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# Recent problems solved by 'rapaljer'

 Sequences-and-series/815181: Dear Team can you please help to get answers on these 2 questions? 1.Select the option for “?” that continues the pattern in each question 2, 7, 26, 101, 400, ? 2.Select the option for “?” that continues the pattern in each question 7, 21, 8, 72, 9, ? 1 solutions Answer 490754 by rapaljer(4670)   on 2013-11-28 09:10:15 (Show Source): You can put this solution on YOUR website! I see a pattern for the first set in which you take the given number and multiply by 4 and subtract 1, then multiply by 4 subtract 2, multiply by 4 subtract 3, mult by 4 and subtract 4, etc. Starting with 2, multiply by 4 subtract 1 giving you 7. Take 7, multiply by 4 and subtract 2 giving you 26. Mult 26 times 4 and subtract 3 giving you 101. Multi by 4 subtract 4 giving you 400. Next would be multiply by 4 and subtract 5 giving 1595. For the second pattern, I'm not sure. You might try starting with 7 *3 = 21. Next, take 8*3^2= 72. Next, take 9*3^3=243. This might be a stretch, but it's all I can think of. Happy Thanksgiving!! Please see my website for FREE math explanations, and practice tests. See www.mathinlivingcolor.com. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Probability-and-statistics/799819: What is the theoretical probability of rolling a 4 or 5 on a number cube? I got 1/4 is my answer correct? 1 solutions Answer 482828 by rapaljer(4670)   on 2013-10-16 15:02:06 (Show Source): You can put this solution on YOUR website! If there are a total of 6 possible faces on the cube, then the probability of getting a 4 or 5 will be TWO possibilities out of SIX. The probability is 2/6 which reduces to 1/3. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Linear-equations/741637: A police academy is training 14 new recruits. Some are working dogs and others are police officers. There are 38 legs in all. How many of each type of recruit are there 1 solutions Answer 452096 by rapaljer(4670)   on 2013-04-25 02:41:33 (Show Source): You can put this solution on YOUR website! Let X=number of police officers (each with 2 legs) y= number of dogs (with 4 legs each) The equation for recruits is x+y=14 The equation of legs is 2x+4y=38 which can be reduced to x+2y=19 Multiply first equation by -1: -x - y = -14 x +2y = 19 Add these equations together, and you get y= 5 dogs Since x+y=14, 5 dogs means there are 9 police, with legs = 20 for dogs, 18 for police for a total of 38 legs. It checks. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Exponential-and-logarithmic-functions/741620: Find the value of that makes the statement true. log20x=-1 1 solutions Answer 452094 by rapaljer(4670)   on 2013-04-25 02:32:09 (Show Source): You can put this solution on YOUR website! translates by the definition of logarithms to Therefore, . Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Probability-and-statistics/741644: A box is filled with 5 red cards, 6 yellow cards, and 7 blue cards. A card is chosen at random from the box. What is the probability that the card is not yellow? Write your answer as a fraction in simplest form. 1 solutions Answer 452093 by rapaljer(4670)   on 2013-04-25 02:26:45 (Show Source): You can put this solution on YOUR website! Probability of a NON-yellow card = , where NON-yellow = 5+7=12 Total = 5+6+7 = 18 . Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Travel_Word_Problems/741643: Please Help Me solve this problem. It took 32 liters of gas to travel 450 km. How many liters would it take to drive 800 km (round it to the nearest tenth). I figured if I took the 450 km times 2 would give 900 km and 64 liters to do this. I guessed it would be between 55 to 60 Liters to do this; but that is my guess and do not know how to work the problem out. Please Help Me! 1 solutions Answer 452091 by rapaljer(4670)   on 2013-04-25 02:20:15 (Show Source): You can put this solution on YOUR website! Set up a ratio: Cross multiply! Since means , the above equation means that Then divide by 450: which rounds to 56.9 liters. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Age_Word_Problems/741165: Phil is 24 years older than WIll. Four years ago he was seven times as old as WIll was then. FInd their ages now. I have tried guess and check and have found the answer but is there a way to get the answer through using a formula? Thank you so much guys! After answering my question treat yourself to a nice warm cup of cocoa and pat your self on the back because you know you just helped a child at need. LOL. Thanks!! @_@ 1 solutions Answer 451875 by rapaljer(4670)   on 2013-04-23 23:18:45 (Show Source): You can put this solution on YOUR website! Let x = Will's age now x+24 = Phil's age now x-4 = Will's age 4 years ago x+24-4 = x+20 = Phil's age 4 years ago. Here is the equation: "Four years ago, Phil was 7 times as old as Will was 4 years ago." x+20 = 7*(x-4) x+20 = 7x -28 x-7x=-28-20 -6x=-48 x=8 = Will now x+24 = 32 = Phil now Check: Four years ago, Will was 4 and Phil was 28, which is 7 times Will's age. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Circles/718623: find the center radius form of the equation of a circle with the center(2,8) and tangent to the x axis 1 solutions Answer 440995 by rapaljer(4670)   on 2013-02-25 12:03:14 (Show Source): You can put this solution on YOUR website! If the center is at (2,8), and it is tangent to the x axis, this means that it just barely touches the x axis from a center that is 8 units above the x-axis. So, the radius of the circle is 8. (x-h)^2 + (y-k)^2 = r^2 (x-2)^2 + (y-8)^2 = 64 For additional help with circles, you may want to see my non-traditional explanation of this and other topics on my own website: www.mathinlivingcolor.com. Click on the link at the very bottom of the page which will take you to my Homepage, and look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "College Algebra" and look in Chapter 2 for the section on Circles. Then, I solved many of my problems IN COLOR, which makes all the difference in the world, to understanding math concepts. Try it for this topic as well as others, and let me know what YOU think. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Polynomials-and-rational-expressions/718666: what is the answer to: -2x-3(x-5)-1 Directions say to simplify. I first thought you would combine like terms but i cannot figure this out. 1 solutions Answer 440992 by rapaljer(4670)   on 2013-02-25 11:37:50 (Show Source): You can put this solution on YOUR website! The first step, if there are parentheses in the problem, is to remove the parentheses by distributive property. -2x -3(x-5) -1 -2x-3x+15-1 Now, combine like terms: -5x + 14 For additional explanations on this type of problem that may be easier to understand than the traditional explanations, please see my own website at www.mathinlivingcolor.com. Then click on the link at the very bottom of the page, which will take you to my Homepage, and look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in Chapter 1 for topics about Signed Numbers, Order of Operations, and especially Distributive Property. You may also really like my explanation of Equation Solving. Also, look for solutions to many of the problems you will find there IN COLOR!! Color really makes a difference in being able to understand what was done in the problem. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Equations/718649: (((n divided by(-7)=4over7))) 1 solutions Answer 440991 by rapaljer(4670)   on 2013-02-25 11:28:50 (Show Source): You can put this solution on YOUR website! Multiply both sides by 7: Divide by -1: n=-4 For an explanation that may be easier than your textbook or web explanations, please see my own website at www.mathinlivingcolor.com. Click on the link at the very bottom of this page that will take you to my Homepage. On my Homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time", click on "Basic Algebra", and look in Chapter 1 for Equation Solving. I think you will like my explanations. My own students liked them before I retired. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Proofs/718648: If ... 1 + 2 = 32 3 + 4 = 712 Then ... 0+5 = ?? 1 solutions Answer 440984 by rapaljer(4670)   on 2013-02-25 10:35:44 (Show Source): You can put this solution on YOUR website! It appears that the pattern is add the digits together to get the first digit, and multiply the digits to get the last digit(s). If this is the correct pattern, then 0+5=50 I'm not sure about this one!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Square-cubic-other-roots/718644: Simplify assuming that variables represent positve real numbers: Square root 9z^6/25 1 solutions Answer 440983 by rapaljer(4670)   on 2013-02-25 10:31:41 (Show Source): You can put this solution on YOUR website! Take the square root of the numbers 9 and 25, which are perfect squares. In the case of variables raised to powers, you have to divide the exponent by 2. Final answer =. For extra help with square roots, please see my own website at www.mathinlivingcolor.com. The link at the bottom of the page will take you to my Homepage. Look for the link on my Homepage called "Basic, Intermediate, and College Algebra." Choose "Basic Algebra" and look in Chapter 5 for a detailed explanation in my own words on Radicals (that is, Square Roots!). I think you will find my website easier to understand than traditional textbooks. Also, there is a FREE video on my website of me teaching this topic a few years ago before I retired. Look for the link "Rapalje Videos in Living Color". Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Miscellaneous_Word_Problems/718632: How many sheets of paper were there in a pack if there were 464 sheets left after Michelle had taken two-sixths of them? Really need help on this one!! 1 solutions Answer 440981 by rapaljer(4670)   on 2013-02-25 10:23:00 (Show Source): You can put this solution on YOUR website! If Michelle took 2/6 or 1/3 of the sheets, this means that 2/3 of the sheets remain. Let x = number of sheets originally in the pack. 2/3*x = 464 To solve the equation for x, multiply both sides of the equation by 3/2 to "undo" the 2/3, x=3/2*464=3*232=696 sheets. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Geometry_Word_Problems/718600: A circular pool has a radius of 15 feet. How many feet is one lap around the edge of the pool? 1 solutions Answer 440971 by rapaljer(4670)   on 2013-02-25 09:11:33 (Show Source): You can put this solution on YOUR website! The distance around a circle is called the circumference of the circle. The formula is , where in this case r=15 feet. feet, where pi= 3.14 approximately. C=94.2 feet approximately I do have a few pages of geometry explanations on my website if you need another explanation of this topic. Go to the website www.mathinlivingcolor.com, then click on the link at the bottom of this page. Then, look on my Homepage for the link "Topics from Geometry." Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Circles/718613: In the circle above, the letter X represents the a radius. b circumference. c diameter. d circle. 1 solutions Answer 440970 by rapaljer(4670)   on 2013-02-25 09:01:39 (Show Source): You can put this solution on YOUR website! I can't see the picture. Does the x distance go all the way across the middle of the circle? If so, the x is the diameter. Does it go from the center of the circle to the edge of the circle? If so, then x is the radius. Usually, x would not be used as the circumference of the circle, unless the x is indicated to go all the way AROUND the circle. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Travel_Word_Problems/718612: dad's car uses 1 litre of of petrol for every 8 kilometres. if dad uses 7 litres of petrol a dat to get to work and come back home again, how far is dad's work from our home? 1 solutions Answer 440969 by rapaljer(4670)   on 2013-02-25 08:58:11 (Show Source): You can put this solution on YOUR website! For each litre he uses, he drives 8 kilometres. If he uses 7 litres, then he must be driving 7 times as far, which is 7*8= 56 kilometres. Dr. Robert J. Rapalje, Retired Seminole State College of Florida USA
 Linear-systems/718605: what is the x-intercept of the line with equation 3y - 4x = 10 1 solutions Answer 440968 by rapaljer(4670)   on 2013-02-25 08:55:15 (Show Source): You can put this solution on YOUR website! The x intercept means that y=0. So, substitute y=0, and you have -4x=10 x= This can be written as a point (-5/2,0). For additional help with graphing and intercepts, please see my own website at www.mathinlivingcolor.com. Click on the link at the bottom of this page which will take you to my homepage. There, look for topics in Basic Algebra in Chapter 4. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 test/718607: Find ∫2 x Sin(x2)dx if c is a constant. 1 solutions Answer 440967 by rapaljer(4670)   on 2013-02-25 08:45:28 (Show Source): You can put this solution on YOUR website! Let u=x^2 du= 2x dx Final answer By the way, I have my own website with a LOT of algebra help. As far as calculus goes, I don't have calculus explanations, but I DO have two sets of practice tests for Calculus I with DETAILED solutions sheets. To see my website use my easy to remember and easy to spell link www.mathinlivingcolor.com. Then click on the link at the bottom of the page, which goes to my Homepage. On my Homepage, look for the link "Practice Tests" and choose the appropriate course level. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Quadratic_Equations/683998: three different ways to graph the quadratic relation, . The three ways include: using a table of values, using x-intercepts, and using the vertex and step pattern. Which method do you like the best to graph ? Why? 1 solutions Answer 423877 by rapaljer(4670)   on 2012-11-22 23:17:57 (Show Source): You can put this solution on YOUR website! My LEAST favorite way is the table of values. I prefer the vertex method using x=-b/2a. Of course, the x-intercepts method is also nice, and also knowing that the vertex is always exactly HALFWAY beteen the two intercepts. Of course, the problem may not have x-intercepts. The vertex, where x=-b/2a, always works. Dr. Robert J. Rapalje, Retired Seminole State College of Florida www.mathinlivingcolor.com.
 Rational-functions/684003: What kind of numbers form the domains for the following types of functions? Also what number should be excluded ? A) Rational functions B) Radical functions C) Logarithmic functions D) Exponential functions 1 solutions Answer 423876 by rapaljer(4670)   on 2012-11-22 23:12:41 (Show Source): You can put this solution on YOUR website! A) Rational functions: Denominators must NEVER be ZERO. B) Radical functions: Radicands must be GREATER than or EQUAL to ZERO. C) Logarithmic functions: For y = log (b, x) base numbers must never be negative, zero, or 1. In other words, b>0 and b not equal to 1. Secondly, x>0. In other words, you can't have the log of a negative number. D) Exponential functions: There are NO restrictions on x. Domain is all real numbers. Dr. Robert J. Rapalje, Retired Seminole State College of Florida www.mathinlivingcolor.com.
 Rate-of-work-word-problems/684008: it takes jack 3.5 hours to complete a job and it takes 2 hours for eleanor to do the same job. How long would it take for them to complete the job working together? 1 solutions Answer 423875 by rapaljer(4670)   on 2012-11-22 23:01:12 (Show Source): You can put this solution on YOUR website! Let x = time it takes them to do the job together. First fraction is UGLY, so multiply numerator and denominator by 2 to clear the decimal: Next, add the fractions with LCD = 14: Invert the fractions: x= 14/11 hours Dr. Robert J. Rapalje, Retired Seminole State College of Florida www.mathinlivingcolor.com.
 Expressions-with-variables/684006: What is 3p + 2 -(2p - 4) 1 solutions Answer 423874 by rapaljer(4670)   on 2012-11-22 22:40:18 (Show Source): You can put this solution on YOUR website! This one is called the Distributive Property. It might help to think of it as 3p + 2 -1(2p - 4) 3p + 2 -2p + 4 3p - 2p + 2 + 4 p + 6 I have a LOT of explanations, examples, and FULL COLOR solutions to problems like this on my own website. To see my website go to www.mathinlivingcolor.com, named after my theme "Math in Living Color." Look for a single link near the bottom of this page that will take you to my Homepage. Once on my Homepage, look for "Basic, Intermediate and College Algebra: One Step at a Time", and select "Basic Algebra". Look in "Chapter 1" for "Section 1.06". If you have questions on other topics, just send me an Email! I'll be glad to help you find the right page on my website. I hope you like my website and that you will recommend it to family and friends! Remember, my goal is to make math EASIER than your own textbook is making it, and it's ALL FREE!!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida www.mathinlivingcolor.com.
 Linear-systems/683842: Suppose two angles are supplements. Fine the measures of both angles if one of the angles is 69 degrees smaller than twice the other angle. I understamd what to do but if the first problem equals to 180 what does the second equation equal to? 1 solutions Answer 423870 by rapaljer(4670)   on 2012-11-22 22:11:25 (Show Source): You can put this solution on YOUR website! Let y="other angle" x= "one of the angles" x+y=180 x=2y-69 Solve by substitution: x+y=180 (2y-69) + y = 180 3y - 69 = 180 3y = 249 y = 83 x=97 Dr. Robert J. Rapalje, Retired Seminole State College of Florida www.mathinlivingcolor.com.
 Linear-equations/684004: Is 6 - 14 -11 or 3 the solution for (-2?) y =5x-4 1 solutions Answer 423868 by rapaljer(4670)   on 2012-11-22 22:00:56 (Show Source): You can put this solution on YOUR website! This means to let x=-2, and find the value of y. y=5x - 4 y=5(-2) - 4 y=-10 - 4 y=-14 Dr. Robert J. Rapalje, Retired Seminole State College of Florida www.mathinlivingcolor.com.
 test/684002: Pls explain to me 1 solutions Answer 423866 by rapaljer(4670)   on 2012-11-22 21:39:37 (Show Source): You can put this solution on YOUR website! You need to state the problem.
 Polynomials-and-rational-expressions/684000: Factor the Polynomial: x^3+7x^2+15x+9 I don't even know where to start, however I made an attempt, by trying to use the factor by grouping method which all I got is: (x^3+7x^2)+(15x+9) x^2(x+7)+3(5x+3) and that's were I stopped because I know that two of them should be the same -thank you in advance :D 1 solutions Answer 423864 by rapaljer(4670)   on 2012-11-22 21:37:53 (Show Source): You can put this solution on YOUR website! This one does NOT work by grouping! You need to use Synthetic Division. Start by looking at the LAST term, which is 9. You need to find a number that is a factor of 9, and do synthetic division by that number until you get a remainder of 0. I can see that one that works here is -1, maybe others as well. I don't know exactly how to lay out a synthetic division problem on this website, but I have quite a few examples on my website in Intermediate Algebra or College Algebra. To see my website go to www.mathinlivingcolor.com, named after my theme "Math in Living Color." Look for a single link near the bottom of this page that will take you to my Homepage. Once on my Homepage, for explanation of Sythetic Division, look for "Basic, Intermediate and College Algebra: One Step at a Time", and select "Intermediate Algebra". Look in "Chapter 2" for "Section 2.10" page 232! College Algebra Chapter 3 has additional explanation about using Synthetic Division in order to factor polynomials. Send me an email if you need additional help with this one. Dr. Robert J. Rapalje, Retired Seminole State College of Florida www.mathinlivingcolor.com.
 percentage/684001: A student took a test composed of 10 questions, with correct answers worth 5 points. If the student received 30 points for his grade, how many questions were correct? I know the answer is 6 but how do I put it in an exquation 1 solutions Answer 423863 by rapaljer(4670)   on 2012-11-22 21:24:53 (Show Source): You can put this solution on YOUR website! For an equation, why don't you set up a ratio: Let x = number of questions Now, means that . means that Now, solve for x by dividing both sides by 5: Dr. Robert J. Rapalje, Retired Seminole State College of Florida www.mathinlivingcolor.com.