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# Recent problems solved by 'josmiceli'

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 Complex_Numbers/555995: what is (3 + 2i) squared?1 solutions Answer 362003 by josmiceli(9654)   on 2012-01-11 20:03:49 (Show Source):
 Mixture_Word_Problems/555788: if 5 ozs of a powdered drug are mixed with 2 ozs of sugar, what part of the total mixture is the drug?1 solutions Answer 361936 by josmiceli(9654)   on 2012-01-11 16:10:20 (Show Source): You can put this solution on YOUR website!( oz. of drug ) / ( oz. of drug + sugar ) = fraction of mixture that is drug answer
 Expressions-with-variables/555758: callie is 4 years older than andrew. in 3 years the sum of their ages will be 52. how old is each now? i have have to solve each problem by creating a chart, writing an algebraic equation and then solving it1 solutions Answer 361935 by josmiceli(9654)   on 2012-01-11 16:08:17 (Show Source): You can put this solution on YOUR website!A key to age problems is the fact that the difference in two peoples ages remains the same throughout their lives. This is obvious, but often overlooked Let = Andrew's age now = Callie's age now = Andrew's age in 3 yrs = Callie's age in 3 yrs You can have columns headed , , , and the last column is Under the last column you have for the sum of their ages Now find with Now work your way back to the 1st 2 columns
 Numbers_Word_Problems/555757: A machine can make 6 parts in 8 minutes. How many can it make in 40 minutes? How do you do this problem above? 1 solutions Answer 361933 by josmiceli(9654)   on 2012-01-11 15:51:38 (Show Source): You can put this solution on YOUR website! parts/min This is of a part in minute parts Note that ( parts/min )*( min ) = parts They can make 30 parts in 40 minutes
 Equations/555661: FACTOR THE TRINOMIAL COMPLETELY: x^2 + x-2 =1 solutions Answer 361887 by josmiceli(9654)   on 2012-01-11 11:54:13 (Show Source): You can put this solution on YOUR website!You can complete the square: Take 1/2 of the coefficient of , square it, and add it to both sides (1) and, also (2) Rewrite (1) and (2) as (1) (2) The factors are:
 Permutations/555629: I am trying to figure out what formula to use on this question and also how to proceed with the formula. A password to a computer is to consist of 2 lower case letters followed by three digits. How many different passwords are possible if repetition of letters and numbers is not permitted?1 solutions Answer 361885 by josmiceli(9654)   on 2012-01-11 11:45:09 (Show Source): You can put this solution on YOUR website!It's better if you reason it out and don't think of it as a formula. ----------------------- Imagine you have 5 empty boxes that you can put things in, but you are restricted as to what you can put in them. ----------------------- There are 26 possible things ( letters ) you can put in the 1st box You have used up a letter, so you only have 25 possible letters you can put in the 2nd box. In the 3rd box, you are allowed 0 - 9, so there are 10 possible things In the 4th box, you have 10 - 1 = 9 possible things allowed In the 5th box, you have 10 - 2 = 8 possible things allowed ------------------------------------------------ The numbers of things allowed in the 5 boxes is: 26, 25, 10, 9, and 8 Now the key to the problem is what to do with these numbers. The general rule is, whenever you have ( x number possible ) AND ( y number possible ) AND ( z number possible ) etc. etc. etc. The resulting possibilities are x times y times z etc. So, the number of possible passwords is:
 Numbers_Word_Problems/555651: The numerator of a fraction is 10 less than the denominator. If the numerator is increased by 5 and the denominator is decreased by 5.The fraction becomes 1. Find the fraction.1 solutions Answer 361883 by josmiceli(9654)   on 2012-01-11 11:27:49 (Show Source): You can put this solution on YOUR website!Let = numerator Let = denominator given: (1) (2) ----------------------- (2) (2) Also, from (1) (1) ---------------- It looks like the fraction can be anything where suppose , then This equals 1, so the fraction can be any
 Travel_Word_Problems/555650: If it takes 15 minutes to drive 4 miles, how fast I MPH am I driving?1 solutions Answer 361881 by josmiceli(9654)   on 2012-01-11 11:13:15 (Show Source): You can put this solution on YOUR website!In just units: ( miles / minute ) x ( minutes / hour ) = miles / hour You are driving 16 mi/hr
 Rational-functions/555642: The graph of the line through (2,3) that is perpendicular to the line with equation x = -1 also goes through which point?1 solutions Answer 361879 by josmiceli(9654)   on 2012-01-11 11:07:52 (Show Source): You can put this solution on YOUR website!The line with equation is a vertical line through ( -1,0 ) Any line perpendicular to this line is a horizontal line If it goes through (2,3), it must also go through (0,3)
 Mixture_Word_Problems/555639: An alloy which weighs 118 kg is 10 percent silver. How much silver must be added to produce a metal that is 25 % silver?1 solutions Answer 361876 by josmiceli(9654)   on 2012-01-11 10:33:15 (Show Source): You can put this solution on YOUR website!Let = kg of silver to be added kg of silver in 10% alloy 23.6 kg of silver must be added check: OK
 Probability-and-statistics/555420: I do not know how to solve this problem correctly. Kate makes 4 free throws every 10 attempts. At this rate how many free throws can she expect to make in 15 attempts?1 solutions Answer 361772 by josmiceli(9654)   on 2012-01-10 19:29:12 (Show Source): You can put this solution on YOUR website!You can set up a ratio Multiply both sides by She can expect to make 6 freethrows in 15 attempts
 Linear-systems/555425: by what number can i multiply 6184 to get 11 solutions Answer 361770 by josmiceli(9654)   on 2012-01-10 19:23:01 (Show Source): You can put this solution on YOUR website!Multiply by
 Age_Word_Problems/555415: George is 3 years older than his sister Janet. In 7 years she will be six-sevenths of his age. How old is George?1 solutions Answer 361769 by josmiceli(9654)   on 2012-01-10 19:21:03 (Show Source): You can put this solution on YOUR website!Let = George's age now Let = Janet's age now given: (1) (2) -------------------- (1) Substitute (1) into (2) (2) (2) (2) (2) (2) and, since (1) (1) (1) George is 14 check answer (2) (2) (2) (2) (2) OK
 Miscellaneous_Word_Problems/555405: There are six digits in a sequence, two 4s, two 5s, and two6s. There is one digit in between the 2 4s, there are 2 digits in between the 2 5s and there are 3 digits in between the 2 s. Write the sequence of numbers.1 solutions Answer 361768 by josmiceli(9654)   on 2012-01-10 19:08:41 (Show Source): You can put this solution on YOUR website!If X represents an unknown digit which is either 4,5, or 6, then I am given: (1) 4 X 4 (2) 5 X X 5 (3) 2 X X X 2 -------- Thje problem is how to shift these 3 sequences around so that the X's are masked out by the digits Suppose I combine (2) and (3) this way: 5 2 X 5 X 2 Now I can combine this with (1) to mask out the X's 5 2 4 5 4 2 answer
 Quadratic_Equations/555084: x2+35x-150=01 solutions Answer 361625 by josmiceli(9654)   on 2012-01-10 09:34:59 (Show Source): You can put this solution on YOUR website! and check answers: close enough You can check the other root
 Expressions-with-variables/555080: For the following system, use the second equation to make a substitution for y in the first equation. 2x + y = 6 y = 3x + 4 What is the resulting equation? 1 solutions Answer 361618 by josmiceli(9654)   on 2012-01-10 08:55:19 (Show Source): You can put this solution on YOUR website!(1) (2) ------------- (1) (1) (1) (1) and (2) (2) (2) (2) (2/5,26/5) check answer: (1) (1) (1) (1) (1) ------------- (2) (2) (2) (2) OK
 Travel_Word_Problems/555001: A plane makes the trip from Acton to Banville at 800 km/h. The return, at 1000 km/h, takes 1/2 hour less than the initial flight. Find the distance between the towns.1 solutions Answer 361603 by josmiceli(9654)   on 2012-01-10 03:26:46 (Show Source): You can put this solution on YOUR website!Let = time in hours for 1st flight Let = distance between towns in km Equation for A to B: Equation for B to A: ---------------------------- Bt substitution: hrs and, since The distance between the towns is 6,000 km check: OK
 Mixture_Word_Problems/555010: What quantity of pure acid must be added to 500 mL of a 25% acid solution to produce a 75% acid solution?1 solutions Answer 361600 by josmiceli(9654)   on 2012-01-10 03:16:39 (Show Source): You can put this solution on YOUR website!let = ml of pure acid needed ml of pure acid in 25% solution ------------------ 1,000 ml of pure acid must be added check answer: OK
 Triangles/554850: Please help me solve this word problem: The sum of all angles in a triangle is always 180 degrees. The measure of the first angle is four times the measure of the second angle. The measure of the third angle is 78° more than the second angle. What is each angle? Thanking you in advance, Student Learner1 solutions Answer 361563 by josmiceli(9654)   on 2012-01-09 22:02:25 (Show Source): You can put this solution on YOUR website!Let the angles be a,b, and c given: (1) (2) (3) -------------- This is 3 equations and 3 unknowns, so it's solvable Substitute (2) and (3) into (1) (1) (1) (1) (1) and, since (2) (2) (2) and (3) (3) (3) The angles are 68, 17, and 95 degrees check: OK
 test/554854: songs are recorded on one side of records that rotate at a rate of 45 rpm, Through how many degrees does one of these records rotate in 20 seconds?1 solutions Answer 361510 by josmiceli(9654)   on 2012-01-09 20:13:29 (Show Source): You can put this solution on YOUR website!In terms of units: ( degrees ) = ( revolutions / minute ) x ( minutes / second ) x ( seconds ) x ( degrees/revolution ) given: degrees = degrees
 Triangles/554847: Given a right triangle with a side of length 4 and a hypotenuse of length 7, find the measure of the two acute angles. (Round to the nearest hundredth.) please help so confused1 solutions Answer 361503 by josmiceli(9654)   on 2012-01-09 20:02:11 (Show Source): You can put this solution on YOUR website!Since it's a right triangle, there is a right angle. That means the sum of the 2 acute angles is 90 degrees. ( 90 + 90 = 180 ) Suppose you want to find the angle which is between the hypotenuse and the side of length 4. ( this reads " a is the angle whose cosine is .5714 " ) and The acute angles are 55.15 and 34.85 degrees
 Expressions-with-variables/554834: if person A can paint a house in 4 hours, and person B can paint the same house in 7 hours... how much time would it take for A and B to paint the same house working together?1 solutions Answer 361494 by josmiceli(9654)   on 2012-01-09 19:49:01 (Show Source): You can put this solution on YOUR website!Add their rates of painting to get their rate working together A's rate: ( 1 house ) / ( 4 hours ) B's rate: ( 1 house ) / ( 7 hours ) Let their time working together = Multiply both sides by Working together, they paint the house in 2 hrs and 33 min
 Percentage-and-ratio-word-problems/554752: If there are 480 students and 5/8 of the students have a sister, how many students do hot have a sister?1 solutions Answer 361479 by josmiceli(9654)   on 2012-01-09 18:39:03 (Show Source): You can put this solution on YOUR website!If 5/8 have a sister, then do not have a sister 180 do not have a sister
 Travel_Word_Problems/554522: Penny's bicycle trip from Colorado Springs to Pikes Peak took 1.5 hours longer than the return trip to Colorado Springs. If she averaged 6 mph on the way to Pikes Peak and 15 mph for the return trip, then how long (in hours) was the ride from Colorado Springs to Pikes Peak?1 solutions Answer 361372 by josmiceli(9654)   on 2012-01-09 11:29:42 (Show Source): You can put this solution on YOUR website!Let = time for return trip in hours Let = distance from C.S. to P.P given: 1st trip: return trip: ----------- By substitution: The ride from C.S. to P.P took 2.5 hours check answer: miles and miles OK
 Quadratic_Equations/554524: Describe the nature and the number of the solutions of 2x^2-7x+9=x+11 solutions Answer 361368 by josmiceli(9654)   on 2012-01-09 11:20:47 (Show Source): You can put this solution on YOUR website!This is determined by what is called the " discriminant " This is in the formula for the roots which is In this case: The discriminant is zero, which means there is 1 solution, which is called a double root. Here's a plot of the equation. Notice it touches the x-axis at 1 point
 Length-and-distance/554259: Lora walks to the library in 1/3 of an hour. The library is 3/4 miles away. What is her pace?1 solutions Answer 361293 by josmiceli(9654)   on 2012-01-08 19:02:52 (Show Source): You can put this solution on YOUR website!Her pace is ( distance ) / ( time ) miles/hour miles/hour mi/hr Her pace is 2 1/4 miles/hour
 Travel_Word_Problems/554257: For every 3 times jake can run around the block myra can bike five times. If they start together, after how many times around the block will they meet at the starting point?1 solutions Answer 361290 by josmiceli(9654)   on 2012-01-08 18:53:08 (Show Source): You can put this solution on YOUR website!If Jakes goes around 3 times, he will meet Myra, who has gone around 5 times.
 Rational-functions/554238: In 1991, the life expectancy of males in a certain country was 61.5 years. In 1995, it was 64.4 years. Let E represent the life expectancy in year t and let t represent the number of years since 1991. The linear function E(t) that fits the data is?1 solutions Answer 361287 by josmiceli(9654)   on 2012-01-08 18:41:37 (Show Source): You can put this solution on YOUR website!A linear function means it is a straight line Plot on the horizontal axis Plot on the vertical axis You are given the points: ( 0,61.5 ) and ( 4,64.4 ) -------- Use the point-slope formula: Multiply both sides by check answer: and OK
 Triangles/554241: one angle of a triangle measuere "f" degrees. One of the other triangles angls measures two times the size, and the third andgle is thrww times the size. Find what each angle measures1 solutions Answer 361279 by josmiceli(9654)   on 2012-01-08 18:26:46 (Show Source): You can put this solution on YOUR website!The sum of the angles of a triangle = 180 degrees given: the angles are: , , and The angles are 30, 60, and 90 degrees
 logarithm/554086: If log a=.5, log b=.3, and log c= 16, solve the following equation for x. a^x b^x=c Can somebody please try to guide me in the right direction? I do not want an answer to the problem, but only some guidance where to start. Thanks!1 solutions Answer 361214 by josmiceli(9654)   on 2012-01-08 13:41:58 (Show Source): You can put this solution on YOUR website! Suppose I say and Then I have . It is true that Take the log of both sides of the original equation Sorry, I did the whole thing.
 Numbers_Word_Problems/554078: 11,600 Universities there are seven times as many students who work full time as there are students who do not. How many students work full time and how many do not?1 solutions Answer 361213 by josmiceli(9654)   on 2012-01-08 13:29:15 (Show Source): You can put this solution on YOUR website!Let = number who do not work full time = number who work full time given: 10150 work full time 1450 do not work full time