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Rectangles/409885: what is the perimeter of a rectangle whose length is 4 ft 8 in and whose width is 2 ft 5 in
1 solutions

Answer 288384 by fractalier(2101) on 2011-02-15 23:29:15 (Show Source):

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P = 2L + 2W =
P = 2(4 ft 8 in) + 2(2 ft 5 in) =
P = 8 ft 16 in + 4 ft 10 in =
P = 12 ft 26 in =
P = 14 ft 2 in

Miscellaneous_Word_Problems/409855: sam invested $2000 at 5.24% annual interest and $3000 at 8.5% annual interest. What percent is he earning on total investment?
1 solutions

Answer 288383 by fractalier(2101) on 2011-02-15 23:27:37 (Show Source):

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In a year, he earned $2000(.0524) = $104.80 plus $3000(.085) = $255, a total of
$359.80 on the $5000 invested. Just divide them...
$359.80 / $5000 = .07196 = 7.196%

test/409853: the carpenter saws a board that is 22 feet long into two pieces. One piece is to be 1 foot longer than twice the length of the shorter piece. Find the length of each piece.
1 solutions

Answer 288382 by fractalier(2101) on 2011-02-15 23:22:52 (Show Source):

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Call the length of the shorter piece x. Then the longer piece will be 1 + 2x.
Together they must be 22 feet...the algebra looks like this:
x + (1 + 2x) = 22
3x + 1 = 22
3x = 21
x = 7
2x + 1 = 15
Your pieces are 7 and 15 feet long.

decimal-numbers/409880: label the place values for the number 191

1 solutions

Answer 288381 by fractalier(2101) on 2011-02-15 23:20:27 (Show Source):

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191 =
1 hundred
9 tens
1 one

decimal-numbers/409881: write 15.014 words.
1 solutions

Answer 288380 by fractalier(2101) on 2011-02-15 23:19:51 (Show Source):

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Fifteen and fourteen thousandths...always use "and" for the decimal point...

decimal-numbers/409882: round 3.74 to the nearest tenth.
1 solutions

Answer 288379 by fractalier(2101) on 2011-02-15 23:18:58 (Show Source):

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3.7 since the digit after the tenths digit is less than five...

Square-cubic-other-roots/409863: what is the simplified form of the expression of the square root of 24 times the square root of 30
1 solutions

Answer 288378 by fractalier(2101) on 2011-02-15 23:18:19 (Show Source):

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Systems-of-equations/409877: solving systems of equations by substitution
-5x+y=-2
-3x+6y=-12
1 solutions

Answer 288377 by fractalier(2101) on 2011-02-15 23:15:49 (Show Source):

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Okay, let's solve the first one for y and substitute that into the second one
-5x+y=-2
-3x+6y=-12
we get
y = 5x - 2
then
-3x + 6(5x - 2) = -12
-3x + 30x - 12 = -12
27x = 0
x = 0
back into eqn #1...
0 + y = -2
y = -2
(0, -2)

Problems-with-consecutive-odd-even-integers/409875: find two consecutive even integers whose sum equals 42. the two integers are?
1 solutions

Answer 288376 by fractalier(2101) on 2011-02-15 23:13:27 (Show Source):

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Let the integers be x and x+2. (Notice they're even)
Now add them and get 42...
x + (x+2) = 42
2x + 2 = 42
2x = 40
x = 20
x + 2 = 22
20 and 22

Linear-systems/409871: what is 9-3t=17+t
1 solutions

Answer 288375 by fractalier(2101) on 2011-02-15 23:11:55 (Show Source):

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Okay, from 9 - 3t = 17 + t, let's get all the t's on one side by adding 3t to both sides...we get
9 = 17 + 4t
Now subtract 17 from both sides...
-8 = 4t
Now divide by 4...
t = -2

Mixture_Word_Problems/409872: How many liters of a 70% alcohol solution must be added to 50 liters of a 40% alcohol solution to produce a 30% alcohol solution?
1 solutions

Answer 288374 by fractalier(2101) on 2011-02-15 23:09:48 (Show Source):

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The setup is this:
x(.70) + 50(.40) = (x+50)(.30)
What a minute...this is impossible...you cannot add a 70% solution to a 40% solution and expect it to be more dilute...trick question!

Systems-of-equations/409866: it takes gary twice as long to mow his lawn as it takes his father to do the same job. if they work together they can complete the job in 1 1/2 hours. how long would it take gary to do the job alone?
1 solutions

Answer 288373 by fractalier(2101) on 2011-02-15 23:07:18 (Show Source):

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The normal setup for a problem like this is:
t%2FA+%2B+t%2FB+=+1

t is the time they work together. A and B are how long they would take working alone. The 1 represents one complete job.
For this problem, we let the first term be Gary...if if it takes Dad A hours, Gary takes 2A...
%283%2F2%29%2F2A+%2B+%283%2F2%29%2FA+=+1

%283%2F2%29%2F2A+%2B+%283%2F2%29%2FA+=+1

Now multiply by 2A and get
3%2F2+%2B+3+=+2A

A = 9/4 = 2 1/4 hours
Therefore it takes Gary 4 1/2 hours alone...

Inequalities/379676: (4/5)x>(2/5)
1 solutions

Answer 269630 by fractalier(2101) on 2010-12-02 14:37:48 (Show Source):

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Okay, from
%284%2F5%29x+%3E+%282%2F5%29

, multiply both sides by 5/4 and get
x+%3E+%285%2F4%29%2A%282%2F5%29

and

Miscellaneous_Word_Problems/379677: A children's store sells a toy racetrack for $94.25. The owner uses a 45% markup based on cost. What was the wholesale cost of the racetrack?
1 solutions

Answer 269629 by fractalier(2101) on 2010-12-02 14:35:45 (Show Source):

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What that means is that the store owner marks up his cost by 45%, so that the final price of the set is 145% of his cost.
Merely dividing $94.25 by 1.45 yields the answer, $65.

Linear-equations/379762: What are the x- and y-intercepts of 2x + 9y = 18?

1 solutions

Answer 269627 by fractalier(2101) on 2010-12-02 14:33:28 (Show Source):

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We find the x-intercept by setting y = 0.
2x + 9(0) = 18
2x = 18
x = 9
We find the y-intercept by setting x = 0.
2(0) + 9y = 18
9y = 18
y = 2

Miscellaneous_Word_Problems/379761: A ball is thrown straight upward from the top of a building 50 feet tall at an initial velocity of 100 feet per second. The equation s=-16^2+100t+50 gives teh heights s of the ball t seconds afer it is thrown. After how many seconds does the ball reach its maximum height?
I started with -100/2(-16) but not sure that is even where to start.
Thank you for your help
Tracy
1 solutions

Answer 269625 by fractalier(2101) on 2010-12-02 14:31:58 (Show Source):

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You were okay.
The key to doing this is to realize that when the ball reaches its maximum height, its velocity is ZERO. We can then find the time it's in the air.
We know v(f) - v(i) = gt. Here v(final) is zero and v(initial) is 100. g = -32.
Therefore -100 = -32t and t = 3.125 seconds.

Number-Line/379694: how do you put x<-9 on a number line.
1 solutions

Answer 269623 by fractalier(2101) on 2010-12-02 14:26:50 (Show Source):

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This means x is less than -9.
Notice that does not include -9, but all numbers less than -9.
So we picture that by an open dot at -9, and then draw an arrow pointing to all points to the left of it, that is, to all points less than -9.

Polynomials-and-rational-expressions/379695: what is xsquared-12x+144 factored completely?
1 solutions

Answer 269622 by fractalier(2101) on 2010-12-02 14:25:01 (Show Source):

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x^2 - 12x + 144 cannot be factored. Please review the problem and restate it.

Age_Word_Problems/379759: A Man is now 3 times as old as his son. He was 30 Years old when the son was born. How old is the son now?
1 solutions

Answer 269621 by fractalier(2101) on 2010-12-02 14:22:57 (Show Source):

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Let m be the man's age and s be the son's age NOW. (always set up age problems in the now...)
Thus m = 3s. We also know he is 30 years older, or m = s + 30.
We can set them equal and get
m = 3s
m = s + 30
Therefore,
3s = s + 30
2s = 30
s = 15

Rectangles/379757: if a square carpet has an area of 9 square meters what is the length of one side?
1 solutions

Answer 269620 by fractalier(2101) on 2010-12-02 14:20:24 (Show Source):

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A square has an area of side-squared, that is, A+=+s%5E2

.
If the area is 9 square meters, we take its square root to find the side.
So sqrt%289%29+=+3

meters.

Problems-with-consecutive-odd-even-integers/379721: the sum of two numbers is 50. The difference between these numbers is 10 than find the numbers

1 solutions

Answer 269618 by fractalier(2101) on 2010-12-02 14:18:56 (Show Source):

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Let's call the two numbers x and y. So,
x + y = 50 and
x - y = 10
We can add these equations and get
2x = 60 (notice the y's drop out)
x = 30
y = 20

Polynomials-and-rational-expressions/379730: Factor out the greatest common factor of 5a(a + 3b) + 4(a + 3b)
1 solutions

Answer 269617 by fractalier(2101) on 2010-12-02 14:17:33 (Show Source):

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Well, from
5a(a + 3b) + 4(a + 3b), we can factor out the (a+3b) and get
(a + 3b)(5a + 4)

Probability-and-statistics/379712: Write the first four terms in the expansion of each of the following.
(a-b)^14
1 solutions

Answer 269615 by fractalier(2101) on 2010-12-02 14:16:25 (Show Source):

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Okay, we can use the binomial theorem for this...
%28a-b%29%5E14

Now work out those coefficients and you're all set...

Linear-systems/379752: What is the linear equation for 4x-2y=-1
1 solutions

Answer 269614 by fractalier(2101) on 2010-12-02 14:11:33 (Show Source):

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What you show, 4x-2y=-1, is a linear equation in standard form. If you need it in slope-intercept form, the most useful form for graphing, we solve for y...
4x - 2y = -1
-2y = -4x - 1
2y = 4x + 1
y = 2x + 1/2

Exponential-and-logarithmic-functions/379727: If log9=0.95 and log2=0.30, then what is log8?
1 solutions

Answer 269612 by fractalier(2101) on 2010-12-02 14:09:38 (Show Source):

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log 8 = log 2^3 = 3 log 2 = 3(.3) = .9

Percentage-and-ratio-word-problems/379719: A man left $72,000 to his wife and son. The ratio of the wife's share to the son's was 5:3. How much did his wife receive?
1 solutions

Answer 269611 by fractalier(2101) on 2010-12-02 14:08:48 (Show Source):

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Since the ratio was 5:3, and we don't know how much that exactly is, we can call their amounts 5x and 3x. Together it must equal $72,000. So...
5x + 3x = 72000
8x = 72000
x = 9000
and the wife's portion is 5x, or $45,000.

Human-and-algebraic-language/379729: an unbiased coin is tossed 5 times. find the probobility that , there are exactly 4 heads
1 solutions

Answer 269610 by fractalier(2101) on 2010-12-02 14:06:31 (Show Source):

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5 coin flips can come up a total of 2^5, or 32 different ways. Only five of those 32 ways have exactly 4 heads...the answer is 5/32.
The proper way is to look at 5%21+%2F%28%284%21%29%281%21%29%29

which equals 5.

real-numbers/379735: 2x/3+2=14
1 solutions

Answer 269607 by fractalier(2101) on 2010-12-02 14:04:21 (Show Source):

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Okay, from
2x%2F3+%2B+2+=+14

,
let us subtract 2 from both sides, then multiply both sides by 3/2...
2x%2F3+=+12

Equations/379737: i am having problems with solving dividing equations here is one of the problems i dont understand 1/2x=3
1 solutions

Answer 269606 by fractalier(2101) on 2010-12-02 14:02:25 (Show Source):

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Not sure whether you mean
%281%2F2%29%2Ax+=+3

Let's go with the first one...
We wish to undo what is being done to x...since it is being multiplied by 1/2, we divide by 1/2 to undo it...we then get
x+=+3%2F%281%2F2%29

Dividing by 1/2 is the same as multiplying by two ("How many half dollars are in three dollars?"), so we get
x = 6

Travel_Word_Problems/379740: One car travels 40 km/hr faster than another. While one travels 150 km, the other goes 350 km. Find the speed of the slower car
1 solutions

Answer 269605 by fractalier(2101) on 2010-12-02 13:57:51 (Show Source):

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The working equation is always distance = rate x time, or d = rt.
If the cars travel for the same time t, and we call the speed of the slower car r, the faster car travels at a speed of r+40.
So
150=rt
350=(r+40)t
Let us solve the first one for t and substitute it into the second, thus solving for r, the speed of the slower car. So...
t = 150/r
and
350=%28r%2B40%29%28150%2Fr%29

km/hr

logarithm/379731: Express as a single logarithm and, if possible, simplify
ln2x+3(lnx-lny)
1 solutions

Answer 269603 by fractalier(2101) on 2010-12-02 13:51:18 (Show Source):

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Okay, from
ln%282x%29+%2B+3%28lnx+-+lny%29

we combine the right part and get
ln%282x%29+%2B+3%2Aln%28x%2Fy%29

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Recent problems solved by 'fractalier'