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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, >>Next
Miscellaneous_Word_Problems/210714: Suppose a fuel mixture is 7% ethanol and 93% gasoline. How much ethanol (in gallons) must you add to one gallon of fuel so that the new fuel mixture is 10% ethanol?
1 solutions
Answer 159184 by stanbon(57967)   on 2009-09-03 11:45:10 (Show Source):
You can put this solution on YOUR website!Suppose a fuel mixture is 7% ethanol and 93% gasoline. How much ethanol (in gallons) must you add to one gallon of fuel so that the new fuel mixture is 10% ethanol?
-------------------------
Equation:
7%ethanol + 100%ethanol = 10%ethanol
0.07(1 gal) + 100%(x gal) = 0.10(1+x)gal
7 + 100x = 10(1+x)
7 + 100x = 10+10x
90x = 3
x = 0.0333.. gallons (amount of 100% ethanol that must be added)
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/210689: The acceleration of a car is proportional tot he hoirsepower of the engine and inversely proportional tot he weight of the passengers
A)Show this relationship as an equation
B)What ahppens to the acceleration of the car if the horsepower of the engine is tripled?
C)What happens tot he acceleration fo the car fi the weight inside is tripled?
1 solutions
Answer 159180 by stanbon(57967) on 2009-09-03 09:57:36 (Show Source):
You can put this solution on YOUR website!The acceleration of a car is proportional tot he hoirsepower of the engine and inversely proportional tot he weight of the passengers
A)Show this relationship as an equation
a = kh/w
-----------------
B)What ahppens to the acceleration of the car if the horsepower of the engine is tripled?
3a = k(3h)/w
----------------------
C)What happens to the acceleration of the car if the weight inside is tripled?
a/3 = kh/(3w)
----------------------
Cheers,
Stan H.
|
Exponents/210686: how would i factor this equation: 2a^2+7a^1-4
1 solutions
Answer 159178 by stanbon(57967) on 2009-09-03 09:49:34 (Show Source):
You can put this solution on YOUR website!factor this equation: 2a^2+7a^1-4
-----------------
Use the AC Method.
a = 2 ; b = 7 ; c = -4
--------------------------
Think of two numbers whose product is AC = 2*-4 = -8
and whose sum or difference is b = 7
========================
The numbers are +8 and -1:
--
Replace the "b" term by 8a - a.
2a^2 +8a - a - 4
---
Factor the 1st two and the last two terms separately:
2a(a+4)-(a+4)
Factor again to get the final answer:
(a+4)(2a-1)
======================
Cheers,
Stan H.
|
Linear-equations/210118: which product represents the solution to the system:
-y+7x=14
-x+4y=1
a)
[1/27 4/27] . [1]
[7/27 1/27] [14]
b)
[-7/3 4/3] . [1]
[-1/3 1/3] [14]
c)
[7/3 -4/3] . [1]
[1/3 -1/3] [14]
d)
[-1/27 -4/27] . [1]
[-4/27 -1/27] [14]
1 solutions
Answer 159131 by stanbon(57967) on 2009-09-02 21:56:01 (Show Source):
You can put this solution on YOUR website!which product represents the solution to the system:
-y+7x=14
-x+4y=1
---------------------
The problem is needlessly confusing. The solution is "a".
=================================================
Cheers,
Stan H.
|
Linear-equations/210120: find the inverse of f(x)=2 sqrt(x+3)
a) f^-1(x)=(x-3/2)^2
b)f^-1(x)= (x+3/2)^2
c)f^-1(x)= 1/2 sqrt(x-3)
d)f^-1(x)= 1/2 sqrt(x+3)
1 solutions
Answer 159126 by stanbon(57967) on 2009-09-02 21:29:33 (Show Source):
You can put this solution on YOUR website!find the inverse of f(x)=2 sqrt(x+3)
---
Interchange x and y then solve for "y":
x = 2sqrt(y+3)
sqrt(y+3) = x/2
y+3 = (x^2/4)
y = (x^2/4)-3
---
That is the inverse but it is not listed as one of your options.
=================================================================
Cheers,
Stan H.
a) f^-1(x)=(x-3/2)^2
b)f^-1(x)= (x+3/2)^2
c)f^-1(x)= 1/2 sqrt(x-3)
d)f^-1(x)= 1/2 sqrt(x+3)
|
Graphs/210588: This question is from textbook algebra 1
please help me solve this problem. y is equal to 3 more than the absolute value of x; x= -2,-1,o,1 and 2
1 solutions
Answer 159120 by stanbon(57967) on 2009-09-02 21:15:20 (Show Source):
You can put this solution on YOUR website!please help me solve this problem. y is equal to 3 more than the absolute value of x; x= -2,-1,o,1 and 2
-------------------------
y = |x| + 3
---
If x = -2 y = 2+3 = 5
If x = -1 y = 1+3 = 4
If x = 0 y = 0+3 = 3
If x = 1 y = 1+3 = 4
If x = 2 y = 2+3 = 5
--------------------------
Cheers,
Stan H.
|
Linear-equations/210158: solve 3y^2+4y-2<= 0
1 solutions
Answer 159119 by stanbon(57967) on 2009-09-02 21:07:46 (Show Source):
You can put this solution on YOUR website!solve 3y^2+4y-2<= 0
-------------------------
Solve the EQUALITY:
y = [-4 +- sqrt(16 - 4*3*-2)]/6
y = [-4 +- sqrt(40)]/6
y = [-4 +- 2sqrt(10)]/6
y = (-2/3)+(1/3)sqrt(10) or y = (-2/3)-(1/3)sqrt(10)
Approximate solutions: y = 0.3874 or y = -1.721
=====================================================
Solve the INEQUALITY:
Draw a number line. Plot the two equality solutions.
Check a value in each of the three intervals formed by those solutions
to see where the solution for the inequality lie.
--------------------
3y^2+4y-2<= 0
Check y = -10 ; 3(-10)^2+4(-10)-2 < 0 ; false
Check y = 0 ; -2 < 0 ; true so solutions in (-1.721,0.3874)
check y = 10 ; 3(10)^2-4(10)-2 < 0 ; false
-------------------------------------------------
Final solution; (-2/3)-(1/3)sqrt(10) <= y <= (-2/3)+(1/3)sqrt(10)
============================================================================
Cheers,
Stan H.
|
Equations/210571: Angle C and Angle D are supplementary. Angle D is four times the measure of Angle C. Find the measure of Angle D and C.
thank you
1 solutions
Answer 159116 by stanbon(57967) on 2009-09-02 20:49:03 (Show Source):
You can put this solution on YOUR website!Angle C and Angle D are supplementary. Angle D is four times the measure of Angle C. Find the measure of Angle D and C.
--------------------------------------------------
C + D = 180
D = 4C
-----------------
Substitute for D to solve for C.
-----
C + 4C = 180
5C = 180
C = 36 degrees
D = 180-36 = 144 degrees
====================================
Cheers,
Stan H.
|
Inequalities/210570: Write each specification as an absolute value inequality...
6.3 <= h <= 10.3
1 solutions
Answer 159105 by stanbon(57967) on 2009-09-02 20:42:01 (Show Source):
You can put this solution on YOUR website!Write each specification as an absolute value inequality...
6.3 <= h <= 10.3
----------------------------
Process: (10.3+6.3)/2 = 16.6/2 = 8.3
------------------------------------------
10.3-8.3 = 2
------------------------------
Absolute:
|h-8.3| <= 2
======================
Cheers,
Stan H.
|
Linear-equations/210564: Write a system of linear equations in two variables having {(-2, 7)} as a solution set. (More than one system is possible.) Make sure that your system has two equations with two variables!
1 solutions
Answer 159086 by stanbon(57967) on 2009-09-02 20:29:48 (Show Source):
You can put this solution on YOUR website!Write a system of linear equations in two variables having {(-2, 7)} as a solution set. (More than one system is possible.) Make sure that your system has two equations with two variables!
-------------------------------------------------
Since:
2*-2 + 3*7 = 17
and
-2 - 2*7 = -16
------------------------
the system:
2x + 3y = 17
x - 2y = -16
---
will have solution (-2,7)
========================================
Cheers,
Stan H.
|
Complex_Numbers/210455: how do you write the expression 2i(5+i)(-2+7i) as a complex number in standard form?
1 solutions
Answer 159082 by stanbon(57967) on 2009-09-02 19:36:22 (Show Source):
You can put this solution on YOUR website!write the expression 2i(5+i)(-2+7i) as a complex number in standard form?
---------------------------------------------------------------
= 2i[-10-7-2i+35i]
---
= 2i[-17+33i]
---
= -66 - 34i
==============================
Cheers,
Stan H.
|
Rational-functions/210537: What is meant by Identify the property that the statement illustraes?
ex. - (-3)(1) = -3 and 1+(3+2)= 1+(2+3)
1 solutions
Answer 159075 by stanbon(57967) on 2009-09-02 18:59:58 (Show Source):
You can put this solution on YOUR website!What is meant by "Identify the property that the statement illustrates"?
------------------------------------------------
- (-3)(1) = -3
----------------
Property: The additive inverse of "a" is "-a"
------------------------------------------------------
1+(3+2)= 1+(2+3)
Property: Real Numbers are commutative over addition.
=============================================================
Cheers,
Stan H.
|
Linear-equations/210408: is the graph of x^2/9 - y^2/25=1 symmetric with respect to the x-axis,neither axis, or both axes.explain please.
1 solutions
Answer 159074 by stanbon(57967) on 2009-09-02 18:51:33 (Show Source):
You can put this solution on YOUR website!is the graph of x^2/9 - y^2/25=1 symmetric with respect to the x-axis,neither axis, or both axes
--------------------------------------
-x can replace x without affecting the graph so symmetric to y-axis
-y can replace y without affecting the graph so symmetric to x-axis
-------------------
Both x and y can be replaced by -x and -y so symmetric to the origin.
=====================================================================
Cheers,
Stan H.
|
Linear-systems/210517: please help me !! I am trying to help my son with an algebra word problem and I do not remember how to do this type of algebraic equation. I do remember: Time = Distance divided by Rate . We have filled in the variables but that is as far as we got. Thanks, here is the question.....
Fastball thrown by.....travels at a speed of 145km/hr toward the batter who is 18.3 meters away. How long does it take the baseball to travel this distance.
Distance divided by Rate = Time
18.3m 145km/hr = t
1 solutions
Answer 159067 by stanbon(57967) on 2009-09-02 18:22:14 (Show Source):
You can put this solution on YOUR website!Fastball thrown by.....travels at a speed of 145km/hr toward the batter who is 18.3 meters away. How long does it take the baseball to travel this distance.
----------------------------------------
Distance divided by Rate = Time
145 km/hr = 145000 meters per hour
----------------------------------------
Equation:
18.3m / 145000 m/hr = 0.0001262...hrs
----
Change to seconds:
0.0001262 hrs = 0.0001262*3600 seconds = 0.4543 seconds
============================================================
Cheers,
Stan H.
|
Numbers_Word_Problems/210519: This question is from textbook Intermediate Algebra
I have tried multiple times to solve this problem, but each time I get the wrong answer ( I've checked in the back of the book).
Question: " The difference of two numbers is 67. The larger number is three less than six times the smaller number. Find the numbers."
I tried solving it like this:
x-y=67
larger number=6y-3
(6y-3)-y=67
The answers in the back of the book says 14 and 81. I am so lost in how they found that answer.
1 solutions
Answer 159059 by stanbon(57967) on 2009-09-02 17:59:11 (Show Source):
You can put this solution on YOUR website!The difference of two numbers is 67. The larger number is three less than six times the smaller number. Find the numbers."
I tried solving it like this:
x-y=67
larger number=6y-3
(6y-3)-y=67
The answers in the back of the book says 14 and 81.
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Since x-y = 67, the "x" must be the larger number.
Equation:
x = 6y-3
-----------------------
Substitute that into x-y=67 to get:
6y-3 - y = 67
5y = 70
y = 14
-------
Substitute that and solve for "x":
x = 6*14 -3
x = 84-3
x = 81
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Cheers,
Stan H.
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Functions/210390: I need help trying to find the difference quotient with this function: 3-5x^2
1 solutions
Answer 159007 by stanbon(57967) on 2009-09-02 13:58:49 (Show Source):
You can put this solution on YOUR website!I need help trying to find the difference quotient with this function: 3-5x^2
-----------------------------------
f(x) = -3x^2 + 3
f(x+h)=-3(x+h)^2 + 3
f(x+h)=-3x^2-6hx-3h^2+3
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f(x+h)-f(x) = -6hx-3h^2
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[f(x+h)-f(x)]h = -6x-3h
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Cheers,
Stan H.
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Numbers_Word_Problems/210394: Find 3 consecutive odd integers such that 3 times the 2nd minus the 3rd is 31 more than the first.
1 solutions
Answer 159006 by stanbon(57967) on 2009-09-02 13:54:14 (Show Source):
You can put this solution on YOUR website!Find 3 consecutive odd integers such that 3 times the 2nd minus the 3rd is 31 more than the first.
---------------------------
1st: 2x-1
2nd: 2x+1
3rd: 2x+3
--------------------------
Equation:
3*(2x+1)-(2x+3) = (2x-1)+31
------------------------------
6x-3 - 2x-3 = 2x+30
---
4x-6 = 2x+30
2x = 36
-----------------
1st: 2x-1 = 35
2nd: 2x+1 = 37
3rd: 2x+3 = 39
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Cheers,
Stan H.
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Percentage-and-ratio-word-problems/210404: of the 958 tornadoes that occurred in the united states during 2006, 25.5% occurred during the month of April. How many tornadoes occurred during april 2006?
1 solutions
Answer 159004 by stanbon(57967) on 2009-09-02 13:46:34 (Show Source):
You can put this solution on YOUR website!of the 958 tornadoes that occurred in the united states during 2006, 25.5% occurred during the month of April. How many tornadoes occurred during april 2006?
-------------------------
0.255*958 = 244.29
Rounding down the answer is 244.
=================================
Cheers,
Stan H.
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Graphs/210405: why is line x=4 a vertical line?
1 solutions
Answer 159002 by stanbon(57967) on 2009-09-02 13:43:57 (Show Source):
You can put this solution on YOUR website!why is line x=4 a vertical line?
---------------------------------------
In a 2-dimentional system x = 4 and the y-values
are unrestricted.
So plot the two points: (4,1) and (4,5)
Then draw a line thru them. It will be a vertical line.
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Cheers,
Stan H.
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percentage/210396: This question is from textbook Longman mathematics for IGCSE book 1
For both sizes of tin for this year calculate the number of grams per penny correct to 4 significant figures. Analyse your answer using percentages. Comment on your result. This table shows contents (in g) and price (in p) for two sizes of tins of baked beans in the UK.
1976 mass (g) 1976 cost (p)
Large tin=794 large tin=28.5
Small tin=142 small tin=7
Please solve my question. It is really urgent. I hope someone would solve it.Thankyou very much indeed.
1 solutions
Answer 159000 by stanbon(57967) on 2009-09-02 13:39:43 (Show Source):
You can put this solution on YOUR website!For both sizes of tin for this year calculate the number of grams per penny correct to 4 significant figures. Analyse your answer using percentages. Comment on your result. This table shows contents (in g) and price (in p) for two sizes of tins of baked beans in the UK.
1976 mass (g) 1976 cost (p)
Large tin=794 large tin=28.5
---
grams per penny = 794/28,5 = 27.86 grams per penny
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Small tin=142 small tin=7
---
grams per penny = 142/7 = 20.29 grams per penny
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The quantitative difference in these prices is 27.86-20.29 = 7.574
The percentage difference is 7.574/20.29 = 0.3733 = 37.33%
==================================================================
Cheers,
Stan H.
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Rational-functions/210400: I have a question regarding a problem. I need to graph x + abs(y) = 3. I have set up a table and have come up with xy points of = 0,3; 1,2; 2,1; 3,0; 4,-1; 5,-2 and 6,-3. Then graphing the following points I come up with a straight line. I am wondering if this is correct. Your feedback is much appreciated.
Lori
1 solutions
Answer 158998 by stanbon(57967) on 2009-09-02 13:25:15 (Show Source):
You can put this solution on YOUR website!I have a question regarding a problem. I need to graph x + abs(y) = 3. I have set up a table and have come up with xy points of = 0,3; 1,2; 2,1; 3,0; 4,-1; 5,-2 and 6,-3. Then graphing the following points I come up with a straight line. I am wondering if this is correct. Your feedback is much appreciated.
---------------------------------------
x + abs(y) = 3
|y| = 3-x
(-3,6), (-2,5), (-1,4), (0,3), (1,2), (2,1), (3,0)
(-3,-6),(-2,-5, (-1,-4),(0,-3),(1,-2),(2,-1)
x cannot be greater than 3 because |y| cannot be negative.
---
Notice that when x < 3, y can have two values.
You need to include that idea in your graphing.
========================================================
Cheers,
Stan H.
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Probability-and-statistics/210381: an integer from 100 through 999 inclusive, is to be chosen at random. What is the probability that the number chosen will have 0 as at least 1 digit?
1 solutions
Answer 158994 by stanbon(57967) on 2009-09-02 13:15:27 (Show Source):
You can put this solution on YOUR website!an integer from 100 through 999 inclusive, is to be chosen at random. What is the probability that the number chosen will have 0 as at least 1 digit?
--------------------------------------
P(at least one zero in 3 digit numbers) = 1-P(no zeroes in 3 digits)
= 1 - 0.9^3
= 1 - 0.729
= 0.271
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Cheers,
Stan H.
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Quadratic_Equations/210401: Give exact and approximate solutions to three decimal places. (x-2)^2=45
1 solutions
Answer 158993 by stanbon(57967) on 2009-09-02 13:09:04 (Show Source):
You can put this solution on YOUR website!Give exact and approximate solutions to three decimal places. (x-2)^2=45
------------------------------------
x-2 = sqrt(45) or x-2 = -sqrt(45)
-----------------------------------------
x = 2+3sqrt(5) or x = 2-3sqrt(5)
============================================
Cheers,
Stan H.
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Probability-and-statistics/210399: A lottery game has balls numbered 1 through 15. What are the odds of selecting an even numbered ball or a 8?
i need help beacsue i am confused how both answers can be the same. numbers 1-15 have 7 even numbers in between meaning this probabilty would be 7:15 but getting an 8 out of 1-15, wouldnt that be 1:8? the choices are between-
A)
15 : -7
B)
7 : 8
C)
7 : 15
D)
8 : 7
1 solutions
Answer 158992 by stanbon(57967) on 2009-09-02 13:05:50 (Show Source):
You can put this solution on YOUR website! A lottery game has balls numbered 1 through 15. What are the odds of selecting an even numbered ball or a 8?
----
P(even or 8) = P(even) + P(8)- P(even and 8)
= 7/15 + 1/15 - 1/15 = 7/15
---------------------------------------------
Cheers,
Stan H.
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I need help because I am confused how both answers can be the same. numbers 1-15 have 7 even numbers in between meaning this probabilty would be 7:15 but getting an 8 out of 1-15, wouldnt that be 1:8? the choices are between-
A)
15 : -7
B)
7 : 8
C)
7 : 15
D)
8 : 7
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Numbers_Word_Problems/210352: Two consecutive odd integers have a product of 99. Find all sets of integers that satisfy this description.
1 solutions
Answer 158956 by stanbon(57967) on 2009-09-02 09:23:58 (Show Source):
You can put this solution on YOUR website!Two consecutive odd integers have a product of 99. Find all sets of integers that satisfy this description.
-----------------
1st: 2x-1
2nd: 2x+1
------------------
Equation:
(2x-1)(2x+1) = 99
4x^2-1 = 99
4x^2 = 100
x^2 = 25
x = 5 or -5
-----------------
If x = 5,
2x-1 = 9
2x+1 = 11
-----------------
If x = -5,
2x-1 = -11
2x+1 = -9
=======================
Cheers,
Stan H.
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Rectangles/210359: Simon drew a rectangle whose width is 6 inches less than its length. The perimeter of the rectangle is 6 feet. What are the dimensions of the rectangle Simon drew?I need length and width in inches! Thanks a Bunch!
1 solutions
Answer 158955 by stanbon(57967) on 2009-09-02 09:19:03 (Show Source):
You can put this solution on YOUR website!6 feet = 72 inches
---------
Simon drew a rectangle whose width is 6 inches less than its length. The perimeter of the rectangle is 6 feet. What are the dimensions of the rectangle Simon drew?I need length and width in inches
--------------------------
Width = L-6
-------------------
Equation:
Perimeter = 2(L + W)
72 = 2(L + L-6)
36 = 2L-6
2L = 42
L = 21 inches (length)
---
W = L-6 = 15 inches (width)
==================================
Cheers,
Stan H.
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Average/210360: The average temperature for a five-day business week was 23 degrees. The temperatures for three of the days were 21 degrees, 30 degrees , and 22degrees respectively. Of the two remaining days, the warmer of the two is 6 degrees more than the cooler of the two. Determine the cooler of the two remaining temperatures.
1 solutions
Answer 158954 by stanbon(57967) on 2009-09-02 09:15:18 (Show Source):
You can put this solution on YOUR website!The average temperature for a five-day business week was 23 degrees. The temperatures for three of the days were 21 degrees, 30 degrees , and 22degrees respectively. Of the two remaining days, the warmer of the two is 6 degrees more than the cooler of the two. Determine the cooler of the two remaining temperatures.
-----------------------
Let the cooler temperature be "x".
Then the warmer is "x+6"
---------------------------------
Equation:
(21+21+21+x+(x+6))/5 = 23
63 + x + 6 = 115
x = 115-69
x = 46 degrees (the cooler day)
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Cheers,
Stan H.
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