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Fombitz answered: 13805 problems
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Expressions-with-variables/335290: Please help me write an algebraic expression for the following word phrase
8 less than the product of a number x and 4
1 solutions

Answer 240341 by Fombitz(13828) About Me  on 2010-08-26 15:30:05 (Show Source):
You can put this solution on YOUR website!

"product of a number x and 4", x%2A4=4x
"8 less than the product of a number x and 4", 4x-8


Radicals/335301: sqrt(1x-1)+8=8x
1 solutions

Answer 240340 by Fombitz(13828) About Me  on 2010-08-26 15:28:53 (Show Source):
You can put this solution on YOUR website!
sqrt%28x-1%29%2B8=8x
sqrt%28x-1%29=8x-8
sqrt%28x-1%29=8%28x-1%29
Square both sides.
x-1=64%28x-1%29%5E2
64%28x-1%29%5E2-%28x-1%29=0
%28x-1%29%2864%28x-1%29-1%29=0
%28x-1%29%2864x-65%29=0
Two solutions:
x-1=0
highlight%28x=1%29
.
.
.
64x-65=0
64x=65
highlight%28x=65%2F64%29


Numbers_Word_Problems/335299: How many whole numbers are there, such that if its digits are reversed and then subtracted from the original number, the result is 198?
1 solutions

Answer 240339 by Fombitz(13828) About Me  on 2010-08-26 15:20:59 (Show Source):
You can put this solution on YOUR website!
Let the original number be ABC, where the numerical value is 100%2AA%2B10%2AB%2BC.
The reverse number would be CBA or numerically 100%2AC%2B10%2AB%2BA.
.
.
100A%2B10B%2BC-100C-10B-A=99A-99C=198
A-C=2
A=C%2B2
A, B, and C can take on values from 0 to 9.
For each value of B, there are 8 A,C values.
0B2
1B3
2B4
3B5
4B6
5B7
6B8
7B9
So there would be 10%2A8 or 80 number pairs that meet this criteria.
If leading zeros aren't allowed (like 012/210), then reduce the B values allowed by 1, and then 9%2A8 or 72 number pairs are allowed.


Human-and-algebraic-language/335307: If a car travels 280 miles at 55 mph, how many hours is that?
1 solutions

Answer 240336 by Fombitz(13828) About Me  on 2010-08-26 15:06:46 (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
R%2At=D
t=D%2FR=280%2F55
Finish the calculation to get the answer in hours.


Mixture_Word_Problems/335306: a certain alloy contails 75% copper and a second alloy 35% copper. how many kilograms of the second alloy must be added to 62 kilograms of the first to form an alloy that is 50% copper?
1 solutions

Answer 240335 by Fombitz(13828) About Me  on 2010-08-26 15:05:46 (Show Source):
You can put this solution on YOUR website!
Let A be the amount of 35% alloy.
62%2875%29%2BA%2835%29=%2865%2BA%29%2850%29
4650%2B35A=3250%2B50A
15A=1400
A=280%2F3kg


Square-cubic-other-roots/335297: How do you write this so that there isn't a fraction in a fraction? (I tried to use the formula to make it show up better but it wouldn't work, so hopefully this way appears right)
1
---------
1-(x/y)

Thanks for the help!
1 solutions

Answer 240332 by Fombitz(13828) About Me  on 2010-08-26 14:49:03 (Show Source):
You can put this solution on YOUR website!
Mutliply numerator and denominator by y.
1%2F%281-x%2Fy%29=y%2F%28y%281-x%2Fy%29%29
1%2F%281-x%2Fy%29=y%2F%28y-x%29%29


Probability-and-statistics/335287: Your statistics tutor wants you to determine a confidence interval estimate for the mean score in next exam. In the past the scores have been distributed normally with a mean of 74.2 and a standard deviation of 30.9. A 95% confidence interval if your class has 30 students is
1. (68.72;79.68)
2. (13.64;34.76)
3. (64.92;83.48)
4. (63.14;85.26)
5. (62.66;85.73)
1 solutions

Answer 240326 by Fombitz(13828) About Me  on 2010-08-26 14:34:10 (Show Source):
You can put this solution on YOUR website!
First find the standard error of the mean,
s=sigma%2Fsqrt%28N%29=30.9%2Fsqrt%2830%29=5.642
.
.
(xave-1.96%2As,xave%2B1.96%2As)=(74.2-1.96%2A5.642,74.2%2B1.96%2A5.642)
.
.
(xave-1.96%2As,xave%2B1.96%2As)=(63.14,85.26)


Graphs/335293: Hello the problem I have is "find the domain of the function."
g(x)=1/(6-7x)
Can you tell me if I have the answer right?
x≠6/7
Thank you for your help! :)
1 solutions

Answer 240324 by Fombitz(13828) About Me  on 2010-08-26 14:27:41 (Show Source):
You can put this solution on YOUR website!
Yes, that's correct, x can be any value except x=6%2F7 since that would lead to the undefined division by zero.


Equations/335291: 9(z-3)=12z
1 solutions

Answer 240323 by Fombitz(13828) About Me  on 2010-08-26 14:26:22 (Show Source):


Square-cubic-other-roots/335292: I can't remember how to do this equation correctly... I need to switch it to a fraction
+3x%5E-1+

Thanks for the help!
1 solutions

Answer 240322 by Fombitz(13828) About Me  on 2010-08-26 14:23:52 (Show Source):


Equations/334318: find all solutions for the equation
absolute value of 6v+3 is equal to 15
1 solutions

Answer 240321 by Fombitz(13828) About Me  on 2010-08-26 14:14:17 (Show Source):
You can put this solution on YOUR website!
abs%286v%2B3%29=15
Two solutions: positive and negative.
6v%2B3=15 and 6v%2B3=-15
6v=12 and 6v=-18
v=2 and v=-3


Exponents/334178: how do i write eachproduct using an exponent, then find the value of the power... to 4.4.4.4
1 solutions

Answer 240320 by Fombitz(13828) About Me  on 2010-08-26 14:12:32 (Show Source):
You can put this solution on YOUR website!
4%2A4%2A4%2A4=4%5E%284%29=256 The exponent signifies how many times to multiply the base together.


Linear-equations/334570: what is the line parallel to the line 2x-5y=0 and with a x-intercept of 6?
1 solutions

Answer 240319 by Fombitz(13828) About Me  on 2010-08-26 14:10:36 (Show Source):
You can put this solution on YOUR website!
The parallel line would have the same left hand side.
2x-5y=a
Find a using the x-intercept information.
When y=0, x=6.
2%286%29-5%280%29=a
a=12
.
.
.
highlight%282x-5y=12%29


Equations/335288: slove for x
7y-2x=9
1 solutions

Answer 240318 by Fombitz(13828) About Me  on 2010-08-26 14:08:34 (Show Source):
You can put this solution on YOUR website!
7y-2x=9
Subtract 7y from both sides.
7y-7y-2x=9-7y
0-2x=9-7y
-2x=9-7y
Divide both sides by %28-2%29.
%28-2x%29%2F%28-2%29=9-7y%2F%28-2%29
%28%28-2%29%2F%28-2%29%29x=-9%2F2%2B%287%2F2%29y
%281%29x=%287%2F2%29y-9%2F2
x=%287%2F2%29y-9%2F2


Square-cubic-other-roots/335286: I need to say what is wrong with this statement:
+sqrt%28x%5E2%2By%5E2%29+=+x%2By+
Would it be that it should be = +x%5E2%2By%5E2+ ?
Thanks for the help!
1 solutions

Answer 240317 by Fombitz(13828) About Me  on 2010-08-26 14:05:40 (Show Source):
You can put this solution on YOUR website!
Square both sides.
x%5E2%2By%5E2=%28x%2By%29%5E2
x%5E2%2By%5E2=%28x%2By%29%28x%2By%29
x%5E2%2By%5E2=x%5E2%2Bxy%2Byx%2By%5E2
x%5E2%2By%5E2=x%5E2%2B2xy%2By%5E2
2xy=0
So the above equality only holds if either x or y or both are zero.
Otherwise you're missing the 2xy term.
sqrt%28x%5E2%2B2xy%2By%5E2%29=sqrt%28%28x%2By%29%5E2%29=x%2By


Proportions/334197: I need to find the LCD for the rational expressions and convert each into equivalent rational expressions with the LCD as the denominator.
Help! I'm stumped! Thank you so very much!
(4)/(x-y),(5x)/(2y-2x)
1 solutions

Answer 240315 by Fombitz(13828) About Me  on 2010-08-26 14:02:04 (Show Source):


Points-lines-and-rays/335282: M is the midpoint of JK (segment) , JM = x/8 and JK = (3x/4) - 6 find MK ?
1 solutions

Answer 240314 by Fombitz(13828) About Me  on 2010-08-26 13:58:17 (Show Source):


Graphs/334204: How do you find the center, radius, and x and y intercepts of 3x^2-3y^2-6x-12y=0?
1 solutions

Answer 240313 by Fombitz(13828) About Me  on 2010-08-26 13:56:22 (Show Source):
You can put this solution on YOUR website!
Complete the square in x and y.
3x%5E2-3y%5E2-6x-12y=0
x%5E2-2x-y%5E2-4y=0
x%5E2-2x%2B1-1=y%5E2%2B4y%2B4-4
%28x-1%29%5E2-1=%28y%2B2%29%5E2-4
%28y%2B2%29%5E2-%28x-1%29%5E2=5
%28y%2B2%29%5E2%2F5-%28x-1%29%5E2%2F5=1
.
.
.
It's not a circle, it's a hyperbola, so it has no radius.
It's centered at (1,2).
.
.
.

.
.
.
x%5E2-2x-y%5E2-4y=0
To find the x-intercepts, set y=0 and solve for x.
x%5E2-2x-y%5E2-4y=0
x%5E2-2x=0
x%28x-2%29=0
(0,0) and (2,0)
.
.
.
To find the y-intercepts, set x=0 and solve for y.
x%5E2-2x-y%5E2-4y=0
-y%5E2-4y=0
y%28y%2B4%29=0
(0,0) and (0,-4)
.
.
.


Quadratic_Equations/335279: Determine the value of y in the following equation: y = sec (3) (0)
1 solutions

Answer 240312 by Fombitz(13828) About Me  on 2010-08-26 13:47:13 (Show Source):
You can put this solution on YOUR website!
Is that the sec(3) multiplied by zero?
y=sec%283%2A0%29=sec%280%29=1%2Fcos%280%29=1%2F1=1


Miscellaneous_Word_Problems/333972: A jar contains quarters and dimes. It contains one more than five times as many quarters as dimes. The money in the jar totals $4.30, how many dimes and quarters are in the jar?
1 solutions

Answer 240311 by Fombitz(13828) About Me  on 2010-08-26 13:46:35 (Show Source):
You can put this solution on YOUR website!
Let D be the number of dimes, Q quarters.
1.Q=5D%2B1
.
.
.
2.10D%2B25Q=430
Substitute eq. 1 into eq. 2,
10D%2B25%285D%2B1%29=430
10D%2B125D%2B25=430
135D=405
highlight%28D=3%29
.
.
.
Then from eq. 1,
Q=5%283%29%2B1
highlight%28Q=16%29
.
.
.
16 quarters and 3 dimes.


Rectangles/334195: the sides of a triangle are in the ratio 3:4:5. what is the length of each side if the permiter of the triangle is 30cm.
1 solutions

Answer 240309 by Fombitz(13828) About Me  on 2010-08-26 13:43:04 (Show Source):
You can put this solution on YOUR website!
3x%2B4x%2B5x=30
12x=30
x=30%2F12=5%2F2
.
.
.
3x=15%2F2cm
4x=10cm
5x=25%2F2cm


Mixture_Word_Problems/335272: Alex received scores of 82 and 88 on his first two quizzes. What average score does he need on the next two quizzes to achieve a final average score of 90, if all four scores are weighted equally?
1 solutions

Answer 240307 by Fombitz(13828) About Me  on 2010-08-26 13:35:40 (Show Source):
You can put this solution on YOUR website!
%2882%2B88%2BC%2BD%29%2F4=90
.
.
170%2BC%2BD=360
.
.
C%2BD=190
.
.
%28C%2BD%29%2F2=95
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.
Alex needs to average a 95 on the final 2 tests.


Linear-systems/335242: Please assist me in solving this system by the addition method.
Thank you.

x + y = 7
x - y = 9
1 solutions

Answer 240306 by Fombitz(13828) About Me  on 2010-08-26 13:33:39 (Show Source):
You can put this solution on YOUR website!
Add the equations together.
x%2By%2Bx-y=16
2x=16
highlight%28x=8%29
Now use either equation to solve for y.
8%2By=7
highlight%28y=-1%29


Linear-systems/335254: Please assist me in solving this system by the addition method.
Thank you.

3x + 5y = -11
x - 2y = 11
1 solutions

Answer 240303 by Fombitz(13828) About Me  on 2010-08-26 13:29:58 (Show Source):
You can put this solution on YOUR website!
1.3x+%2B+5y+=+-11
2.x+-+2y+=+11
Multiply eq. 2 by (-3) and add the equations,
3x%2B5y-3x%2B6y=-11-33
11y=-44
highlight%28y=-4%29
Then use either equation to solve for x.
x-2%28-4%29=11
x%2B8=11
highlight%28x=3%29


Linear-equations/335261: x/x^2-9 + 4/x+3 = 3/x^2-9
My answer is x^2=9
May I please ask for assistance? Thank you in advance.
1 solutions

Answer 240301 by Fombitz(13828) About Me  on 2010-08-26 13:26:47 (Show Source):
You can put this solution on YOUR website!
You don't show any steps of how you got to your answer and it's not a final answer either.
x%5E2=9 cannot be solution since it would lead to a division by zero.
.
.
.
Use the common denominator, x%5E2-9=%28x-3%29%28x%2B3%29
x%2F%28x%5E2-9%29+%2B+4%2F%28x%2B3%29+=+3%2F%28x%5E2-9%29+
x%2F%28x%5E2-9%29+%2B+%284%28x-3%29%29%2F%28%28x%2B3%29%28x-3%29%29+=+3%2F%28x%5E2-9%29+
%28x%2B4%28x-3%29-3%29%2F%28x%5E2-9%29=0
%28x%2B4x-12-3%29%2F%28x%5E2-9%29=0
%285x-15%29%2F%28x%5E2-9%29=0
%285%28x-3%29%29%2F%28%28x-3%29%28x%2B3%29%29=0
5%2F%28x%2B3%29=0
No solution.


Probability-and-statistics/335273: The ages of 25 employees in a company are listed below in a stem and leaf plot. What is the probability that a worker chosen at random will have an age greater than or equal to 30 and less than or equal to 39?
2 0 2 6 7 9
3 0 3 4 5 6 8 8 9 9
4 2 4 5 6 7
5 2 3 4 7
6 1 3
1 solutions

Answer 240299 by Fombitz(13828) About Me  on 2010-08-26 13:21:25 (Show Source):
You can put this solution on YOUR website!
There are 25 total values.
There are 9 values between 30 and 39.
P%2830-39%29=9%2F25


Equations/335269: a bank teller has 125 $10 and $5 bills to start a day. If the total value of the bills was $1000, how many $5 bills did the teller have?
1 solutions

Answer 240298 by Fombitz(13828) About Me  on 2010-08-26 13:19:36 (Show Source):
You can put this solution on YOUR website!
Let T be the number of $10 bills, and F be the number of $5 bills.
1.T%2BF=125
2.10T%2B5F=1000
Multiply eq. 1 by -5 and add the two equations.
-5T-5F%2B10T%2B5F=-625%2B1000
5T=375
highlight%28T=75%29
Then from eq. 1,
75%2BF=125
highlight%28F=50%29
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75 $10 bills and 50 $5 bills.


Circles/335270: The diameter of a circle is 1.3 X 10-^12 meters, then what is its radius.
1 solutions

Answer 240297 by Fombitz(13828) About Me  on 2010-08-26 13:16:25 (Show Source):
You can put this solution on YOUR website!
The radius is 1/2 of the diameter.


Square-cubic-other-roots/335271: log 5th SQRT (10)
1 solutions

Answer 240296 by Fombitz(13828) About Me  on 2010-08-26 13:15:56 (Show Source):


Numeric_Fractions/334255: (a^-3b^2c)^-2/(ab^-2c^3)^-1
1 solutions

Answer 240276 by Fombitz(13828) About Me  on 2010-08-26 11:04:52 (Show Source):
You can put this solution on YOUR website!

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Polynomials-and-rational-expressions/334201: Hi,
I am having issues solving this kind of problems. Any help and suggestion is greatly appreciated.
Simplify the expression, using only positive exponents in your answer:
x^-8+y^-8
---------
x^-1+y^-1
Thanks!
1 solutions

Answer 240274 by Fombitz(13828) About Me  on 2010-08-26 10:59:34 (Show Source):
You can put this solution on YOUR website!
Multiply numerator and denominator by x%5E8y%5E8 and simplify.