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Recent problems solved by 'stanbon'
stanbon answered: 57239 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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53010..53039 , 53040..53069 , 53070..53099 , 53100..53129 , 53130..53159 , 53160..53189 , 53190..53219 , 53220..53249 , 53250..53279 , 53280..53309 , 53310..53339 , 53340..53369 , 53370..53399 , 53400..53429 , 53430..53459 , 53460..53489 , 53490..53519 , 53520..53549 , 53550..53579 , 53580..53609 , 53610..53639 , 53640..53669 , 53670..53699 , 53700..53729 , 53730..53759 , 53760..53789 , 53790..53819 , 53820..53849 , 53850..53879 , 53880..53909 , 53910..53939 , 53940..53969 , 53970..53999 , 54000..54029 , 54030..54059 , 54060..54089 , 54090..54119 , 54120..54149 , 54150..54179 , 54180..54209 , 54210..54239 , 54240..54269 , 54270..54299 , 54300..54329 , 54330..54359 , 54360..54389 , 54390..54419 , 54420..54449 , 54450..54479 , 54480..54509 , 54510..54539 , 54540..54569 , 54570..54599 , 54600..54629 , 54630..54659 , 54660..54689 , 54690..54719 , 54720..54749 , 54750..54779 , 54780..54809 , 54810..54839 , 54840..54869 , 54870..54899 , 54900..54929 , 54930..54959 , 54960..54989 , 54990..55019 , 55020..55049 , 55050..55079 , 55080..55109 , 55110..55139 , 55140..55169 , 55170..55199 , 55200..55229 , 55230..55259 , 55260..55289 , 55290..55319 , 55320..55349 , 55350..55379 , 55380..55409 , 55410..55439 , 55440..55469 , 55470..55499 , 55500..55529 , 55530..55559 , 55560..55589 , 55590..55619 , 55620..55649 , 55650..55679 , 55680..55709 , 55710..55739 , 55740..55769 , 55770..55799 , 55800..55829 , 55830..55859 , 55860..55889 , 55890..55919 , 55920..55949 , 55950..55979 , 55980..56009 , 56010..56039 , 56040..56069 , 56070..56099 , 56100..56129 , 56130..56159 , 56160..56189 , 56190..56219 , 56220..56249 , 56250..56279 , 56280..56309 , 56310..56339 , 56340..56369 , 56370..56399 , 56400..56429 , 56430..56459 , 56460..56489 , 56490..56519 , 56520..56549 , 56550..56579 , 56580..56609 , 56610..56639 , 56640..56669 , 56670..56699 , 56700..56729 , 56730..56759 , 56760..56789 , 56790..56819 , 56820..56849 , 56850..56879 , 56880..56909 , 56910..56939 , 56940..56969 , 56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>NextSquare-cubic-other-roots/248486: I am trying to help my child with his homework. The problem is "Gary is going to stain a square board on one side only. The width of the board is 2 YARDS. A half pint of stain covers approx. 30 square FEET. If Gary wants to put on 2 coats of stain, haw many pints of stain dows he need?"
We keep coming up with 2 answers that appear right, depending on if you change the YARDS to FEET at the beginning or end of the equation. What is the proper way to do this problem??
Thank you,
Confused Mom
1 solutions
Answer 181093 by stanbon(57307)   on 2009-12-10 20:16:31 (Show Source):
You can put this solution on YOUR website!I am trying to help my child with his homework.
The problem is "Gary is going to stain a square board on one side only. The width of the board is 2 YARDS.
A half pint of stain covers approx. 30 square FEET.
If Gary wants to put on 2 coats of stain, haw many pints of stain does he need?"
We keep coming up with 2 answers that appear right, depending on if you change the YARDS to FEET at the beginning or end of the equation. What is the proper way to do this problem??
-------------------------------
2 yrds = 6 feet
Area of the board is 6' by 6' = 36 sq feet
Two coats would require you cover 72 sq feet.
-----------------------------------------------
A half pint covers 30 sq ft.
So a pint covers 60 sq ft.
-----------------------------
# of pints needed = 72 sq ft/60 sq ft = 18/15 = 1 1/5 pints
==============================================================
Cheers,
Stan H.
|
Probability-and-statistics/248451: how many versions of a test are required to cover all possible question arrangements if there are 9 open ended questions?
1 solutions
Answer 181089 by stanbon(57307) on 2009-12-10 20:09:03 (Show Source):
You can put this solution on YOUR website!how many versions of a test are required to cover all possible question arrangements if there are 9 open ended questions?
-----------
Ans: 9! = 362,880
Cheers,
Stan H.
===================
|
absolute-value/248423: what would happen to a graph if you take the absolute value of just x in a x,y graph?
the points are (-3,0)(-2,2)(0,1)(1,1)(1,3)
1 solutions
Answer 181080 by stanbon(57307) on 2009-12-10 19:57:30 (Show Source):
You can put this solution on YOUR website!Points on the left side of the y-axis would move
to the right side of the y-axis.
Ex: (-3,0) would move and become (+3,0)
===========================================
Cheers,
Stan H.
|
Polygons/248421: if the measure of each interior angle of a polygon is 140 then how many sides does it have ?
1 solutions
Answer 181032 by stanbon(57307) on 2009-12-10 18:30:32 (Show Source):
You can put this solution on YOUR website!if the measure of each interior angle of a polygon is 140 then how many sides does it have ?
Each exterior is 180-140 = 40 degrees.
360/40 = 9 exterior angles
Therefore there are 9 sides.
Cheers,
Stan H.
|
Polygons/248416: How do you find the number of sides of a regular polygon when only given the measure of the Interior Angle?
1 solutions
Answer 181030 by stanbon(57307) on 2009-12-10 18:28:49 (Show Source):
You can put this solution on YOUR website!How do you find the number of sides of a regular polygon when only given the measure of the Interior Angle?
---
Make use of the fact that the sum of the exterior angles is 360 degrees.
=====================================
Example: If an interior angle is 120, the corresponding exterior angle
is 60.
If the polygon is regular all the exterior angles are 60.
The number of exterior angles is 360/60 = 6
So the number of sides is 6.
=====================================
Cheers,
Stan H.
|
Polygons/248417: How do find the measures of an interior angle and an exterior angle for each regular Polygon? Example....
Number 11. Quadrilateral
Number 12. Pentagon
Number 13. Dodecagon
1 solutions
Answer 181028 by stanbon(57307) on 2009-12-10 18:25:39 (Show Source):
You can put this solution on YOUR website!How do find the measures of an interior angle and an exterior angle for each regular Polygon? Example....
Number 11. Quadrilateral
Each interior/exterior pair is supplementary.
--------------------------------------------------
Number 12. Pentagon
If it is a regular pentagon each exterior angle is 360/5 = 72 degrees
The corresponding interior angles will be 180-72 = 108 degrees.
--------------------------------------------------
Number 13. Dodecagon
If it is a regular regular dodecagon each exterior angle is 360/10
= 36 degrees. The corresponding interior angles will be 180-36 = 144 degrees.
=================================
Cheers,
Stan H.
|
Linear-systems/248391: solve by the elimination method.
5x+2y=-11
7x-3y=17
1 solutions
Answer 181026 by stanbon(57307) on 2009-12-10 18:18:39 (Show Source):
You can put this solution on YOUR website!solve by the elimination method.
5x+2y=-11
7x-3y=17
--------------
Multiply thru 1st by 3 and thru 2nd by 2:
15x + 6y = -33
14x - 6y = 34
--------------------
29x = 1
x = 1/29
--------------
Substitute into 5x+2y = -11 to solve for "y":
5(1/29) + 2y = -11
Multiply thru by 29 to get rid of the denominator:
5 + 58y = -319
58y = -324
y = -162/29
=======================
Cheers,
Stan H.
|
Graphs/248384: how to find solve an equation when it has an undefined slope
1 solutions
Answer 181017 by stanbon(57307) on 2009-12-10 17:45:40 (Show Source):
You can put this solution on YOUR website!how to find solve an equation when it has an undefined slope
--------
If the slope is undefined the equation can be
written in the form x = k where k is some Real Number.
---
The solution is x=k.
------------
Cheers,
Stan H.
|
Expressions-with-variables/248307: 4c= 3d + 3
c= d-1
The book says use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions.
1 solutions
Answer 180952 by stanbon(57307) on 2009-12-10 14:57:30 (Show Source):
You can put this solution on YOUR website!4c= 3d + 3
c= d-1
The book says use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solution or infinitely many solutions.
--------------
Substitute for "c" and solve for "d":
4(d-1) = 3d+3
4d-4 = 3d+3
d = 7
-------------
Since c = d-1, c = 6
==========================
Cheers,
Stan H.
|
Triangles/248305: Leg xy of the right triangle shown in the diagram below is twice as ling as leg yz. if the area of the triangle is 36 cm^2, what is the length, in cm, of leg xy
1 solutions
Answer 180951 by stanbon(57307) on 2009-12-10 14:55:19 (Show Source):
You can put this solution on YOUR website!Leg xy of the right triangle shown in the diagram below is twice as long as leg yz. if the area of the triangle is 36 cm^2, what is the length, in cm, of leg xy
------------
Let yz = x
Then xy = 2x
---------------------
Area = (1/2)bh
36 = x(2x)
18 = x^2
x = 3sqrt(2)cm
----------------
2x = 6sqrt(2)cm
=======================
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/248303: Find the coordinates of the center and the radius of each circle whose equation is given. Then draw the graph.
#31)
I am confused about what to do after expanding the y^2+6y part to (y+6y+9)^2. The "-14x" is also confusing me.
Any help would be greatly appreciated!
1 solutions
Answer 180950 by stanbon(57307) on 2009-12-10 14:51:55 (Show Source):
You can put this solution on YOUR website!Find the coordinates of the center and the radius of each circle whose equation is given. Then draw the graph.
#31)
I am confused about what to do after expanding the y^2+6y part to (y+6y+9)^2. The "-14x" is also confusing me.
-----------------------------
Rewrite:
x^2 + 14x + ? + y^2 + 6y + ? = -50 + ?
---
Complete the square on the x-terms and on the y-terms:
x^2 + 14x + 49 + y^2 + 6y + 9 = -50 + 49 + 9
------------------------------------------------
(x+7)^2 + (y+3)^2 = 8
---------
Center at (-7,-3)
Radius = sqrt(8) = 2sqrt(2)
===============================================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/248299: Peanuts cost $3 per pound, almonds $4 per pound and cashews $8 per pound. How many pounds of each should be used to produce 140 pounds of mixture costing $6 per pound, in which there are twice as many peanuts as almonds?
1 solutions
Answer 180949 by stanbon(57307) on 2009-12-10 14:46:23 (Show Source):
You can put this solution on YOUR website!Peanuts cost $3 per pound, almonds $4 per pound and cashews $8 per pound. How many pounds of each should be used to produce 140 pounds of mixture costing $6 per pound, in which there are twice as many peanuts as almonds?
---------------------------------------------------------------
Equations:
p = 2a
p + a + c = 140
3p + 4a + 8c = 6*140
-------------------------
Substitute into the 2nd and the 3rd equation:
3a + c = 140
10a+8c = 840
--------------------
Multiply thru the 1st Eq by 8:
24a + 8c = 8*140
10a + 8c = 840
-----
Subtract the 2nd from the 1st and solve for "a":
14a = 280
a = 20 (amt. of almonds in the mix)
p = 2a = 40 (amt of peanuts in the mix)
c + 3a = 140
c + 60 = 140
c = 80 (amt of cashews in the mix)
===========================================
Cheers,
Stan H.
|
Probability-and-statistics/248270: What is the probablility of picking a chosen whole number out of 1000 in 10 guesses
1 solutions
Answer 180947 by stanbon(57307) on 2009-12-10 14:30:44 (Show Source):
You can put this solution on YOUR website!What is the probablility of picking a chosen whole number out of 1000 in 10 guesses
-----
Assuming the selections are independent,
P(success) = 1/1000
P(failure) = 999/1000
--------------------------
Your Problem:
Binomial with n=10, p = 1/1000, x=1
P(success in 10 tries) = 1 - P(no success in 10 tries)
---
P(no success in 10 tries) = (999/1000)^10 = 0.9900
------------
P(at least one success in 10 tries) = 1-0.99 = 0.01
=======================================================
Cheers,
Stan H.
|
Trigonometry-basics/248292: Find all the zeros of the function
F(x) = x^3 - 5x^2 +17x - 13
1 solutions
Answer 180946 by stanbon(57307) on 2009-12-10 14:20:03 (Show Source):
You can put this solution on YOUR website!Find all the zeros of the function
F(x) = x^3 - 5x^2 +17x - 13
-----------
Again, x=1 is a zero because f(1) = 0
-------------------------------------------
1)....1....-5....17....-13
.......1.....-4....13...|..0
----------------------------------
Quotient: x^2 - 4x + 13
Remainder: 0
----------------------------
Find the zeroes of x^2-4x+13
x = [4 +- sqrt(16-4*1*13)]/2
---
x = [4 +- sqrt(-36)]/2
---
x = 2+3i or x = 2-3i
==========================
Cheers,
Stan H.
|
Triangles/248295: find all the zeros of the function
f(x) = x^3 - 2x^2 - 5x + 6
1 solutions
Answer 180945 by stanbon(57307) on 2009-12-10 14:14:39 (Show Source):
You can put this solution on YOUR website!find all the zeros of the function
f(x) = x^3 - 2x^2 - 5x + 6
---------
The coefficients add up to zero so x = 1 is a zero.
============
1)....1....-2....-5....6
.......1.....-1....-6..|..0
Quotient: x^2 -x -6
Remainder: 0
==========================
Find the zeroes of x^2-x-6
---
(x-3)(x+2) = 0
x = 3 or x = -2
-------------------------
Solutions: x = 1,x = 3, x = -2
====================================
Cheers,
Stan H.
|
Probability-and-statistics/248281: a box contains 3 defective lights and 5 non-defective lights. The lights are tested one at a time without replacement. What is the probability that the 3 defective bulbs will be found in the first 3 tests?
1 solutions
Answer 180943 by stanbon(57307) on 2009-12-10 14:09:54 (Show Source):
You can put this solution on YOUR website!a box contains 3 defective lights and 5 non-defective lights. The lights are tested one at a time without replacement. What is the probability that the 3 defective bulbs will be found in the first 3 tests?
---------------
P(3 defective) = (3/5)(2/4)(1/3) = 2/20 = 1/10
=====================================================
Cheers,
Stan H.
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Rectangles/248274: 1. Is there a number that 1 compares to such that that number compares to itself plus 1? 1/x = x/x+1
Find me 2 solutions (non factorable)
1 solutions
Answer 180936 by stanbon(57307) on 2009-12-10 13:25:39 (Show Source):
You can put this solution on YOUR website!1/x = x/x+1
Cross-multiply and solve for "x":
x^2 = x+1
x^2-x-1 = 0
x = [1 +- sqrt(1-4*1*-1)]/2
---
x = [1 +- sqrt(5)]/2
--------------------------
x = (1+sqrt(5))/2 or x = (1-sqrt(5))/2
===========================================
Cheers,
Stan H.
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Triangles/248265: A highway that has a 6% grade rises 6 ft vertically for every 100 ft horizontally. Which trigonometric ratio is being used in reporting the 6% grade? Explain why.Draw the answer out.
1 solutions
Answer 180933 by stanbon(57307) on 2009-12-10 13:10:37 (Show Source):
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Money_Word_Problems/248263: How much intrest is earned in 3 years on $3500.00 in an account paying 6% interest compounded quarterly
1 solutions
Answer 180925 by stanbon(57307) on 2009-12-10 12:57:19 (Show Source):
You can put this solution on YOUR website!How much interest is earned in 3 years on $3500.00 in an account paying 6% interest compounded quarterly
-----------------------
A(t) = P(1+(r/n))^(nt)
----------------------------
A(t) = 3500(1+(0.06/4))^(4*3)
A(t) = 4184.66
---
Interest earned is 4184.66-3500 = $684.66
=============================================
Cheers,
Stan H.
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Radicals/248264: Virginia's phone has a range of 1000 ft. Her apartment is 180 ft high (where the base of the phone is located). She must go down and walk on a sidewalk that is 600 ft and turn left and walk 400ft to reach the community pool. Will Virginia be able to use her phone at the pool?
(This one was hard to describe because it had a picture showing the directions she is going and how many feet. The last question I answered from this section used the pythagorean equation to figure the answer but in the figure for this question it was not shaped like a triangle... so I do not know what to do?)
1 solutions
Answer 180924 by stanbon(57307) on 2009-12-10 12:52:22 (Show Source):
You can put this solution on YOUR website!Virginia's phone has a range of 1000 ft. Her apartment is 180 ft high (where the base of the phone is located). She must go down and walk on a sidewalk that is 600 ft and turn left and walk 400ft to reach the community pool. Will Virginia be able to use her phone at the pool?
(This one was hard to describe because it had a picture showing the directions she is going and how many feet. The last question I answered from this section used the pythagorean equation to figure the answer but in the figure for this question it was not shaped like a triangle... so I do not know what to do?)
Her building is on the west, the picture shows and arrow going down her building 180ft then it starts going east 600 ft and the another arrow is pointing north at 400ft.
----------------------
You have a ground-level right triangle with legs of 400 and 600 feet.
Find the ground-level diameter to the base of Virginia's building.
d = sqrt(400^2+600^2)
d = 721.11 ft
--------------------
Now you have a right triangle whose height is 180 ft and ground-level
leg is 721.11 ft.
---
Find the diagonal line from the pool to the phone.
D^2 = 180^2 + 721.11^2
D = 743.24 ft.
=====================
Cheers,
Stan H.
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Quadratic_Equations/248262: Can you please help with these word problems I am terrible at word problems. I listed the problems below along with what I could figure out. Thanks in advance.
Solving Quadratic Equations by Factoring
1. Address book. The perimeter of the cover of an address book
is 14 inches, and the diagonal measures 5 inches. What are
the length and width of the cover?
x^2+14=5^2
x^2+x^2+14=25
2x^2+14=25
-14=-14
2x^2=11 don't know if this is right thus far and where to go from here.
2. Throwing a wrench. An angry construction worker throws
his wrench downward from a height of 128 feet with an
initial velocity of 32 feet per second. The height of the
wrench above the ground after t seconds is given
by S(t)-16t^2-32t+128.
-16(t+4)(t-2)is what I have so far!!
a) What is the height of the wrench after 1 second?
b) How long does it take for the wrench to reach the
ground?
1 solutions
Answer 180923 by stanbon(57307) on 2009-12-10 12:49:28 (Show Source):
You can put this solution on YOUR website!Solving Quadratic Equations by Factoring
1. Address book. The perimeter of the cover of an address book
is 14 inches, and the diagonal measures 5 inches. What are
the length and width of the cover?
---
Equations:
P = 2(L + W)
L^2 + W^2 = 5^2
---------------------
7 = L + W
L = 7-W
----------------
Substitute for "L" and solve for "W":
(7-W)^2 + W^2 = 25
49 - 2W + 2W^2 = 25
2w^2 - 2w + 24 = 0
w^2 - w + 12 = 0
(w-4)(w+3) = 0
Positive solution:
W = 4 (width)
---
Then L = 3 (length)
=========================
2. Throwing a wrench. An angry construction worker throws
his wrench downward from a height of 128 feet with an
initial velocity of 32 feet per second. The height of the
wrench above the ground after t seconds is given
by S(t)= -16t^2-32t+128.
-16(t+4)(t-2)is what I have so far!!
a) What is the height of the wrench after 1 second?
Solve S(1) = -16-32+128 = -48+128 = 80 ft.
------------------------------------------------
b) How long does it take for the wrench to reach the
ground?
When the wrench is on the ground S(t) is zero.
So -16t^2-32t+128 = 0
-16(t+4)(t-2) = 0
Positive solution:
t = 2 seconds
======================
Cheers,
Stan H.
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Proportions/248248: Hello, kind tutor!
Having a work problem concerning dilutions, and therefore ratios.
We took 30 microliters of a stock, and added it to 270 microliters of saline to make 300 microliters of a 1:10 dilution. We then took this 300 microliters and added 100 microliters of another solution to that to form 400 microliters total.
2 questions regarding this: What would the second dilution (300 microliters + 100 microliters) be considered? 3:4?
And, what would the final dilution be?
My boss and another coworker said it would end up being 1:13.3, (roughly 1:13), but I could not understand how they arrived at that number.
Thank you very much for your kind assistance,
Lauren
1 solutions
Answer 180920 by stanbon(57307) on 2009-12-10 12:32:27 (Show Source):
You can put this solution on YOUR website!Having a work problem concerning dilutions, and therefore ratios.
-----------------------------
We took 30 microliters of a stock, and added it to 270 microliters of saline to make 300 microliters of a 1:10 dilution.
We then took this 300 microliters and added 100 microliters of another solution (with no active ingrediant) to that to form 400 microliters total.
2 questions regarding this: What would the second dilution (300 microliters + 100 microliters) be considered? 3:4?
And, what would the final dilution be?
-----------------------
Equation:
active + active = active
0.10*300 + 0*100 = x(300+100)
30 + 0 = 400x
x = 30/400
x = 3/40
The ratio of active ingrediant to non-active in the final solution is 3:40
or 1:13 1/3
------
Congratualate your co-workers
=================
Cheers,
Stan H.
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Sequences-and-series/248240: Find the third, sixth and eighth terms of the sequence A(n) = 6 + (n - 1)(-2). Step by step please, how do I get there ?
1 solutions
Answer 180916 by stanbon(57307) on 2009-12-10 12:03:47 (Show Source):
You can put this solution on YOUR website!Find the third, sixth and eighth terms of the sequence A(n) = 6 + (n - 1)(-2). Step by step please, how do I get there ?
---------------------
A(n) = 6 + (n - 1)(-2)
A(3) = 6 + 2(-2) = 2
A(6) = 6 + 5(-2) = -4
A(8) = 6 + 7(-2) = -8
--------------------------
Cheers,
Stan H.
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Polynomials-and-rational-expressions/248231: 1).
Factor the following:
y3 - 1
2). What is the answer from the following?
(6y4 + 15y3 + 28y + 6) ÷ (y + 3)
3).Find all the numbers for which the rational expression below is NOT defined:
x^2-16/x^2-7x+12
4). simplify
1 1
--------------------------- + ------------------------------
a2 + 7a + 12 a2 + a - 6
--------------------------------------------------------------------------------
1 1
--------------------------- + ------------------------------
a2 + 2a - 8 a2 + 5a + 4
1 solutions
Answer 180908 by stanbon(57307) on 2009-12-10 11:09:54 (Show Source):
You can put this solution on YOUR website!1).
Factor the following:
y^3 - 1
---
(y-1)(y^2+y+1)
======================
2). What is the answer from the following?
(6y^4 + 15y^3 + 28y + 6) ÷ (y + 3)
Synthetic Division:
-3)....6....15.....0....28....6
........6.....-3....9.....1...|..3
Quotient: 6x^3 - 3x^2 + 9x + 1
Remainder: 3
============================
3).Find all the numbers for which the rational expression
below is NOT defined:
x^2-16/x^2-7x+12
---
Solve: x^2-7x+12 = 0
(x-6)(x+3) = 0
x = 6 or x = -3
Not defined for x = 6 or x = -3
--------------------------------------
4). simplify
1 1
---------------- + -----------
a^2 + 7a + 12 a^2 + a - 6
]--------------------------------------------------------------------------------
1 1
--------------------------- + ------------------------------
a^2 + 2a - 8 a^2 + 5a + 4
===============================================================================
{1/[(a+3)(a+4)] + 1/[a+3)(a-2)]} / {1/[(a+4)(a-2)] + 1/[(a+4)(a+1)]
-----------------------------------------------------------------------
[(a-2)/lcm + (a+4)/lcm] / [(a+1)/lcm + (a-2)/lcm]
----
[(2a+2)/lcm] / [(2a-1)/lcm]
----
Invert the denominator and multiply:
2(a+2)/[(a+3)(a+4)(a-2)] * [(a+4)(a-2)(a+1)]/(2a-1)
-------------------------------------------------------
Cancel where you can to end up with:
[2(a+2)(a+1)]/[(2a-1)(a+3)]
=============================
Cheers,
Stan H.
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Trigonometry-basics/248226: Can you check my answer to see if im right or which one i need to correct this the last subject. I need to past to graduate.
1). cot 0 = 1/tan0 is a
A. confuction idenity
B. reciprocal idenity
C. inverse idenity
2). cos^-1 0.5 =
A. 1/cos 0
B. cos(90-0)
C. 60
3). sin 20 =
A. 2sin 0 cos 0
B. cos^2 0 - sin^2 0
C. 1- cos^2 0
4). cos 20 =
A. 1 - 2sin^2 0
B. 1- 2cos^2 0
C. cos 0 - sin 0
I got for numbers
1. B
2. c
3. A
4. A
Is im correct or which one do i have to go back and do
1 solutions
Answer 180903 by stanbon(57307) on 2009-12-10 10:41:34 (Show Source):
You can put this solution on YOUR website!Can you check my answer to see if im right or which one i need to correct this the last subject. I need to past to graduate.
1). cot 0 = 1/tan0 is a
A. confuction idenity
B. reciprocal idenity
C. inverse idenity
Ans: B
------------------------
2). cos^-1 0.5 =
A. 1/cos 0
B. cos(90-0)
C. 60
Ans: C
-----------------------
3). sin 20 =
A. 2sin 0 cos 0
B. cos^2 0 - sin^2 0
C. 1- cos^2 0
Ans: A
-----------------------
4). cos 20 =
A. 1 - 2sin^2 0
B. 1- 2cos^2 0
C. cos 0 - sin 0
Ans: A
----------------------
I got for numbers
1. B
2. c
3. A
4. A
Is im correct or which one do i have to go back and do
--------------
Your answers seem correct to me.
--------------
Cheers,
Stan H.
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Probability-and-statistics/248207: Ten percent of adults say oatmeal raisin is their favorite cookie. You randomly select 12 adults and ask each to name his or her favorite cookie. Find the probability that the number who say oatmeal raisin is their favorite cookie is
a. Exactly four
b. At least four
c. Less than four
1 solutions
Answer 180897 by stanbon(57307) on 2009-12-10 10:15:12 (Show Source):
You can put this solution on YOUR website!Ten percent of adults say oatmeal raisin is their favorite cookie. You randomly select 12 adults and ask each to name his or her favorite cookie.
---
Binomial: n=12 ; p=0.10 ; x varies
---
Find the probability that the number who say oatmeal raisin is their favorite cookie is
a. Exactly four
P(x=4) = 12C4(0.10)^4(0.90)^8 = 0.0213
------
b. At least four
P(4 <= x <= 12) = 1 - binomcdf(12,0.1,3) = 0.0256
---------------------
c. Less than four
P(0 <= x <= 3) = 0.9744
===========================
Cheers,
Stan H.
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