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# Recent problems solved by 'edjones'

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 Equations/252829: One of two positive integers is 8 more than the other. If the product of the two integers is 84, find the integers. Must be solved in an algebraic solution.1 solutions Answer 184945 by edjones(7569)   on 2009-12-31 15:23:01 (Show Source): You can put this solution on YOUR website!Let the numbers be x and x+8 x(x+8)=84 x^2+8x-84=0 (x+14)(x-6)=0 x=6, x+8=14 . Ed
 Distributive-associative-commutative-properties/252727: Find the solution to the equation. Remember there will be two solutions. |x - 2| + 3 = 10 1 solutions Answer 184788 by edjones(7569)   on 2009-12-30 16:16:29 (Show Source): You can put this solution on YOUR website!|x - 2| + 3 = 10 . x-2=7 x=9 . x-2=-7 x=-5 . Ed
 Rate-of-work-word-problems/252653: One pipe can fill a pool in 8 hours. The drain can empty it in 14 hours. With the pipe on and the drain open, how long will it take the pool to be filled? 1 solutions Answer 184679 by edjones(7569)   on 2009-12-29 23:14:36 (Show Source): You can put this solution on YOUR website!1/8 pool filled in 1 hour. 1/14 pool drained in 1 hr. 1/8 - 1/14 =7/56 - 4/56 = 3/56 pool filled in 1 hr. 56/3 hrs to fill the entire pool. . Ed
 Volume/252603: The triangle that forms the base is a right triangle whose legs are 1 foot long. The height of the Prism is 5 feet. Find the volume.1 solutions Answer 184605 by edjones(7569)   on 2009-12-29 16:09:51 (Show Source): You can put this solution on YOUR website!A=.5ab=.5*1*1=.5 V=Ah=.5*5=2.5 ft^3 . Ed
 Square-cubic-other-roots/252569: what is 4 times the square root of 140 in simplest radical form?1 solutions Answer 184579 by edjones(7569)   on 2009-12-29 15:03:14 (Show Source): You can put this solution on YOUR website!140=4*35 4sqrt(140) =8sqrt(35) . Ed
 Probability-and-statistics/252587: A student is selected at random from 100 students where 50 are taking history, 50 are taking politics and 11 are taking history and politics. Find the probability that a student is taking history or politics but not both.(answer to two places of decimals1 solutions Answer 184575 by edjones(7569)   on 2009-12-29 14:57:31 (Show Source): You can put this solution on YOUR website!Check the Venn diagram below. (not drawn to scale) The entire red circle is 50 as is the entire green circle 50. The intersection of the circles is 11 The red circle left of the intersection is 50-11=39 as is the green circle right of the intersection=39 39+39+11=89 This is the union of the 2 circles which includes the intersection. Out side this union but inside the rectangle is the final 11. They took neither history nor politics. .78=probability that a student is taking history or politics but not both. This is the answer correct for sure unless you copied the question wrong. . Ed .
 Probability-and-statistics/252540: In a certain federal prison it is known that 2/3 of the inmates are under 25 years of age. It is also known that 3/5 of the inmates are male and the 5/8 of the inmates are female or 25 years of age or older. What is the probability that a prisoner selected at random from this prison is female and at least 25 years old?1 solutions Answer 184504 by edjones(7569)   on 2009-12-29 08:09:38 (Show Source): You can put this solution on YOUR website!For this problem old means 25 or older and F means female. Refer to the Venn diagram below. 2/5 are female, the entire red circle. 1/3 are old, the entire green circle 5/8 are F or old. This is a union of the red and green circles and includes the intersection of the circles. Let the intersection of the circles be x. The red circle left of the intersection is 2/5 - x. The green circle to the right of the intersection is 1/3 - x. . (2/5 - x) + (1/3 - x) + x = 5/8 -x + 11/15 = 5/8 -x=-13/120 x=.1083... Probability prisoner selected at random is F and old. . Ed .
 Numbers_Word_Problems/252535: What is the last digit of 2^2005 ? (a) 0 (b) 2 (c) 4 (d) 5 (e) 61 solutions Answer 184499 by edjones(7569)   on 2009-12-29 07:02:08 (Show Source): You can put this solution on YOUR website!There is a repetition of four numbers 2, 4, 8, and 6 2005/ 4=501.25 1/4=.25 the same remainder as 501.25 2^1=2 so the last digit is 2. . Ed
 Functions/252531: if f(x) = x + 4 and g(f(x)) = 2x + 1 then g(x)= ? a 2x -7 b 8x+3 c 2x+9 d 2x^2 + 5x + 4 e cannot be determined1 solutions Answer 184498 by edjones(7569)   on 2009-12-29 06:52:44 (Show Source): You can put this solution on YOUR website!f(x) = x + 4 and g(f(x)) = 2x + 1 then g(x)= ? 2(x+4)=2x+8 so g(x)=2x-7 in order to get 2x+1 . Ed
 Miscellaneous_Word_Problems/252532: the floor of a square hall is tiled with unbroken square tiles . along the two diagonals there are 125 tiles altogether . how many tiles are there in the hall? a 15625 b 15624 c 1537 d 2985 e 39691 solutions Answer 184497 by edjones(7569)   on 2009-12-29 06:14:59 (Show Source): You can put this solution on YOUR website!Draw a diagram of a square with 25 equal squares in it. Count the squares along the 2 diagonals. There are 9. because you didn't count the central square twice. If you add 1 and divide by 2 you get the number of squares on each side. 125+1=126 126/2=63 tiles on a side 63^2=3969 tiles in the hall. . Ed
 Miscellaneous_Word_Problems/252529: In how many ways can a committee of at least four but not more than six people be chosen from a group of seven ? a 24 b 63 c 210 d 343 e 84001 solutions Answer 184496 by edjones(7569)   on 2009-12-29 05:27:52 (Show Source): You can put this solution on YOUR website!nCr=n!/((n-r)!r!) Combination of n things r at a time. . 7C4=35 7C5=21 7C6= 7 ------------ ===>63 . Ed
 Inverses/250829: what is the inverse of f(x) = 5x-10?1 solutions Answer 184412 by edjones(7569)   on 2009-12-28 14:55:49 (Show Source): You can put this solution on YOUR website!f(x) = 5x-10 y=5x-10 x=5y-10 the key step, switch x and y. Then solve for y. 5y=x+10 y=x/5 +2 f^(-1)(x)=x/5 +2 . Ed
 Rational-functions/250850: i need help on how to solve problems that are roots and rational exponents liek for example 4radical 36. or -2x exponent-3y2 over 5 x raised to the third power times -3 over 21 solutions Answer 184410 by edjones(7569)   on 2009-12-28 14:51:12 (Show Source): You can put this solution on YOUR website!4sqrt(36) =4*6 =24
 Quadratic-relations-and-conic-sections/250802: Solve the system? 1. y^2+x^2=61 -x+y=1 1 solutions Answer 184409 by edjones(7569)   on 2009-12-28 14:47:44 (Show Source): You can put this solution on YOUR website!y^2+x^2=61 -x+y=1 . y=x+1 (x+1)^2+x^2=61 x^2+2x+1+x^2=61 2x^2+2x-60=0 x^2+x-30=0 (x+6)(x-5)=0 x=-6, y=-5 x=5, y=6 . Ed
 Expressions-with-variables/250807: when solving 3x^2=75 do you multiply 3 times x then square it, or do you multiply three times the squared number to find 751 solutions Answer 184406 by edjones(7569)   on 2009-12-28 14:38:29 (Show Source): You can put this solution on YOUR website!inside parentheses 1st then exponents then * / then + - In this problem only the x is squared. The 3 is multiplied time x^2. (3x)^2 is different from 3x^2. 3x^2=75 x^2=25 x=+-5 . Ed
Rate-of-work-word-problems/252467: First I just hope I'm in the right section, I have been trying to figure out how to solve this problem but I just can't come up with the right formula.

An office has an old copying machine and a new one. Working together it takes both machines 6 hours to make all the copies of the annual financial report. Working alone the old machine takes 15 hours longer than the new machine. How long would it take the new machine to make all the copies working alone?
1 solutions

Answer 184389 by edjones(7569)   on 2009-12-28 13:25:13 (Show Source):
You can put this solution on YOUR website!
Let n=time it takes for new machine to do the job.
Old does 1/(n+15) the job in 1 hr
together: 1/n + 1/(n+15)=1/6 (in one hour)
6(n+15)+6n=n(n+15) multiply each side by 6n(n+15) (LCM) to eliminate fractions.
6n+90+6n=n^2+15n
12n+90=n^2+15n
n^2+3n-90=0 subtract the left side from the right.
.
Ed
.
 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 : . Discriminant d=369 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 8.10468635614927, -11.1046863561493. Here's your graph:

 Divisibility_and_Prime_Numbers/250946: The expression n2 + n + 11 does not represent a prime number if n equals: A.2 B.4 C.5 D.7 E.101 solutions Answer 184385 by edjones(7569)   on 2009-12-28 13:05:35 (Show Source): You can put this solution on YOUR website!n^2+n+11 When n=10 100+10+11=121 121=11*11 . Ed
 expressions/252450: a number is 8 more than the ratio of q and 2 what is 3/4 the number in terms of q1 solutions Answer 184383 by edjones(7569)   on 2009-12-28 12:55:36 (Show Source): You can put this solution on YOUR website!x=(q/2)+8 (I changed your question so that it made sense to me.) 3x/4=3/4((q/2)+8) =3q/8 +8 . Ed
 Age_Word_Problems/252386: 1) if the product (2x+3)(x+k)is 2x to the 2nd power + 13x+15 find the value of k 2)write a quadratic expression that is the difference of two squares. 3)factor 15m to the 4 power - 6m to the 2nd power + 9m 4)14x to the 5th power - 49x to the 8th power 5) subtract (-8x to the 4th power +3x)-(5x-4-x to the 4th power)1 solutions Answer 184264 by edjones(7569)   on 2009-12-27 14:05:46 (Show Source): You can put this solution on YOUR website!3*k=15 k=5 . Ed
 Triangles/252398: In right triangle ABC where angle A is 90 degrees, AC = 3x and BC = 5x. if the perimeter of triangle ABC is 84, then what is x?1 solutions Answer 184262 by edjones(7569)   on 2009-12-27 13:59:55 (Show Source): You can put this solution on YOUR website!b=3x, c=5x a^2+b^2=c^2 a^2+9x^2=25^2 a^2=16x^2 a=4x 3x+4x+5x=84 12x=84 x=7 . Ed
 Quadratic_Equations/252391: I am having trouble solving: Y= -3x^2-6x-5, I have to graph it, so I need to know the x values, the y values, the x intercepts, the y itercepts and vertex1 solutions Answer 184256 by edjones(7569)   on 2009-12-27 13:14:55 (Show Source): You can put this solution on YOUR website!y= -3x^2-6x-5 . Use whatever x values you wish and calculate the y values. . x intercepts (when y=0) -3x^2-6x-5=0 There are none. There are no real zeros. Quadratic formula. . y intercepts (when x=0) y=-5 . vertex at x: -b/2a x= -(-6)/2(-3) =6/-6=-1 at y=-3+6-5=-2 . . Ed
 Linear-systems/252392: A 31-inch-square TV is on sale at the local electronics store. If 31 inches measure of the diagonal of the screen, use the Pythagorem to find the legnth of the side of the screen.1 solutions Answer 184254 by edjones(7569)   on 2009-12-27 12:47:00 (Show Source): You can put this solution on YOUR website!Let a=one of the sides 2a^2=31^2 Pythagoras a^2=961/2=480.5 a=21.92" . Ed
 Travel_Word_Problems/252390: An army, lined up single file, is one mile long. It starts marching at a uniform rate. It marches exactly one mile and then stops. At exactly the time it started marching, a messenger at the back of the line begins jogging toward the front of the line at a uniform rate. When he reaches the front of the line he instantaneously drops off a message and turns around and heads back to the end of the line just as the army stops marching. What distance did the messenger travel?1 solutions Answer 184251 by edjones(7569)   on 2009-12-27 12:39:15 (Show Source): You can put this solution on YOUR website!3 mi by the time he gets back to the end of the line.
 Expressions-with-variables/252389: i dont have a problem its more of a question with expression i know you have to do the same opperation to each side but how do you figure out wich number to use, allong with what action * - + or/? 1 solutions Answer 184250 by edjones(7569)   on 2009-12-27 12:36:04 (Show Source): You can put this solution on YOUR website!Good question! We usually want to get an unknown variable (x for instance) on the left hand side of the equation and everything else on the right. We + - * / accordingly until the mission is accomplished. a+b=c/d Find a, c and d. . a=c/d -b (subtract b from each side) . c=d(a+b) Multiply each side by d . d=c/(a+b) multiply each side by d/(a+b) . Ed
 Quadratic_Equations/252356: given 3x- 4y = 7 and x+ cy = 13 for what value of c will this system of equations NOT have a solution? a -4 b -4/3 c -3/4 d 3/4 e 4/31 solutions Answer 184247 by edjones(7569)   on 2009-12-27 12:23:34 (Show Source): You can put this solution on YOUR website!3x- 4y = 7 x+ cy = 13 . -4y=-3x+7 y=3x/4 -7/4 . cy=13-x y=13/c - x/c . There would be no answer if the equations had the same slope: 3x/4=-x/c Let the slope of the 2nd equal the slope of the 1st. c/4=-x/3x Multiply each side by c/3x c=-4/3 . Ed
 Points-lines-and-rays/252351: The line passing through (7, y) and (1,0) is parallel to the line joining (4,4) and (-2,1). Find y1 solutions Answer 184206 by edjones(7569)   on 2009-12-27 01:52:07 (Show Source): You can put this solution on YOUR website!(4-1)/(4-(-2)) =3/6 = 1/2=m=slope (y-0)/(7-1)=y/6 y=3 because slope must be 1/2. . Ed
 Probability-and-statistics/252282: Please help me solve the following problem as soon as possible. Thank you very much. A plant has 4 workshops. The production of workshop 1,2,3 & 4 account for 1/3, 1/4, 1/4 and 1/6 ,respectively, of the total output of the plant. The error rates of defective products correspond to the 4 workshops are 0.15, 0.08, 0.05, 0.01 respectively. a)Find the probability to extract one random product that is a good product. b)Find the probability to extract 7 random products that have 2 defective products. 1 solutions Answer 184205 by edjones(7569)   on 2009-12-27 00:17:03 (Show Source): You can put this solution on YOUR website!a) 1/3 * .15 = .05 1/4 * .08 = .02 1/4 * .05 = .0125 1/6 * .01 = .0167 ------------------------- =========>.08417 . 1-.08417=.91583 prob 1 random product is a good one. . . b) Let g=.91583 and d=.08417 (g+d)^7 nCr = n!/((n-r)r!) to find the coefficient of (g^5d^2) 7C2=21 21*.91583^5*.08417^2=.09585 prob that 2 out of 7 randomly selected will be defective. . Ed
 Probability-and-statistics/252250: The sales Manager of an Automobile dealer estimated 80% of the new cars delivered by them have no defect and so will not be brought back immediately for repair. He sells a fleet of 10 cars to an important customer. What i» the probability that — (i) No car will be brought back (ii) Exactly two cars will be brought back. (iii) At least two cars will be brought back. b) State the laws of probability. c) Describe giving examples different types of events.1 solutions Answer 184069 by edjones(7569)   on 2009-12-25 12:59:16 (Show Source): You can put this solution on YOUR website!Binomial expansion: (a+b)^10=a^10+10a^9b+45a^8b^2+... This is the only part of the expansion that we need. Let a=.8, b=.2 . No car returned: .8^10=.107 . Exactly 2 returned: 45*.8^8*.2^2=.302 . At least 2 returned: 10*.8^9*.2=.268 (exactly 1 returned) 1-.107-.268=.624 (1-one or none returned=at least 2 are returned.) . Ed
 Divisibility_and_Prime_Numbers/252201: What are the prime factors of 54541 solutions Answer 183996 by edjones(7569)   on 2009-12-24 15:15:19 (Show Source): You can put this solution on YOUR website!5454/2=2727 2727/3=909 909/3=303 303/3=101 2 * 3^3 * 101 are the prime factors. . Ed
 Probability-and-statistics/252181: The sales Manager of an Automobile dealer estimated 80% of the new cars delivered by them have no defect and so will not be brought back immediately for repair. He sells a fleet of 10 cars to an important customer. What i»the probability that — (i) No car will be brought back (ii) Exactly two cars will be brought back. (iii) At least two cars will be brought back.1 solutions Answer 183980 by edjones(7569)   on 2009-12-24 11:43:45 (Show Source): You can put this solution on YOUR website!Binomial expansion: (a+b)^10=a^10+10a^9b+45a^8b^2+... This is the only part of the expansion that we need. Let a=.8, b=.2 . No car returned: .8^10=.107 . Exactly 2 returned: 45*.8^8*.2^2=.302 . At least 2 returned: 10*.8^9*.2=.268 (exactly 1 returned) 1-.107-.268=.624 (1-one or none returned) . Ed
 Linear_Equations_And_Systems_Word_Problems/252153: As a restaurant owner there are many decisions that you need to make on a daily basis, such as inventory levels. You wish to replenish your stock of dishes by purchasing 250 sets for your restaurant. You have available two different dish designs. One design costs \$20 per set and the other \$45 per set. If you only have \$6,800 to spend, how many of each design should you order? Hint: Let x = the number of \$20 dishes and y = the number of \$45 dishes.1 solutions Answer 183935 by edjones(7569)   on 2009-12-23 19:14:55 (Show Source): You can put this solution on YOUR website!x+y=250 20x+45y=6800 . y=250-x 20x+45(250-x)=6800 20x+11250-45x=6800 -25x=-4450 x=178 y=72 . Ed