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# Recent problems solved by 'rapaljer'

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 Numbers_Word_Problems/682532: Find the value of 327 in the mod 7 system. 1 solutions Answer 423222 by rapaljer(4667)   on 2012-11-18 23:21:06 (Show Source): You can put this solution on YOUR website!Divide by 7, and see what the remainder is. 327 divided by 7 gives you 46 with a remainder of 5, right?? so 327(mod 7) = 5. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Probability-and-statistics/682541: the probability that her age will fall between 55 and 60 years is____ the probability that her age will fall between 47 and 53 years is___ the probability that her age will be less than 35 years is____ the probability that her age will exceed 41 years is___1 solutions Answer 423219 by rapaljer(4667)   on 2012-11-18 23:15:07 (Show Source): You can put this solution on YOUR website!Were you given the mean and standard deviation of the population??? Dr. Robert J. Rapalje, Retired
 Miscellaneous_Word_Problems/682506: Hi. Can you help me solve this? I'm stuck. How many teams are in a league that schedules 45 games in such a way that each team plays every other team only once? Thanks.1 solutions Answer 423214 by rapaljer(4667)   on 2012-11-18 22:15:35 (Show Source): You can put this solution on YOUR website!Let x = number of teams in the league. Since each game includes 2 teams, you are looking for a COMBINATION problem, C(x,2) = 45. In other words, Now, if you are an algebra student, you should multiply out the left side to obtain x^2 - x = 90, and solve the quadratic equation. x^2 - x - 90 = 0 (x-10)(x+9)=0 x= 10 or x=-9, reject the negative answer. There are 10 teams in the league. If you are a statistics student, you should ask yourself, what number times one more that the number would give you a product of 90. Probably pretty obvious that the numbers would be 9 and 10. To analyze the answer, what you have is 10 teams in the league, and each team has 9 opponents. Lest you think this gives you 90 games, remember that Team A playing Team B is the same as Team B playing Team A, so you have to divide by 2 in order to eliminate the duplication of games. Dr. Robert J. Rapalje, Retired Seminole State College of Florida P.S. Check out my website for full color explanations and lots of practice tests with detailed solutions for all levels of math at www.mathinlivingcolor.com.
 Rate-of-work-word-problems/682497: A hose takes 15 minutes to fill a swimming pool and the drain empties the pool in 20 minutes. How long will it take to fill the pool if the drain is left open? I thought my teacher said the answer was 80 minutes but I only could figure out 1/15-1/20=1/60 making it 60 minutes. Can you explain my mistake please?1 solutions Answer 423209 by rapaljer(4667)   on 2012-11-18 21:52:10 (Show Source): You can put this solution on YOUR website!I'm sorry but I can't see how it could be 80 minutes, and I don't see anything wrong with your equation. Let x = time it takes for the pool to fill given that the drain is open and the hose is turned on. 1/15 = amount of the pool filled in 1 minute with hose only and drain closed. 1/20 = amount of the pool emptied in 1 minute with the drain open and no hose. , solve for x. The LCD is 60x, and the answer is x=60. Why don't you re-post the problem. Maybe someone else has another idea on this one. Dr. Robert J. Rapalje, Retired Seminole State College of Florida P.S. Check out my website for full color explanations and lots of practice tests with detailed solutions for all levels of math at www.mathinlivingcolor.com.
 Rational-functions/682492: How to rewrite g(x) to look like f(x) and f(x) to look like g(x)? g(x)=0.25^(1-x) f(x)= 4^(x-1)1 solutions Answer 423204 by rapaljer(4667)   on 2012-11-18 21:37:58 (Show Source): You can put this solution on YOUR website! Converting f(x) to g(x) will be a similar process, somewhat in reverse! Dr. Robert J. Rapalje, Retired Seminole State College of Florida P.S. Check out my website for full color explanations and lots of practice tests with detailed solutions for all levels of math at www.mathinlivingcolor.com.
 Equations/632843: solve y^2+14y=32 by completing the square,..thnks1 solutions Answer 398511 by rapaljer(4667)   on 2012-07-29 08:26:15 (Show Source): You can put this solution on YOUR website!Take HALF of the coefficient of y, which is 7, and SQUARE it to get 49. Add this to each side of the equation: y^2 + 14y + 49 = 32 + 49 (y+7)^2 = 81 Take the square root of each side: Calculate each value: y=-7 +9 =2 y=-7-9 = -16 Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Geometry_Word_Problems/632353: If you wrap a piece of wire 8 times around a pipe and the length of the pipe is 20cm and the circumference is 6cm, what is the length of the wire?1 solutions Answer 398239 by rapaljer(4667)   on 2012-07-27 09:36:49 (Show Source): You can put this solution on YOUR website!When I first read this problem, I'm afraid that I interpreted incorrectly. This is actually supposed to be a wire wrapped AROUND and UP the pipe in a spiral manner (this is called a HELIX in case you want to look into this for additional explanation), Begin by picturing a vine or a wire wrapped 6 times around a tree trunk that is 20 feet high and whose circumference is 8 feet. If the circumference is 8 feet, then the DIAMETER of the trunk of the tree is 8/pi. Now, suppose you cut the tree off at the base, and lay the tree flat on the ground, and UNWRAP the vine or wire by fastening the vine at the top of the tree and rolling the tree on the ground. When the vine is completely unwrapped, the vine will form the hypotenuse of a right triangle, where the first leg (the height of the triangle!) is the original position of the tree on the ground, which is 20 feet, and the second leg (the base of the triangle!) is the path traced out by the base of tree as it was rolled to unwind the vine. Can you picture this? The tricky part to figure is the length of the second leg of the right triangle. Each time you rolled the tree to unwrap one complete wrapping of the vine, the tree rolls ONE circumference, which would be 8 feet. Since the vine wrapped a total of 6 times around the tree, this means that the total distance the tree rolls to completely unwrap the vine will be 6*8 feet or 48 feet. So, picture a right triangle whose height is 20 feet and whose base is 48 feet. The total length of the vine is the hypotenuse, which is Of course, change the feet to cm for this particular problem. The final answer is . Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Travel_Word_Problems/632280: A vehicle is traveling 35 mph. It takes that vehicle 12 minutes to reach its destination. How far away is that distance (in miles). I am unsure how to do this type of math problem. Can you please explain it to me. 1 solutions Answer 398174 by rapaljer(4667)   on 2012-07-26 22:46:08 (Show Source): You can put this solution on YOUR website!The key is to make sure the units in the problem are the same throughout the problem. Since you have 35 mph, you need to change the 12 minutes to 12/60 = 1/5 hour. Now, use the famous formula D=RT, where R=35 mi/hr and T=1/5 hour. D=RT D=35*1/5 = 7 miles Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Radicals/631626: sqrt2,3sqrt3,6sqrt6,12sqrt12 which is smallest explain it1 solutions Answer 397718 by rapaljer(4667)   on 2012-07-24 23:23:28 (Show Source): You can put this solution on YOUR website!sqrt 2 has the smallest coefficient AND also the smallest radicand. Therefore it must be the smallest quantity. For additional help with a variety of algebra topics, please see my own FREE website which can be found at the easy-to-remember and easy-to-spell link: www.mathinlivingcolor.com. Click on the link near the bottom of the page, which will take you to my Homepage. Near the top of the papge, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Angles/631625: The sum of the measures of a complement and supplement of an angle is 200. What is the measure of the angle?1 solutions Answer 397714 by rapaljer(4667)   on 2012-07-24 23:11:26 (Show Source): You can put this solution on YOUR website!Let x=the angle 90-x=the compliment 180-x=the supplement 90-x + 180-x = 200 270 - 2x =200 -2x = -70 x=35 The angle 90-x =55 The Complement 180-x = 145 The Supplement Check: 55 + 145 = 200 It checks!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Finite-and-infinite-sets/631589: Use the addition principle for counting to solve the problem: If n(A)=20, n(A U B)=58, and n(A "intersection" B)=16, Find n(B)1 solutions Answer 397690 by rapaljer(4667)   on 2012-07-24 20:23:55 (Show Source): You can put this solution on YOUR website!In order to get the UNION of two sets, you can ADD the number of members of the two sets together, and SUBTRACT the OVERLAP. The OVERLAP is actually the INTERSECTION. This gives the following formula: n(A) + n(B)-n(A intersection B)=n(AUB) 20 + n(B) -16 = 58 4 + n(B) = 58 n(B) = 58-4 = 54 Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Linear_Equations_And_Systems_Word_Problems/631574: S=a+b/2h for h1 solutions Answer 397688 by rapaljer(4667)   on 2012-07-24 20:16:12 (Show Source): You can put this solution on YOUR website! Multiply both sides of the equation by the denominator 2h: To solve for h, divide both sides by 2S: For additional help with Literal Equations, please see my own FREE website which can be found at the easy-to-remember and easy-to-spell link: www.mathinlivingcolor.com. Click on the link near the bottom of the page, which will take you to my Homepage. Near the top of the Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose Intermediate Algebra, and look in Chapter 3 for the section on Literal Equations. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 sets-and-operations/631585: Write each statement in symbolic form using the indicated letters to represent the corresponding components. Snoopy is not an aviator (~a), or the Sopwith Camel is an airplane( p). 1 solutions Answer 397686 by rapaljer(4667)   on 2012-07-24 20:04:46 (Show Source): You can put this solution on YOUR website!~aVp For additional help with Logic, please see my own FREE website which can be found at the easy-to-remember and easy-to-spell link: www.mathinlivingcolor.com. Click on the link near the bottom of the page, which will take you to my Homepage. About halfway down the Homepage, look for the link "Topics from Logic." Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 sets-and-operations/631584: Section 3.3: #6. Find the truth value of the following statement: If 2 + 2 = 22, then 8 = 4 + 41 solutions Answer 397685 by rapaljer(4667)   on 2012-07-24 19:58:51 (Show Source): You can put this solution on YOUR website!If the hypothesis of an if-then statement is FALSE, then the truth value of the statement is ALWAYS TRUE!! For additional help with LOGIC, please see my own FREE website which can be found at the easy-to-remember and easy-to-spell link: www.mathinlivingcolor.com. There is an entire section on "Topics from Logic" that may be helpful. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Functions/630458: Please help me with this problem, using the piecewise function: f(x)= \$5o if o< x < 60 4/3x - 30 if x > 60 this function describes the rate of a computer repairman. The question is what is the cost if the repairman works for 45 minutes? Thanks.1 solutions Answer 396922 by rapaljer(4667)   on 2012-07-20 22:42:24 (Show Source): You can put this solution on YOUR website!Since 45 minutes is BETWEEN 0 and 60 minutes, you use the first half of the formula, which is a flatrate \$50. However, if the computer repairman runs OVER 60 minutes, then you use the rate of 4/3 x - 30. In other words, if it takes more than 60 minutes, they charge EXTRA, depending upon how long it takes. For example, if it takes 66 minutes, then you calculate 4/3*66-30, which is \$58. For additional help with most algebra topics, please see my own FREE website which can be found at the easy-to-remember and easy-to-spell link: www.mathinlivingcolor.com. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Miscellaneous_Word_Problems/630292: AB + BA= 1A4 in the correctly worked addition problem above, A and B represent two different digits. what digit does A represent? *please include explanations1 solutions Answer 396814 by rapaljer(4667)   on 2012-07-20 12:26:23 (Show Source): You can put this solution on YOUR website!The value of AB is 10A + B, while the value of BA is 10B + A. In the equation, AB + BA = 1A4, substitute the values of AB and BA above: (10A + B) + (10B + A) = 100 + 10A + 4 Subtract 10A from each side: B+ 10B + A = 104 11B + A = 104 Subtract A from each side: 11B = 104 - A Since B must be an integer, this means that you must subtract an integer value of A from 104 and obtain a multiple of 11. If A = 1, you have 11B=103. 103 is not a multiple of 11. If A = 2, you have 11B=102. If A = 3, you have 11B=101. If A = 4, you have 11B=100. If A = 5, you have 11B=99, so B = 9. It works!! Check: AB= 59, BA= 95, AB + BA = 1A4 59 + 95 = 154, so it checks!! Congratulations on a NICE PROBLEM!! I liked this one VERY MUCH!! For additional help with this topic and other algebra topics, please see my own FREE website at www.mathinlivingcolor.com. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Circles/630246: Calculate the radius of a circle whose area is equal to the sum of the areas of three? circles of radii 2 cm, 3 cm and 4 cm.1 solutions Answer 396809 by rapaljer(4667)   on 2012-07-20 12:10:41 (Show Source): You can put this solution on YOUR website! Area of three circles = Area of unknown circle = Divide both sides by pi: For additional help with this topic and other algebra topics, please see my own FREE website at www.mathinlivingcolor.com. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Linear-equations/630254: Is (1,-3) a solution of y=-2x-1?1 solutions Answer 396806 by rapaljer(4667)   on 2012-07-20 11:29:04 (Show Source): You can put this solution on YOUR website!The point (1,-3) means to substitute x=1, and see if y=-3. y=-2x-1 y=-2(1)-1 y=-2-1=-3. YES!! Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Probability-and-statistics/630275: How many different teams of 2 people each can Joshua select from a group of 5 people? please include explanations!1 solutions Answer 396805 by rapaljer(4667)   on 2012-07-20 11:24:19 (Show Source): You can put this solution on YOUR website!Since you are choosing members of a team (the key word here is "CHOOSE"!), it is a COMBINATION problem, a combination of 5 people, taken 2 at a time. C(5,2) = = 10. Most calculators of today will calculate combinations and permuations for you. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Triangles/630277: the length of the base of a triangle, x-8, is less than the height of triangle, 12.1 solutions Answer 396803 by rapaljer(4667)   on 2012-07-20 11:20:04 (Show Source): You can put this solution on YOUR website!What was the question? Is there more information or a diagram in this problem? Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 absolute-value/630278: |x + 2| + 16 = 141 solutions Answer 396802 by rapaljer(4667)   on 2012-07-20 11:18:19 (Show Source): You can put this solution on YOUR website!In order to isolate the absolute value, subtract 16 from each side. This gives Since absolute value cannot equal a negative number, there is NO SOLUTION. Dr. Robert J. Rapalje, Retired Seminole State College of Florida
 Functions/614727: Under what circumstances would the domain be something other than all real numbers? Provide an example. 1 solutions Answer 386670 by rapaljer(4667)   on 2012-05-24 22:54:19 (Show Source): You can put this solution on YOUR website!For functions in which there are NO DENOMINATORS and NO SQUARE ROOTS, the DOMAIN is ALL REAL NUMBERS. An example would be y=x^2. However, if you have a variable in a DENOMINATOR, like , then the domain is all values of x except x=5. If you have a square root, like , then there is a restriction that the radicand, which is x-5, must be greater than or equal to zero. That is, . This means . I have a similar explanation with more details on my website. You might want to see my own NON-TRADITIONAL explanation of FUNCTIONS, DOMAIN, and RANGE on my own website. To find my website, use the easy-to-spell and easy-to-remember link www.mathinlivingcolor.com. This link takes you to a single page with a single link near the bottom of the page. Click on this link, and it takes you to my Homepage. Once you are on my Homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Intermediate or College Algebra", and look in "Chapter 5" for Intermediate Algebra, and Chapter 2 for College Algebra. Then, the hardest of the problems in these sections are solved IN COLOR on the Math in Living Color page for the respective sections. On the topic of Functions, Domain and Range, I also have VIDEOS of me teaching this topic a few years before I retired. To find the videos, look on my Homepage for "Rapalje Videos in Living Color." Look in Intermediate or College Algebra respectively for the video on Functions, Domain, and Range. The videos, like everything else on my website, are all FREE!!! Check it out!! Math is usually not as hard as it looks if you get a decent explanation of it!! I hope this is helpful. For ANYONE interested in using my FREE website for ANY TOPIC in math, just send me an Email at rapaljer@seminolestate.edu. Dr. Robert J. Rapalje, Retired Seminole State College of Florida Altamonte Springs Campus