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# Recent problems solved by 'robertb'

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 Rational-functions/353796: 3^2x+3^x-2=01 solutions Answer 252906 by robertb(4012)   on 2010-10-09 03:52:58 (Show Source): You can put this solution on YOUR website!The equation is actually a quadratic equation in . It is factorable. , , This means , or . The first equation has no solution, because , while the second gives . Only will satisfy this equation.
 Miscellaneous_Word_Problems/353716: 1. Addition and subtraction are examples of what are BEST called ____________.1 solutions Answer 252895 by robertb(4012)   on 2010-10-09 01:54:15 (Show Source): You can put this solution on YOUR website!Arithmetical operations.
 Probability-and-statistics/353779: A community meeting was attended by 37 parents along with 26 students. A committee is to be formed consisting of 8 people: 4 parents and 4 students. If you are one of the students at the meeing, what is the probability that you will be chosen for the committee1 solutions Answer 252894 by robertb(4012)   on 2010-10-09 01:45:22 (Show Source): You can put this solution on YOUR website!If I were one of the students and it is certain that I'll be a member of the committee, then 3 more students are needed to be selected from the remaining 25 students. It can be done in ways. Then 4 parents had to be selected from 37 parents. This can be done in . There are ways of selecting 8 people out of people. The probability is then .
 Rate-of-work-word-problems/353752: a drain can empty a swimming pool in 16 days. A drain can empty this pool in 8 days. In how much time will the two drains working together empty the pool?1 solutions Answer 252856 by robertb(4012)   on 2010-10-08 21:25:24 (Show Source): You can put this solution on YOUR website!The equation is . Solving, , , days.
 sets-and-operations/353728: A student has a test average of 74% after taking six exams. The student wants to get an 80% average to earn a B for the course. The student has 1 more exam to take, is it possible to earn a B.1 solutions Answer 252855 by robertb(4012)   on 2010-10-08 21:20:36 (Show Source): You can put this solution on YOUR website!From the equation , we get , the sum of all his scores from the 6 exams. let x = his score on the 7th exam. Thus, . (Note that he has to get an 80 out of an hundred to get a B.) . . Therefore he has to get 116 out of 100 in his last exam, which is impossible (at least on paper! haha)
 Linear-systems/353734: Please help me solve this. Find the value of k such that the system of linear equations is inconsistent. 4x + 2y = 6 −6x + ky = −8 1 solutions Answer 252853 by robertb(4012)   on 2010-10-08 21:04:36 (Show Source): You can put this solution on YOUR website!You can form the augmented matrix for this system, reduce it to echelon form, and find out that k should be equal to -3. Done by your usual substitution method, the first equation leads to . Put into the 2nd equation, we get. . , . the denominator will be undefined if , or .
 Equations/353743: (x+(x+2)+ x+4)3=x(x+2)+ 181 solutions Answer 252850 by robertb(4012)   on 2010-10-08 20:43:02 (Show Source): You can put this solution on YOUR website! , , , , , or .
 Probability-and-statistics/353741: If a person tosses a coin 22 times; in how may ways can he get exactly 20 heads?1 solutions Answer 252848 by robertb(4012)   on 2010-10-08 20:38:27 (Show Source): You can put this solution on YOUR website!There are exactly C(22, 20) ways of getting exctly 20 heads in 22 tosses of a single coin. .
 Rate-of-work-word-problems/353742: If you are planning to make a 24 mile round trip while canoeing in a river with a current of 2 mph, how fast will you have to paddle to make the trip in 4.5 hours?1 solutions Answer 252846 by robertb(4012)   on 2010-10-08 20:35:08 (Show Source): You can put this solution on YOUR website!distance up the river = 12 miles let x = speed of canoe. Rate of canoe with respect to the river = x-2 distance down the river = 12 miles. rate of canoe with respect to the river = x+2. From the formula . Thus . The equation is the same as after simplification. . . . Thus miles per hr.
 Linear-equations/353523: Find numerical values for all simultaneous solutions of: X^2+3y^2=27 xy=6 and illustrate with a graph1 solutions Answer 252591 by robertb(4012)   on 2010-10-08 02:10:51 (Show Source): You can put this solution on YOUR website! (1) (2) From equation (2), . Substituting into (1), , , Multiplying both sides by , we get , or . Treating the equation as a quadratic equation in , and applying the quadratic formula, we get , . Hence , or . The values that we get from the first x-value are or . from the second x-value, we get the negatives: or . The corresponding y-values are (obtained from equation (2)) 1.2758, 2.7152, -1.2758, -2.7152.
 Travel_Word_Problems/353518: a plane flying with the wind flew 460 miles in 2 hours. flying against the same wind, the same plane flew 340 miles in 2 hours. find the speed of the wind.1 solutions Answer 252590 by robertb(4012)   on 2010-10-08 01:41:13 (Show Source): You can put this solution on YOUR website!Let P = speed of the plane, and W = speed of the wind. Using the formula , or distance = speed x time, we get , and . These are the same as and . Adding corresponding sides, we get , or . Thus the speed of the wind is miles per hour.
 Length-and-distance/353515: Find the measure of line segment KL if K is between J and L, JK = 5x-3 and KL=7x+8 and JL=651 solutions Answer 252589 by robertb(4012)   on 2010-10-08 01:28:20 (Show Source): You can put this solution on YOUR website!K is between J and L, so . Hence, , from the given. , , . Therefore segment KL is units long.
 Probability-and-statistics/353513: A Manufacturer makes three models of a television set, models A, B and C. A store sells 40% of a model A sets, 40% of a model B sets, and 20% of model C sets. Of model A sets, 3 % have stereo sound; of model B sets, 7 % have stereo sound; and of model C sets, 9% have stereo sound. If a set is sold at random, find the probability that it has stereo sound.1 solutions Answer 252588 by robertb(4012)   on 2010-10-08 01:15:57 (Show Source): You can put this solution on YOUR website!The probability that a set taken is A is 0.40. Since 3% of these have stereo, the probability that a set taken is A with stereo is . Similarly, the probability that a set taken is B with stereo is , and the probability that a set taken is C with stereo is . Since these events are mutually exclusive, or disjoint, the probability that a set taken has stereo is .
 Mixture_Word_Problems/353498: how much 60% antifreeze solution must be mixed with a 40% antifreeze solution to produce 25 gallons of a 52% disinfectant solution.1 solutions Answer 252586 by robertb(4012)   on 2010-10-08 01:05:08 (Show Source): You can put this solution on YOUR website!let x = # gallons 60% antifreeze sol'n that has to be added. Then , , , . Therefore 15 gallons of 60% antifreeze has to be added.
 Age_Word_Problems/353507: Nathan is 8 years older than Steven. Steven is 3 years older than Megan. Megan is 11 years younger than Nathan. The sum of their ages is 65. How old is Megan?1 solutions Answer 252584 by robertb(4012)   on 2010-10-08 00:57:20 (Show Source): You can put this solution on YOUR website!From the given, (1) (2) (3) (4) Putting equation (3) into (4), we get Thus (5) Putting equation (1) into (5), , , , or . Thus Steven is 20 years old. from equation (2), , or . Therefore megan is 17 yrs old.
 Geometry_Word_Problems/353510: Phyllis invested 33000 dollars, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 7 percent per year. After one year the total interest earned on these investments was 2090 dollars. How much money did she invest at each rate? 1 solutions Answer 252580 by robertb(4012)   on 2010-10-08 00:45:57 (Show Source): You can put this solution on YOUR website!Let x = portion earning at 5% per year. Then 33000 - x = portion earning at 7%. Then , the total interest after 1 year. , , is the investment at 5%, and is the investment at 7%.
 Geometry_Word_Problems/353509: A rectangular room is 1.4 times as long as it is wide, and its perimeter is 33 meters. Find the dimension of the room1 solutions Answer 252578 by robertb(4012)   on 2010-10-08 00:40:02 (Show Source): You can put this solution on YOUR website!From the given, . Also, . By direct substitution, . , , meters. The length of the room is 9.625 meters.
 Probability-and-statistics/353428: an unprepared student makes a random guesses on all questions if her multiple choice test. If there are 17 questions and each question has 4 possible answers, what is the probability she will answer at least one answer right1 solutions Answer 252526 by robertb(4012)   on 2010-10-07 20:43:00 (Show Source):
 Evaluation_Word_Problems/353429: The sumof the squares of three consecutive positive integers is 77. Find the integers. The book gives a hint: if one integer is x, the next consecutive positive integer is x+1, and the third is x+21 solutions Answer 252519 by robertb(4012)   on 2010-10-07 20:38:04 (Show Source): You can put this solution on YOUR website!, , , , , after dividing both sides by 3. , This implies that or . We reject the -6 as a solution. Therefore the three consecutive positive integers are 4, 5, 6.
 Human-and-algebraic-language/353393: A rice trader mixes commercial rice that costs 29/kilo with that which costs 33/kilo. How many kilos of each should he mix to produce 200 kilos of a mixture that costs 30/kilo?1 solutions Answer 252514 by robertb(4012)   on 2010-10-07 20:32:13 (Show Source): You can put this solution on YOUR website!Let x = # kilos from 29/kilo rice. Then 200 - x = # kilos from 33/kilo rice. Then . , , , . Therefore he should mix 150 kilos of the 29/kilo rice and 50 kilos of the 33/kilo rice.
 Graphs/353080: solve: (2x-1)^1/3 -3=0 x=? 1 solutions Answer 252297 by robertb(4012)   on 2010-10-07 03:58:52 (Show Source): You can put this solution on YOUR website! after cubing both sides.
 Subset/353047: how many subsets does 100 sets have?1 solutions Answer 252283 by robertb(4012)   on 2010-10-06 23:54:27 (Show Source): You can put this solution on YOUR website!Maybe you meant, how many subsets does a 100-element set have? In this case there are subsets.
 Rational-functions/352989: (2/3x)+1/4 = (11/6x)-1/3 What is the value for x?1 solutions Answer 252282 by robertb(4012)   on 2010-10-06 23:51:38 (Show Source): You can put this solution on YOUR website! . Thus, , or, after cross-multiplication, , .
 Complex_Numbers/353044: (2+i)(3-i)(2-3i) i=imaginary unit I know we're supposed to do FOIL, but in what order?1 solutions Answer 252280 by robertb(4012)   on 2010-10-06 23:43:59 (Show Source): You can put this solution on YOUR website!You can do it in any order--Multiplication of complex numbers is commutative. = = = = =
 Mixture_Word_Problems/353023: The sum of 2 consecutive integers is 203 less than 8 times the smallest integer. Find the SMALLEST of the integers.1 solutions Answer 252276 by robertb(4012)   on 2010-10-06 23:36:45 (Show Source): You can put this solution on YOUR website!Let x = smallest integer. The next integer is x + 1. Thus .
 Quadratic_Equations/353026: Algebra: Find the vertex, symmetry, maximum, and minimum of f(x)=-x^2+12x+1.1 solutions Answer 252274 by robertb(4012)   on 2010-10-06 23:32:17 (Show Source): You can put this solution on YOUR website!Here, , , . The x-coordinate of the vertex is . The y-coordinate of the vertex is . . . The axis of symmetry is the vertical line . There is no max value. (The parabola opens upward.) The minimum value is .
 Probability-and-statistics/353036: The probability that a salesperson will make a sale is 0.8. What is the probability (assuming independence) that on two calls made in a day the salesperson will: a. make two sales? b. Make at least one sale? c. Make no sales?1 solutions Answer 252269 by robertb(4012)   on 2010-10-06 23:09:12 (Show Source): You can put this solution on YOUR website!Probability of making a sale = 0.8 Probability of not making a sale = 0.2 a) Probability of making two sales = b) probability of making at least one sale = c) probability of making no sales =
 Travel_Word_Problems/352959: the bus to washington has traveled 5/6 of the way there. if it has traveled 80 miles, how much farther does it have to go?1 solutions Answer 252231 by robertb(4012)   on 2010-10-06 21:07:53 (Show Source): You can put this solution on YOUR website!Let x = the total distance. Then So there's still 96 miles - 80 miles = 16 miles to go.
 Miscellaneous_Word_Problems/352946: When 3 times a certain number n is added to 6, the sum is 20 more than the original number. What is n1 solutions Answer 252227 by robertb(4012)   on 2010-10-06 21:02:37 (Show Source): You can put this solution on YOUR website!Let n = unknown number. Then "3 times a certain number n is added to 6" is . "20 more than the original number" is . Hence, . .
 Linear_Equations_And_Systems_Word_Problems/352947: To rent a van it intially costs \$87 down plus \$.031 per mile. Write a fuction that describes the total cost of renting the van. I dentify the independent and dependent variables and tell what each one represents. How far can you drive the van if you have \$275? What is the cost if you drive 1358 miles?1 solutions Answer 252223 by robertb(4012)   on 2010-10-06 20:57:21 (Show Source): You can put this solution on YOUR website!Let C = total cost of renting the van. This is the dependent variable. Let x = number of miles the van was driven. This is the independent variable. Then . If , then . miles. If \$.
 Probability-and-statistics/352933: a girl has 10 yellow, 10 red, and 10 green marbles. She picks two marbles out at random and gives them to her sister a.) what is the probability of choosing 2 yellow marbles? b.) of the marbles left what is the probability of choosing a green marble next? c.)of the marbles left, what color has the probability of 1/3 of being picked? explain how you determined your answer. 1 solutions Answer 252217 by robertb(4012)   on 2010-10-06 20:46:40 (Show Source): You can put this solution on YOUR website!The number of ways of getting 2 marbles out of 30 is C(30, 2). The number of ways of getting 2 yellow marbles out of 10 yellow marbles is C(10, 2). a.) Thus The probability of choosing 2 yellow marbles is b.) Of the marbles left there are 8 yellow, 10 red , 10 green. Thus the probability of choosing 1 green marble next is . c.) After picking a green marble, there are 8 yellow, 10 red, 9 green marbles left. So there are 27 marbles remaining. Of these the green colored marble has probability of being picked.