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# Recent problems solved by 'fractalier'

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 Sequences-and-series/41934: Find four geometric means between 4096 and 972. Thank you1 solutions Answer 27070 by fractalier(2101)   on 2006-06-13 11:37:46 (Show Source): You can put this solution on YOUR website!You divide 972 by 4096 and then take the fifth root to find the common ratio r...since you need four intermediate geometric means, there will be five increments...when you do that you find that r = 3/4...so that your sequence looks like... 4096, 3072, 2304, 1728, 1296, 972
 Sequences-and-series/41935: Find the sum of a geometric series for which a(1)=1, r=2, and n=6 Thanks you1 solutions Answer 27069 by fractalier(2101)   on 2006-06-13 11:34:38 (Show Source): You can put this solution on YOUR website!The terms of the series are 1 + 2 + 4 + 8 + 16 + 32 = 63
 Divisibility_and_Prime_Numbers/41690: Can someone help me with this problem? Is the following set of numbers a perfect triple? 8, 10, and 12 Thanks, Ashley1 solutions Answer 27067 by fractalier(2101)   on 2006-06-13 11:30:57 (Show Source): You can put this solution on YOUR website!It is not a Pythagorean triple, since 8^2 + 10^2 ≠ 12^2
 Graphs/41857: find the slopes, if they exist, of the linecontaining these points? (-5,4)and(1-2) (3,2)and(-5,0)1 solutions Answer 27059 by fractalier(2101)   on 2006-06-13 11:03:40 (Show Source): You can put this solution on YOUR website!Slope m is found by the formula m = (y2 - y1) / (x2 - x1) So for (-5,4) and (1,-2), we have m = (-2 - 4) / (1 -(-5)) = m = -6 / 6 = -1 And for (3,2) and (-5,0), we have m = (0 - 2) / (-5 - 3) = m = -2 / -8 m = 1/4
 Linear-equations/41928: what does the equation y=mx+c mean?1 solutions Answer 27058 by fractalier(2101)   on 2006-06-13 11:01:00 (Show Source): You can put this solution on YOUR website!This is a linear function showing a relationship between x and y. For y = mx + c, we have y expressed as a function of x, whereby any increase in x is calculated to be an (m times x) increase in y. The c value is the value of y when x = 0. If this function is graphed as a line, m is the slope of that line and c is the y-intercept.
 Probability-and-statistics/41886: The time a group of high school students arrive home from school each day was found to be normally distributed. The mean time was 3:15 PM and the times had a standard deviation of 15 minutes. What is the probability that a student chosen at random arrives home from school before 2:30 PM?1 solutions Answer 27056 by fractalier(2101)   on 2006-06-13 10:58:09 (Show Source): You can put this solution on YOUR website!Well 2:30 pm represents three sigmas below the mean...so look up on your normal distribution table a z-score of -3.00 and find the probability of .0013. Thus the probability is .13% that a student chosen at random arrives before 2:30 pm.
 Equations/41890: Find the equation of the line containing the point (-1,3) and perpendicular to hte line 2x+4y=-11 solutions Answer 27054 by fractalier(2101)   on 2006-06-13 10:54:51 (Show Source): You can put this solution on YOUR website!We need a line perpendicular to 2x + 4y = -1 Let us find the slope of this line first... 4y = -2x - 1 y = (-1/2)x - 1/4 The slope here is -1/2. The slope of the perpendicular to it is the negative reciprocal, or +2. Now use the point-slope form y - y1 = m(x - x1) y - 3 = 2(x + 1) y - 3 = 2x + 2 y = 2x + 5
 Polynomials-and-rational-expressions/41854: The volume of the box is represented by (x^2 + 5x + 6) (x+5). Find the polynomial that represents the area of the bottom of the box.1 solutions Answer 27053 by fractalier(2101)   on 2006-06-13 10:48:15 (Show Source): You can put this solution on YOUR website!Since x^2 + 5x + 6 factors into (x + 2)(x + 3), thus any pair of factors of (x + 2)(x + 3)(x + 5) could represent the area of the base...just multiply them to get the polynomial...
 Polynomials-and-rational-expressions/41915: having problem with fractions 1/2x^2+5x+25/2=0 show work1 solutions Answer 27051 by fractalier(2101)   on 2006-06-13 10:41:42 (Show Source): You can put this solution on YOUR website!Your best bet with fractional equations to to multiply eveyrthing by the lowest common denominator in order to clear the fractions...so for 1/2x^2 + 5x + 25/2 = 0 we multiply by 2 and get x^2 + 10x + 25 = 0 Now factor and solve as usual... (x + 5)^2 = 0 x = -5 (double root)
 Surface-area/41925: Question As many 8-cm diameter discs as possible are cut from a sheet of rectangular cardboard measuring 170 cm by 90 cm. Find the area of the sheet that is left. Please help to solve this question. Thank you very much.1 solutions Answer 27049 by fractalier(2101)   on 2006-06-13 10:36:24 (Show Source): You can put this solution on YOUR website!Well 21 discs one way and 11 disks the other way can be cut...231 disks in total...let's find thier total area and subtract it from the area of the original sheet... A = 231 * ((pi)r^2) A = 231 * 16pi A = 3696*pi sq cm The original sheet was 90 x 170 or 15300 sq cm. Now subtract to get the leftover area Leftover = 15300 - 3696(pi) or about 3689 sq cm
 Probability-and-statistics/41887: During a clothing sale, 1/4 of the store merchandise is reduced in price, Find the probability that 3 of 5 randomly-selected shirts have reduced prices.1 solutions Answer 27048 by fractalier(2101)   on 2006-06-13 10:30:05 (Show Source): You can put this solution on YOUR website!I believe this one is done like this... P(3 of 5 have reduced price) = C(5,3)*(1/4)^3*(3/4)^2 = 10 * 1/64 * 9/16 = 45/512
 Functions/41922: What is the slope of a binomial 2x+3'1 solutions Answer 27047 by fractalier(2101)   on 2006-06-13 10:26:59 (Show Source): You can put this solution on YOUR website!If you mean y = 2x + 3 then the slope is 2.
 Polynomials-and-rational-expressions/41867: This question is from textbook A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane's speed in still air? Thanks!1 solutions Answer 27046 by fractalier(2101)   on 2006-06-13 10:25:01 (Show Source): You can put this solution on YOUR website!In problems like this, we always use distance = rate * time, or D = RT. Thus T = D/R. Let R be the plane's speed in still air. Going against the wind, we have T1 = 720 / (R - 30) and T2 = 720 / (R + 30) But these two times add to 10 hours, so we have 720 / (R - 30) + 720 / (R + 30) = 10 Now multiply everything by (R+30)(R-30) to clear fractions... 720(R+30) + 720(R-30) = 10(R+30)(R-30) Now solve for R... 720R + 21600 + 720R - 21600 = 10(R^2 - 900) 1440R = 10(R^2 - 900) 144R = R^2 - 900 R^2 - 144R - 900 = 0 (R - 150)(R + 6) = 0 R = 150 mph
 Probability-and-statistics/41881: Two cards are drawn from a standard deck of cards. Find the probability that a king or a red card is drawn.1 solutions Answer 27045 by fractalier(2101)   on 2006-06-13 10:15:21 (Show Source): You can put this solution on YOUR website!Since the question is an OR case, we add the probabilities... The probability of picking a king is 4/52 or 1/13 and the probability of picking a red card is 26/52 or 1/2, we add 1/13 + 1/2 = 2/26 + 13/26 = 15/26 Thus 15/26 is the probability of any one card be a king or red. To do it twice (after first replacing the card), one would then multiply 15/26 by itself, giving us 225/676. To do it in either card, we add 15/26 + 15/26 = 15/13...or a certainty... It is not clear how we draw the two cards.
 Equations/41869: What is the value of the discriminant? X(squared) - 3x - 12 = 0 The teacher collected the textbooks today, the final is tomorrow.1 solutions Answer 27044 by fractalier(2101)   on 2006-06-13 10:11:06 (Show Source): You can put this solution on YOUR website!For x^2 - 3x - 12 = 0 we examine the discriminant as b^2 - 4ac...here that is (-3)^2 - 4(1)(-12) = 9 + 48 = 57
 Exponents-negative-and-fractional/41870: I am doing school from home. The name of my school is penn foster. Reduce fraction 6x/12x to lowest terms. My answer was 1/2 but was not right.1 solutions Answer 27043 by fractalier(2101)   on 2006-06-13 10:08:08 (Show Source): You can put this solution on YOUR website!Yes it is. 6x/12x = 1/2 Either the book is wrong or you copied something incorrectly...
 Age_Word_Problems/41901: Hello! Can somebody help please? My question is: Last time it was the kids birthdays I noticed that even though they were born only one year apart, when I squared their ages and then added the sum of the ages they would total 1105. How old are my kids? Thanks. Your help and time are much appreciated. marangeo1 solutions Answer 27042 by fractalier(2101)   on 2006-06-13 10:05:50 (Show Source): You can put this solution on YOUR website!Okay let their ages be x and x+1, since they are a year apart. Then we have x^2 + (x+1)^2 + x + x+1 = 1105 Now solve this... x^2 + x^2 + 2x + 1 + x + x + 1 = 1105 2x^2 + 4x + 2 = 1105 2x^2 + 4x - 1103 = 0 This is not factorable, so we use the quadratic formula to get x = (-4 ± sqrt(16 + 8824)) / 4 x = (-4 ± sqrt(8840)) / 4 x = (-4 ± 2*sqrt(2210)) / 4 x = (-2 ± sqrt(2210)) / 2 x is about 22.5 years old x+1 is about 23.5 years old I have a feeling there is something wrong with the problem...
 Polynomials-and-rational-expressions/41911: solve 8x(4.7)=0 show work1 solutions Answer 27040 by fractalier(2101)   on 2006-06-13 09:58:38 (Show Source): You can put this solution on YOUR website!Since we have a product equalling zero, the only way that can happen is if one of the numbers involved IS zero...thus for 8x(4.7) = 0 x must be zero.
 Polynomials-and-rational-expressions/41912: solve 8x^2=5x show work1 solutions Answer 27038 by fractalier(2101)   on 2006-06-13 09:57:11 (Show Source): You can put this solution on YOUR website!Okay, from 8x^2 = 5x let's subtract the 5x and then factor giving us 8x^2 - 5x = 0 x(8x - 5) = 0 so that x = 0 or 8x - 5 = 0 The second one can be solved giving us 8x = 5 x = 5/8 as the second solution...
 Polynomials-and-rational-expressions/41913: solve 2x^3-10x^2=0 show work1 solutions Answer 27037 by fractalier(2101)   on 2006-06-13 09:55:12 (Show Source): You can put this solution on YOUR website!2x^3 - 10x^2 = 0 factor out 2x^2 and get 2x^2(x - 5) = 0 Therefore x = 0 and x = 5
 Equations/41917: Can someone help me solve this problem? Subtract: 8 gal. 7 qt. - 3 gal. 2 qt. Thanks, Sher1 solutions Answer 27035 by fractalier(2101)   on 2006-06-13 09:23:28 (Show Source): You can put this solution on YOUR website! 8 gal. 7 qt. - 3 gal. 2 qt. __________________ 5 gal. 5 qt. which equals 6 gal. 1 qt.
 Polynomials-and-rational-expressions/41723: Simplify. -125 to the -3/2 power1 solutions Answer 26976 by fractalier(2101)   on 2006-06-12 12:30:26 (Show Source): You can put this solution on YOUR website!Okay, we can express -125 as (-5)^3, so we have (-125)^(-3/2) = ((-5)^3)^(-3/2) = (-5)^(-9/2) = 1 / (-5)^(9/2) = 1 / [(-5)^4 * (-5)^(1/2)] = 1 / 625i*sqrt(5) Now we have to rationalize by multiplying top and bottom by -i*sqrt(5) and we get -i*sqrt(5) / 3125
 Radicals/41725: This question is from textbook Elementary Algebra Please help me to simplify this problem: (7/2)^2 Thanks!1 solutions Answer 26974 by fractalier(2101)   on 2006-06-12 12:25:01 (Show Source): You can put this solution on YOUR website!Okay... (7/2)^2 means (7/2) * (7/2) = 49/4 or 12 1/4
 Graphs/41729: To solve y-7=3x for y, undo the subtration by adding 7. What do you get1 solutions Answer 26973 by fractalier(2101)   on 2006-06-12 12:23:48 (Show Source): You can put this solution on YOUR website!From y - 7 = 3x we add 7 to both sides and get y - 7 + 7 = 3x + 7 y = 3x + 7
 Linear_Equations_And_Systems_Word_Problems/41732: Use a system of equations to solve the following: The sum of two numbers is 54. The difference of the two numbers is 18. Find the two numbers.1 solutions Answer 26972 by fractalier(2101)   on 2006-06-12 12:20:31 (Show Source): You can put this solution on YOUR website!Let the numbers be x and y...then we have x + y = 54 and x - y = 18 Now add the equations and get 2x = 72 and x = 36 From this you can see that y = 18 and we're done...
 Sequences-and-series/41805: A scout troop will prepare trail mix for their next hike. They have decided to mix one type of nut, one type of dried fruit, and one type of granola. The local store carries 8 types of nuts, 6 types of dried fruit, and 5 types of granola. How many different trail mixes are possible? Thanks1 solutions Answer 26971 by fractalier(2101)   on 2006-06-12 12:17:07 (Show Source): You can put this solution on YOUR website!For every nut type, we have 6 fruit and 5 granola...thus 30 for each nut type and there are 8 nut types, so the answer turns out to be 8 * 6 * 5 = 240 mixes
 Probability-and-statistics/41810: From a group of 6 men and 4 women, a committee of 3 is to be selected at random. Find P(at least 2 women).1 solutions Answer 26970 by fractalier(2101)   on 2006-06-12 12:12:26 (Show Source): You can put this solution on YOUR website!We can add up the possibilities... start with having all three women...how many ways can we choose that? Well 4 chosen three at a time is C(4,3) = 4 ways Now, let's look at just two women...how many ways can we choose them? Well, C(4,2) = 6 ways...but for each of these ways, we can have any of six men, so there's a total of 36 ways this can happen... Thus the grand total is 40 different ways. Let me complete the problem... How many total ways are there altogether? Well if we complete the ananlysis by looking at C(4,1)*C(6,2), we get 4*15 = 60 one woman committees and C(6,3) = 20 no woman committees, so there are a grand total of 120 possible committees, and thus P(at least two women) = 40/120 = 1/3
 Probability-and-statistics/41809: A red and a blue die are tossed. What is the probability that the red die shows an odd number and the blue die shows a 1 or 2? Thanks1 solutions Answer 26969 by fractalier(2101)   on 2006-06-12 12:09:07 (Show Source): You can put this solution on YOUR website!Assuming fair six-sided dice, we multiply the individual probabilities because we are asked to find the AND case... so we have a 3 out of 6 for an odd on the red and we have a 2 out of 6 for a 1 or a 2 on the blue... multiplying we get 3/6 * 2/6 = 6/36 = 1/6
 Probability-and-statistics/41808: If the probability that an event will occur is 8/13, what are the odds that it will occur?1 solutions Answer 26968 by fractalier(2101)   on 2006-06-12 12:06:47 (Show Source): You can put this solution on YOUR website!8 out of every 13 tries...in the long run...
 Probability-and-statistics/41807: Evaluate C(12,10). thanks1 solutions Answer 26967 by fractalier(2101)   on 2006-06-12 12:05:50 (Show Source): You can put this solution on YOUR website!C(12,10) or 12C10 is expressed as (12!) / [(12-10)!(10!)] = (12*11) / (2*1) = 66
 Sequences-and-series/41806: Students are given a list of ten vocabulary words to learn. In how many ways could four of the words be listed on a test?1 solutions Answer 26966 by fractalier(2101)   on 2006-06-12 12:04:11 (Show Source): You can put this solution on YOUR website!We say that is "ten chosen four at a time," and can be expressed as 10C4, or (10!) / [(10-4)!(4!)] = (10*9*8*7) / (4*3*2*1) = 210