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robertb answered: 4011 problems
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Travel_Word_Problems/390906: The distance from a star to a planet is 9.1 X 10^18 m. How long does it take light, traveling at 10^16 m/year, to travel from the star to the planet?
1 solutions
Answer 277259 by robertb(4012) About Me  on 2011-01-05 05:04:23 (Show Source):
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%28%289.1%2910%5E18%29%2F10%5E16+=+%289.1%29+10%5E2 years, or 910 years.

Functions/390884: find the domain and range of each relation .
[(-3, -7),(-1, -3),(0,-1),(2,3),(4,7)]
1 solutions
Answer 277258 by robertb(4012) About Me  on 2011-01-05 05:01:08 (Show Source):
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Domain = {-3, -1, 0, 2, 4}
Range = {-7, -3, -1, 3,7}

Inverses/390918: 1/1.4+1/4.7+1/7.10+1/10.13+1/13.16=?
1 solutions
Answer 277257 by robertb(4012) About Me  on 2011-01-05 04:57:53 (Show Source):

Miscellaneous_Word_Problems/390919: Express the area A of a square in terms of its perimeter p
1 solutions
Answer 277255 by robertb(4012) About Me  on 2011-01-05 04:56:10 (Show Source):

Inverses/390917: 1/1.4+1/4.7+1/7.10+1/10.13+1/13.16
1 solutions
Answer 277253 by robertb(4012) About Me  on 2011-01-05 04:54:25 (Show Source):

Inverses/390915: 1/2+1/6+1/12+1/20+1/30...1/n(n+1)
1 solutions
Answer 277252 by robertb(4012) About Me  on 2011-01-05 04:40:24 (Show Source):
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1%2F2%2B1%2F6%2B1%2F12%2B1%2F20%2B1%2F30+...+1%2F%28%28n-1%29n%29+%2B+1%2F%28n%28n%2B1%29%29
=+...+%281%2F%28n-1%29+-+1%2Fn%29+%2B+%281%2Fn+-+1%2F%28n%2B1%29%29
=1+-++1%2F%28n%2B1%29 because of "telescoping" property.

Trigonometry-basics/389458: A box has the dimensions of 2 inches by 3 inches by 4 inches. Determine the approximate angle formed by the diagonal of the 2 X 3 side and the diagonal of the 3 X 4 side to the nearest degree?
1 solutions
Answer 277251 by robertb(4012) About Me  on 2011-01-05 04:33:35 (Show Source):
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Let the length of the base be 4 inches, the width of the base be 3 inches, and the height, 2 inches. Then the measure of the diagonal of the 2x 3 face is sqrt%2813%29, the measure of the diagonal of the 3x 4 face is 5, and the measure of the diagonal of the 2x 4 face is 2sqrt%285%29. The three diagonals form a triangle. Then from the cosine law,
20+=+25+%2B+13+-+2%2A5%2Asqrt%2813%29%2Acos%28theta%29
===>+-18+=+-10sqrt%2813%29cos%28theta%29
===>cos%28theta%29+=+%289sqrt%2813%29%29%2F65
===> theta+=+60degrees, to the nearest degree.

test/390913: if 5/7 of a number is 35.what is the number?










1 solutions
Answer 277249 by robertb(4012) About Me  on 2011-01-05 04:03:13 (Show Source):
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Since %285%2F7%29%2A49+=+35, the number is 49.

Travel_Word_Problems/390874: A car goes at v mph for a hours then goes in the opposite direction at u mph for b hours. How far is the car from where it started at the end?
1 solutions
Answer 277248 by robertb(4012) About Me  on 2011-01-05 04:00:55 (Show Source):
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|u*b - v*a| miles.

Travel_Word_Problems/390886: Two jets are traveling toward each other and are 4000 km apart. The rate of one jet is 100 km/h faster than the rate of the other. If the jets pass each other after 2.5 hours, what is the rate of the faster jet?
1 solutions
Answer 277247 by robertb(4012) About Me  on 2011-01-05 03:56:44 (Show Source):
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2.5x + 2.5(x+ 100) = 4000
===> 2.5x + 2.5x +250 = 4000
===> 5x = 3750
===> x = 750 kph, the rate of one jet,
x + 100 = 850 kph, the rate of the faster jet.

Linear-equations/390911: If f(x) = 2x - 3, evaluate the following:
( a ) f(-2) =
( b ) f(t)
( c ) f(a - 2)

1 solutions
Answer 277246 by robertb(4012) About Me  on 2011-01-05 03:47:06 (Show Source):
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f(-2) = 2*-2 - 3 = -4-3 = -7.
f(t) = 2t - 3.
f(a-2) = 2*(a-2) - 3 = 2a - 4 - 3 = 2a - 7.

Proportions/390893: Jeremy bought a souvenir while on vacation. The item cost $22.00, but the otal bill was $23.43, What percent was the sales tax?
Use a percent equation and Use a proportion
1 solutions
Answer 277245 by robertb(4012) About Me  on 2011-01-05 03:45:20 (Show Source):

Percentage-and-ratio-word-problems/390895: Wayne has milk that is 5% butterfat and skim milk without butterfat. How much 5% milk and how much skim milk should he mix to make 200 gallons of milk that is 3.5% butterfat?
1 solutions
Answer 277244 by robertb(4012) About Me  on 2011-01-05 03:40:56 (Show Source):
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0.05x + 0.00*(200 - x) = 0.035*200 ===> 0.05x = 7 ===> x = 140 gallons of the 5% milk, and 60 gallons of the skim milk.

Proportions/390892: "If the 481 children's books represent 13% of the books in the library, how many total books are in the library?"
Use a percent equation and Use a proportion

1 solutions
Answer 277243 by robertb(4012) About Me  on 2011-01-05 03:32:02 (Show Source):
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0.13x = 481 ===> x = 481/0.13 = 3700 books.

Probability-and-statistics/390910: in a cellular phone area, company A accounts for 70% of the cellular phone market, while company B accounts for the remaining 30% of the market. Of the cellular calls made with company A, 2% of the calls will have some sort of interference, while 3% of the cellular calls with company B will have interference. if a cellalar call is selected at , the probability that it will not have interference is........
1 solutions
Answer 277242 by robertb(4012) About Me  on 2011-01-05 03:30:05 (Show Source):
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0.7*0.98 + 0.3*0.97 = 0.977

Percentage-and-ratio-word-problems/390889: A pharmacist needs 500 milliliters of a 10% phenorbarbital solution. She only has 5% and 25% solutions available. How many milliliters of each solution should she mix to obtain the desired solution?

1 solutions
Answer 277241 by robertb(4012) About Me  on 2011-01-05 03:24:18 (Show Source):
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0.05*x + 0.25*(500 - x) = 0.10*500;
0.05x + 125 - 0.25x = 50;
-0.20x = -75;
x = 375 milliliters of the 5% solution, and
500 - x = 125 milliliters of the 25% solution.

Trigonometry-basics/390905: Hello,
Please hep me to solve this problem: Find all exact value solutions [o,360) for sin^2x-2sinx-3 = 0
My work:
x^2-2x-3 = 0
sinx = 3
sinx = -1
sin^-1(3) = None
sin^-1(-1) = -90

1 solutions
Answer 277239 by robertb(4012) About Me  on 2011-01-05 02:47:07 (Show Source):
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sin^-1(-1) = -90 is actually correct, BUT -90 is not in [0, 360), so the desired solution is -90 + 360 = 270.

test/390908: The differences between primitive root and primitive element of a finite field. And also the difference between primitive element and generator of a finite field.
1 solutions
Answer 277238 by robertb(4012) About Me  on 2011-01-05 02:42:21 (Show Source):
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Hmm. Look at http://en.wikipedia.org/wiki/Primitive_element_%28finite_field%29. You must be a math major in 2nd, 3rd year college? Or a college math professor? Ha ha. There are some excellent books in abstract algebra/Galois theory you can look at, like Gallian, Fraleigh, Hungerford, Artin, to name a few.

Proportions/390900: if a,b,c are in continued proportion, prove that:
(a^2+b^2+c^3)/(a+b+c)=a-b+c
and hence find three numbers in continued proportion so that their sum is 14 and the sum of their squares is 84

1 solutions
Answer 277237 by robertb(4012) About Me  on 2011-01-05 02:37:18 (Show Source):
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You definitely mean %28a%5E2%2Bb%5E2%2Bc%5E2%29%2F%28a%2Bb%2Bc%29=a-b%2Bc.
The given is a%2Fb+=+b%2Fc, that is, a,b,c are in continued proportion . One consequence of this condition is the fact that ac+=+b%5E2, which we will use later.
To start off, consider %28a%2Bb%2Bc%29%28a-b+%2B+c%29. Upon expansion, this is equal to .
But ac+=+b%5E2, so after substitution,
%28a%2Bb%2Bc%29%28a+-b+%2B+c%29+=+a%5E2+%2B+b%5E2+%2B+c%5E2. Assuming that the sum a+b+c is not equal to zero, then we divide by a+b+c, and the result follows.
Consider a = 8, b = 4, and c = 2. Then %2864%2B16+%2B+4%29%2F%288%2B4%2B2%29+=+6.

Evaluation_Word_Problems/390610: A biology class did a survey of an open field for the number of visible insects per square ft. of ground. The results were normally distributed. The mean was 28 insects and the standard deviation was 5. What values are 1 standard deviation from the mean?
1 solutions
Answer 277231 by robertb(4012) About Me  on 2011-01-04 22:58:07 (Show Source):
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Use the z-score formula:
z+=+%28X+-+mu%29%2Fsigma. Hence we want
+/-1+=+%28X+-+28%29%2F5, or +/-5 = X - 28, or X = 23, 33.

Travel_Word_Problems/390875: Express the area A of a square in terms of its perimeter p.
1 solutions
Answer 277228 by robertb(4012) About Me  on 2011-01-04 22:51:21 (Show Source):

Mixture_Word_Problems/390739: How many milliliters of water must be added to 60 mL of a 15% iodine solution in order to dilute it to a 10% iodine solutioN?
1 solutions
Answer 277225 by robertb(4012) About Me  on 2011-01-04 22:41:32 (Show Source):
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60*0.15 + x*0.00 = (60 + x)*0.10;
9 = 6 + 0.10x;
3 = 0.10x;
x = 30 mL of water must be added.

Travel_Word_Problems/390873: A car travels y miles in t hours, what is its speed?
1 solutions
Answer 277224 by robertb(4012) About Me  on 2011-01-04 22:39:03 (Show Source):
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y/t miles per hour AVERAGE speed.

Travel_Word_Problems/390734: one car travels west at 72 mph and another car travels north at 21 mph whats their distance after an hour
1 solutions
Answer 277223 by robertb(4012) About Me  on 2011-01-04 22:36:59 (Show Source):
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The distance is sqrt%2872%5E2+%2B+21%5E2%29+=+sqrt%285625%29+=+75 miles apart.

Percentage-and-ratio-word-problems/390740: If 50 million people traveled for 2010 and only 14 million traveled by air; what percentage traveled by air?
1 solutions
Answer 277222 by robertb(4012) About Me  on 2011-01-04 22:34:17 (Show Source):
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(14/50)*100% = 28% traveled by air.

Permutations/390858: Signals are made by running five colored flags up a mast. How many different signals can be made if there is an unlimited supply of flags of seven colors?
1 solutions
Answer 277218 by robertb(4012) About Me  on 2011-01-04 22:31:11 (Show Source):
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7%2A7%2A7%2A7%2A7+=+7%5E5+=+16807 signals assuming repetition of colors.

Travel_Word_Problems/390857: A car travels 140 miles in 2 hours at constant speed. What was the speed?
1 solutions
Answer 277216 by robertb(4012) About Me  on 2011-01-04 22:28:35 (Show Source):
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140/2 = 70 miles per hour.

Travel_Word_Problems/390861: A car travels for t hours at 100 mph how far does it go?
1 solutions
Answer 277215 by robertb(4012) About Me  on 2011-01-04 22:27:50 (Show Source):

Probability-and-statistics/390733: What proportion of the data is between the first and third quartiles?
1 solutions
Answer 277210 by robertb(4012) About Me  on 2011-01-04 22:22:23 (Show Source):
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The 1st quartile Q1 demarcates the lowest 25% of the distribution from the higher 75%.
The 3rd quartile Q3 demarcates the lower 75% of the distribution from the highest 25%.
(We are assuming here that the values of the RV are either in increasing or decreasing order.)
What is in between the Q1 and Q3 then, is exactly 50% of the distribution. (Think of it this way: Exclude the lowest 25% of the distribution and the highest 25% of the distribution and you get exactly the middle 50% of the distribution.)

test/390728: The quadratic parent function is translated 2 units left and 1 unit up. What is the new quadratic equation, in vertex form?
1 solutions
Answer 277203 by robertb(4012) About Me  on 2011-01-04 22:10:40 (Show Source):
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If the quadratic "parent" function is y+=+a%28x-h%29%5E2+%2B+k, then the "offspring" function is y+=+a%28x+-+h+%2B+2%29%5E2+%2B+k+%2B+1.

Mixture_Word_Problems/390845: a juice bar mixes apple juice and cranberry juice. how much should you charge if you mix 8 l of apple juice selling 45 cents/liter with 10 l of cranberry juice for $1.08/liter?
1 solutions
Answer 277199 by robertb(4012) About Me  on 2011-01-04 22:06:12 (Show Source):
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8*0.45 + 10*1.08 = 18*x;
14.4 = 18x;
x = $0.80 per liter.