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# Recent problems solved by 'solver91311'

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 Permutations/273156: In the United Kingdom's National Lottery you must correctly select a group of 6 numbers from 49. Suppose that the contest were changed to selecting 7 numbers. How many more ways would there be to select the numbers?1 solutions Answer 199578 by solver91311(17077)   on 2010-02-23 01:36:24 (Show Source): You can put this solution on YOUR website! John
 Inequalities/273161: Solve: (x-5)(x+3)<=0 Thanks!1 solutions Answer 199577 by solver91311(17077)   on 2010-02-23 01:31:06 (Show Source): You can put this solution on YOUR website! Critical points are at (0,5) and (1,-3). These two points separate the -axis into three regions. Select -values from each of the three regions that are not the critical point -values. Let Let Let So: On the interval [-3,5] John
 Complex_Numbers/273148: how do you write the problem 3i(2-3i) in a+bi form?1 solutions Answer 199568 by solver91311(17077)   on 2010-02-23 00:03:11 (Show Source): You can put this solution on YOUR website! Use the distributive property: Remember: John
 Permutations/273140: in many lotteries, contestants choose 6 out of 50 numbers, without replacement. find the probability of winning this kind of lottery with one set of numbers.1 solutions Answer 199565 by solver91311(17077)   on 2010-02-22 23:51:26 (Show Source): You can put this solution on YOUR website! The numerator of your probability fraction is 1 and the denominator is the number of ways to select 6 things from 50 things. The number of ways to select things from things, , is calculated by: For your problem: You can do your own arithmetic. John
 Linear-equations/273142: find the value of C such that each pair of points is 5 units apart (0,C) (3,1)1 solutions Answer 199564 by solver91311(17077)   on 2010-02-22 23:44:05 (Show Source): You can put this solution on YOUR website! Use the distance formula: Solve: For And the question is mis-stated. It should read: "Find the values of C..." John
 Volume/273139: hi. can you help me to solve this problem.? thanks a lot A propane tank is constructed by welding hemispheres to the ends of a right circular cylinder. Write the volume V of the tank as a function of r and l, where r is the radius of the cylinder and hemispheres, and l is the length of the cylinder.1 solutions Answer 199563 by solver91311(17077)   on 2010-02-22 23:38:04 (Show Source): You can put this solution on YOUR website! The volume of a sphere of radius is given by: Each hemisphere is half of that volume, but you have two hemispheres, so you have one whole sphere. The volume of a cylinder with radius and length is: The total volume is the sum of the two: Which can be left as it is or manipulated as desired. I would use: or perhaps John
 Quadratic_Equations/273093: write an equation in standard form of the quadratic function that has a vertex (3,4) and whose graph passes through the poing (-1,-6)1 solutions Answer 199562 by solver91311(17077)   on 2010-02-22 23:26:01 (Show Source): You can put this solution on YOUR website! You are looking for a function: Such that , , and, because of symmetry, Hence: So solve the system: for the ordered triple <> which coordinates are the coefficients of the desired function. Note: This response was corrected some 24 hours after initial posting John
 Geometry_proofs/272927: how do you solve: Given: angle LOM is congruent to angle NPM LM is congruent to NM Prove: triangle LOM is congruent to angel NPM1 solutions Answer 199475 by solver91311(17077)   on 2010-02-22 17:25:53 (Show Source): You can put this solution on YOUR website! In the first place, you either have to include a diagram or at the very least give an extremely detailed description of the figure. In the second place, no matter what your figure looks like you cannot prove that a triangle is congruent to an angle -- that would be like trying to prove that belly button lint is the same as a hard-boiled egg. John
 Linear_Equations_And_Systems_Word_Problems/272869: How do I write and solve an equation for c mows the lawn three times faster than j. How long will it take to finish the job? (do you need the acerage? It would be 2)1 solutions Answer 199432 by solver91311(17077)   on 2010-02-22 15:56:54 (Show Source): You can put this solution on YOUR website! Without knowing specifically how long it takes either one of the participants to do the entire job (or some specified portion of the job) all you can tell is the proportional difference between the amount of time it would take j working alone vs. c working alone vs. the two of them working together. Let represent the number of time periods it would take c working alone. Then represents the number of time periods it would take j working alone. c can do of the job in one time period. Likewise, j can do of the job in one time period. Then, working together they can do: of the job in one time period. Hence, they would take: time periods to do the entire job. So, however long it takes c to do the entire job by herself is the value of and three-fourths of that is the time it would take the two of them working together. John
 Expressions-with-variables/271715: A thief steals a number of rare plants from a nursery. On his way out, the thief meets three security guards, one after another. To each security guard the thief is forced to give one-half the plants that he still has, plus two more. Finally, the thief leaves the nursery with no plants. How many plants were originally stolen?1 solutions Answer 198866 by solver91311(17077)   on 2010-02-19 10:53:51 (Show Source): You can put this solution on YOUR website! He gave the last guard everything, which was half of what he had plus 2. So 2 had to be the other half of what he had -- hence he had 4 when he met the last guard. The guard before then got 2 more than half, so half must have been 6, and he had 12 after his encounter with the first guard. 12 plus 2 is 14, times 2 is 28 which is the number he had at the start. John
 percentage/271713: In a certain company, 30 percent of the men and 20 percent of the women attend night school. If 40 percent of all employees are men, what percent of all the employees attend night school? 1 solutions Answer 198862 by solver91311(17077)   on 2010-02-19 10:44:07 (Show Source): You can put this solution on YOUR website! If 40% of the employees are men, then 60% must be women (unless there is some third gender I don't know about), so 30% of 40% is 0.3 times 0.4 = 0.12 = 12%. The men night school students represent 12% of the employee population. Likewise 0.2 times 0.6 = 0.12 = 12% so the women night school students also represent 12% of the employee population. So, 12% plus 12% is 24%. John
 Probability-and-statistics/271712: determine the probability of randomly guessing 40 questions correct out of 60 questions on a multiple choice test with possible selections a,b,c,d,e; by guessing1 solutions Answer 198861 by solver91311(17077)   on 2010-02-19 10:35:00 (Show Source): You can put this solution on YOUR website! The probability of exactly successes in trials where the probability of success on any given trial is is given by: Where is the number of ways to select things from a collection of things and is equal to Since there are 5 responses to each question, the probability of a random correct response on any given question is . Just plug in the numbers... And do the arithmetic. John
 Numbers_Word_Problems/271619: I am a 2 digit number greater than30 but less than 70 I am a mutiple of 2 and 4 but not a multiple of 6 I am squqre number1 solutions Answer 198860 by solver91311(17077)   on 2010-02-19 10:22:19 (Show Source): You can put this solution on YOUR website! The perfect squares greater than 30 but less than 70 are 36 (divisible by 2 and 4, but also by 6), 49 (not divisible by 2, 4, or 6), and 64. 64 has to be the answer. John
 Polynomials-and-rational-expressions/271377: I'm trying to put this polynomial in standard form: y-7y^3+15y^8. I started to reorder it and got 15y^8-7y^3+y. Can I subtract 7y^3 from 15y^8 and get 8y^5? That would make my solution 8y^5-y. Am I right?1 solutions Answer 198711 by solver91311(17077)   on 2010-02-18 17:14:31 (Show Source): You can put this solution on YOUR website! No, no, no! A thousand times NO! Just for the sake of argument, let's assign the value 2. By your theory: Not in my math classroom, thank you very much. The only thing you could possibly do with: would be to factor out a , leaving you with: John
 Inverses/271385: what is 6r-1+6r=111 solutions Answer 198704 by solver91311(17077)   on 2010-02-18 17:01:07 (Show Source): You can put this solution on YOUR website! A single variable linear equation. John
 Travel_Word_Problems/271381: Dr. Pepper left Oakville at 9am. and drove the central city at 60km/h. H. Salt left Oakville at 11am and traveled the same route to Central City. If both men arrived in Central City at 4pm, at what rate did H. Salt travel? .. please i cannot find a way to write the equations needed! please help..?1 solutions Answer 198702 by solver91311(17077)   on 2010-02-18 16:58:53 (Show Source): You can put this solution on YOUR website! Pepper left at 9 am and arrived at 4 pm -- 7 hours. 7 hours times 60 miles per hour is 420 miles. Salt left two hours later, but arrived at the same time, so his travel time was 5 hours for the same 420 miles. 420 divided by 5 is 84 mph. Lucky he didn't get a ticket. John
 Probability-and-statistics/271350: If you have a bag of marbles; 7 red, 5 green, and 8 blue, what's the probability of getting at least 2 red marbles in 3 draws from the bag, with replacement? Thanks...this is all new to me!1 solutions Answer 198697 by solver91311(17077)   on 2010-02-18 16:51:01 (Show Source): You can put this solution on YOUR website! Here you are looking for the probability of success for a number of trials where the probability of success is constant for each independent trial. The probability is constant because you are replacing the drawn marble each time. The probability on any given trial is the number of red marbles divided by the total number of marbles. You'll have to compute that first. For now, I'm going to call that number . You also need to know the probability of NOT drawing a red marble on any given trial. Two ways to get this: Either count the total number of marbles that aren't red and divide by the total number of marbles or calculate . We'll call this second number . The probability of exactly successes out of trials is given by: where is the number of ways to select things from a collection of things and is equal to: But you don't want the probability of exactly 2 red out of 3 draws, you want at least 2 red out of 3 draws. So you need the probability of exactly 2 red out of 3 draws PLUS the probability of exactly 3 red out of 3 draws. So, substitute the values you calculated for and into: and Then add the two results. John
 expressions/271345: How do I add -4/5 + (-3/4)?1 solutions Answer 198680 by solver91311(17077)   on 2010-02-18 15:59:06 (Show Source): You can put this solution on YOUR website! 5 and 4 have no factors in common so the LCD is just the product, namely 20. Therefore: All of which makes good sense because: and and and John
 Equations/271341: Please help me solve.. 1+1/x=90/x^21 solutions Answer 198672 by solver91311(17077)   on 2010-02-18 15:50:04 (Show Source): You can put this solution on YOUR website! Multiply by Add -90 to both sides: Now just solve the easily factorable quadratic. John
 Travel_Word_Problems/271332: Please help me with these word problems... 1. A boat goes 240 miles downstream in the same time it can go 160 miles upstream. The speed of the current is 9 miles per hour. Find the speed of the boat in still water. 2. To determine the number of fish in a lake, a park ranger catches 200 fish, tags them, and returns them to the lake. Later, 144 fish are caught, and it is found that 40 of them are tagged. Estimate the number of fish in the lake. 3. Frank can type a report in 4 hours and James takes 6 hours. How long will it take the two of them typing together?1 solutions Answer 198665 by solver91311(17077)   on 2010-02-18 15:40:08 (Show Source): You can put this solution on YOUR website! 1. Solve for 2. Solve for 3. If A can do a job in time periods and B can do a job in time periods, then A can do of the job in 1 time period and B can do of the job in 1 time period. Then, working together they can do: of the job in one time period. Therefore they can do the whole job in: time periods. Next time, one question per post please. John
 Linear-equations/271328: Please show me how to graph 15x-5y=45 using the x- and y-intercepts. What is the slope and the y intercept in the problem?1 solutions Answer 198660 by solver91311(17077)   on 2010-02-18 15:31:51 (Show Source): You can put this solution on YOUR website! Substitute 0 for and then solve what is left for , giving you some value for such as . (Determining the value of is left as an exercise for the student). That gives you the coordinates of one ordered pair, , which happens to lie somewhere on the -axis -- hence the name -intercept. Now repeat the same process substituting 0 for and creating a second ordered pair, interestingly enough called the -intercept, of the form . Again, the value of is up to you. Plot both points. Draw a line extending all the way across your graph through the two points. John
 Polynomials-and-rational-expressions/271325: I'm trying to factor -x^2+6x-8 please.1 solutions Answer 198657 by solver91311(17077)   on 2010-02-18 15:25:08 (Show Source): You can put this solution on YOUR website! Factor out -1 to start: Now note that -2 times -4 is +8 and -2 plus -4 is -6, so: John
 Linear-equations/271321: what is the eguation of a line with slope -2,that passes through (1,1)1 solutions Answer 198651 by solver91311(17077)   on 2010-02-18 15:18:39 (Show Source): You can put this solution on YOUR website! I don't know what an eguation is, but if you want an equation of a line with a slope of -2 that passes through the point (1,1), then you should use the point-slope form of the equation of a line: where are the coordinates of the given point and is the given slope. Note that this will not give you the equation of the desired line, it will only give you an equation of the specified line. There is no such thing as the equation of a line since there are an infinity of equivalent representations for any given line. John
 Triangles/271106: A flower bed in the shape of a right triangle is to be made in the corner of a yard, with sides 15 feet and 20 feet. a) The label the fertilizer I plan to use for the flower bed says to use 2 cups for each 100 square feet. How much will I need? The answer I got was 6 cups. b) I want to add 6 inches of topsoil on the flower bed, which comes in bags that hold 2 cubic feet each. How many bags will I need? c)How many feet of fencing will be needed to completly surround the flower bed? The answer I got was 145ft. Please help me with the (B) question and correct (A and C) if I got those wrong. Thanks so much. 1 solutions Answer 198508 by solver91311(17077)   on 2010-02-18 00:26:04 (Show Source): You can put this solution on YOUR website! A: The area of a triangle is given by where is the measure of the base and is the measure of the height (aka altitude). In a right triangle, the base and height are the same as the legs of the triangle. So in your case: Then B: From part A, the area is 150 ft². If you want the topsoil to be 6 inches deep, you use one-half cubic foot for every square foot of area. Or 75 cubic feet for the entire 150 ft² garden. 75 divided by 2 is 37.5, so you need 38 bags of soil unless you can get someone to sell you half a bag. C: The perimeter is just the sum of the measures of the sides. 15 is to 20 as 3 is to 4, so this is actually a 3-4-5 right triangle, and the hypotenuse is 25. (if you want to check this, use Pythagoras: ) The perimeter is then 15 + 20 + 25 = 65 feet. John
 Geometry_Word_Problems/271024: joan bought a garden hose from the hardware store. the hose measured 50 meters in length. which measurement is closest to the lenghth of the hose, in feet?1 solutions Answer 198424 by solver91311(17077)   on 2010-02-17 20:23:54 (Show Source): You can put this solution on YOUR website! Wow! That is some garden hose. One meter is roughly 3.28 feet, so 50 meters is just a touch over 164 feet. I've never seen a garden hose longer than 100 feet. John
 Quadratic_Equations/271022: discriminant of each equation and tell if the solutions are real or imaginary for example how would you do y=x^2+10X-25 also tell how many solutions1 solutions Answer 198417 by solver91311(17077)   on 2010-02-17 20:20:46 (Show Source): You can put this solution on YOUR website! For a quadratic equation in standard form, namely: the discriminant, , is given by: Two real and unequal roots. If the discriminant is a perfect square, the roots are rational. Otherwise not. One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. A conjugate pair of complex roots of the form where is the imaginary number defined by John
 Volume/271020: Suppose a box has a volume of 1 yd3. What is its volume in cubic feet?1 solutions Answer 198415 by solver91311(17077)   on 2010-02-17 20:16:04 (Show Source): You can put this solution on YOUR website! John
 Circles/271014: In circle C, QR is a diameter, and Q(1,8) and C(3.5, 2) are points on a coordinate plane. Find and state the coordinates of point R.1 solutions Answer 198414 by solver91311(17077)   on 2010-02-17 20:13:39 (Show Source): You can put this solution on YOUR website! C must be the center of the circle, so since QR is a diameter, C must be the mid-point of QR. Use the mid-point formulae to determine the coordinates of R. and Where are the coordinates of C, are the coordinates of Q, and are the coordinates of R. Substitute what you know and then solve: and John
 expressions/271008: a algebraic expression for a number increased by nine using the letter x1 solutions Answer 198410 by solver91311(17077)   on 2010-02-17 20:07:58 (Show Source): You can put this solution on YOUR website! John
 Equations/270998: Have I done this correctly? (I am writing it out in words; have tried twice to write it, once using formula plotting system) 5 minus m over 7 minus m equals 2 over 3 5 minus m equals 2 times 7 minus m over 3 2 m minus m equals 14 minus 5 over 3 m equals 9 over 3 m equals 3 Thank you, Elizabeth1 solutions Answer 198405 by solver91311(17077)   on 2010-02-17 20:03:33 (Show Source): You can put this solution on YOUR website! A gallant effort, Elizabeth, but not quite right. Here's how I know: You say . If that is true, then: must be a true statement. But You were on the right track on the second step, but where you went from there I cannot fathom. You multiplied both sides of the equation by the denominator on the left to get: Your next step should have been to distribute the 2 in the numerator on the right, thus: Then you can multiply both sides by 3, the denominator on the right: Distribute the 3: Add to both sides: Add -15 to both sides: Multiply both sides by -1: Check the answer: Yep, it checks. John
 Geometry_Word_Problems/270960: hello tutor my name is faisal and i have 2 important questions to ask u 1) if the perimeter of a right traingle is 3 meters and the hypotenuse is 145 cm, what is the length of the other 2 sides. 2) A picture's area is 10cm by 8cm and the width is also uniform, it is going to be placed on a mat that is twice the area of the picture, what is the width of the mat?1 solutions Answer 198404 by solver91311(17077)   on 2010-02-17 19:47:24 (Show Source): You can put this solution on YOUR website! #1: Let represent the measure of one leg of your triangle. Let represent the measure of the other leg. Since the perimeter is 3 meters, which is to say 300 cm, we can write: It will be convenient to solve for at this point: Since this is a right triangle, we can also write: Substituting: Just solve for . You will get two positive roots, one will be one leg of the triangle and the other root will be the other leg of the triangle. #2: Let represent the width of the mat. If the picture is 10 by 8, the mat has to be by . Now the only question is whether the area of the mat mentioned in the problem is the overall area of the mat before you cut the hole for the picture, or the area that remains after you cut the hole for the picture. If it is the first way: which simplifies to: if it is the second way (and this is probably the correct interpretation): Which simplifies to: Either way, solve for . Either way you get a positive and a negative root. Discard the negative root because you are looking for a positive measure of length. John