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Recent problems solved by 'oberobic'
oberobic answered: 2303 problems
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1 solutions
Answer 341718 by oberobic(2304)   on 2011-10-05 18:10:03 (Show Source):
You can put this solution on YOUR website!Profit = Total Revenue - Total Cost
.
Total Cost = Variable Cost per Unit * Number of Units Produced + Fixed Costs
.
Total Revenue = Sales Price * Units Sold
.
x = number of candles
.
TC = $1/candle * x candles + $100
.
TR = $5/candle * x
.
We want to find the point where TC =TR, which is the break-even point.
.
1x + 100 = 5x
100 = 4x
x = 25
.
So when you sell 25 candles at $5, you achieve $0 profitability.
Of course, that means you have paid your fixed costs ($100).
In turn that means the rest of your candles sales contribute profit.
.
In the following graph, the red line is TC and the green line is TR.
.
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Linear-equations/510120: If x=4, how do you find the slope and y-intercept?
1 solutions
Answer 341711 by oberobic(2304) on 2011-10-05 17:54:53 (Show Source):
You can put this solution on YOUR website!If x=4 there is no slope and there is no y-intercept.
.
x=4 defines a vertical line that goes through x=4.
.
y can take on any value from -infinity to +infinity, but there is no defined slope
.
Recall the slope = change in y / change in x
There is no change in x, so we are attempting to divide by 0.
Dividing by zero is undefined.
.
In slope-intercept form: y = mx+b,
the y-intercept is 'b', defining the point (0,b).
.
But we're told x=4, so there is no point where x=0.
.
Done.
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Linear_Algebra/510119: y=3x-2
How do you get to the slope? is this right?
-2/.6
if this is wrong, how do i get the right answer?
1 solutions
Answer 341706 by oberobic(2304) on 2011-10-05 17:49:08 (Show Source):
You can put this solution on YOUR website!y = mx + b is in slope-intercept form
.
m = slope
m = change in y / change in x
m = coefficient of 'x' in y = mx+b
.
b = y-intercept, which is the point (0, b)
.
so...
.
y = 3x -2
.
slope = 3
A positive slope means the line slants up from the lower left to the upper right.
With m=3, there is a change of 3 in 'y' for a change of 1 in 'x'.
So the line is "rising" 3 times as fast as it is "running."
.
y-intercept = (0,-2)
.
To find the x-intercept, simply set y=0 and solve for 'x'.
.
0 = 3x -2
add 2 to both sides
2 = 3x
so
3x = 2
divide both sides by 3
x = 2/3
.
x-intercept = (2/3, 0)
.
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Numbers_Word_Problems/510110: The sum of two whole numbers is 19. The product of the number is 84. What are the two numbers?
1 solutions
Answer 341705 by oberobic(2304) on 2011-10-05 17:41:47 (Show Source):
You can put this solution on YOUR website!x + y = 19
so
x = 19-y
.
x*y = 84
so
x = 84/y
.
substitute
.
84/y + y = 19
.
multiply both sides by 'y'
.
84 + y^2 = 19y
.
rearrange
.
y^2 -19y +84 = 0
.
factor
.
(x-12)(x-7) = 0
.
x = 12 or x=7
.
which means the other number is either 7 or 12, respectively.
.
12*7 = 84
12+7 = 19
Correct.
.
Answer: The two numbers are 7 and 12.
.
Done.
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Graphs/510113: How do you graph 2x+y=3 and 4x+2y=6
1 solutions
Answer 341703 by oberobic(2304) on 2011-10-05 17:31:28 (Show Source):
You can put this solution on YOUR website!Reformat both equations to slope-intercept form: y=mx+b.
Determine two points on each line.
Draw the two lines.
.
2x + y = 3
y = -2x + 3
(x=0, y= 3)
(x=5, y=-7)
.
4x + 2y = 6
is
2x + y = 3
which is the same line
.
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Travel_Word_Problems/509618: How long will it take you of your going 3 miles per hour, going 2 miles? HELP!
1 solutions
Answer 341515 by oberobic(2304) on 2011-10-04 21:14:59 (Show Source):
You can put this solution on YOUR website!d = r*t is the fundamental distance equation.
.
you need to know 2 of these to calculate the 3rd.
.
3 mph = r
2 mph = r
.
but unless you know 'd', you cannot calculate 't'
.
Say d = 9
.
9 = 3t
t = 9/3 = 3 hr : It takes 3 hr at 3 mph to go 9 miles
.
9 = 2t
t = 9/2 = 4 1/2 : It takes 4 1/2 hr at 2 mph to go 9 miles.
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And so forth.
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Miscellaneous_Word_Problems/509606: Write an equation and solve for the word problem: Rico spent $18.50 to rent a lawn mower. The fee for the first hour was $8. Each additional hour cost $3.50. For how many hours did he rent the mower?
I figured out the answer is 4 hours, but what is the equation that goes with this word problem?
1 solutions
Answer 341513 by oberobic(2304) on 2011-10-04 21:09:02 (Show Source):
You can put this solution on YOUR website!rental is for 'x' hrs
price is 'y'
.
y = 3.5(x-1) + 8
.
y = 3.5x -3.5 + 8
.
y = 3.5x + 4.5
.
He spent 18.50
.
18.50 = 3.5x + 4.5
3.5x = 18.50 -4.5
x = 14/3.5
x = 4
.
check using the facts
hr 1 = 8
hr 2, 3 & 4 = 3.50
3*3.50 = 10.5
8 + 10.5 = 18.5
.
Answer: He rented it for 4 hr.
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Graphs/509549: solve equation for y
-6x+y=11
1 solutions
Answer 341489 by oberobic(2304) on 2011-10-04 20:04:33 (Show Source):
You can put this solution on YOUR website!Solve the equation
-6x +y = 11
for y
.
That means to get it into slope-intercept form: y = mx+b
.
Then you can define two points and draw a line.
.
You also can define the slope, y-intercept, and x-intercept.
.
To get started,
add 6x to both sides
.
y -6x + 6x = 11 + 6x
.
y = 6x + 11
.
There is no need to go further.
.
The slope is 6, which means it goes steeply up to the right. There is a change of 6 in y for a change of 1 in x.
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The y-intercept occurs when x = 0, so you can see it is the point: (0, 11).
'b' is the y-intercept
.
The x-intercept occurs when y = 0. If x=-11/6, then 6x = -11.
y = 6(-11/6) + 11
y = 0
This defines the point (-11/6,0).
.
With two points you can draw a straight line.
You also can check the intercepts to see if they cross where they are supposed to.
.
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Linear-equations/509540: solve the problem:
The worlds largest taco contained approximately 1 kg of onion for every 6.6 kg of grilled steak. The total weight of these two ingredients was 617.6 kg. To the nearest tenth of a kilogram, how many kilograms of each ingredient were used to make the taco?
I am struggling with turning the story problem into the actual equation.
1 solutions
Answer 341488 by oberobic(2304) on 2011-10-04 20:02:34 (Show Source):
You can put this solution on YOUR website!The ratio of onions to grilled steak was 1:6.6 kg.
.
In this case, 'k' is simply an constant multiplier.
.
1k + 6.6k = 617.6
.
7.6k = 617.6
.
k = 617.6/7.6
.
k = 81.3
.
So the taco contained about 81.3 kg of onions and 6.6*81.3 = 536.3 kg of grilled steak.
.
Done.
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Polynomials-and-rational-expressions/509424: A circular pool is surrounded by a brick walkway 3m wide. Find the radius of the pool if the area of the walkway is 198 m^2.
The walkway is 3 m wide, and A of walkway = 193 m^2....
I think I need to find the area of the entire circle and subtract the area of the walkway from it, and figure out the radius from there, but I have no idea how to do so.
I'D LOVE any additional advice on polynomial word problems - rate-time-distance problems, problems involving area...
Any tips, please??
Much appreciated! Thank you !!
1 solutions
Answer 341464 by oberobic(2304) on 2011-10-04 19:11:20 (Show Source):
You can put this solution on YOUR website!The walkway and pool are circular, so the inside circumference of the walkway is less than the outside circumference. So, you can take the area of the inner circle (which is the pool, actually) and subtract it from the area of the outer circle.
.
pi*r^2 = area of the pool
.
pi*(r+3)^2 = area of the pool + walkway
.
pi*r^2 = pi*(r+3)^2 - 198
.
pi*r^2 = pi*(r^2 +6r +9) - 198
.
pi*r^2 = pi*r^2 + pi*6r + pi*9 -198
.
0 = pi*6r + pi*9 -198
.
pi*6r + pi*9 = 198
.
pi*(6r + 9) = 198
.
6r + 9 = 198/pi = 63.0253575
.
6r = 63.0253575 -9 = 54.0253575
.
r = 54.0253575/6
.
r = 9.00422624
.
r+3 = radius to outer edge of walkway
.
r+3 = 12.00422624
.
inner area = pi*(9.00422624^2)
inner area = 254.708049
.
outer area = pi*(12.00422624^2)
outer area = 452.708049
.
walkway area = 452.708049 - 254.708049 = 198
.
Correct.
.
Answer: The radius of the pool is 9.00422624 or about 9 meters.
.
Done.
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Functions/509414: how do you find the domain and range of g(x)=(4x-20)/(3x-18)
1 solutions
Answer 341440 by oberobic(2304) on 2011-10-04 17:56:45 (Show Source):
You can put this solution on YOUR website!The domain of g(x) is limited by the denominator. Division by 0 is undefined, so x=6 results in an undefined value.
.
Therefore the domain is all x from -infinity to +infinity, except for x = 6.
The range is -infinity to +infinity.
.
Done.
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Word_Problems_With_Coins/509404: Josiah has three less than twice as many nickles as dimes. If the total value of hsi coins was $1.45 how many of each kind of coin did he have?
1 solutions
Answer 341436 by oberobic(2304) on 2011-10-04 17:53:14 (Show Source):
You can put this solution on YOUR website!n = number of nickels
5n = value of nickels in cents
d = number of dimes
10d = value of dimes in cents
.
n = 2d -3
.
5n + 10d = 145 cents
.
substitute
.
5(2d-3) + 10d = 145
.
10d -15 + 10d = 145
.
20d = 160
.
d = 8
.
n = 2(8) -3
.
n = 13
.
Check the value to see if this is the correct answer.
.
5(13) + 10(8) = 65 + 80 = 145
Correct.
.
Answer: Josiah has 8 dimes and 13 nickels.
.
Done.
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Linear-equations/509400: Find the equation of a line through the point (-1,9) and parallel to 2x-4y=7.
1 solutions
Answer 341428 by oberobic(2304) on 2011-10-04 17:46:40 (Show Source):
You can put this solution on YOUR website!A line parallel to 2x-4y = 7 will have the same slope.
2x-4y = 7
-4y = -2x +7
y = (-2/-4)x + (7/-4)
y = 1/2x - 7/4
.
Slope = 1/2
so the sought equation will have slope = 1/2.
.
y = 1/2x + b
.
We want it go through the point (-1,9),
so we use that point to define 'b'.
.
9 = 1/2(-1) + b
9 = -1/2 + b
b = 9 + 1/2
b = 18/2 + 1/2
.
y = 1/2x + 19/2
.
In the following graph, the first equation is in red, the second is in green.
.
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Problems-with-consecutive-odd-even-integers/508965: find three consecutive odd intergers such that if six times the first is subtracted from the sum of twice the second plus five times the third, the result is 53
1 solutions
Answer 341201 by oberobic(2304) on 2011-10-03 21:46:06 (Show Source):
You can put this solution on YOUR website!x, y and z are three consecutive odd integers.
.
-6x +2y +5z = 53
.
We can redefine the integers to use only one unknown
x
x+2
x+4
.
substitute
.
-6(x) +2(x+2) +5(x+4) = 53
-6x +2x +4 +5x +20 = 53
x + 24 = 53
x = 29
x+2 = 31
x+4 = 33
.
Answer: The three numbers are 29, 31, and 33.
.
Done.
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Word_Problems_With_Coins/508966: A parking meter will accept dimes and quarters only. At the end of the day, the meter attendants collected 55 coins whose total value was $10.75. How many coins of each type where there?
1 solutions
Answer 341197 by oberobic(2304) on 2011-10-03 21:39:22 (Show Source):
You can put this solution on YOUR website!d = number of dimes
10d = value of the dimes in cents
q = number of quarters
24q = value of the quarters in cents
.
d + q = 55
so
d = 55-q
.
10d + 25q = 1075 cents
.
substitute d = 55-q
.
10(55-q) + 25q = 1075
550 -10q + 25q = 1075
15q = 525
q = 35
.
d = 55-q
d = 55-35
d = 20
.
Check to determine if the value is correct.
25(35) = 875 cents
10(20) = 200 cents
875 + 200 = 1075 cents
Correct.
.
Answer: The meter had 35 quarters and 20 dimes.
.
Done.
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Permutations/508959: How many different 4-letter radio call letters can be made using the 26 capital letters of the English alphabet (Examples: WJBR, KDKA, WSTW) if the first letter must be K or W and no letter may be repeated.
1 solutions
Answer 341190 by oberobic(2304) on 2011-10-03 21:31:54 (Show Source):
You can put this solution on YOUR website!The first letter has 2 possibilities: K and W.
The second letter has 24 possibilities given you cannot reuse K or W.
Once you take that letter, then the third letter has only 23 possibilities.
After you pick the third letter, then you only 22 choices for the last letter.
.
2*24*23*22 = 24288
.
BUT in your example you showed WSTW, which suggests the K and the W can be repeated as one of the other three letters. In turn, that means your total patterns are:
.
2*26*25*24 = 31200
.
Done.
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Angles/508930: The supplement of an angle is 26 more than five times its complement. what is the measure of your angle?
1 solutions
Answer 341176 by oberobic(2304) on 2011-10-03 21:14:14 (Show Source):
You can put this solution on YOUR website!A = the angle
C = its complement
C = 90-A
S = its supplement
S = 180-A
.
S = 5*C + 26
.
S = S
so
180-A = 5*C+26
.
substitute C = 90-A
.
180-A = 5(90-A) + 26
.
180-A = 450 -5A + 26
.
180-A = 476 -5A
.
4A = 296
.
A = 74
.
C = 90-74 = 16
.
S = 180-74 = 106
.
Check to see if this solution is the answer.
.
5C + 26 = 5(16) + 26 = 106
Correct.
.
Answer: The angle is 74 degrees.
.
Done.
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Geometry_Word_Problems/508896: Ali paints with watercolors on a sheet of paper 20 in. wide by 15 in. high. He then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 118 in. How wide is the strip of the mat showing around the picture?
1 solutions
Answer 341171 by oberobic(2304) on 2011-10-03 20:57:26 (Show Source):
You can put this solution on YOUR website!p = perimeter of the mat
p = 2(length + width)
p = 118
.
l = 15 + 2x, where x is the width of the strip
w = 20 + 2x
.
2(15+2x+20+2x) = 118
.
30 + 4x +40 + 4x = 118
.
8x + 70 = 118
.
8x = 48
.
x = 6 in, which is the width of the border.
.
Check to ensure the solution is the answer.
.
l = 15 + 12 = 27
w = 20 + 12 = 32
32 + 27 = 59
p = 2*59 = 118
Correct.
.
Answer: The width of the strip showing around the picture is 6 inches.
.
Done.
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Functions/508898: Let f(x)=x^2-4 and g(x)=-5X+3
f(x)= -3x^2+ -4, g(x)=x3+3X^2
1 solutions
Answer 341165 by oberobic(2304) on 2011-10-03 20:27:32 (Show Source):
You can put this solution on YOUR website!OK. But what do you want to do with them?
(f + g)x?
(f - g)x?
(f * g)x?
(f / g)x?
(f o g)x?
.
f(x) = x^2 -4
f(x) = (x-2)(x+2)
.
g(x) = 5x + 3
.
You can graph them. f(x) is red; g(x) is green.
.
.
OR you can set them = to each other.
.
f(x) = g(x)
.
x^2-4 = 5x + 3
subtract 5x from both sides
x^2 -5x -4 = 3
subtract 3 from both sides
x^2 -5x -7 = 0
Which can only be solved using the quadratic equation.
But you can graph it.
.
.
OR you can add them.
.
f(x) + g(x) = (f+g)x
.
f(x) = x^2 -4
g(x) = 5x + 3
.
(f+g)x = x^2 +5x -7
.
So, you need to re-read the question to see what they're asking you do with f(x) and g(x).
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Triangles/508891: The lengths of the three sides of a trianlge are in the ratio 3:5:6. The perimeter of the triangle is 21 cm. How can you find the length of each side of the triangle.
1 solutions
Answer 341163 by oberobic(2304) on 2011-10-03 20:25:25 (Show Source):
You can put this solution on YOUR website!Let 'x' be the unknown measurement.
.
Perimeter of a triangle = sum of sides.
.
3x + 5x + 6x = 21
.
14x = 21
.
x = 21/14 = 3/2
.
3x = 3(3/2) = 9/2
5x = 5(3/2) = 15/2
6x = 6(3/2) = 18/2
.
9/2 + 15/2 + 18/2 = 42/2 = 21
.
The three sides are: 9/2, 15/2 and 18/2
or 4.5, 7.5, and 9.
.
Done.
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Linear-equations/508881: Contains (5,1) and is parallel to y=3
1 solutions
Answer 341161 by oberobic(2304) on 2011-10-03 20:21:54 (Show Source):
You can put this solution on YOUR website!y =3 has a slope=0, which means it is a horizontal line. It contains all x from -infinity to +infinity.
.
A line parallel to it will be horizontal, too.
.
y = 1 will contain all x values from -infinity to +infinity, so it doubtless contains (5,1).
.
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