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# Recent problems solved by 'oberobic'

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 Age_Word_Problems/530525: David is y years old. Tom is 2 years younger than David. What is Tom's age?1 solutions Answer 350155 by oberobic(2304)   on 2011-11-12 22:08:22 (Show Source): You can put this solution on YOUR website!y = David's age . Tom is 2 years younger than David. . y-2 = Tom's age
 Linear_Equations_And_Systems_Word_Problems/530562: The enrolment in a school this year is 552.this is an increase of 15% over last year's enrolment.how many were enrolled last year?1 solutions Answer 350154 by oberobic(2304)   on 2011-11-12 22:06:43 (Show Source): You can put this solution on YOUR website!A 15% increase means the schools' current enrollment = 115% of last year's enrollment. x = last year's enrollment 115% * x = 552 1.15*x = 552 x = 552/1.15 x = 480
 Numbers_Word_Problems/530521: Find three consecutive odd intergers such that the sum of all three is 36 less than the product of the smaller two. Show the equation and all the steps.1 solutions Answer 350153 by oberobic(2304)   on 2011-11-12 22:03:15 (Show Source): You can put this solution on YOUR website!Three consecutive odd integers can be defined as: x x+2 x+4 . The sum of these three number is 36 less than the product of the smaller two. . x +x+2 +x+4 +36 = x*(x+2) . Solve . 3x + 42 = x^2 + 2x . x^2 -x -42 = 0 . Factor . (x-7)(x+6) = 0 . x = 7 or -6 . -6 is not odd, so we select 7 as the answer. . x = 7 x+2 = 9 x+4 = 11 . Check the values. 7*9 = 63 7+9+11 = 27 27+36 = 63 Correct . Answer: The numbers are 7, 9, and 11. . Done.
 test/530557: Two cars leave delhi at the same time ,travelling in opposite directions.if the average speed of one car is 5km/hr more than that of the other and they are 425 km apart at the end of 5hrs,what is the average speed oe each?1 solutions Answer 350151 by oberobic(2304)   on 2011-11-12 21:55:02 (Show Source): You can put this solution on YOUR website!The two cars are moving in opposite directions, so they are separating at the sum of their speeds. Looking at the fundamental distance equation, d = rt, we know: d = 425 km t = 5 hr So, the combined rate = 425/5 = 85 km/hr One car goes 5 km/hr faster than the other, which means we can define their speeds as x and x+5. x + x+5 = 85 2x +5 = 85 2x = 80 x = 40, which is the speed of one car x+5 = 45, which is the speed of the other car
 Linear-systems/530555: Solve the system shown. Put your answer in (x, y) format with no spaces. 2x + 9y = 0 3x + 5y = 171 solutions Answer 350148 by oberobic(2304)   on 2011-11-12 21:49:45 (Show Source): You can put this solution on YOUR website!2x + 9y = 0 3x + 5y = 17 . multiply the first equation by 3 and the second by 2; then subtract . 6x + 27y = 0 6x + 10y = 34 -------------- 17y = -34 . y = -2 . substitute to find 'x' . 2x + 9(-2) = 0 2x -18 = 0 2x = 18 x = 9 . check by substituting these values into the other equation . 3(9) + 5(-2) = 17 ?? 27 -10 = 17 correct . Answer: (9,-2) . Done.
 Word_Problems_With_Coins/530546: Ben has eight 5 cent coins and three 10 cent coins. How much does he have altogether? (I need a step by step solution please)1 solutions Answer 350147 by oberobic(2304)   on 2011-11-12 21:48:33 (Show Source): You can put this solution on YOUR website!5 cent coins are called nickels. 10 cent coins are called dimes. . 8 nickels = 8 * 5 cents = 40 cents 3 dimes = 3 * 10 cents = 30 cents 40 cents + 30 cents = 70 cents . Done.
 Linear-systems/530554: Solve the system shown. Put your answer in (x, y) format with no spaces. 2x + 9y = 0 3x + 5y = 171 solutions Answer 350146 by oberobic(2304)   on 2011-11-12 21:41:42 (Show Source): You can put this solution on YOUR website!2x + 9y = 0 3x + 5y = 17 . multiply the first equation by 3 and the second by 2; then subtract . 6x + 27y = 0 6x + 10y = 34 -------------- 17y = -34 . y = -2 . substitute to find 'x' . 2x + 9(-2) = 0 2x -18 = 0 2x = 18 x = 9 . check by substituting these values into the other equation . 3(9) + 5(-2) = 17 ?? 27 -10 = 17 correct . Answer: (9,-2) . Done.
 Parallelograms/530544: One of two consecutive angles of a parallelogram measures six more than twice as much as the other. Find the measures of the angles.1 solutions Answer 350145 by oberobic(2304)   on 2011-11-12 21:38:42 (Show Source): You can put this solution on YOUR website!The consecutive angles of a parallelogram are supplementary. Call these angles x and y. x + y = 180 x = 2y+6 substitute 2y+6 +y = 180 3y = 174 y = 58 x = 2*58 + 6 = 122 Done.
Probability-and-statistics/530501: Out of 100 students, (49 girls, 51 boys) if three children are selected what is the probability that at least one is a girl?
I am missing a key point to this equation because I keep getting 49/97 which I believe is wrong
Thanks for any help
1 solutions

Answer 350103 by oberobic(2304)   on 2011-11-12 19:58:14 (Show Source):
You can put this solution on YOUR website!
The probability of picking a girl on the first pick is: 49/100.
.
The probability of picking a girl on the second pick depends on whether a girl was picked first.
If a girl was picked initially, then the probability of picking a girl on the second pick is : 48/99.
If a boy was picked initially, then the probability of picking a girl on the second pick is: 49/99.
.
The probability of picking a girl first and second is: 49/100 * 48/99.
.
And so forth.
.
You need to determine the conditional probabilities to find the chance of picking at least 1 girl.
.
1st Pick      2nd Pick      3rd Pick         Probability             Description
P(girl)=49/100      P(girl)=48/99      P(girl)=47/98      P=0.113939394 (A) 3 girls
" " P(boy)=51/98 P=0.123636364 (B) 2 girls, 1 boy
" P(boy)=51/99 P(girl)=48/98 P=0.123636364 (C) 2 girls, 1 boy
" " P(boy)=50/98 P=0.128787879 (D) 1 girl, 2 boys
P(boy)=51/100 P(girl)=49/99 P(girl)=48/98 P=0.123636364 (E) 2 girls, 1 boy
" " P(boy)=50/98 P=0.128787879 (F) 1 girl, 2 boys
" P(boy)=50/99 P(girl)=49/98 P=0.128787879 (G) 1 girl, 2 boys
" " P(boy)=49/98 P=0.128787879 (H) 3 boys

The total probability = 1.00, as you can see.
.
P(at least 1 girl) = A+B+C+D+E+F+G = 0.871212121
.
OR
.
You could see the problem in terms of the chance of picking 3 boys. If you do not pick 3 boys, then you have to pick at least 1 girl.
.
P(picking 3 boys) = 51/100 * 50/99 * 49/98 = 0.128787879
.
P(picking at least 1 girl) = 1.0 - 0.128787879 = 0.871212121
.
Same answer. Two ways to get there.
.
Done.

 Numbers_Word_Problems/530410: What number Am I? 1)I have 4 digits. 2)Each digit is either a 2 or a 4. 3)The numbers in the ones and tenths places are the same. 4)The numbers in the tens and hundredths places are also the same. 5)I have a 4 in the hundredths place. 1 solutions Answer 350098 by oberobic(2304)   on 2011-11-12 19:15:35 (Show Source): You can put this solution on YOUR website!5) The number in the hundredths place is 4. so the number is: xy.z4 . 4) The number in the tens and hundreths place are the same. . 4y.z4 . 3) The number in the ones and tenths are the same. . Of course they can be 2's or 4's. So, the number can be either 42.24 or 44.44 . 2) The numbers can be only 2's or 4's. OK. , 1) The number has 4 digits. OK. . So the number can be 42.24 or 44.44. . Done.
 Functions/530417: what is f(.75) for the function f(x)= 7x?1 solutions Answer 350094 by oberobic(2304)   on 2011-11-12 19:02:55 (Show Source): You can put this solution on YOUR website!f(x) = 7*x . x = .75 . f(x) = 7*.75 = 5.25
 Average/530495: Can I please get some help to solve this word problem? Enrollment at a local university is 8500. There are one third as many students over the age of 25 as there are 25 and under. How many students are 25 and under and how many are over 25?1 solutions Answer 350093 by oberobic(2304)   on 2011-11-12 18:59:02 (Show Source): You can put this solution on YOUR website!x = number of students 25 and under y = number of students over 25 . x + y = 8500 so x = 8500 -y . y = 1/3x so x = 3y . substitute . x = 3(8500-x) . x = 25500 -3x . 4x = 25500 . x = 6375 . 8500-x = 2125 . The number of students 25 and under is 6375. . The number of students over 25 is 2125. . The number of students over 25 = 2125/6375 = 1/3 the number of students 25 and under. . Done.
 Graphs/530464: solve for y. 6x+y=41 solutions Answer 350050 by oberobic(2304)   on 2011-11-12 16:47:34 (Show Source): You can put this solution on YOUR website!6x+y = 4 y = -6x + 4 . This equation defines a line. . The y-intercept is (0,4) . To find the x-intercept, set y=0 and solve for 'x'. . 0 = -6x + 4 6x = 4 x = 2/3 which is the point (2/3,0) . With two points you can draw a line. .
 test/530426: The graph of the following system yields perpendicular lines. x + 2y = -10 -4y = 2x + 20 true or false?1 solutions Answer 350049 by oberobic(2304)   on 2011-11-12 16:44:52 (Show Source): You can put this solution on YOUR website!Get both equations into slope-intercept form and determine if their slopes are inverse reciprocals. . x +2y = -10 2y = -x -10 y = -1/2*x -5 . -4y = 2x + 20 y = -2/4*x + 20/-4 y = -1/2*x - 5 . The lines' slopes are equal, so the lines are parallel. In fact, the lines lie one on top of the other such that they appear to be same line. . Answer: False. The lines are not perpendicular. . The graph is useful. . . Done.
 Linear-equations/530460: Find the slope-intercept equation for the line with the indicated slope and y-intercept. Slope -4; y-intercept (0,-3/5) 1 solutions Answer 350048 by oberobic(2304)   on 2011-11-12 16:36:25 (Show Source): You can put this solution on YOUR website!m = -4, so the basic equation will be y = -4x + b . We're given the y-intercept, which is the point (0,b). . y = -4x -3/5 . A graph is useful. .
 Miscellaneous_Word_Problems/530447: oe has a collection of nickels and dimes that is worth \$7.65. If the number of dimes was doubled and the number of nickels was increased by 35, the value of the coins would be \$14.30. How many nickels and dimes does he have?1 solutions Answer 350047 by oberobic(2304)   on 2011-11-12 16:30:27 (Show Source): You can put this solution on YOUR website!With coin problems you have to keep track of the count of each coin and the value. n = number of nickels 5n = value of the nickels in cents d = number of dimes 10d = value of the times in cents . 5n + 10d = 765 cents . 2(10d) + 5(n+35) = 1430 cents 20d + 5n + 165 = 1430 20d + 5n = 1265 . With two equations and two unknowns, you can solve the system of equations. . 5n + 10d = 765 5n + 20d = 1265 ---------------- -10d = -500 . d = 50 . Substitute d = 50 to find n. . 5n + 10d = 765 5n + 10(50) = 765 5n = 265 n = 53 . Check the values to make sure the above solution is the correct answer. . 5(53) = 265 10(50) = 500 265 + 500 = 765 cents . Check the other equation, too. . 2(10(50)) + 5(53+35) = 1430 ?? 2(500) + 265 + 175 = 1430 Correct. . Answer: Joe has 53 nickels and 50 dimes. . Done.
 test/530458: 3x=-3x+12 x=___1 solutions Answer 350044 by oberobic(2304)   on 2011-11-12 16:19:02 (Show Source): You can put this solution on YOUR website!3x=-3x+12 . Add 3x to both sides. . 6x = 12 . Divide both sides by 6. . x = 2
 Travel_Word_Problems/530455: Two trains leave simultaneously from stations that are 360 miles apart. If one train is traveling at 40 miles per hour and the other is traveling 50 miles per hour, how far (along the track) from the nearest station will they meet?1 solutions Answer 350043 by oberobic(2304)   on 2011-11-12 16:15:24 (Show Source): You can put this solution on YOUR website!I assume the trains are heading toward each other from the two different stations. That means they are converging at a combined speed of 90 mph. When they meet, they will have covered the 360 miles. The fundamental distance equation is d = rt. In this case we know d = 360 miles and r = 40+50 = 90 mph. Therefore, t = 360/90 = 4 hr The train going 40 mph will have covered 4*40 = 160 miles at the time they meet. The train going 50 mph will have traveled 4*50 = 200 miles at the time they meet. 160+200 = 360 miles, so that checks. Re-reading the question, it asks for how far from the nearest station they will be. Well, both of them will be 160 miles from the nearest station. One train will heading toward the nearest station and the other will be heading away from it. Done.
1 solutions

Answer 350042 by oberobic(2304)   on 2011-11-12 16:04:54 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -20 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -20 is + or - . The solution is Here's your graph:

 test/530452: 7x+12=9 X=_____1 solutions Answer 350041 by oberobic(2304)   on 2011-11-12 16:01:50 (Show Source): You can put this solution on YOUR website!7x + 12 = 9 . subtract 12 from both sides . 7x = -3 . divide both sides by 7 . x = -3/7 . Done.
 Linear-equations/530434: What is the equation of a line perpendicular to the line y=2x - 4 and going through the point (-1,3).1 solutions Answer 350040 by oberobic(2304)   on 2011-11-12 15:58:28 (Show Source): You can put this solution on YOUR website!y = 2x-4 . A line perpendicular to this line will have a slope that is the inverse reciprocal of 2, which is -1/2. . y = -1/2x + b . To determine 'b', use the point you want to go through. . 3 = -1/2(-1) + b 3 = 1/2 + b b = 2 1/2 = 5/2 . A graph usually helps. The red line is y = 2x-4; the green line is y = -1/2x + 5/2. . .