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Recent problems solved by 'robertb'

robertb answered: 4011 problems
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Numeric_Fractions/408728: Find the least common multiple of 14 and 84. 1 solutions Answer 287849 by robertb(4012)   on 2011-02-13 21:10:09 (Show Source): You can put this solution on YOUR website! 14 = 2*7 84 = Hence LCM is .

Numeric_Fractions/408723: Jessica ate 5/12 of her orange before lunch and 5/12 of her orange after lunch. How much of her orange did she eat? 1 solutions Answer 287847 by robertb(4012)   on 2011-02-13 21:08:16 (Show Source): You can put this solution on YOUR website! After lunch, she has eaten . Hence all in all she has eaten of her orange. Well, think about it: Before lunch she ate 5/12 of the orange, which leaves 7/12 of the orange BEFORE lunch. AFTER lunch, she ate 5/12 of the remaining 7/12, and that is . That is the portion eaten AFTER lunch. So the portion eaten BEFORE lunch, PLUS the portion eaten AFTER lunch must be of the orange.

Miscellaneous_Word_Problems/408675: In each of the following cases, would the mean or the median probably be higher, or would they be about the same? 1. Ages at which residents of a suburban city die, including everything from infant deaths to the most elderly 2. Shoe sizes of adult women 1 solutions Answer 287846 by robertb(4012)   on 2011-02-13 21:03:07 (Show Source): You can put this solution on YOUR website! 1. The distribution would tend to skew to the left (meaning a lot more people die in the older ages than in the younger ages), hence the median would be higher than the mean. 2. My opinion is that the mean and the median would be just about the same, because there's really not a lot of variation across shoe sizes of women.

Problems-with-consecutive-odd-even-integers/408702: there are two pairs of consecutive integers such that their product is three less than three times their sum. 1 solutions Answer 287844 by robertb(4012)   on 2011-02-13 20:55:24 (Show Source): You can put this solution on YOUR website! x(x+1) = 3(x+x+1)-3 <==> <==> <==> <==> ==> x = 0, 5 If x = 0, x +1 = 1 ==> {0,1} If x = 5, x+1 = 6 ==> {5,6}.

Trigonometry-basics/408715: sin(a+b)-sin(a-b)=2cosasinb How do I solve this problem? I am so close to a break down over this. Help!! 1 solutions Answer 287843 by robertb(4012)   on 2011-02-13 20:49:13 (Show Source): You can put this solution on YOUR website! The left-hand side reduces to sina*cosb + cosa*sinb - sina*cosb + cosa*sinb = 2cosa*sinb. Hence the equation is an identity, and all values for a , b are solutions.

Inequalities/408713: what does 3(x+2)less than or equal to 3x+2 equal? 1 solutions Answer 287842 by robertb(4012)   on 2011-02-13 20:46:12 (Show Source): You can put this solution on YOUR website! Nothing. <==> <==> , a contradiction.

Linear_Equations_And_Systems_Word_Problems/408711: Tickets to a local movie were sold at $4 for adults and $2.50 for students. If 59 tickets were sold for a total of $222.50, how many student tickets were sold? 1 solutions Answer 287840 by robertb(4012)   on 2011-02-13 20:44:20 (Show Source): You can put this solution on YOUR website! 4x + 2.50(59 - x) = 222.50 4x + 147.50 - 2.50x = 222.50 1.50x = 75 x = 50, the number of adult tickets sold, and 59 - x = 9, the number of student tickets sold.

Human-and-algebraic-language/408681: 500 people were surveyed at a blood drive; 215 gave blood, 153 set-up and 89 did both, how many people did neither? How would I set this up? 1 solutions Answer 287838 by robertb(4012)   on 2011-02-13 20:41:50 (Show Source): You can put this solution on YOUR website! 500 - (215 + 153 - 89) = 221.

Square-cubic-other-roots/408688: can someone please help me uderstand how to do this. thank you for your time value of the discriminant 18 x^2+2x+12=0 1 solutions Answer 287836 by robertb(4012)   on 2011-02-13 20:38:30 (Show Source): You can put this solution on YOUR website!

Human-and-algebraic-language/408708: 5 times the sum of a number and -10 divided by the number 1 solutions Answer 287833 by robertb(4012)   on 2011-02-13 20:34:43 (Show Source): You can put this solution on YOUR website!

test/408264: Show 5n+3 and 7n+4 are relatively prime for all n 1 solutions Answer 287832 by robertb(4012)   on 2011-02-13 20:33:42 (Show Source): You can put this solution on YOUR website! As a corollary to Euclid's algorithm, there are integers s and t such that as + bt = gcd(a,b). Hence if we're able to find integers s,t, such that s(5n + 3) + t(7n + 4) = 1, then we've shown that 5n + 3, 7n + 4 are relatively prime for all n. ==> (5s + 7t)n + (3s + 4t) = 1. It's enough to see if the system 5s + 7t = 0 3s + 4t = 1 has integer solutions. Indeed, the solutions are s = 7, and t = -5. Therefore 5n + 3, 7n + 4 are relatively prime for all n.

Miscellaneous_Word_Problems/408030: The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the triangle is increasing at a rate of 3 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 88 square centimeters? 1 solutions Answer 287559 by robertb(4012)   on 2011-02-12 06:58:01 (Show Source): You can put this solution on YOUR website! ==> , . When a = 7 cm and A = , b = . Now you got everything you need to find . Good luck!

Length-and-distance/408064: John's height increased from 5'2'' to 5'7'' during the past year. what is the rate of increase ( to the nearest whole percent) of John's height over the past year? 1 solutions Answer 287558 by robertb(4012)   on 2011-02-12 06:45:18 (Show Source): You can put this solution on YOUR website! %, to the nearest whole percent.

Linear_Algebra/408072: A 30 liter solution is 80% antifreeze. How much water should be added to produce a solution that is 60% antifreeze? I want to cross multiply, but that seems to easy. 1 solutions Answer 287557 by robertb(4012)   on 2011-02-12 06:39:47 (Show Source): You can put this solution on YOUR website! 0.80*30 + 0.00*x = 0.60*(30 + x) 24 = 18 + 0.60x 6 = 0.60x x = 10 liters of water should be added.

Probability-and-statistics/408052: The number of baby deliveries in a small hospital was sampled over 12 hour periods. Below is the sample: 18 21 9 16 8 4 21 16 9 5 12 16 5 9 7 25 14 9 17 From this data set, compute the sample mean, median, mode and midrange. Compute the 1st quartile and 3rd and interpret their meanings. 1 solutions Answer 287556 by robertb(4012)   on 2011-02-12 06:34:35 (Show Source): You can put this solution on YOUR website! 4 5 5 7 8 9 9 9 9 12 14 16 16 16 17 18 21 21 25 Mean is 241/19 = 12.68421, to 5 decimal places. Median is the 10th entry, 12 Mode is 9. Midrange is (4 + 25)/2 = 14.5 The 1st quartile is between the 4th and 5th terms: (7+8)/2 = 15/2 = 7.5. The 3rd quartile is between the 14th and 15th terms: (16+17)/2 = 16.5. The 1st quartile 7.5 separates the lowest 25% of the distribution from the rest. The 3rd quartile 16.5 separates the highest 25% of the distribution from the rest.

Probability-and-statistics/408045: Given that P(A) = 0.4, P(B) = 0.8, and P(A and B) = 0.10, determine P(A|B) (Points : 3) 0.08 0.32 0.25 0.125 1 solutions Answer 287555 by robertb(4012)   on 2011-02-12 06:19:18 (Show Source): You can put this solution on YOUR website! P(A|B) = P(A and B)/P(B) = 0.10/0.80 = 1/8 = 0.125

Probability-and-statistics/408019: Given the least-square regression equation Y hat=a+bX , which letter corresponds to each of the following? Regression coefficient Predictor variable Regression constant Dependent variable 1 solutions Answer 287554 by robertb(4012)   on 2011-02-12 06:16:25 (Show Source): You can put this solution on YOUR website! a = Regression constant b = Regression coefficient X = Predictor variable Y^ = Dependent variable

Probability-and-statistics/408046: If P(A or B) = 0.8, P(A) = 0.8 and P(B) = 0.5, determine P(A and B). (Points : 3) 0.35 0.50 0.64 0.13 1 solutions Answer 287553 by robertb(4012)   on 2011-02-12 06:12:21 (Show Source): You can put this solution on YOUR website! P(A and B) = P(A) + P(B) - P(A U B) = 0.8 + 0.5 - .8 = 0.5

Probability-and-statistics/408049: Given the situation described, identify the type of sampling involved. A vegan food and clothing store polls every 17th customer about the selection of desserts offered. random sampling systematic sampling convenience sampling stratified sampling cluster sampling 1 solutions Answer 287552 by robertb(4012)   on 2011-02-12 06:10:22 (Show Source): You can put this solution on YOUR website! systematic sampling

Probability-and-statistics/408051: Scripps Hospital surveyed 10 patients on each floor every day in February. Did this study use a sample or the population? 1 solutions Answer 287551 by robertb(4012)   on 2011-02-12 06:07:10 (Show Source): You can put this solution on YOUR website! Sample

Probability-and-statistics/408080: 95% of households have microwaves.If you randomly sample 3 households,what is the probability that the first two have microwaves an the last one doesn't? is this right? 3(.95+.95+.05) 1 solutions Answer 287550 by robertb(4012)   on 2011-02-12 06:02:11 (Show Source): You can put this solution on YOUR website! 0.95*0.95*0.05 = 0.045125

Complex_Numbers/408067: 1)how to Find the complex conjugate of (3+5i)/(1+2i) 2)how to Find all the seventh roots of (3+4i). 1 solutions Answer 287549 by robertb(4012)   on 2011-02-12 05:48:10 (Show Source): You can put this solution on YOUR website! 1) ==> the complex conjugate is . 2) , letting and . ==> , using de Moivre's theorem. All roots will be obtained when you let n = 0,1,2,3,4,5,6. is obtained as arctan(4/3), or .

Functions/407741: let f be a function with domain (-2,positive infinity) and range [-3,4]. Find the domain and range of y=-f(x+2)-3 1 solutions Answer 287356 by robertb(4012)   on 2011-02-11 03:38:27 (Show Source): You can put this solution on YOUR website! f(x+2) corresponds to a horizontal shift of the y-axis 2 units to the right, and so the new domain is (-4, ). -f(x+2)-2 implies reflection across the x-axis, and then vertical shift of x-axis 3 units up, and so the new range is [3 - 3, -4 - 3], or [0, -7].

Money_Word_Problems/407748: find the original price of a pair of shoes if the increased price is $80 after a 25% increase 1 solutions Answer 287355 by robertb(4012)   on 2011-02-11 03:30:55 (Show Source): You can put this solution on YOUR website! 1.25p = 80 ==> p = $64, the original price of a pair of shoes.

Numbers_Word_Problems/407764: The number in the tens place is even, and it is greater than 6. The digit in the ones places is odd, and it is between 3 and 7. Which number matches the clues? A. 95 B. 94 C. 85 D. 82 1 solutions Answer 287352 by robertb(4012)   on 2011-02-11 02:57:09 (Show Source): You can put this solution on YOUR website! c. 85

Complex_Numbers/407765: Hi please can someone help and break this down, im really struggling. By Expressing (1+j) in polar form and using De Mioivres Theorem, show that (1+j)^24= 2^12 Obtain (1-j)^24. Thank You 1 solutions Answer 287351 by robertb(4012)   on 2011-02-11 02:50:33 (Show Source): You can put this solution on YOUR website! , using de Moivre's Theorem. Hence . Now, ==> ==>

logarithm/407766: if x^2 + y^2 = 6xy prove that: 2log(x+y) = log x + log y +3log 2 plz i want the answer quickly 1 solutions Answer 287350 by robertb(4012)   on 2011-02-11 02:39:24 (Show Source): You can put this solution on YOUR website! Hmm. Since you abbreviated please with the letter "z", I'll solve the problem for you, for your "enlightenment", hahaha. <==> ==> Take logs of both sides: , after applying additive property of logs. Hence it follows that .

Linear-equations/407733: solve and check the linear equation 9x-(8x-1)=2 1 solutions Answer 287342 by robertb(4012)   on 2011-02-10 23:27:42 (Show Source): You can put this solution on YOUR website! 9x - 8x + 1 = 2 ==> x + 1 = 2 ==> x = 1. 9*1 - (8*1 - 1) = 9 - 7 = 2, checks out.

absolute-value/407716: 2|d+4|=8 1 solutions Answer 287340 by robertb(4012)   on 2011-02-10 23:26:26 (Show Source): You can put this solution on YOUR website! |d+4| = 4, d+4 = 4, or d+4 = -4 ==> d = 0, or d = -8.

test/407539: What happens to the graph of y=x as you change the y intercept? Written and diagram explanation please! 1 solutions Answer 287339 by robertb(4012)   on 2011-02-10 23:23:35 (Show Source): You can put this solution on YOUR website! The slope of y = x is 1, and the y-intercept is 0. Fixing the value of the slope to 1, if we change the y-intercept to b > 0, then the x-intercept becomes -b <0. Changing the y-intercept to b < 0, the x-intercept becomes -b > 0. Hence if we increase the y-intercept, there is a corresponding DECREASE in the x-intercept (in the same numerical amount.) If we decrease the y-intercept, there is a corresponding INCREASE in the x-intercept (in the same numerical amount.)

Parallelograms/407605: the diagonals of a parallelogram intersect at (1,1). two vertices are located at (-6,4) and (-3,-1). find the coordinates of the other vertices. 1 solutions Answer 287337 by robertb(4012)   on 2011-02-10 23:08:40 (Show Source): You can put this solution on YOUR website! Since the diagonals of a parallelogram bisect each other, then we can use the midpoint formula in reverse. For the vertex opposite (-6,4), we get: ==> 2 = x - 6 ==> x = 8, ==> 2 = y + 4 ==> y = -2. Therefore the vertex opposite (-6,4) is (8, -2). For the vertex opposite (-3,-1), we get: ==> 2 = x - 3 ==> x = 5, ==> 2 = y - 1 ==> y = 3. Therefore the vertex opposite (-3,-1) is (5,3).