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# Recent problems solved by 'drk'

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 test/255374: The sum of the squares of two consecutive odd positive integers is 202. Find the integers.1 solutions Answer 187643 by drk(1908)   on 2010-01-10 14:58:22 (Show Source): You can put this solution on YOUR website!let x = positive odd integer and x + 2 be the next positive odd integer. we get x^2 + (x+2)^2 = 202 foiling the left and combining like terms, we get 2x^2 + 4x + 4 = 202 and then 2x^2 + 4x - 198 = 0 divide by 2 to get x^2 + 2x - 99 = 0 factor to get (x+11)(x-9) = 0 solving for x, we get x = -11 and x = 9 we get (-11,-9) OR (9,11)
 Probability-and-statistics/255362: The probability that an American CEO can transact business in a foreign language is .20. Ten American CEOs are chosen at random. (a) What is the probability that none can transact business in a foreign language? (b) That at least two can? (c) That all 10 can? (d) Sketch the probability distribution and discuss its appearance. 1 solutions Answer 187640 by drk(1908)   on 2010-01-10 14:53:17 (Show Source): You can put this solution on YOUR website!P(speak foreign language) = .20 P(NOT speak foreign language) = .80 (a) What is the probability that none can transact business in a foreign language? answer: we want zero "YES" and 10 "NO" so, nCr*(no)^10*(yes)^0 or 10c0*.8^10*.2^0 ~ .1074 -- (b) That at least two can? answer: This means that 0 or 1 cannot. It is easier to do this in negation. 1 - p(0 not) + p(1 not) = 1 - 10c0(.8)^0*(.2)^10 + 10c1*(.8)^1*(.2)^9 ~ .99999 -- (c) That all 10 can? answer; we want all 10 yes, so, 10c10*(.2)^10 ~ 1.02 x 10^-7 (d) Sketch the probability distribution and discuss its appearance. The sketch should be a normal curve with cum sum = 1.
 Human-and-algebraic-language/255365: What is the slope of a line that is perpendicular to a line that has no slope? Explain the answer.1 solutions Answer 187634 by drk(1908)   on 2010-01-10 14:40:55 (Show Source): You can put this solution on YOUR website!If a line has no slope then it can be expressed as 1/0 or in general as a/0, where a not = 0. A perpendicular slope is the negative reciprocal. So, 1/0 turns into -0/1 = 0, or in general a/0 turns into -0/a = 0.
 Human-and-algebraic-language/255369: what is the unit rate of change of y with respect to x if the slope of the graph of the equation for y in terms of x is 1/4?1 solutions Answer 187633 by drk(1908)   on 2010-01-10 14:38:53 (Show Source): You can put this solution on YOUR website!For every 1 increase in y, we increase x by 4. unit rate of change of y with respect to x = rise information over run information.
 Quadratic_Equations/255366: (x*-3x)+8=0 cant figure out how to do the last part of question after I get here x= 3 + - square root -23 over 2 1 solutions Answer 187632 by drk(1908)   on 2010-01-10 14:37:33 (Show Source): You can put this solution on YOUR website!Your original equation was: suppose * = 2. then we have a quadratic of the form which can easily be solved using the quadratic formula as which is simplified as From here you have one of two ways to go. (1) if you have never been shown imaginary numbers, then say no solution. (2) If you have been shown imaginary numbers, then say ,
 Exponents/255363: please help me solve this problem... 4^x=(1/2)^3x+51 solutions Answer 187630 by drk(1908)   on 2010-01-10 14:33:05 (Show Source): You can put this solution on YOUR website!If you mean , then simplify as . multiplying both sides by 8^x, we get in this case, there is no x value which is true. -- If you mean simplifies as . Multiply both sides by 8 to get In this case, there is no x value which is true. -- If you mean then rewrite the right side as the 4 can be expressed as 2^2, so we get cancel the base 2's to get solve for x to get
 Angles/255357: The measure of the supplement of an angle exceeds three times the measure of half the compliment of the angle by 12. Find the measure of half the supplement1 solutions Answer 187625 by drk(1908)   on 2010-01-10 14:20:04 (Show Source): You can put this solution on YOUR website!Let x be an angle. 180-x is the supplement. 90 - x is the compliment. So, we get By distributive prperty, we get combining like terms on the right we get and simplifying we get The supplement of 66 is 114. Half of 114 is 57. So answer is 57.
 Graphs/255361: how do i write an equation in slope-intercept form for the lone that is perpendicular to the given lone and passes through the given point y=-3x+4;(6,-2)1 solutions Answer 187624 by drk(1908)   on 2010-01-10 14:15:41 (Show Source): You can put this solution on YOUR website!step 1 - solve the equation for y. That is already done and given as (i) step 2 - find the slope of (i) and we get m = 3. step 3 find perpendicular slope. m = 3, so perpendicular means flip and change sign. Perp m = -1/3. step 4 - using new slope and (6,-2) we put that information into to get step 5 - write the answer as
 Equations/255360: (4.2y)/0.2-84=y1 solutions Answer 187623 by drk(1908)   on 2010-01-10 14:12:28 (Show Source): You can put this solution on YOUR website! step 1 - divide 4.2 by .2 to get step 2 - subtract 21y from both sides to get step 3 - divide by -20 to get
 Equations/255356: 25n-(-15n-4)=28n1 solutions Answer 187622 by drk(1908)   on 2010-01-10 14:09:54 (Show Source): You can put this solution on YOUR website! step 1 - distribute the negative through to get step 2 - combine like terms on the left to get step 3 - subtract 40n from both sides to get step 4 - divide to get
 Travel_Word_Problems/255359: Two airplanes start toward each other at the same time from airports located 1950 km apart. One plane flies at an average speed of 360 km/h. What should the average speed of the plane be if they meet in 3 hours? Show all work.1 solutions Answer 187621 by drk(1908)   on 2010-01-10 14:07:29 (Show Source): You can put this solution on YOUR website!This is a RTD problem. Here is the table based on given information: airplane . . . . . . . . .rate . . . . . . . . .time . . . . . . . . .distance A . . . . . . . . . . .. . . .360 . . . . . . . . .3 . . . . .. . . . . .. . 1080 B . . . . . . . . . . . . . . .R . . . . . . . . . . .3 . . . . . . .. . . . .. . 3R totals . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1950 The distance of A + distance of B = total distance. So, 1080 + 3R = 1950 3R = 870 R = 290 km/h
 Functions/255355: write in standard form, m= 5 and b = -51 solutions Answer 187620 by drk(1908)   on 2010-01-10 14:03:23 (Show Source): You can put this solution on YOUR website!Lets start with slope intercept form as we know m = 5 and b = -5, so we get (i) standard form requires 2 things (1) no decimals (2) X and Y stuff on the same side and the # by itself. From (i) subtract 5x to get (ii) This is standard form.
 Word_Problems_With_Coins/255358: You have two U.S. coins with a total value of \$.35, and one of them is not a quarter. What are the coins?1 solutions Answer 187619 by drk(1908)   on 2010-01-10 14:00:52 (Show Source): You can put this solution on YOUR website!This is a trick question. If one cannot be a quarter, the other one CAN be a quarter. So, we have dime and then quarter.
 Equations/255352: how do you write 5580 in scientific notation. 1 solutions Answer 187618 by drk(1908)   on 2010-01-10 13:59:54 (Show Source): You can put this solution on YOUR website!Notice there is no decimal. IF you don't see one, it is all the way to the right. We want a number expressed in the following form: where 0 < a < 10 and b is an integer. step 1 - move the decimal left 3 jumps to get 5.580 step 2 - ask yourself how many jumps and in which direction? # jumps = 3 direction = left OUr answer is: 5.580 x 10^3
 Rational-functions/255299: solve using the rational zero theorem and descarte rule:x^4-5x^3-54x^2-80x-32=01 solutions Answer 187617 by drk(1908)   on 2010-01-10 13:54:51 (Show Source): You can put this solution on YOUR website!x^4 - 5x^3 - 54x^2 - 80x - 32 = 0 step 1 - set up P, N, i P are the number of sign changes you see when (x) is placed into the equation. We get P = 1. N are the number of sign changes you see when (-x) is placed into the equation. We get N = 3. Now 1 + 3 = 4. P . . . 1 . . . . 1 N . . . 3 . . . . 1 i . . . .0 . . . . .2 Notice that i = 0 or 2. Imaginary numbers always travel in conjugate pairs. Now on to rational zeros. or P/Q P = +-(1, 2, 4, 8, 16, 32) Q = +-(1) We can find that x = -4 and x = -1 give us 2 zeros. By synthetic division, using x = -4, we get (x^3-9x^2-18x-8) and this divided by x = -1 gets us (x^2-10x-8) setting this = 0 and solving gets us or or simplified as SO our four answers are: x = -4, x = -1, x = 5 +-sqrt(33)
 Graphs/255314: Flying against the wind, a plane makes a 1050km trip in 3.5 hours. On the return trip, the flight takes 30 minutes less. What is the rate of the plane in calm air?1 solutions Answer 187591 by drk(1908)   on 2010-01-10 12:11:30 (Show Source): You can put this solution on YOUR website!This is an rtd problem with currents. Here is a table based on the given information: plane . . . . . .rate . . . . . . . . . . . time . . . . .distance against . . . .r-c=1050 . . . . . . . .3.5 . . . . . . 3675 with . . . . . .r+c . . . . . . . . .. . . .. 3 . . .. . . . .3675 we know (i) r-c = 1050. solve with for r+c, we get (ii) r+c = 1225 adding (i) and (ii) together, we get (iii) 2r = 2275 r = 1137.5 c then is 87.5 Kph
 Linear-equations/255303: ((x^2 - x) / (x^2 + 3x + 2)) / ((x^2 + 2x)/ (x^2 -1)) or http://www.thea.nesinc.com/images/math/tasp_image335.gif 1 solutions Answer 187590 by drk(1908)   on 2010-01-10 12:06:45 (Show Source): You can put this solution on YOUR website!OUr expression is: step 1 - factor each part separately: x^2-x = x(x-1) x^2 + 3x + 2 = (x+2)(x+1) x^2+ 2x = x(x+2) x^2-1 = (x+1)(x-1) we get / step 2-Multiply the top fraction by the reciprocal of the bottom fraction to get * step 3 - cancel where possible to get
 Linear-equations/255309: how do you find the slope of a line when your only given two points? we are required to solve it algebralicly with out graphing. i know that there is an equation to solve it but im not sure what it is or how it works.1 solutions Answer 187588 by drk(1908)   on 2010-01-10 11:59:49 (Show Source): You can put this solution on YOUR website!Suppose you are given 2 coordinates: A (x1,y1) and B (x2,y2). We can find the slope with the dollowing equation: -- EX: A(1,4) B (-3,9) using the slope formula we get = 5/-4 so m = -5/4
 Polynomials-and-rational-expressions/255307: ((C+5)/7)+((C-30)/4)=5/14 I KEEP COMING UP WITH BIG NUMBERS EVEN THOUGHT THE SOLUTION IS SUPPOSED TO BE "1"1 solutions Answer 187587 by drk(1908)   on 2010-01-10 11:57:09 (Show Source): You can put this solution on YOUR website! step 1 - find the common denominator. It is 28. step 2 - multiply every number by 28 to get and then step 3 - combine like terms on the left to get add 190 to both sides to get c= 18.1818.... -- checking, we get 3.3116 - 2.9545 ~ .357054 ; 5/14 = .3571428
 Inequalities/255281: n is an integer a) Write down the values of n which satisfy the inequality -2 < n ≤ 3 b) Solve the inequality 3x + 2 ≤ 4 Thanks everyone :D1 solutions Answer 187559 by drk(1908)   on 2010-01-10 09:47:50 (Show Source): You can put this solution on YOUR website!(a) the values of n are: -1, 0, 1, 2, and 3. We can't use -2 because it is not =. (b) 3x + 2 ≤ 4 step 1 - subtract 2 to get 3x <=2 step 2 - divide by 3 to get x<= 2/3 If you want the set of integers then (- 00, 0]
 Miscellaneous_Word_Problems/255273: A staircase has 5 steps. You can walk up the staircase by taking one or two steps at a time. How many different ways can you walk up the staircase? 1 solutions Answer 187552 by drk(1908)   on 2010-01-10 09:16:14 (Show Source): You can put this solution on YOUR website!we have 1,1,1,1,1 1,1,1,2 1,1,2,1 1,2,1,1 2,1,1,1 1,2,2 2,1,2 2,2,1 so, it appears we have 8 ways
 Numbers_Word_Problems/255261: show that (x+2)squared(x-2)squared is equal to x to the fourth-8x squared + 16?1 solutions Answer 187551 by drk(1908)   on 2010-01-10 09:14:21 (Show Source): You can put this solution on YOUR website! this is the same as now (x+2)(x-2) = x^2-4, so we get squaring this gets us
 Miscellaneous_Word_Problems/255259: What is the largest positive integer k so that 5k divides 26!? 1 solutions Answer 187549 by drk(1908)   on 2010-01-10 09:10:47 (Show Source): You can put this solution on YOUR website!Part of 26! are the numbers: 5, 10, 15, 20, and 25. 5*1 = 5 5*2 = 10 5*3 = 15 5*4 = 20 5*5 = 25 factor out the 5's from the left and we have 5(1*2*3*4*5) or 5*120. So, k = 120
 Geometric_formulas/255276: A circular archery target is 122 cm in diameter and consists of a bull's eye of diameter 12.2 cm, surrounded by nine evenly spaced concentric circles. Assume that an arrow that hits a target is equally likely to land anywhere on the target. What's the probability that the arrow will A) hit the bulls eye B) Land somewhere in the outmost four circles. C) Land within the fifth ring in from the outer edge. ---Please help on this problem! THANKS!1 solutions Answer 187548 by drk(1908)   on 2010-01-10 09:07:44 (Show Source): You can put this solution on YOUR website!Let's call the bulls eye - circle 1 including circle #1, there are 10 concentric circles. radius of circle 1 = 6.1 radius of circle 2 = 12.2 or 6.1 * 2. and so on. A) hit the bulls eye P(bulls eye) = pi*6.1^2 = 37.21pi cm^2 B) Land somewhere in the outmost four circles. P(outer 4 circles) = p(whole target - inner 6 circles) = pi*R^2 - pi*r^2 = pi*61^2 -pi*36.6^2. The 36.6 is the radius of the first 6 circles or 6.1 * 6. This gives us 2381.44pi cm^2 C) Land within the fifth ring in from the outer edge. P(5th ring) = p(5th ring - p(4th ring). We want only the fifth ring so all other inner rings must be subtracted out. We get pi*R^2 - pi*r^2 = pi*30.5^2 -pi*24.4^2 = 334.89pi cm^2
 Rectangles/255278: The length of a rectangle is x + 4 The width of a rectangle is x - 1 The perimeter is 46 cm Calculate the length of the diagonal of the rectangle Please help?!1 solutions Answer 187546 by drk(1908)   on 2010-01-10 08:57:30 (Show Source): You can put this solution on YOUR website!The length of a rectangle is x + 4 The width of a rectangle is x - 1 The perimeter is 46 cm -- We can use th perimter formula as: (i) replacing x + 4 for L, x - 1 for W, and 46 for P, we get (ii) we solve for x as (iii) (iv) (v) (vi) Now, the length = 14, and the width is 9. -- Using the Pythagorean theorem: we get the diagonal, c, ~ 16.64
 Trigonometry-basics/255277: Simplify: (sec^2xcscx)/(sec^2x + csc^2x)1 solutions Answer 187545 by drk(1908)   on 2010-01-10 08:52:15 (Show Source): You can put this solution on YOUR website!Simplify (i) turn everything into sin and cos as (ii) simplify the denominator to get (iii) Notice cos^2x + sin^2 x = 1. Multiply by the reciprocal to get (iv) and simply (v)
 Rectangles/255275: A rectangle has a width of 10 inches and an area of 5 square inches. what is the length of the rectangle?1 solutions Answer 187542 by drk(1908)   on 2010-01-10 08:43:56 (Show Source): You can put this solution on YOUR website!We have 1 formula: (i) A = L x W step 1 - replace A = 5 and W = 10 to get (ii) 5 = 10L step 2 - divide by 10 to get (iii) 1/2 = L Length = 1/2 in.
 Parallelograms/255124: How do you find the perimeter of a parallelogram when you have the base of 4m, height of 3m and don't have side length?1 solutions Answer 187438 by drk(1908)   on 2010-01-09 15:22:14 (Show Source): You can put this solution on YOUR website!I assume it is isosceles. We can use Pythagorean theorem a^2 + b^2 = c^2 and then 3^3 + 4^2 = c^2 9 + 16 = c^2 25 = c^2 5 = c. The perimeter is 3 + 4 + 5 + 5 = 17 m.
 real-numbers/255128: Is 3 over pie an irrational number?1 solutions Answer 187437 by drk(1908)   on 2010-01-09 15:20:21 (Show Source): You can put this solution on YOUR website!Yes, since PI is irrational, a rational / irrational is irrational.
 Equations/254924: A= 1/2h (a+b) for b1 solutions Answer 187282 by drk(1908)   on 2010-01-08 19:48:06 (Show Source): You can put this solution on YOUR website!A= 1/2h (a+b) for b. step 1 - multiply both sides by 2 to get step 2 - divide by h to get subtract a to get
 Square-cubic-other-roots/254941: Solve for n: cube root of (n + 9) - cube root of (n - 9) = 31 solutions Answer 187277 by drk(1908)   on 2010-01-08 19:36:29 (Show Source): You can put this solution on YOUR website! To solve this via algebraic means may get messy, but the answer is rather simple: n = 4sqrt(5)