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# Recent problems solved by 'josmiceli'

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 logarithm/686808: ln (x-8) - ln (x+7)= ln (x-10) - ln (x+8)1 solutions Answer 424907 by josmiceli(9817)   on 2012-11-28 23:49:48 (Show Source): You can put this solution on YOUR website! Multiply both sides by ---------- I'm doubtful that this is the right solution. It works for But it doesn't work for There is no log to a positive base that gives me or --------------------------- I would get a 2nd opinion on this one
 Money_Word_Problems/686813: A plumber earns 25 dollars per hour more than his apprentice. For a 40-hour week, their combined earnings were \$2600. What is the hourly rate for each?1 solutions Answer 424904 by josmiceli(9817)   on 2012-11-28 23:28:34 (Show Source): You can put this solution on YOUR website!Let = the hourly rate of the apprentice in dollars/hr = the hourly rate of the plumber in dollars/hr given: The hourly rate of the apprentice is \$20/hr The hourly rate of the plumber is \$45/hr
 Age_Word_Problems/686829: i dont understnad this question it is about direct varaitons can you please help me out If y = negative 4 when x=10, find y when x = 2 can you please help me with this im am not understanding this thanks 1 solutions Answer 424902 by josmiceli(9817)   on 2012-11-28 23:15:25 (Show Source): You can put this solution on YOUR website!the 1st part says Then it says Multiply both sides by
 logarithm/686832: Log(base3)27=x1 solutions Answer 424901 by josmiceli(9817)   on 2012-11-28 23:09:37 (Show Source): You can put this solution on YOUR website! I can rewrite this as: --------- You can see this is true, but doing the mechanics: take the log to base of both sides
 Linear_Algebra/686822: In my math book the directions say ; Write an equation for a linear function f that has the given values. Example number 24 ; f(-2)=-2, f(4)=-8 I dont understand how to do this, could you explain it step by step & why? Thank you.1 solutions Answer 424900 by josmiceli(9817)   on 2012-11-28 22:59:06 (Show Source): You can put this solution on YOUR website!Given: ------------ A linear equation will have the form (1) ------------------- (2) ----------------- Now I have 2 equations with 2 unknowns, so it's solvable (1) (1) and (2) (2) ------------------- Subtract (1) from (2) (2) (1) and (1) (1) (1) (1) The function is: --------------- check answer: OK OK
 Expressions-with-variables/686675: There were 213 tickets sold to a school dance. Tickets cost \$5 with an activity sticker and \$8 without. Tickets sales totaled \$1,254. Find the number of each type of ticket sold.1 solutions Answer 424866 by josmiceli(9817)   on 2012-11-28 19:36:33 (Show Source): You can put this solution on YOUR website!Let = number of \$5 tickets bought Let = number of \$8 tickets bought ----------- (1) (2) ---------------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) 150 \$5 tickets were bought 63 \$8 tickets were bought
 Complex_Numbers/686643: one of the questions to my homewok that i am having trouble with answering was r^2-3r/5+2/25=0 and the homework asks to find the value of the discriminant and describe the nature of the roots of each quadratic equation Then solve the equation and ive tried various ways but i have no confidence so o=if you can help that would be great1 solutions Answer 424863 by josmiceli(9817)   on 2012-11-28 19:13:50 (Show Source): You can put this solution on YOUR website!When you have the equation in the form , the the discriminant is The rules are: (1) If , then there are 2 imaginary roots (2) If , then there are 2 real roots (3) If , then there is a single real root ( called a double root ) ----------------------- Your equation is: ( note that this is saying , which means that the values of that you find will be the x-crossings which are the roots ) ------------------------ The fact that you have and not doesn't matter The form is still Now just plug these into the discriminant This is a positive result, so there are 2 roots, and they are real Now to solve equation: ( I could see the result by inspection ) and are the solutions But here's solution by completing the square: take the square root of both sides But, also I can say that Taking the negative square root of (1/10)^2 I get the same answers I hope this helps
 Percentage-and-ratio-word-problems/686599: Three sevenths of the pizza was eaten.what percent of the pizza was not eaten?1 solutions Answer 424858 by josmiceli(9817)   on 2012-11-28 18:39:19 (Show Source): You can put this solution on YOUR website!the whole pizza = 1 1 = 7/7 ( whole pizza ) - ( portion that is eaten ) = ( portion not eaten ) 7/7 - 3/7 = 4/7 4/7 of the pizza was not eaten
 Miscellaneous_Word_Problems/686600: Maria has a piece of rope that is 3 feet long. She cuts 6 inches off the end of the rope. hat is the length of the remaining rope? Is it a multiplication? or divide? I need to now before Nov 29,2012!!!!!!!!1 solutions Answer 424849 by josmiceli(9817)   on 2012-11-28 17:54:51 (Show Source): You can put this solution on YOUR website!3 feet is 2 feet plus 12 inches 2 feet + 12 inches minus 6 inches = 2 feet + 6 inches
 Age_Word_Problems/686588: an oriental rug is 52 years old and a persian rug is 16 years old. how many years ago was the oriental rug 4 times as old as the persian rug?1 solutions Answer 424846 by josmiceli(9817)   on 2012-11-28 17:51:46 (Show Source): You can put this solution on YOUR website!Let = number of years ago that the oriental rug 4 times as old as the persian rug given: 4 years ago, the oriental rug was 4 times as old as the persian rug check: OK
 Rate-of-work-word-problems/686116: Working together, Bob, Sally, and Harry can dig a hole in 3.5 hours. Working alone, Harry can do it in 7 hours. Bob can do it 3/4 hours fasters than Sally. How long will it take for Sally to dig a hole alone?1 solutions Answer 424715 by josmiceli(9817)   on 2012-11-27 22:13:08 (Show Source): You can put this solution on YOUR website!Add their rates of working to get their time working together = Bob's time to dig hole in hours working alone = Sally's time to dig hole in hours working alone = Harry's time to dig hole in hours working alone ------------- given: (1) (2) (3) ----------------- Substitute (2) and (3) into (1) (1) (1) Multiply both sides by (1) (1) (1) Solve using quadratic equation Sally can dig the hole alone in 14 hrs and 23 min check: (1) (1) (1) (1) I think error is due to rounding off OK
 Quadratic_Equations/686131: two cars traveled in opposite directions from the same starting point. The rate of one car was 10km less than the rate of the other. After 4 hours the cars were 600km apart. Find the rate of each car1 solutions Answer 424707 by josmiceli(9817)   on 2012-11-27 21:34:17 (Show Source): You can put this solution on YOUR website!I think of one car as standing still and the other car moving away from it at the sum of their speeds Let = the speed of the faster car in km/hr = the speed of the slower car in km/hr --------------- The speeds of the cars were 80 km/hr and 70 km/hr check: and and OK
 Numeric_Fractions/686125: :Louise read 5\8ths of the pages in her book, then read 18 more pages and found that she had 1/3 of the pages left, how many pages are in her book. Wouldn't it be 5/8x + 18 = 1/3x to figure if out. Been a while for me. Lol1 solutions Answer 424703 by josmiceli(9817)   on 2012-11-27 21:17:55 (Show Source): You can put this solution on YOUR website!I have to take it slow and step-by-step. Let = the number of pages in her book She read 5/8 of the pages in her book So there are 3/8 of the pages left. Now she reads 18 pages, so she has 3/8 of the pages - 18 pages OK, so far this is wha she has left to read: and now Multiply both sides by There are 432 pages in her book check: She read pages left and OK
 real-numbers/685837: PLEASE HELP If a and b are negative integers, determine whether each of the following is positive or negative: a)-a(a+b) b)(b-a) c) (a+b) d) -a/b thank you so much! 1 solutions Answer 424603 by josmiceli(9817)   on 2012-11-27 14:14:24 (Show Source): You can put this solution on YOUR website!It is less confusing, I think if I just replace a and b with negative numbers ---------- a) -a(a+b) -(-3)*( -3-5 ) 3*(-8) -24 negative ------- b) (b-a) ( -5-(-3) ) -5 + 3 -2 ( the only reason this is negative, is because I picked b to be more negative than a ) ------- c) (a+b) ( -3 -5 ) (-8) negative ------- d) -a/b -(-3) / (-5) 3/(-5) -(3/5) negative
 Rate-of-work-word-problems/685827: A and B working together can finish a job in T days. If A works alone and completes the job, he will take T + 5 days. If B works alone and completes the same job, he will take T + 45 days. What is T? 1 solutions Answer 424600 by josmiceli(9817)   on 2012-11-27 14:02:27 (Show Source): You can put this solution on YOUR website!A's rate working alone is B's rate working alone is Working together: Multiply both sides by
 Travel_Word_Problems/685815: Jane's work commute is 6 miles. When the roads are icy, she travels 20mph slower and takes 9 minutes (or 3/20 hours) longer to get to work. How long does it take her to get to work when the roads are icy?1 solutions Answer 424595 by josmiceli(9817)   on 2012-11-27 13:23:48 (Show Source): You can put this solution on YOUR website!You need 2 equations, one for regular commute and one for icy roads Let = her regular speed in mi/hr Let = her regular time in hrs ------------ given: For regular commute: (1) For icy roads: (2) ----------------------------- (2) Make these substitutions: (1) and (1) -------------- (2) (2) Multiply both sides by (2) (2) Use quadratic formula ( ignore the negative square root ) hrs min When roads are icy, When roads are icy, it takes 18 minutes check: (1) (1) (1) and (2) (2) (2) (2) OK
 percentage/685630: what percent of 55 is 221 solutions Answer 424518 by josmiceli(9817)   on 2012-11-27 03:29:54 (Show Source): You can put this solution on YOUR website!" per cent " means " per one-hundred " ( in latin ), so " what / 100 = 22/55 " X/100 = 22/55 X = ( 22/55 ) * 100 X = 20 22 is 20 % of 55
 logarithm/685646: how do you solve the logarithmic equation log9(x-6)+log9(x-6)=11 solutions Answer 424517 by josmiceli(9817)   on 2012-11-27 03:22:02 (Show Source): You can put this solution on YOUR website!The trick is to make the substitution: --------- Only is valid. If you plug in , then You can't have a log to a positive base that gives you a negative number
 Equations/685650: Can you please help me to understand how Re=1-(1-R)(1-R) becomes Re=2R-R^2. I multiplied out the brackets and was left with 1-1-R-R+R^2, which gave me -2R+R^21 solutions Answer 424515 by josmiceli(9817)   on 2012-11-27 03:10:09 (Show Source): You can put this solution on YOUR website!Re=1-(1-R)(1-R) Re = 1 - ( 1 - 2R + R^2 ) Re = 1 - 1 + 2R - R^2 Re = 2R - R^2
 logarithm/685649: write the expression as a single logarithm. Express powers as factors. In(x/x-7)+In(x+7/x)-In(x^2-49)1 solutions Answer 424514 by josmiceli(9817)   on 2012-11-27 03:04:54 (Show Source):
 Exponential-and-logarithmic-functions/685572: log5(x+7)+log5(x-7)=21 solutions Answer 424500 by josmiceli(9817)   on 2012-11-26 22:59:02 (Show Source): You can put this solution on YOUR website!The trick is to use , then ( There is a negative solution, too, but I can't use it since that would give me log( 5, negative number ) , and there is no log to a positive base that can give me a negative number. -------------- check answer: I think the error is due to rounding off
 Linear-equations/685360: Find the equation of the line through the y-intercept of y = x^4 – 3x^5 – 8 + x^2 and the x-intercept of y = 2x – 18. If anyone can explain how to do this that would be awesome! I'm so confused. Thanks!1 solutions Answer 424413 by josmiceli(9817)   on 2012-11-26 18:02:56 (Show Source): You can put this solution on YOUR website!Find the y-intercept of Important rule: The y-intercept occurs where Note that really is a function of , then there is only ONE y-intercept -------------------------- It is important to note that this intercept is the point (0,-8) -------------- Now find the x-intercept of The x-intercept occurs where This is the x-intercept. Note that a valid function can have MANY x-intercepts, but a straight line like this one has only ONE x-intercept. This intercept is at the point (9,0) ---------------------------- Now you need to find the equation that goes through these points (0,-8) and (9,0) Use the general point-slope formula. Multiply both sides by ---------------- check answer: Does it go through (0,-8) ? ---------- Does it go through (9,0) ? OK
 logarithm/684805: solve for x Log3x+log3(x-4)=1 hint: all 3 are subscripts (I don't know how to put subscript here please tell me all i know is writing superscript like this symbol(^).whats for subscript?1 solutions Answer 424232 by josmiceli(9817)   on 2012-11-25 20:26:28 (Show Source): You can put this solution on YOUR website!The format for subscript looks like log( 3,x ), and when you put it in the "" symbols you get ------------ The trick here is to say use the quadratic formula check answer: close enough You can also go back and use the negative square root of 28 and get another answer
 Functions/684797: you go to dinner and decide to leave an 18% tip for the server. you had \$72 when you entered the restaurant. write a function rule f(m) where m is the amount of money that the meal costs before the tip and the function represents the total amount of the meal with the tip included. what is the possible domain of the function (rounded to the nearest cent)? what is possible range (rounded to the nearest cent)? (assume tax is not applicable.)1 solutions Answer 424212 by josmiceli(9817)   on 2012-11-25 18:22:39 (Show Source): You can put this solution on YOUR website! = cost of meal before tip = cost of meal plus tip ----------- ----------- It is given that ----------- If I say that The domain of the function is ------------------- The range of is
 Linear_Algebra/684479: An elementary-school-age child wants to have a lemonade stand. She wants to sell each glass of lemonade for \$0.25. She has determined that each glass of lemonade costs about \$0.15 to make (for lemons and sugar). It costs her \$20.00 for materials to make the lemonade stand. How many glasses of lemonade must she sell to break even?1 solutions Answer 424110 by josmiceli(9817)   on 2012-11-24 22:53:13 (Show Source): You can put this solution on YOUR website!She breaks even when profit = 0 Let = profit Let = number of glasses sold She must sell 200 glasses to break even
 Complex_Numbers/684433: Find two complex numbers whose sum equals 15 and whose product equals 90. How would I go about putting it into the format z=___ +- ___i ???? Any help would be greatly appreciated1 solutions Answer 424098 by josmiceli(9817)   on 2012-11-24 20:37:49 (Show Source): You can put this solution on YOUR website!To end up with only real numbers for product and sum, the complex numbers have to be of the form and given: and The complex numbers are: and check: close enough
 Evaluation_Word_Problems/684385: The population growth of an animal species is described by P(t)=400log(2t+6). How long will it take for the population to grow to 750? (t is measured in months)1 solutions Answer 424091 by josmiceli(9817)   on 2012-11-24 19:37:51 (Show Source): You can put this solution on YOUR website! Find the left side on your calculator and solve for
 Money_Word_Problems/684409: Sales of a soft drink produces profits in accordance with: P(x)= -0.001x^2+3x-1800 per day, where P is profits in dollars and x is quantity of cans. What is the maximum profits per day & how many cans must it sell to gain maximum profits??1 solutions Answer 424090 by josmiceli(9817)   on 2012-11-24 19:28:47 (Show Source): You can put this solution on YOUR website! The x-co-ordinate of the maximum is at They must sell 1500 cans to maximize profit ---------------- Their maximum profit per day is \$450 check answer: OK
 Human-and-algebraic-language/684212: The number of traffic fatalities increased by 12 times from 1912 to 2008. There were 34,000 more deaths in 2008 than in 1912. Find the number of traffic fatalities in each of the two years. Note that the number of vehicles on the road increased from 1 million to 255 million between 1912 to 2008. 1 solutions Answer 423999 by josmiceli(9817)   on 2012-11-24 03:33:58 (Show Source): You can put this solution on YOUR website!Let = number of fatalities in 1912 = number of fatalities in 2008 also = number of fatalities in 2008 so, and The number of fatalities in 1912 was 3091 The number of fatalities in 2008 was 37091 This is plus or minus one
 Expressions-with-variables/684223: i have a prob involving linear equations using 2 points (1,3)(5,7). i solved point-slope form, slope-intercept and standard form. y=x+2; y-3=(x-1); x-y=-2 respectively. i need a REAL LIFE SCENARIO FOR MY EQN., with slope and y-int(1 and 2 respectively) AND independent and dependent variables. Can't think of a good one. stuck at this step. My mom came up with sisters' age difference, being 2 years. is this ok? seems like there's something better. 1 solutions Answer 423997 by josmiceli(9817)   on 2012-11-24 03:21:12 (Show Source): You can put this solution on YOUR website!A pretty standard one would be time on the horizontal axis and distance on the vertical axis. The slope of the line would be velocity. The y-intercept would be the starting point at time = 0. If you just consider the 2 given points, they are ( time[1], distance[1] ) and ( time[2], distance[2] ) You can pick whatever units you want, like meters and seconds. Hope this helps
 Travel_Word_Problems/684235: I rode my bike 30 miles. If I had increased my average speed by 3 mph, I would have decreased my travel time by 20 minutes. How many miles per hour was my original speed? I tried to use d= r* t so 3x=30? I don't know what else to do1 solutions Answer 423993 by josmiceli(9817)   on 2012-11-24 02:49:07 (Show Source): You can put this solution on YOUR website!There are 2 equations. One is for the actual bike riding the other is the option with higher speed. Let = original speed in mi/hr Let = original time in hrs given: (1) (2) ( note that 20 min is 1/3 hr ) --------------------------- (2) and (1) Substitute (1) into (2) ( note also that ) (2) Subtract from both sides, then add to both sides (2) Multiply both sides by (2) (2) Complete the square: (2) (2) (2) (2) Take the square root of both sides ( ignore the negative square root ) (2) (2) (2) Your original speed was 15 mi/hr check: (1) (1) (1) and (2) (2) (2) (2) (2) (2) OK