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checkley75 answered: 3664 problems
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Equations/105828: This is the reflection coefficient formula,
r=(L-O)/(L+O)
I need to solve for L:
please help,
Thank You.
1 solutions

Answer 77026 by checkley75(3666) on 2007-10-23 16:09:11 (Show Source):

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R=(L-0)/(L+0) CROSS MULTIPLY
R(L+0)=L-0
RL=L
RL-L=0
L(R-1)=0
L=0/(R-1)
L=0 ANSWER.

Linear_Equations_And_Systems_Word_Problems/105776: If the inventor charges $4 per unit then her profit for producing and selling x units is given by the function. p(x)= 2.2 5x-700
A. what is her profit if she sells 2000 units?
b. what is her profit is she sells 5000 units?
c. what is the break-even point for sales?
1 solutions

Answer 77024 by checkley75(3666) on 2007-10-23 16:03:46 (Show Source):

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IS THERE A SIGN BETWEEN THE 2.2 & THE 5X???????

Linear-equations/105785: The length of a rectangle is 8 in. more than twice its width. If the perimeter of the rectangle is 64 in., find the width of the rectangle.
1 solutions

Answer 77023 by checkley75(3666) on 2007-10-23 16:01:09 (Show Source):

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2L+2W=PERIMETER.
L=3W+8
2(3W+8)+2W=64
6W+16+2W=64
8W=64-16
8W=48
W=48/8
W=6CM FOR THE WIDTH.
L=3*6+8
L=18+8
L=26 CM FOR THE LENGTH.
PROOF
2*26+2*6=64
52+12=64
64=64

Miscellaneous_Word_Problems/105824: The length of a rectangle is 8cm more then 3 times the width. The perimeter of the rectangle is 64cm. What are the dimensions of the rectangle?
1 solutions

Answer 77021 by checkley75(3666) on 2007-10-23 15:56:53 (Show Source):

Linear-systems/105803: 3x-5y=7
-9x+15y=-21
solve for x and y
1 solutions

Answer 77019 by checkley75(3666) on 2007-10-23 15:48:32 (Show Source):

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3X-5Y=7
-5Y=-3X+7
Y=-3X/-5+7/-5
Y=3X/5-7/5 (RED LINE)
-9X+15Y=-21
15Y=9X-21
Y=9X/15-21/15
Y=3X/5-7/5 (GREEN LINE)
THESE TWO EQUATIONS ARE IDENTICAL THEREFORE THERE IS NO UNIQUE SOLUTION.
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y+=+3x%2F5+-7%2F5%2C+y+=+3x%2F5+-7%2F5%29+

+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y+=+3x%2F5+-7%2F5%2C+y+=+3x%2F5+-7%2F5%29+

(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = 3x/5 - 7/5 and y = 3x/5 -7/5).

expressions/105815: This question is from textbook Algerbra 1 Concepts and Skills
Evaluate the expression for the given value
of the variiable.
3x+14 when x=4
1 solutions

Answer 77018 by checkley75(3666) on 2007-10-23 15:40:43 (Show Source):

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3*4+14=12+14=26 ANSWER.

Problems-with-consecutive-odd-even-integers/105819: twice the greater of two consecutive odd integers is thirteen less than three times the lesser number?
1 solutions

Answer 77017 by checkley75(3666) on 2007-10-23 15:38:05 (Show Source):

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LET X & X+2 BE THE 2 ODD INTEGERS.
2(X+2)=X+13
2X+4=X+13
2X-X=13-4
X=9 ANSWER FOR THE SMALLER INTEGER.
9+2=11 IS THE LARGER INTEGER.
PROOF
2(11)=9+13
22=22

Percentage-and-ratio-word-problems/105820: I could use some help please.I am taking an on line couase and this did not come out of my text book. It came off my on line test.

The question is For the following function,C computes the cost in millions of dollars of implementing a city recycling project when x percent of the citizens particapte. C(x)=1.5x/100-x. Using this model approximately what is the cost if 60% ofthe citizens participate?
This is what I tried. C(60%)=1.5(60%)/100-60%, .9/66.66=.014 C=.014
Thank You for your help.
I found that I am totally lost
1 solutions

Answer 77016 by checkley75(3666) on 2007-10-23 15:32:48 (Show Source):

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C(.6)=1.5*.6/(100-.6)
C(.6)=.9/99.4
C(.6)=.009 MILLION IS THE COST.
OR
C(.6)=1.5*.6/(100-60)
C(.6)=.9/.4
C(.6)=2.25 MILLION IS THE COST.

Mixture_Word_Problems/105816: How much pure acid should be mixed with 2 gallons of a 50% acid solution in order to get an 80% acid solution?
1 solutions

Answer 77012 by checkley75(3666) on 2007-10-23 15:18:46 (Show Source):

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sorry for the mistake. I used 5% instead of 50%.
below is the corrected solution & 3 is the answer.
---------------------------------------------------------------------
.5*2+X=.8(X+2)
1+X=.8X+1.6
X-.8X=1.6-1
.2X=.6
X=.6/.2
X=3 GALLONS NEEDED OF THE PURE ACID.
PROOF
.5*3+3=.8(3+2)
1.5+3=.8*5
4=4

Mixture_Word_Problems/105817: Melissa invested a sum of money at 3% annual simple interest. She invested three times that sum at 5% annual simple interest. If her total yearly interest from both investments was $7200, how much was invested at 3%?
1 solutions

Answer 77011 by checkley75(3666) on 2007-10-23 15:13:10 (Show Source):

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.03X+.05(3X)=7200
.03X+.15X=7,200
.18X=7,200
X=7,200/.18
X=40,000 IS THE AMOUNT INVESTED @ 3%
3*40,000=120,000 INVESTED @ 5%
PROOF
.03*40,000+.05*120,000=7200
1,200+6,000=7,200
7,200=7,200

Divisibility_and_Prime_Numbers/105804: I don't know how to do this question.
Factor the monomial of the following.
8a2b,30x2y2, 45m3n2,84b2c3d.
The 2's and 3's are to the power, but I don't know how to display that on the computer. I don't know what monomial is, either.
1 solutions

Answer 77009 by checkley75(3666) on 2007-10-23 15:08:32 (Show Source):

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8A^2B=4*2*A*A*B THESE ARE ALL THE FACTORS.
30*X^2Y^2=2*3*5*X*X*Y*Y.
45M^3N^2=3*3^5*M*M*M*N*N
84B^2C^3D=2*2*3*7*B*B*C*C*C*D

Average/105450: 1) 3/16= (?)% x 3/4

2) 5.5/20%=

3) slove for N. N/3=6/9
I need help in trying to solve these probelms, thank you.
1 solutions

Answer 76784 by checkley75(3666) on 2007-10-21 18:47:55 (Show Source):

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3/16=X*3/4 DIVIDE BOTH SIDES BY 3/4
X=(3/16)/(3/4) NOW INVERT THE DENOMINATOR & MULTIPLY
X=3/16*4/3
X=12/48
X=1/4 OR .25 OR 25% ANSWER.
----------------------------------------
5.5/20%
5.5/.2
2.75 ANSWER.
--------------------------------
N/3=6/9 CROSS MULTIPLY
9N=18
N=18/9
N=2 ANSWER.

Linear-equations/105451: A chemist has a 25% and a 50% acid solution. How much of each solution should be used to form 200 mL of a 35% acid solution?

1 solutions

Answer 76782 by checkley75(3666) on 2007-10-21 18:39:57 (Show Source):

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.50X+.25(200-X)=.35*200
.50X+50-.25X=70
.25X=70-50
.25X=20
X=20/.25
X=80 ML OF 50% SOLUTION.
200-80=120 ML OF 30& SOLUTION.
PROOF
.50*80+.25*120=.35*200
40+30=70
70=70

Equations/105498: 2/9X = 1/7
round to hundredths
1 solutions

Answer 76781 by checkley75(3666) on 2007-10-21 18:33:56 (Show Source):

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(2/9)X=1/7 CROSS MULTIPLY
7*2X=9
14X=9
X=9/14
X=.64

Inequalities/105500: On an NBA team the two forwards measure 6'8" and 6'6" and the two guards measure 6'0" and 5'9" tall. How tall a center should they hire if they wish to have a starting team average height of at least 6'5"?
1 solutions

Answer 76780 by checkley75(3666) on 2007-10-21 18:31:14 (Show Source):

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6-8
6-6
6-0
5-9 NOW ADD
-----------------------
23-23 OR WE HAVE 23 FEET 23 INCHES OR 24 FEET 11 INCHES.
TO AVERAGE 6-5 FOR ALL 5 PLAYERS WE NEED A TOTAL OF
5(6-5)=30-25 OR 30 FEET 25 INCHES OR 32 FEET 1 INCH
NOW SUBTRACTING WHAT WE HAVE (24-11) FROM WHAT WE NEED (32-1) WE GET
32-1 WHICH HAS TO BE CONVERTED TO
31-13 SO WE CAN SUBTRACT.
-(24-11)
-----------------
7-2 IS WHAT WE NEED FOR THE CENTER.
PROOF:
6-8
6-6
6-0
5-9
7-2 NOW ADD THE TEAM HEIGHTS
--------------
30-25 OR 32+1 WHICH IS EXACTLY WHAT WE NEED
32*12+1=5*77 (CONVERTING FIGURES TO INCHES)
384+1=385

Equations/105495: 3x2-6x + 9
x= -2
(thats suppose to be square x (x2) not sure how to show it that way
1 solutions

Answer 76779 by checkley75(3666) on 2007-10-21 18:18:23 (Show Source):

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3X^2-6X+9
3*-2^2-6*-2+9
3*4+12+9
12+12+9=33 ANSWER.

expressions/105480: -8(2n-4)+5
1 solutions

Answer 76778 by checkley75(3666) on 2007-10-21 18:10:53 (Show Source):

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-8(2N-4)+5
-16N+32+5
-16N+37

Finance/105490: Can you please explain the foil system to me I didnt understand it in school?
Thank you,
1 solutions

Answer 76777 by checkley75(3666) on 2007-10-21 18:08:51 (Show Source):

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FOIL IS FIRST, OUTER, INNER & LAST.
THAT'S HOW YOU MULTIPLY TERMS LIKE (X+2)(X-3)
(FIRST+2)(FIRST-3) OR X*X=X*2
(OUTER 2)(X OUTER) OR -3X
(X INNER)(INNER -3) OR 2X
(X LAST)(X LAST) OR 2-3=-6
WITH PRACTICE YOU'LL GET IT.

Word_Problems_With_Coins/105489: This question is from textbook
i have eight more quarters than dimes.if the coins are worth 6.20 how many dimes are there?
1 solutions

Answer 76775 by checkley75(3666) on 2007-10-21 18:01:06 (Show Source):

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Q=D+8
.10D+.25(D+8)=6.20
.10D+.25D+2=6.20
.35D=6.20-2
.35D=4.2
D=4.20/.35
D=12 NUMBER OF DIMES
Q=12+8=20 QUARTERS
PROOF
.10*12+.25*20=6.20
1.20+5.00=6.20
6.20=6.20

Travel_Word_Problems/105482: Tom and John drive 258 miles in 5 hours. Tom drives for the first part, and John drives for the second part. How long did Jon drive for?
1 solutions

Answer 76774 by checkley75(3666) on 2007-10-21 17:52:25 (Show Source):

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T=53mph & J=51mph.
T*H+J(5-H)=258
53H+51(5-H)=258
53H+255-51H=258
2H=258-255
2H=3
H=3/2
H=1.5 HOURS IS TOM'S DRIVING TIME.
5=1.5=3.5 IS JOHN'S DRIVING TIME.
PROOF
53*1.5+51*3.5=258
79.5+178.5=258
258=258

Equations/105465: The states of Hawaii and Pennsylvania spend a total of $60.9 million for tourism. The state of Hawaii spends 8.1 million less than twice the amount of money that Pennsylvania spends.
Find the amount that each state spends on tourism
1 solutions

Answer 76773 by checkley75(3666) on 2007-10-21 17:48:24 (Show Source):

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LET X BE THE SPENDING FOR PENN.
THEN THE SPENDING FOR HAWAII=2X-8.1
TOGETHER THEY SPEND 60.9.
THUS WE HAVE X+(2X-8.1)=60.9
X+2X-8.1=60.9
3X=60.9+8.1
3X=69
X=69/3
X=$23 MILLION IS SPENT BY PENN.
2*23-8.1=46-8.1= 37.9 MILLION IS SPENT BY HAWAII.
PROOF
23+37.9=60.9
60.9=60.9

expressions/105479: -7n+4(-6+3n)

1 solutions

Answer 76771 by checkley75(3666) on 2007-10-21 17:38:46 (Show Source):

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-7N+4(-6+3N)
-7N-24+12N
5N-24

Mixture_Word_Problems/105478: This question is from textbook beginning & Intermediate Algebra
Suppose a chemist is mixing two acid solutions, one of 20% concentration and the other of 30% concentration.Which one of the following concentrations could not be obtaioned?
A. 22% B. 24% C. 28% D. 32%
1 solutions

Answer 76770 by checkley75(3666) on 2007-10-21 17:37:13 (Show Source):

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D)32% BECAUSE THIS IS GREATER THAN EITHER OF THE MIXTURES.
THE MIXTURE MUST BE BETWEEN 20% & 30%.

Equations/105468: 2x
-- = 40
5

1 solutions

Answer 76769 by checkley75(3666) on 2007-10-21 17:34:56 (Show Source):

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2X/5=40 NOW CROSS MULTIPLY
2X=5*40
2X=200 NOW DIVISDE BY 2
X=200/2
X=100 ANSWER.

Percentage-and-ratio-word-problems/105475: determine which two equations represent parallel lines.
a. y= 5/4x+3
b. y= 4/5x+5
c. y= 4/5x-5
d. y= -5/4x+5
1 solutions

Answer 76768 by checkley75(3666) on 2007-10-21 17:32:58 (Show Source):

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B & C HAVE THE SAME SLOPE (4/5) THEREFORE THEY ARE PARALLEL LINES.

Percentage-and-ratio-word-problems/105472: If there are 500 people in a town. 22% have dogs and cats, 44% only have dogs, 28% only have cats. 6% have neither. How many people doesn't have a cat or a dog.
1 solutions

Answer 76766 by checkley75(3666) on 2007-10-21 17:30:07 (Show Source):

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SEEING AS THERE ARE 6% WHO HAVE NEITHER THAN .O6*500=30 PEOPLE HAVE NEITHER DOG NOR CAT.

Graphs/105474: Determine which two equations represent perpendicular lines.
a. y= 9x-3
b. y= 1/9x+3
c. y= -1/9x+3
d. y= 1/9x-3
1 solutions

Answer 76762 by checkley75(3666) on 2007-10-21 17:22:13 (Show Source):

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A & C BECAUSE THEY HAVE SLOPES THAT ARE NEGATIVE RECIPROCALS OF EACH OTHER
9 & -1/9

Exponents/105469: 3x to the negative 6 power y to the negative 5 power
1 solutions

Answer 76761 by checkley75(3666) on 2007-10-21 17:20:45 (Show Source):

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(3X)^-6Y^-5
3^-6X^-6Y^-5 OR
1/(3^6X^6Y^5)
1/(729X^6Y^5)

Quadratic_Equations/105453: The product of two numbers is 5 and the sum of their reciprocals is 9/10. Find the numbers.
1 solutions

Answer 76759 by checkley75(3666) on 2007-10-21 17:14:51 (Show Source):

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XY=5 OR X=5/Y
1/X+1/Y=9/10
NOW REPLACE X BY 5/Y & SOLVE FOR Y IN THE SECOND EQUATON.
1/(5/Y)+1/Y=9/10 NOW INVERT THE DENOMINATOR OF THE FIRST FRACTION.
Y/5+1/Y=9/10 NOW COMBINE THE FRACTIONS.
(Y*2+5)/5Y=9/10 NOW CROSS MULTIPLY
10Y^2+50=45Y
10Y^2-45Y+50=0
5(2Y^2-9Y+10)=0
5(2Y-5)(Y-2)=0
2Y-5=0
2Y=5
Y=5/2 OR 2.5 ANSWER
X*2.5=5
X=5/2.5
X=2 ANSWER.
PROOF
2*2.5=5
1/2.5+1/2=9/10
(5+4)/10=9/10
9/10=9/10

Systems-of-equations/105460: Match the graph with one of the equations.
Crosses at (0,2) & (2,0)

A) y = –x – 2
B) y = x – 2
C) y = –x + 2
D) y = x + 2

1 solutions

Answer 76757 by checkley75(3666) on 2007-10-21 16:40:06 (Show Source):

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FIRST WE FIND THE SLOPE
SLOPE=(Y2-Y1)/(X2-X1)
SLOPE=(0-2)/(2-0)=-2/2=-1
NOW WE SUBSTITUTE ONE SET OF (X,Y) POINTS & SOLVE FOR b THE Y INTERCEPT.
2=-1*0+b
b=2
THUS THE EQUATION IS [Y=-X+2]
THE ANSWER IS C)

Systems-of-equations/105462: One number is 3 less than another. If 7 times the smaller number minus 3 times the larger number is 7, find the two numbers.
1 solutions

Answer 76756 by checkley75(3666) on 2007-10-21 16:34:52 (Show Source):

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X=Y+3
7Y-3X=7
7Y-3(Y+3)=7
7Y-3Y-9=7
4Y=7+9
4Y=16
Y=16/4
Y=4 ANSWER.
X=4=3
X=7 ANSWER.
PROOF
7*4-3*7=7
28-21=7
7=7

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