[x-16y]
=============
Cheers,
Stan H.
|
Probability-and-statistics/79346: Mr. Thibodeaux is teaching probability to his class of 48 students. He has 12 decks of cards and 18 pairs of six-sided dice. He wants to divide his class into equal-sized groups. He plans to give each group the same number of decks of cards and the same number of pairs of dice. He also wants to use all of his manipulatives and to have no more than 20 students in each group. How many equal-sized groups are possible? Explain results please.
1 solutions
Answer 56948 by stanbon(57347) on 2007-04-23 22:45:37 (Show Source):
You can put this solution on YOUR website!The greatest common divisor of 48,12, and 18 is 6
----------
If 6 groups; 8 students in a group ; 2 card decks in each grp ; 3 pair of dice
If 3 groups; 16 students in a grp ; 4 card decks in each grp ; 2 pair of dice
If 2 groups; 24 students in a grp ; 6 card decks in each grp ; 9 pair of dice
============
Note that 2 and 3 are factors of six, the gcd of 48,12, and 18.
Cheers,
Stan H.
|
Complex_Numbers/79297: A dog is tethered to the corner of a ten-foot-by-ten-foot square pen by a leash that is 14 feet long. In how much area outside the pen can the dog roam?
1 solutions
Answer 56943 by stanbon(57347) on 2007-04-23 22:13:51 (Show Source):
You can put this solution on YOUR website!A dog is tethered to the corner of a ten-foot-by-ten-foot square pen by a leash that is 14 feet long. In how much area outside the pen can the dog roam?
-----------
The area of that circle is (pi)14^2
-----------
The area of the ten-foot square pen is 100 sq ft.
--------------------
The area of the part outside the square = (pi)14^2-100 = 515.75 sq ft.
================
Cheers,
Stan H.
|
Expressions-with-variables/79345: Find the constant of variation k m varies directly with n; m=144 when n=8
1 solutions
Answer 56940 by stanbon(57347) on 2007-04-23 21:54:11 (Show Source):
You can put this solution on YOUR website!Find the constant of variation k m varies directly with n; m=144 when n=8
-------
If m varies directly with n, m=kn
The constant of variation is "k".
EQUATION:
144=k*8
k=18
That is the consant of variation.
=======
Cheers,
STan H.
|
Linear-equations/79339: How do I go about finding the slope of of the line through the following pairs of points? (-5, -3) and (-5, 2)
I am guessing that the answer to the second one is -5/2..Am I right? Please explain, Thank You...
1 solutions
Answer 56937 by stanbon(57347) on 2007-04-23 21:51:27 (Show Source):
You can put this solution on YOUR website!It's -5/0
Notice that the x-values are the same on the two points.
So the "change is x" is 0
---------
The line has an "undefined" slope or infinite slope.
It is a vertical line.
=========
You can see this if you plot the two points and draw a line thru them.
========
Cheers,
Stan H.
|
Numbers_Word_Problems/79332: Hi, I've been trying to set up an appropriate system of equations for quite some time, and I've had no luck. The question is as follows;
The sum of the digits of a certain three digit number is nine. The sum of the hundreds and the tens digits is equal to the ones digit minus one. The number, divided by nine, equals three times the ones digit. What is the number? All I have so far is x+y+z=9. Could you show me how to set the problem up please?
1 solutions
Answer 56936 by stanbon(57347) on 2007-04-23 21:48:01 (Show Source):
You can put this solution on YOUR website!The sum of the digits of a certain three digit number is nine. The sum of the hundreds and the tens digits is equal to the ones digit minus one. The number, divided by nine, equals three times the ones digit. What is the number? All I have so far is x+y+z=9. Could you show me how to set the problem up please?
-----------
The number is x(10^2+y(10)+z
The digits are x,y,z
--------
EQUATIONS:
x+y+z=9
x+y=z-1
(100x+10y+z)/9 = 3z
-------------
x+y+z=9
x+y-z=-1
100x+10y-26z=0
==========
Ans: x=1; y=3; z=5
=========
Cheers,
Stan H.
|
Exponential-and-logarithmic-functions/79329: According to the CDC, if one member of the household contracts the chickenpox, 90% of family member who have never had the disease or a vaccine will contract the chickenpox. Suppose four members are exposed for the first time. What is the probability that three or fewer family members contract the chickenpox?
1 solutions
Answer 56934 by stanbon(57347) on 2007-04-23 21:38:02 (Show Source):
You can put this solution on YOUR website!According to the CDC, if one member of the household contracts the chickenpox, 90% of family member who have never had the disease or a vaccine will contract the chickenpox. Suppose four members are exposed for the first time. What is the probability that three or fewer family members contract the chickenpox?
----------
It's a binomial problem with n=4, p=0.9, 0<=x<=3
If you have a TI calculator use binomcdf(4,0.9,3)=0.3439
---------
If you do not have a TI calculator use 1-P(4 contract the chickpox)
=1-4C4 (0.9)^4(0.1)^0= 1-0.6561=0.3439
=============
Cheers,
Stan H.
|
Linear-equations/79316: This question is from textbook
Graph each compound inequality. Due tonight.
4x - 3y < 3 or
2x + y > 2
(Please note that the greater than and less than signs are underlined).
1 solutions
Answer 56931 by stanbon(57347) on 2007-04-23 21:25:49 (Show Source):
You can put this solution on YOUR website!4x - 3y <= 3 or
2x + y >= 2
------------
You first have to graph the EQUALITIES:
y=(1/3)(4x-3=(4/3)x-1
y=-2x+2
-------------
==========================
Now you need to find the half-plane solution set for each INEQUALITY:
Pick a test point that is not on the boundary line y=(4/3)x-1
Pick (0,0)
Substitute that into the INEQUALITY, y>(4/3)x-1 to see if the side of the line
that contains (0,0) satisfies the INEQUALITY:
0>(3/4)*0-1
This is true so the half-plane containing (0,0) is the solution set for
4x - 3y <= 3; shade that half-plane that is above the boundary line.
--------
Pick a test point that is not on the boundary line for y=2x+2.
Pick (0,0)
Substitute that into the INEQUALITY, 2x + y >= 2 :
2*0+0>2; 0>2
That is false so the half-plane that does NOT contain (0,0) is the solution
set for 2x+y>2; shade that half-plane.
------------
Finally, find the intersection of the two shaded half planes to get
the solution for the system of inequalities.
============
Cheers,
Stan H.
|
Linear-systems/79323: A square room has a square rug in it. The area of the room not covered by the rug is 51 sq feet. The sum of the lenght of a side of the rug and the lenght of a side of the room is 17 feet. Find the dimensions of the room.
I know Area=LenghtxWidth and Perimeter is 2Lenght + 2 Width, but I can't figure out this one. Please help.
1 solutions
Answer 56928 by stanbon(57347) on 2007-04-23 21:08:05 (Show Source):
You can put this solution on YOUR website!A square room has a square rug in it. The area of the room not covered by the rug is 51 sq feet. The sum of the lenght of a side of the rug and the lenght of a side of the room is 17 feet. Find the dimensions of the room.
----------
Draw the picture of the square room with the square rug in it.
Hint: put the square in the corner of the square room.
-----------
Let a side of the square rug be x ft.
Let a side of the square room be y ft.
EQUATION:
x+y=17 ft
y=17-x
------------
The area of the square room is y^2=(17-x)^2
The area of the square rug is x^2
-----------
EQUATION:
Area of room - Area of rug = 51 sq ft.
(17-x)^2-x^2=51
17^2-34x+x^2-x^2=51
17^2-51=34x
x=238/34
x=7 ft (the rug is 7'x7'
17-x=17-7=10 (the room is 10'x10')
==============
Cheers,
Stan H.
|
real-numbers/79324: What is 2 to the negative 1.8 power rounded to nearest hundredth?
What is e to the 3.79 power rounded to the nearest hundredth?
1 solutions
Answer 56925 by stanbon(57347) on 2007-04-23 20:53:47 (Show Source):
You can put this solution on YOUR website!What is 2 to the negative 1.8 power rounded to nearest hundredth?
------
2^-1.8=0.28717....
=========
What is e to the 3.79 power rounded to the nearest hundredth?
e^3.79 = 44.256...
==========
Cheers,
Stan H.
|
Rational-functions/79289: Identify all asymptotes and holes in the graph of each rational function:
f(x)= 3x^2+x-4/x^2+2x-3
please help if you can! all i know how to do is to factor the denominator
1 solutions
Answer 56917 by stanbon(57347) on 2007-04-23 17:57:19 (Show Source):
You can put this solution on YOUR website!Identify all asymptotes and holes in the graph of each rational function:
f(x)= 3x^2+x-4/x^2+2x-3
f(x)=[3x^2+4x-3x-4]/[(x+3)(x-1)]
f(x)=[x(3x+4)-(3x+4)]/[(x+3)(x-1)]
f(x)=[(3x+4)(x-1)]/[(x+3)(x-1)]
=============
Since there is an (x-1) factor in the numerator and denominator
f(x) has a hole at x=1.
There is a vertical asymptote at x=-1.
=====================
Cheers,
Stan H.
|
Radicals/79285: Please help!!!!!!
1) (3x+14)^2+25=0
2) 25x^2=13
3) 2(x-5)^2=3
4) x^2+4x+4=7
Thanks!!!!!!
1 solutions
Answer 56915 by stanbon(57347) on 2007-04-23 17:47:02 (Show Source):
You can put this solution on YOUR website!Please help!!!!!!
1) (3x+14)^2+25=0
FYI: a^2+b^2=(a+bi)(a-bi)
Your Problem:
[3x+14+5i][3x+14-5i]
x=(1/3)(-145-5i) or x=(1/3)(-14+5i)
==========================
2) 25x^2=13
x^2=13/25
x=(sqrt13)/5 or x=-(sqrt13)/5
============================
3) 2(x-5)^2=3
(x-5)^2=3/2
(x-5)=sqrt(3/2) or x-5=-(sqrt(3/2))
x=5+(sqrt6)/6 or x=5-[(sqrt6)/6]
=============================
4) x^2+4x+4=7
(x+2)^2=7
(x+2)=sqrt7 or (x+2)=-sqrt7
x=-2+sqrt7 or x=-2-sqrt7
==============
Cheers,
Stan H.
|
Coordinate-system/79260: I have to find the coordinates of the vertex. and then sketch the graph...
the problem is:
y=x^2+6x+12
I'm assuming the x^2 means x sq?
1 solutions
Answer 56906 by stanbon(57347) on 2007-04-23 15:34:30 (Show Source):
You can put this solution on YOUR website!find the coordinates of the vertex. and then sketch the graph...
the problem is:
y=x^2+6x+12
You have a quadratic with a=1, b=6
The vertex is at x=-b/2a=-6/2=-3
The y value when x=-3 is (-3)^2+6*(-3)+12 = 3
The vertex is at (-3,3)
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Cheers,
Stan H.
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Finite-and-infinite-sets/79263: what is the leghnth of the diagonal of a square with area 40.5 square inches?
1 solutions
Answer 56904 by stanbon(57347) on 2007-04-23 15:29:49 (Show Source):
You can put this solution on YOUR website!what is the length of the diagonal of a square with area 40.5 square inches?
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Draw the picture.
Let each side of the square be "x".
Then x^2=40.5
Then, diagonal^2 = side^2 + side^2
diagonal^2 = 40.5 + 40.5 = 81
diagonal = 9 inches
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Cheers,
Stan H.
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Polynomials-and-rational-expressions/79257: Use the remainder theorem to evaluate the function at x=3.
F(x)=4x^3-5x^2+7x+2
1 solutions
Answer 56901 by stanbon(57347) on 2007-04-23 12:18:00 (Show Source):
You can put this solution on YOUR website!Use the remainder theorem to evaluate the function at x=3.
F(x)=4x^3-5x^2+7x+2
Divide by x-3 to get the Remainder which equals f(3);
using synthetic division you get:
=============================
3...4....-5....7....2
... .4....7....28,|,,86
=========================
f(3)=86
Cheers,
Stan H.
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Quadratic_Equations/79245: help me someone please? i am so lost with this.
Construction. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path?
1 solutions
Answer 56892 by stanbon(57347) on 2007-04-23 10:25:06 (Show Source):
You can put this solution on YOUR website!A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path?
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Draw the picture of the garden; Draw the path inside the perimeter of the garden.
Let the width of the path be "x".
Note: The area of the garden is now less than what it was before the
path was built.
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EQUATIONS:
New area of the garden is (30-2x)(20-2x)=4[(15-x)(10-x)]sq. ft.
This remaining garden area is 400 sq ft.
4(15-x)(10-x)=400
(15-x)(10-x)=100
x^2-25x+150=100
x^2-25x+50=0
x=[25+-sqrt(625-4*50]/2
x=[25+-sqrt425]/2
x=[25+-5sqrt17]/2
x=(25+5sqrt17)/2 = 22.81 ft or x=(25-5sqrt17)/2= 2.19 ft
Only reasonable answer = 2.19 ft.
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Cheers,
Stan H.
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Quadratic_Equations/79243: how do i find two consecutive positive integers such that the sum of their squares is 85?
1 solutions
Answer 56884 by stanbon(57347) on 2007-04-23 09:52:36 (Show Source):
You can put this solution on YOUR website!how do i find two consecutive positive integers such that the sum of their squares is 85?
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The consecutive integers are "x" and "x+1".
EQUATION:
x^2+(x+1)^2=85
x^2+x^2+2x+1=85
2x^2+2x+1=85
2x^2+2x=84
x^2+x=42
x^2+x-42=0
(x+7)(x-6)=0
The only positive answer is x=6; then x+1=7
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Cheers,
Stan H.
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Sequences-and-series/79225: A quiz has 8 questions with answer options A and B for each. What is the probability that by pure guess work a student answer at least 6 correctly?
1 solutions
Answer 56883 by stanbon(57347) on 2007-04-23 09:46:49 (Show Source):
You can put this solution on YOUR website!A quiz has 8 questions with answer options A and B for each. What is the probability that by pure guess work a student answer at least 6 correctly?
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It is a binomial problem with n=8, p=1/2, 6<=x<=8
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If you have a Ti calculator use 1- binomcdf(8,1/2,5)= 0.145
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If you do not have a TI you need to figure 8C6(1/2)^6(1/2)2+8C7(1/2)^7(1/2)
+8C8(1/2)8 = 37*(1/2)^8=0.145
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Cheers,
Stan H.
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Inequalities/79190: Graph the solution set of x>5. Please help me with this one. when it ssy graph do that mean I need to draw the line
1 solutions
Answer 56872 by stanbon(57347) on 2007-04-23 00:17:40 (Show Source):
You can put this solution on YOUR website!Graph the solution set of x>5.
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Draw a line, any line.
Pick any point on the line and label it "5".
Draw a small circle around that point.
Draw an arrow going to the right starting at the point x=5.
That is the graph of x>5
Cheers,
Stan H.
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Pythagorean-theorem/79168: This question is from textbook geometry
an escalator lifts people to the secomd floor, 25ft above the first floor. the escalator rises at a 30 degree angle. how far does a person travel from the bottom to the top of the escalator?
1 solutions
Answer 56871 by stanbon(57347) on 2007-04-23 00:13:01 (Show Source):
You can put this solution on YOUR website!an escalator lifts people to the secomd floor, 25ft above the first floor. the escalator rises at a 30 degree angle. how far does a person travel from the bottom to the top of the escalator?
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Draw the picture.
You have a right triangle with side opposite the 30 degree angle being
length 25 ft.
The escalator follows the path of the hypotenuse.
The hypotenuse is twice the side opposite the 30 degree angle or 50 ft.
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Cheers,
Stan H.
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Exponents/79222: This is a homework assignment and I have been trying to solve it with no luck. The problem is as follows:
(x^7y^-4z^0/5^-2x^3y^-8z^-9)^2 All exponents in final answers should be positive. Final answers should have all single connecting signs and be arranged in descending order. This is what I have so far, but do not know if it is right. Homework is due Tuesday, April 24,2007.
(x^7y^-4z^0/5^-2x^3y^-8z^-9)^2
= (x^7x^3/y^45^2y^8z^9)2
=(x^7)^2x^3(2)/(y^4)^2(5^2)^2(y^8)^2(z^9)^2
= x^14x^6/y^85^4y^16z^18
=x^14y^16z^185^4/x^6y^8
=5^4 x^14-6Y^16-8z^18
= 625z^18x^8y^8
Is this correct? If not, what am I doing wrong? Your reply and help is greatly appreciated. Thank you.
1 solutions
Answer 56870 by stanbon(57347) on 2007-04-23 00:07:13 (Show Source):
You can put this solution on YOUR website![(x^7) (y^-4) (z^0) /(5^-2) (x^3) (y^-8) (z^-9)]^2
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= [5^2 (x^4) (y^4) (z^9)]^2
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= 625 x^8 y^8 z^18
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Cheers,
Stan H.
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Rational-functions/79143: Graph the following polynomials by using the zero product property and end behavior.
y= -(x+5)(x-3)(x-6)
y= (x+4)^2(x-1)(x-3)
1 solutions
Answer 56869 by stanbon(57347) on 2007-04-22 23:57:22 (Show Source):
You can put this solution on YOUR website!y= -(x+5)(x-3)(x-6)
The zeroes are x=-5, x=3, x=6
Mark those points on the x-axis.
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If you were to multiply out the right side the highest power term
would be -x^3 and the y=intercept would be at -5*-3*-6=-90
Therefore as x gets larger y gets very negative
So off toward the right of x=6 sketch the curve going down
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Also as x gets more and more negative y gets very positive
So off to the left of x=--5 sketch the curve coming down to the
x-axis from above.
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So, from left to right:
The curve comes down to x=-5
It crosses the x-axis at x=-5
It crosses the y-axis at -90
it crosses the x axis at x=3
It turns around and crosses the x-axis at x=6
It gets more and more negative as x gets more and more positive.
================
Cheers,
Stan H.
y= (x+4)^2(x-1)(x-3)
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Polynomials-and-rational-expressions/79219: I need to see how this was solved: x/x-1 - 2/1-x^2 = 8/x+1
Thank you
1 solutions
Answer 56868 by stanbon(57347) on 2007-04-22 23:45:09 (Show Source):
You can put this solution on YOUR website!I need to see how this was solved: x/x-1 - 2/1-x^2 = 8/x+1
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x/(x-1) + 2/(x^2-1) -8/(x+1)
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lcd is x^2-1 which is (x+1)(x-1)
Write each fraction with the lcd as its denominator:
--------
x(x+1)/lcd +2/lcd -8(x-1)/lcd
Combine the numerators and write over the lcd:
[x^2+x+2-8x+8]/lcd
[x^2-7x+10]/lcd
[(x-2)(x-5)]/[(x+1)(x-1)]
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Cheers,
Stan H.
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Polynomials-and-rational-expressions/79097: c...
is this correct
it is two different fractions both fractions need to be multiplied.
multiply: (3x-30)/(x^2-4x) times (8x)/(10-x)
My answer: (-6)/(x)
PROBLEM #2
Simplify
(m^2)/(8) divdied by (m^5)/(16)
my answer: (2)/(m^4)
1 solutions
Answer 56867 by stanbon(57347) on 2007-04-22 23:38:55 (Show Source):
You can put this solution on YOUR website!multiply: (3x-30)/(x^2-4x) times (8x)/(10-x)
Factor where you can to get:
[3(x-10)/x(x-4)]
Cancel where you can to get:
[3/(x-4)]
Multiply to get:
[-24/(x-4)
====================
PROBLEM #2
Simplify
(m^2)/(8) divdied by (m^5)/(16)
Invert the denominator to get:
(m^2)/8 times 16/(m^5)
Cancel where you can to get:
2/(m^3)
================
Cheers,
Stan H.
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Linear_Equations_And_Systems_Word_Problems/79140: This question is from textbook Algebra:Structure and Method
Find the coordinates of the vertex and the equation of the axis of symmetry of the graph of the eqution. y=6+4x-1/2 x squared
1 solutions
Answer 56865 by stanbon(57347) on 2007-04-22 23:26:51 (Show Source):
You can put this solution on YOUR website!Find the coordinates of the vertex and the equation of the axis of symmetry of the graph of the eqution. y=6+4x-1/2 x squared
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Put the equation in vertex form:
-1/2 x^2 +4x = y-6
(-1/2)(x^2- 8x + 4^2) = y-6-(1/2)*16
(-1/2)(x-4)^2= y-14
Vertex at x=4,y=14
Axis of symmetry is x=4
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Cheers,
Stan H.
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Probability-and-statistics/79182: Sale of eggs that are contaminated with salmonella can cause food poisoning among consumers. A large egg producer takes an SRS of 200 eggs from all the eggs shipped in one day. The laboratory reports that 11 of these eggs had salmonella contamination. Unknown to the producer, 0.2% (two-tenths of one percent) of all eggs shipped had salmonella. In this situation
0.2% is a parameter and 11 is a statistic.
11 is a parameter and 0.2% is a statistic.
both 0.2% and 11 are statistics.
both 0.2 % and 11 are parameters.
1 solutions
Answer 56863 by stanbon(57347) on 2007-04-22 23:17:04 (Show Source):
You can put this solution on YOUR website!0.2% is a statement about the population, so it is a parameter
11 is a statement about the sample, so it is a statistic
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cheers,
Stan H.
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