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# Recent problems solved by 'alicealc'

alicealc answered: 281 problems
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 Equations/463422: simplify 1 solutions Answer 317524 by alicealc(281)   on 2011-06-22 06:35:35 (Show Source): You can put this solution on YOUR website! = =
 Linear-equations/463432: 5F+17=1471 solutions Answer 317523 by alicealc(281)   on 2011-06-22 06:32:58 (Show Source): You can put this solution on YOUR website!5F + 17 = 147 5F = 147 - 17 5F = 130 F = 130/5 = 26
 Age_Word_Problems/463435: Please answer as soon as possible... 1) 3 graduating students who are applying for a part-time job have ages which sum up to 60. The sum of the ages of the first 2 students less the age of the third student gives 12. If the third student is 5 yrs. older than the first student, find their ages.1 solutions Answer 317522 by alicealc(281)   on 2011-06-22 06:31:40 (Show Source): You can put this solution on YOUR website!1st student's age = a 2nd student's age = b 3rd student's age = c a + b + c = 60 a + b - c = 12 c = 5 + a a + b + c = 60 a + b - c = 12 --------------- (-) 2c = 48 c = 48/2 = 24 c = 5 + a 24 = 5 + a a = 24 - 5 = 19 a + b + c = 60 19 + b + 24 = 60 43 + b = 60 b = 60 - 43 = 17 so, 1st student's age = 19 2nd student's age = 17 3rd student's age = 24
 Mixture_Word_Problems/463117: A cleaning solution was made by mixing 10 qt of a 4% baking soda solution and 8 qt of a 45% soap solution. Find the concentration of the cleaning solution.1 solutions Answer 317355 by alicealc(281)   on 2011-06-21 09:01:47 (Show Source): You can put this solution on YOUR website!baking soda = 4/100 * 10 qt = 40/100 qt = 0.4 qt soap = 45/100 * 8 qt = 360/100 qt = 3.6 qt concentration = (0.4+3.6)/(10+8) * 100% = 4/18 * 100% = 400/18 % = 22.22 %
 Probability-and-statistics/463118: Two six sided dice, with sides numbered 1 through 6 are rolled. If the dice are rolled 9000 times, about how many times would you expect the dice to have a sum of 8?1 solutions Answer 317354 by alicealc(281)   on 2011-06-21 08:58:50 (Show Source): You can put this solution on YOUR website!2 dice = 6*6 = 36 possibilities sum of 8: (2,6) (3,5) (4,4) (5,3) (6,2) probability = 5/36 expectation frequency = 5/36 * 9000 = 45000/36 = 5000/4 = 1250 times
 Average/463115: F.E.U Cooperative Store sold 1,200 copies of this Workbook this first semester, 500 copies remain unsold. What percent of the total number of copies did the store sell?? Please help.... 1 solutions Answer 317353 by alicealc(281)   on 2011-06-21 08:56:10 (Show Source): You can put this solution on YOUR website!the book sold = 1200 - 500 = 700 percent sold = 700/1200 * 100% = 7/12 * 100% = 700/12 % = 58.33%
 Rectangles/463116: A room has an area of 352 ft2. One dimension is 6 ft more than the other. Find the dimensions of the room.1 solutions Answer 317352 by alicealc(281)   on 2011-06-21 08:53:50 (Show Source): You can put this solution on YOUR website!length = l width = w l = 6 + w area = 352 l*w = 352 (6 + w)*w = 352 (w + 22)*(w - 16)= 0 w + 22 = 0 w = - 22 or w - 16 = 0 w = 16 because the dimension can't be a negative number, then: w = 16 l = 6 + 16 = 22 so the room is 16 ft wide and 22 ft long
 Age_Word_Problems/463081: Reggie is 5 years old than Lani. Five years ago the sum of their ages was 25. How old are they now?1 solutions Answer 317349 by alicealc(281)   on 2011-06-21 08:50:28 (Show Source): You can put this solution on YOUR website!Reggie = R Lani = L if it means that Reggie is 5 years older than Lani, then: R = 5 + L Five years ago: R - 5 + L - 5 = 25 5 + L - 5 + L - 5 = 25 2L - 5 = 25 2L = 25 + 5 2L = 30 L = 30/2 = 15 R = 5 + 15 = 20 so, now Reggie is 20 years old, Lani is 15 years old
 Mixture_Word_Problems/463083: To a sugar solution of 3 liters containing 40% sugar one liter of water is added. The percentage of sugar in the new solution is 1 solutions Answer 317348 by alicealc(281)   on 2011-06-21 08:47:33 (Show Source): You can put this solution on YOUR website!sugar = 40/100 * 3 = 120/100 = 1.2 liters percentage of new sugar = 1.2/(3+1) * 100% = 1.2/4 * 100% = 0.3 * 100% = 30%
 Exponential-and-logarithmic-functions/463110: 1 solutions Answer 317347 by alicealc(281)   on 2011-06-21 08:44:48 (Show Source):
 Linear-equations/463095: Write the slope-intercept equation for the line that passes through (14, -2) and is perpendicular to 7x – 10y = 181 solutions Answer 317345 by alicealc(281)   on 2011-06-21 08:36:56 (Show Source): You can put this solution on YOUR website!7x - 10y = 18 -10y = -7x + 18 divide all by -10 y = 7/10 x - 18/10 the slope of this equation is 7/10 if 2 lines are perpendicular then slope 1 * slope 2 = -1 7/10 * slope 2 = -1 slope 2 = -1 * 10/7 = -10/7 line equation for the line with slope m and passes through (x1, y1): y - y1 = m*(x - x1) m = -10/7 x1 = 14 y1 = -2 y - (-2) = -10/7 * (x - 14) y + 2 = -10/7 x + 140/7 multiply all by 7: 7y + 14 = -10x + 140 10x + 7y + 14 - 140 = 0 so the equation will be: 10x + 7y - 126 = 0
 Numbers_Word_Problems/463105: I am a number greater than 50,000 but less than 70,000. My ones digit and tens digit are the same. My ten thousands digit is three times the sum of my ones digit and tens digit. Both my thousands digit and hundreds digit are half my ten thousands digit. What number am I?1 solutions Answer 317344 by alicealc(281)   on 2011-06-21 08:29:58 (Show Source): You can put this solution on YOUR website!let the number = abcde (a, b, c, d, and e should be whole numbers/integers) the number is greater than 50,000 but less than 70,000, so the possibility of the value of "a" is 5 or 6 ones digit and tens digit are the same: e = d ten thousand digit is three times the sum of ones and tens digits: a = 3*(e + d) a = 3*(d + d) a = 3*2d a = 6d thousands digit and hundreds digit are half of ten thousand digit b = 1/2 * a = 1/2 * 6d = 3d c = 1/2 * a = 1/2 * 6d = 3d if a = 5 then 5 = 6d -> d = 6/5 (not a whole number) so a = 6 6 = 6d -> d = 6/6 = 1 e = d = 1 b = 3d = 3*1 = 3 c = 3d = 3*1 = 3 so, the number is 63311
 Miscellaneous_Word_Problems/463106: A farmer has 318 feet of fence with which to make a corral. If he arranges it into a rectangle that is twice as long as it is wide, what are the dimensions1 solutions Answer 317340 by alicealc(281)   on 2011-06-21 08:21:28 (Show Source): You can put this solution on YOUR website!length = l width = w perimeter = 318 divide all by 2: l + w = 159 2w + w = 159 3w = 159 w = 159/3 w = 53 l = 2w = 2 * 53 = 106 so, the dimension will be: 106 feet long and 53 feet wide
 Probability-and-statistics/309757: You roll a number cube . what is the probability that you roll a 2 or an even number ? 1 solutions Answer 221537 by alicealc(281)   on 2010-05-30 05:53:33 (Show Source): You can put this solution on YOUR website!even numbers in a dice = 2, 4, 6 (2 is included) so, the probability of rolling 2 or even numbers = probability of rolling even numbers = 3/6 = 1/2 = 0.5
 Percentage-and-ratio-word-problems/309758: The price of a telephone was first increased by 10% and then the new price was decreased by 25%. The final price was what percent of the initial price A 78% B 80% C 82.5% D 85% E 87.5% 1 solutions Answer 221536 by alicealc(281)   on 2010-05-30 05:51:56 (Show Source): You can put this solution on YOUR website!initial price = p increased by 10% -> the price will be: p + 10% * p = p + 0.1p = 1.1p decreased the new price by 25% -> the price will be: 1.1p - 25% * 1.1p = 1.1p - 0.25 * 1.1p = 1.1p - 0.275p = 0.825p = 82.5% * p (C)
 absolute-value/309759: | 2 - x | < 3 , which of the following is a possible value of x ? a 4 b 5 c 6 d 7 e 8 1 solutions Answer 221535 by alicealc(281)   on 2010-05-30 05:49:10 (Show Source): You can put this solution on YOUR website!|2 - x| < 3 means: -3 < 2 - x < 3 subtract all by 2: -3 - 2 < 2 - x - 2 < 3 - 2 -5 < -x < 1 multiply all by -1 5 > x > -1 so the value of x must between -1 and 5. then the correct answer is 4 (a)
 Surface-area/309678: FInd the lateral area and surface area of a right cone with radius 8 in. and height 15 in. Give your answers in terms of pie or pi1 solutions Answer 221531 by alicealc(281)   on 2010-05-29 23:57:44 (Show Source): You can put this solution on YOUR website!radius (r) = 8 in height (h) = 15 in slant height (s) = = = = = 17 lateral area = square inches surface area = base area + lateral area = = = = square inches
 Surface-area/309677: find the number of vertices, faces, and edges for the regular hexagonal pyramid1 solutions Answer 221530 by alicealc(281)   on 2010-05-29 23:52:11 (Show Source): You can put this solution on YOUR website!number of vertices = 6 (hexagon) + 1 (the top) = 7 number of face = 1 (base) + 6 (the lateral faces) = 7 number of edges = 6 (base's edges) + 6 (the edges connecting each base's vertices to the top) = 12
 Quadratic_Equations/309681: The width is 2 ft less than the length. The area is 8ft^2. What is the length and width?1 solutions Answer 221529 by alicealc(281)   on 2010-05-29 23:46:43 (Show Source): You can put this solution on YOUR website!assuming that it's a rectangle: width = w length = l w = l - 2 area = l * w 8 = l * (l - 2) 0 = (l - 4)*(l + 2) l - 4 = 0 or l + 2 = 0 l = 4 or l = -2 because the length can't be in negative number, so: length= 4 ft width = l - 2 = 4 - 2 = 2 ft
 Probability-and-statistics/309698: Guillermo wants to create several different 7-character screen names. He wants to use arrangements of the first 3 letters of his first name (Gui), followed by arrangments of 4 digits in 1947 the year of his birth. How many differnet screen names can he create in this way?1 solutions Answer 221527 by alicealc(281)   on 2010-05-29 23:40:47 (Show Source): You can put this solution on YOUR website!number of ways of arrangement the 3 letters (Gui) = 3! = 3 * 2 * 1 = 6 number of ways of arrangement the 4 numbers (1947) = 4! = 4 * 3 * 2 * 1 = 24 if the arrangement started by the letters than followed by the numbers, then number of ways of arrangement 7-character screen name is: 6 * 24 = 144 ways
 Probability-and-statistics/309699: On certain day the chance of rain is 80% in San Francisco and 30% in Sydney. Assume that the chance of rain in the 2 cities is independent What is the probability that it will not rain in either city? 1 solutions Answer 221523 by alicealc(281)   on 2010-05-29 23:36:21 (Show Source): You can put this solution on YOUR website!probability not rain in San Fransisco = 100% - 80% = 20% = 0.2 probability not rain in Sydney = 100% - 30% = 70% = 0.7 probability not rain in either city (the chance of rain in the 2 cities is independent) = 0.2 * 0.7 = 0.14 = 14%
 Word_Problems_With_Coins/309710: The St. Mark Community babecue served 250 dinners. Achilds plate cost \$3.50 and an adult plate is \$7.00. A total of \$1347.50 was collected. How many of each type of plate was served? Please show work. Thanks1 solutions Answer 221521 by alicealc(281)   on 2010-05-29 23:33:08 (Show Source): You can put this solution on YOUR website!child's plate = c adult's plate = a (1) c + a = 250 (2) 3.5c + 7a = 1347.50 multiply equation (1) by 7 (1) 7c + 7a = 1750 (2)3.5c+ 7a = 1347.50 ---------------------- (-) 3.5c = 402.5 c = 402.5/3.5 = 4025/35 = 115 c + a = 250 115 + a = 250 a = 250 - 115 = 135 so, child's plates reserved = 115 plates adult's plate reserved = 135 plates
 Graphs/309719: A gas stattion sells 4820 gallons of gas on a day when they charge \$1.35 per gallon, and they sell 3880 gallons on a day when they charge \$1.40. Find the equation for the line whose graph depicts this data.1 solutions Answer 221520 by alicealc(281)   on 2010-05-29 23:27:57 (Show Source): You can put this solution on YOUR website!price = x number of gallons sold = y y = ax + b (1) 4820 = 1.35a + b (2) 3880 = 1.40a + b --------------------- (-) 940 = -0.05a a = 940/-0.05 a = 94000/-5 = -18800 4820 = 1.35a + b 4820 = 1.35*(-18800) + b 4820 = -25380 + b b = 4820 + 25380 = 30200 so, the line equation for the problem is: y = -18800x + 30200
 Travel_Word_Problems/309711: Deep thought granola is 25% nuts and dries fruit. Oat Dream Granola is 10% nuts and dried fruit. How much of deep thought and how uch of oat dream should be mixed to form a 20-lb batch of granola that is 19%nuts and dried fruit? Please show work.Thanks1 solutions Answer 221515 by alicealc(281)   on 2010-05-29 23:15:36 (Show Source): You can put this solution on YOUR website!Deep thought Granola = x lb -> nuts = 25/100 * x = 0.25x Oat Dream Granola = y lb -> nuts = 10/100 * y = 0.1y (1) x + y = 20 (2) 0.25x + 0.1y = 0.19 * 20 -> 0.25x + 0.1y = 3.8 multiply equation (1) by 0.25: (1) 0.25x + 0.25y = 5 (2) 0.25x + 0.1 y = 3.8 ------------------------ (-) 0.15y = 1.2 y = 1.2/0.15 = 120/15 = 8 x + y = 20 x + 8 = 20 x = 20 - 8 x = 12 so, deep thought granola needed = 12 lb oat dream granola needed = 8 lb
 Graphs/309565: Find the slope-intercept equation for the line with the indicated slope and y-intercept. Slope 3/4; y-intercept (0, 35)1 solutions Answer 221419 by alicealc(281)   on 2010-05-29 07:43:45 (Show Source): You can put this solution on YOUR website!slope (m) = 3/4 intercept (x1, y1) = (0, 35) this formula can be used to find the equation: y - y1 = m * (x - x1) y - 35 = 3/4 * (x - 0) y - 35 = 3/4 * x multiply both sides by 4: 4y - 140 = 3x 3x - 4y + 140 = 0
 Probability-and-statistics/309573: A bag contains 2 red marbles , 4 green marbles , 4 blue marbles you choose one marble at random , put the marble back in the bag, then choose a second marble at random . What is the probability that you choose 2 red marbles.1 solutions Answer 221418 by alicealc(281)   on 2010-05-29 07:39:44 (Show Source): You can put this solution on YOUR website!2 red marbles , 4 green marbles , 4 blue marbles total, there are 10 marbles probability to get: 1st red marble = 2/10 = 0.2 then the red marble is put back in the bag, so the probability to get the 2nd red marble is same as the probability to get 1st red marble, that is 0.2 so, the probability to get 2 red marbles for this problem is 0.2 * 0.2 = 0.04
 Permutations/309574: Five blocks are painted red, blue, green, yellow, and white. In how many different ways can the blocks be arranged in a row if the red block is always first?1 solutions Answer 221417 by alicealc(281)   on 2010-05-29 07:36:12 (Show Source): You can put this solution on YOUR website!the red block is always first, it means the arrangement is made only for the rest 4 colors. So, there will be 4! = 4 * 3 * 2 * 1 = 24 different ways
 expressions/309582: How can I determine whether this relation is a function or not? Need help {(3,6),(4,6),(10,6),(12,6)}1 solutions Answer 221416 by alicealc(281)   on 2010-05-29 07:34:05 (Show Source): You can put this solution on YOUR website!a relation is a function if there is only one solution for each domain member, that means no repeating value of a domain member in a solution set. A domain member is the left part of the coordinate system, a solution for the domain member is the right part of the coordinate system. Example: {(1, 2), (1, 4), (2, 5)} in not a function since a domain member, that is 1 have more than one solution, 2 and 4 so, if we have {(3, 6),(4, 6),(10, 6),(12, 6)} it is a function, because there aren't any domain members that have more than one solution (the domain members are 3, 4, 10, and 12)
 Triangles/309578: How many different triangles are there for which the lengths of the sides are 3, 8, and n, where n is an integer and 3 < n < 8?1 solutions Answer 221415 by alicealc(281)   on 2010-05-29 07:24:32 (Show Source): You can put this solution on YOUR website!to make a triangle, the sum of two smaller sides must be greater than the third side. so, if the side are 3, 8, and n, and 3 < n < 8 the possible values of n are 6 and 7 (3 + 6 > 8 and 3 + 7 > 8) so, there will be 2 different triangles (triangle 1 with sides of 3,8,6 and triangle 2 with sides of 3,8,7)
 Probability-and-statistics/309580: For the set of numbers 2, 2, 4, 5, and 12, which statement is true? (A) Mean = Median (B) Mean > Mode (C) Mean < Mode (D) Mode = Median (E) Mean = Mode 1 solutions Answer 221414 by alicealc(281)   on 2010-05-29 07:20:46 (Show Source): You can put this solution on YOUR website!2, 2, 4, 5, and 12 mean = (2 + 2 + 4 + 5 + 12) / 5 = 25/5 = 5 median = 4 (the value in the middle of the sequence) mode = 2 (appears twice) so, the correct answer is mean > mode (B)
 Percentage-and-ratio-word-problems/309581: A company produced 300 appliances in the first week of the month. Because it received additional machinery, its production increased 50% from the first week to the second week. How many appliances did the company produce the second week ? 1 solutions Answer 221413 by alicealc(281)   on 2010-05-29 07:16:48 (Show Source): You can put this solution on YOUR website!the increase = 50% * 300 = 50/100 * 300 = 0.5 * 300 = 150 so in the second week, the company can produce 300 + 150 = 450 appliances