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# Recent problems solved by 'richard1234'

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 Surface-area/582625: Sides of the triangle 15ft 12ft need area and peremeter1 solutions Answer 372236 by richard1234(5390)   on 2012-03-05 21:49:15 (Show Source): You can put this solution on YOUR website!Insufficient info...you need either all three sides, or two sides plus the included angle, or some other piece of information.
 Square-cubic-other-roots/582768: What is a rational exponent? How are rational exponents related to radicals? Give an example of how an expression with a rational exponent can be rewritten as a radical expression. Please do not provide the formula, your example should contain numbers/letters. 1 solutions Answer 372235 by richard1234(5390)   on 2012-03-05 21:47:08 (Show Source): You can put this solution on YOUR website!Rational exponent = an exponent that is a rational number For example,
 Equations/582693: how many tires does it take to make m minivans if each one has a spare1 solutions Answer 372176 by richard1234(5390)   on 2012-03-05 19:21:28 (Show Source): You can put this solution on YOUR website!5 tires for each minivan 5m tires for m minivans
 Numbers_Word_Problems/582681: i have been trying to figure this out but no luck! 3 times the sum of a number and 4 is 8 less than one half the number 1 solutions Answer 372164 by richard1234(5390)   on 2012-03-05 19:14:29 (Show Source): You can put this solution on YOUR website!No luck involved. Translate into an algebra problem (this requires practice) where x is the number Subtract x/2 from both sides Subtract 12 from both sides
 Numbers_Word_Problems/582523: 1) I am a 2-digit number less than 90. 2) Three more than my value is an even number. 3) The sum of my digits is a multiple of 8.1 solutions Answer 372081 by richard1234(5390)   on 2012-03-05 16:19:19 (Show Source): You can put this solution on YOUR website!2) Three more than my value is an even number. This is just a "tricky" way of saying "I am an odd number." 3) The sum of my digits is a multiple of 8. Since we have a 2-digit number, the digit sum must be either 8 or 16 (24 is too large). If it is 8, then we have 71, 53, 35, 17. If it is 16, we have 79 (97 is too large). Therefore all the possible numbers are 17, 35, 53, 71, and 79.
 Miscellaneous_Word_Problems/582299: Prove by induction that if n distinct dice are rolled, then the number of outcomes where the sum of the faces is an even integer equals the number of outcomes where the sum of the faces is an odd integer?1 solutions Answer 372080 by richard1234(5390)   on 2012-03-05 16:17:13 (Show Source): You can put this solution on YOUR website!Base case n=1 is obviously true. Suppose that the statement is true for n dice (n>1). If we add another die that is distinguishable from the other n dice, then for each sequence of n dice rolls , we can let is even if and only if S is even and the (n+1)th roll is even, or if S is odd and the (n+1)th roll is odd. If we look at this from a probabilistic view, we have P(S even) = 1/2 because there are as many even outcomes as odd outcomes P((n+1)th roll even) = 1/2 because 2,4,6 are even Therefore P(S even and (n+1)th roll even) = 1/4. Similarly, P(S odd and (n+1)th roll odd) = 1/4, so P(S + a_(n+1) even) = 1/2, which is half of all the possible outcomes. Hence we are done.
 Linear-systems/582269: Please set this up as y=mx+b: Discount Cell Phones charges $19.99 per month and$0.15 per text message.....thank you1 solutions Answer 372009 by richard1234(5390)   on 2012-03-05 00:12:08 (Show Source): You can put this solution on YOUR website!The independent variable (x) is the number of text messages and the 19.99 per month is the "constant" term. y = .15x + 19.99
 test/581541: What is 3gallons=to ______ pints 1 solutions Answer 372008 by richard1234(5390)   on 2012-03-05 00:10:56 (Show Source): You can put this solution on YOUR website!1 gallon = 8 pints 3 gallons = 24 pints
 Trigonometry-basics/582048: how do i find the value of cotx if secxsinx= 21 solutions Answer 372007 by richard1234(5390)   on 2012-03-05 00:09:39 (Show Source): You can put this solution on YOUR website!We have We can invert both sides to get .
 Travel_Word_Problems/581717: Integrate with respect to x : \int_{0}^{1}4xdx1 solutions Answer 372006 by richard1234(5390)   on 2012-03-05 00:07:35 (Show Source): You can put this solution on YOUR website! evaluated at x=1, minus the value evaluated at x=0. This becomes 2(1)^2 - 2(0)^2 = 2.
 Polynomials-and-rational-expressions/582095: I need help factoring. I just don't get it. 8x^2y+34xy-84y1 solutions Answer 372004 by richard1234(5390)   on 2012-03-05 00:06:02 (Show Source): You can put this solution on YOUR website!First you can factor out 2y: The 4x^2 + 17x - 42 is a bit tricky to factor; the best way to learn is by experience and simply being able to "see" the correct factorization. 4x^2 + 17x - 42 can be factored into a product (ax + b)(cx + d). We want ac = 4, so a,c can equal 2 or 1,4. However, if a = c = +/- 2, the x coefficient will be even, so try a=1, c=4. We can kind of "guess and check" based on the factorization of -42 to obtain the factorization , in which the complete answer would be . Again, this takes lots of practice. Another way you could factor it is to find the roots of 4x^2 + 17x - 42 by the quadratic formula: Then you could factor it as . However, the leading coefficient is 4 so we can multiply the first term by 4.
 Polynomials-and-rational-expressions/582155: According to Newton's universal gravitation, the attractive force F between two bodies is given by where m1 and m2 are the mass of the two bodies, r is the distance between the two bodies, and G is the gravitational constant = newtons meter squared kilogram squared. Suppose an object is traveling directly from Earth to the moon. The mass of Earth is kilograms, the mass of the moon is kilograms, and the mean distance from Earth to the moon is 384000 kilometers. For an object between Earth and the moon, how far from Earth is the force on the object due to the moon greater than the force on the object due to Earth? Thank you!1 solutions Answer 372002 by richard1234(5390)   on 2012-03-04 23:55:39 (Show Source): You can put this solution on YOUR website!Suppose d is the distance between this object and Earth, m_1 is the mass of the object, m_2 and m_3 are the masses of the Earth and moon, respectively. Then r-d or 384000-d is the distance between the object and the Moon. We want the following inequality to be true: G and m_1 cancel, leaving Since m_2, m_3, and r are known, solve the quadratic in terms of d (you will have to expand, simplify first), replace m_2, m_3, r in, and find the smallest d such that the gravitational force from the Moon is greater than the force from the Earth.
 Probability-and-statistics/581518: There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores are approximately Normal with mean μ = 21.5 and standard deviation σ = 5.4. SAT scores are reported on a scale from 600 to 2400. The SAT scores are approximately Normal with mean μ = 1509 and standard deviation σ = 321. Tonya scores 1770 on the SAT. Jermaine scores 28 on the ACT. Assuming that both tests measure the same thing, who has the higher score? Report the z-scores for both students. (Round your answers to two decimal places.) Tonya's score standardizes to z = . Jermaine's score standardizes to z = . Therefore,.......... has the higher score. 1 solutions Answer 371956 by richard1234(5390)   on 2012-03-04 19:16:41 (Show Source): You can put this solution on YOUR website!Tonya's z-score is Jermaine's z-score is Jermaine has the higher z-score, and scores "higher."
 Polygons/581522: How many different ways can you find the area of a regular octagon with all sides equal to 3 meters? Describe each method and use it to find the area. Are the answers the same? Should the answers be the same?1 solutions Answer 371906 by richard1234(5390)   on 2012-03-04 16:04:19 (Show Source): You can put this solution on YOUR website!Suppose the vertices of the octagon are A,B,C,...,H in counterclockwise order with AB = 3 m, and O is the center. 1. Divide up the octagon into four triangles and five rectangles (draw lines AF, BE, CH, DG). Find the area of each shape using your knowledge about 45-45-90 triangles. 2. Think of the octagon as a square with four right isosceles triangles cut off. Find the area of the square, then subtract off the areas of the triangles. 3. Divide up the octagon into eight congruent isosceles triangles (OAB, OBC, etc.). Use the area formula A = (1/2)ab sin C where a = b = the radius of the circumscribed circle, and C = 45 deg. You may need additional theorems, such as law of sines. There are many other ways, but most of them are similar to the above three. You should obtain the same answer in each case.
 decimal-numbers/581769: in your lesson "This Lesson (WHAT IS a decimal)" i believe you may have a typo at the very end. 2.2/5=2.2 but i think it should be 2.2/5=2.4 hope this helps and if i'm wrong please email me or even if i'm right that would be cool thanks1 solutions Answer 371902 by richard1234(5390)   on 2012-03-04 15:58:25 (Show Source): You can put this solution on YOUR website!Whoops, didn't see the link to the lesson. Yes, 2/5 = .4, not .2. I didn't write that lesson, so you can email the author of the website (who is also the owner of this website) if you wish, at ichudov@algebra.com. Make sure that you are clear with your notation; 2.2/5 is usually interpreted as 2.2 over 5 (or .44), while 2 2/5 means 2 and 2/5 (or 2.4), which is probably what you want.
 Numbers_Word_Problems/581445: if the largest 4 digit even number subtracted to smallest 3 digit odd number with the digits 2,8,6,3,the difference will be?1 solutions Answer 371900 by richard1234(5390)   on 2012-03-04 15:56:49 (Show Source): You can put this solution on YOUR website!Largest 4-digit even number = 9998 Smallest 3-digit odd number with 2,8,6,3 = 223 (depending on how you interpret the question) 9998 - 223 = 9775
 Inequalities/581926: How would you solve the inequality: x^2 is greater than or equal to 15x? Thank you for your time1 solutions Answer 371896 by richard1234(5390)   on 2012-03-04 15:49:47 (Show Source): You can put this solution on YOUR website! This factors If x = 0 or x = 15, the inequality becomes an equality. It can easily be checked that all x >= 15 and x <= 0 satisfy the inequality.
 Probability-and-statistics/581090: The scatter plot shows the average temperature each month in a particular city. What is a good prediction for the temperature in July if the temperature continues to increase until then?1 solutions Answer 371470 by richard1234(5390)   on 2012-03-02 00:29:31 (Show Source): You can put this solution on YOUR website!You forgot one thing...the scatterplot.
 Probability-and-statistics/581007: a researcher is investigating the effectiveness of a new study-skills training program1 solutions Answer 371469 by richard1234(5390)   on 2012-03-02 00:18:58 (Show Source): You can put this solution on YOUR website!Okay. And?