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# Recent problems solved by 'josmiceli'

josmiceli answered: 9646 problems
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 Money_Word_Problems/439582: Gerry wants to put enough money aside to pay all of his july and august utility bills. His summer gas bills are usually about half of his winter bills. His winter gas bills average \$142 per month. His electric bills are about \$26 higher each month in summer than in winter. His winter electric bills average \$52 per month. About how much should Gerry put aside to pay his july and august utility bills?1 solutions Answer 303773 by josmiceli(9649)   on 2011-04-23 17:32:16 (Show Source): You can put this solution on YOUR website!Let = average monthly summer gas bill Let = average monthly winter gas bill Let = average monthly summer electric bill Let = average monthly winter electric bill given: (1) (2) (3) (4) ----------------- There are 4 equations and 4 unknowns, so it's solvable Substitute (1) in (3) (3) Substitute (2) in (4) (4) ------------ For July and August, he should set aside \$298
 Money_Word_Problems/439570: Erica earned \$12,000 last year. He invested part of her money at 3% and the rest at 4% single interest. In one year she earned \$440.00 in interest. How much did she invest at each rate1 solutions Answer 303770 by josmiceli(9649)   on 2011-04-23 17:11:13 (Show Source): You can put this solution on YOUR website!Let = amount invested @ 3% interest Let = amount invested @ 4% interest given: (1) (2) ------------------- (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) \$4,000 = amount invested @ 3% interest \$8,000 = amount invested @ 4% interest check answer: (2) (2) OK
 logarithm/438613: A lawyer has determined that the number of people P(t) in a city of 1.4 million people who have been exposed to a news item after t days is given by the function P(t) = 1,400,000(1 − e−0.03t). How many days after a major crime has been reported has 35% of the population heard of the crime? I tried -0.03t=ln 35/14000001 solutions Answer 303251 by josmiceli(9649)   on 2011-04-20 20:29:24 (Show Source): You can put this solution on YOUR website! given: ---------------- During the 15th day 35% have heard of the crime check answer: OK
 Linear-equations/438459: Where do the two graphs and intersect?1 solutions Answer 303207 by josmiceli(9649)   on 2011-04-20 14:37:29 (Show Source): You can put this solution on YOUR website!They intersect where There can be no intersection, because there is no way the left side can equal the right can only be positive ------------------- Here's the graph:
 Money_Word_Problems/438460: Amy paid \$69.99 for a pair of running shoes during a 15% off sale. What was the regular price?1 solutions Answer 303201 by josmiceli(9649)   on 2011-04-20 14:22:38 (Show Source): You can put this solution on YOUR website!Let = theregular price given: The regular price was \$82.34
 Numbers_Word_Problems/438433: how many three digit numbers have the sum of their digits equal to 22?1 solutions Answer 303200 by josmiceli(9649)   on 2011-04-20 14:18:44 (Show Source): You can put this solution on YOUR website!(1) None of the digits can be , , or , since the sum of any arrangement of is too small What is left is all possible arrangements of: 994 985 976 886 877 ---- The arrangements are: 994 949 499 - 3 possible --- 985 958 895 859 598 589 - 6 possible --- 976 - 6 possible 886 - 3 possible 877 - 3 possible -------------- There are 21 3-digit numbers whose digits add up to 22
 Travel_Word_Problems/438390: When Frank Gresham drove 150 miles in the city, the fuel efficiency rating for his car was 18 miles/gallon. For highway driving, the fuel efficiency rating is 24 miles/gallon. How far will Frank have to drive on the highway for his car to have a fuel efficiency rating of 20 miles/gallon. My teacher gave us this problem to work on over break and he gave us the answer of 100 miles but i dont know how to get there. I checked this website and the problem has already been answered but in the explanation it says 24 - 20 is 3 which it is obviously not so i still need help setting up the problem. thank you :D1 solutions Answer 303189 by josmiceli(9649)   on 2011-04-20 13:54:58 (Show Source): You can put this solution on YOUR website!Let = highway miles he has to drive In words: (total miles driven)/(gallons used) = efficiency in mi/gal ------------- given: Gallons of gas used in city = Gallons of gas used on highway = Multiply both sides by Multiply both sides by He has to drive 100 miles on the highway check answer: OK
 Proportions/438426: what is the slope of a binomial 2x+31 solutions Answer 303183 by josmiceli(9649)   on 2011-04-20 13:32:41 (Show Source): You can put this solution on YOUR website!The slope is Here's the plot:
 Quadratic_Equations/438421: Solve: 10x^2 = 20x+30 What are the solutions to the equation? Can someone please help me with this? Thanks1 solutions Answer 303182 by josmiceli(9649)   on 2011-04-20 13:30:34 (Show Source): You can put this solution on YOUR website! Subtract from both sides Divide both sides by Now you can complete the square. Take 1/2 of the coefficient of , square it, and add it to both sides Both sides are now a perfect square Take the square root of both sides ( this is the (+) square root) and (this is the (-) square root) The solutions are and
 Equations/438404: At the fruit market, a box of 16 peaches costs \$2.01 more than a bag of 12 apples. Bobby bought 2 boxes of peaches and 5 bags of apples. He paid \$46.11, which included 6% sales tax. What is the price of each box of 16 peaches and what is the price of each bag of 12 apples?1 solutions Answer 303181 by josmiceli(9649)   on 2011-04-20 13:22:38 (Show Source): You can put this solution on YOUR website!Let = the price of a box of 16 peaches Let = the price of a bag of 12 apples Let = the price of 2 boxes of peaches and 5 bags of apples given: (1) (in cents) (2) (in cents) (in cents) ( in cents) ----------------------- (1) (2) Multiply both sides of (1) by and add (1) and (2) (1) (2) and, since (1) Each box of 16 peaches costs \$7.65 Each bag of 12 apples costs \$5.64 check: (2) (2) OK
 Rectangles/438331: im stumped; can you help? "The perimeter of a rectangle is twice the sum of its length and its width. The perimeter is 46 meters and its length is 2 meters more than twice its width. what is the length?"1 solutions Answer 303169 by josmiceli(9649)   on 2011-04-20 11:26:39 (Show Source): You can put this solution on YOUR website!Let width = Let length = given: By substitution: the length is 16 m
 Probability-and-statistics/438328: If two cards are drawn at random without replacement from a standard deck, find the probability that the second card is red, given that the first card was a heart. Please and thankyou very much.1 solutions Answer 303156 by josmiceli(9649)   on 2011-04-20 10:31:11 (Show Source): You can put this solution on YOUR website!There are 26 red cards and 26 black cards in a deck Hearts and diamonds are red, so if the 1st card is a heart, it is red. There are then 25 red cards left, and there are 25 + 26 = 51 cards left. The probability of drawing a 2nd card that is red is
 Age_Word_Problems/438274: If the digits of Fathers present age are reversed then get the age of his son.If 1 year ago his age was twice as that of his son.Find his present age1 solutions Answer 303155 by josmiceli(9649)   on 2011-04-20 10:23:15 (Show Source): You can put this solution on YOUR website!Let the 10s digit of Father's age = Let the units digit of Father's age = given: Father's age = Age of Son = This is 1 equation and 2 unknowns, so it's not solvable directly. I see that . I also see that the left side will always be even, so must be odd for that to be. So, can be 3,5,7 ( can't be , since can be even or odd --------------------- does not divide for any ------------------------ does not divide for any ------------------------ --------- The father is 73 and the son is 37 check: OK
 Inequalities/438287: write an equation of the line through the given point with the given slope write the equation in slope intercept form (4,4);m= -5/71 solutions Answer 303147 by josmiceli(9649)   on 2011-04-20 09:33:26 (Show Source): You can put this solution on YOUR website!(4,4) The formula is: Multiply both sides by check: Does the line go through (4,4) ? OK
 test/437906: On a buying trip in L.A,Don ordered 120 peices of jewelry:a number of bracelets \$5 each and a number of necklaces at \$14 each.He wrote a check for \$1230 to pay for the order.How many braclets and how many necklaces did Don purchase. Larry1 solutions Answer 302920 by josmiceli(9649)   on 2011-04-19 14:56:49 (Show Source): You can put this solution on YOUR website!Let = number of necklaces Let = number of bracelets given: (1) (2) ---------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and (1) Don bought 70 necklaces and 50 bracelets check: (2) (2) OK
 Exponential-and-logarithmic-functions/437896: log8 x^2 = (log8 x)^21 solutions Answer 302918 by josmiceli(9649)   on 2011-04-19 14:48:09 (Show Source): You can put this solution on YOUR website! Let --------- and -------------- check answers: and OK
 Average/437898: If Christina Makes a 80, 84, and 72 on her report card, what grade must she make on her last quarter to make an 85 average?1 solutions Answer 302910 by josmiceli(9649)   on 2011-04-19 14:22:27 (Show Source): You can put this solution on YOUR website!Let = the grade she needs Looks like she can't do it unless she gets a 104
 Exponential-and-logarithmic-functions/437888: solve for x log(base4)(x^2-3x) = 11 solutions Answer 302908 by josmiceli(9649)   on 2011-04-19 14:12:27 (Show Source): You can put this solution on YOUR website!Get logs on both sides. First, express as a log to the base Rewrite the equation: -------------- check answers: and
 Linear-equations/437878: can you please help me with this problem if line j is perpendicular to line k.If the slope of line j is 5/2,what is the slope of line k 1 solutions Answer 302903 by josmiceli(9649)   on 2011-04-19 14:03:17 (Show Source): You can put this solution on YOUR website!The letter used for slope is . If the slope of a given line is , then any line perpendicular to this line will have a slope equal to given: slope of perpendicular line =
 Numbers_Word_Problems/437868: Three batteries are connected in series so that the total voltage is 54 volts. The voltage of the first battery is twice the voltage of the second and 1/3 the voltage of the third battery. Find the actual voltage of each battery. 1 solutions Answer 302897 by josmiceli(9649)   on 2011-04-19 13:53:57 (Show Source): You can put this solution on YOUR website!Let = voltage of 2nd battery = voltage the 1st battery = voltage of 3rd battery The batteries are 6v, 12v, and 36v
 Inequalities/437877: can you please help me on this question what are all the negative odd integers that satisfy the inequality -3x +1≤ 171 solutions Answer 302892 by josmiceli(9649)   on 2011-04-19 13:43:48 (Show Source): You can put this solution on YOUR website! This says that is greater than or equal to minus 5 1/3. The negative odd integers that satisfy this are -5, -3, and -1 -------------- check: OK
 Travel_Word_Problems/437871: A co-worker posed this problem this morning that his daughter had. I'm not sure enough information is given to arrive at a solution. A lady drives to her destination one day at 40 mph. Another day she drives at 56 mph. She arrived at her destination the second day 2 hrs quicker than the first trip. What was the distance of her trip?1 solutions Answer 302888 by josmiceli(9649)   on 2011-04-19 13:35:08 (Show Source): You can put this solution on YOUR website!The 1st day: The 2nd day: ------------ Since the distance are the same: and, since The distance was 280 mi check answer: OK
 Permutations/437758: The man picks 1 from each of the following short stories every night and reads one short story from each of the following catagories: 1 of 5 mysteries, 1 of 4 non-fiction, 1 of 6 teen tales, 1 of 3 Robin Cook books, and and 1 of 5 historical novels. How many options does he have if he must start and end with either a mystery or a teen tale?Can you help with an explanation of how to go about solving a simpler problem too? I am so stuck. I think it is a permutation???1 solutions Answer 302840 by josmiceli(9649)   on 2011-04-19 10:07:20 (Show Source): You can put this solution on YOUR website!I think it may be simpler than it looks. The man could choose from the categories in any order he wishes except for the 1st and last night. ------------------ The problem is hard to interpret. I think they are talking about 5 successive nights that he reads a single short story. I don't think I can go beyond 5 successive nights because I don't know how many short stories are in each book. ------------------- I'll use 1 letter for each category: M - 5 N - 4 T - 6 R - 3 H - 5 ------ total - 23 --------------- The 1st night, he chooses between M - 5 T - 6 ------- total - 11 ways to choose 2nd night: there are 23 - 1 = 22 possible ways he can choose 3rd night: there are 23 - 2 = 21 possible ways he can choose 4th night: there are 23 - 3 = 20 possible ways he can choose 5th night: there are 11 - 1 = 10 possible ways he can choose -------- The choices must be multiplied to get all the possible orders There are 1,016,400 possible orderings of short stories he can read on 5 successive nights ------------------------- You should get a 2nd opinion on this, too. These kind of problems can be very tricky, but they are good for the brain.
 Percentage-and-ratio-word-problems/437497: Melissa earns 10% more per hour than her friend Jonathan. Louise makes 25% less per hour than Jonathan. What us the ratio of Louise's salary to Melissa's? 1 solutions Answer 302657 by josmiceli(9649)   on 2011-04-18 18:36:15 (Show Source): You can put this solution on YOUR website!Let = Melissa's earnings/hr Let = Jonathan's earnings/hr Let = Louise's earnings/hr (1) (2) ----------- (2) (1) (1) (1) (1)
 Numbers_Word_Problems/437413: A small pipe can fill an oil tank in 6 min more time than it takes a larger pipe to fill the same tank. Working together both pipes can fill a tank in 4 min. How long would it take each pipe working alone to fill the tank?1 solutions Answer 302609 by josmiceli(9649)   on 2011-04-18 15:49:27 (Show Source): You can put this solution on YOUR website!Let = time for larger pipe to fill oil tank given: = time for smaller pipe to fill tank --------- Add their rates of filling to get rate working together Multiply both sides by The solutions are (can't use negative time) and The smaller pipe takes 12 min The larger pipe takes 6 min
 Linear-equations/437425: Cheap Truck rentals charges \$15/day plus 0.12 cents per mile. Trucks 4 Less charges \$20/day plus 0.10 cents per mile. How many miles would you need to drive in order for the cost of both rental companies be the same and what would that cost be?1 solutions Answer 302601 by josmiceli(9649)   on 2011-04-18 15:36:09 (Show Source): You can put this solution on YOUR website!Let = miles driven Let = rental cost given: Cheap Truck: Trucks 4 Less: Set the costs equal to each other The costs are the same driving 250 miles check: and OK
 Numbers_Word_Problems/437284: The sum of two numbers is 17. When the larger is divided by the smaller the quotient is 3 and the remainder is 1. Find the numbers.1 solutions Answer 302475 by josmiceli(9649)   on 2011-04-18 10:19:51 (Show Source): You can put this solution on YOUR website!Let the larger number = Let the smaller number = given: (1) (2) ---------------- Multiply both sides of (2) by (2) Substitute this into (1) (1) (1) and (1) The numbers are 4 and 13
 test/437295: What is the value of the discriminant of the equation 6x^2-5x-3=0?1 solutions Answer 302472 by josmiceli(9649)   on 2011-04-18 10:11:11 (Show Source): You can put this solution on YOUR website!When the equation has the form , The discriminant is In your equation, , discriminant = 97
 test/437148: Express 4173 in scientific notation1 solutions Answer 302362 by josmiceli(9649)   on 2011-04-17 21:46:48 (Show Source): You can put this solution on YOUR website!Scientific notation always looks like: a.aaa * 10^b There is only 1 digit to the left of the decimal point You can do it in steps: answer
 logarithm/437149: How to find what y value in log(y)=.9311 solutions Answer 302359 by josmiceli(9649)   on 2011-04-17 21:39:43 (Show Source): You can put this solution on YOUR website!Remember that logs are exponents The way you read this is: The exponent that gives me is .931, and the base of the exponent is