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# Recent problems solved by 'josmiceli'

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 logarithm/529650: how does 8x^3=e^18 equal 2x=e^61 solutions Answer 349648 by josmiceli(9817)   on 2011-11-10 14:38:51 (Show Source): You can put this solution on YOUR website! Take the cube root of both sides Note that
 Expressions-with-variables/529648: My question is whats substition I keep hearing about? How does it work? Can you tell me how to solve a problem using substition?1 solutions Answer 349645 by josmiceli(9817)   on 2011-11-10 14:31:32 (Show Source): You can put this solution on YOUR website!Sure. Suppose you have 2 equations with 2 unknowns. It definitely should be solvable, and one way is by substitution. Say the equations are (1) (2) ----------------------- From(1), I get (1) Now I will Substitute this value of into equation (2) (2) (2) (2) (2) (2) The solutions are (10,0) and (5,-5)
 Rational-functions/529620: Please help! I have to solve by factoring. Not sure how to get the answer to these: x^3 -10x + 25x = 0 and 2x^3 -8x = 0 Thanks for the help 1 solutions Answer 349644 by josmiceli(9817)   on 2011-11-10 14:14:34 (Show Source): You can put this solution on YOUR website! Either of these 2 factors must be , so is a solution and This is a perfect square is also a solution --------------------- is a solution also and are both solutions
 Probability-and-statistics/529602: If two cards are drawn from a standard 52 card deck without replacement, in how many different ways is it possible to obtain a heart on the first draw and an ace on the second?1 solutions Answer 349640 by josmiceli(9817)   on 2011-11-10 13:33:12 (Show Source): You can put this solution on YOUR website!I'd get a 2nd opinion on this, but here's my view: There are 13 ways that you can draw a heart first Having drawn the heart, there are 4 ways to draw an ace, so there are ways to get this combination. But what if the 1st card is the Ace of hearts. Then there are only 3 ways to draw an Ace. So I have to subtract the one combination that I counted twice, that is Ace of hearts and Ace of hearts again. There are then 51 ways to draw a heart and then an Ace. Hope I got it.
 percentage/529617: how to do percentages.1 solutions Answer 349635 by josmiceli(9817)   on 2011-11-10 13:17:16 (Show Source): You can put this solution on YOUR website!You need to fix in your mind that per cent means "per one-hundred" Think of the % sign as saying: you need to divide this number by 100. ------------------------- Suppose I say 67% % means to divide it by 100, so what I really have is 67/100 = .67 ------------------------ Another problem you will see is: convert .67 to a percent The algebra for this is .67 = x/100 This says: .67 is what percent ? Multiply both sides by 100 67 = x, so 67/100 = 67 percent Hope this helps
 percentage/529379: If my portfolio grows by 10% then i now havw 150\$.How much did I originally have?1 solutions Answer 349585 by josmiceli(9817)   on 2011-11-09 23:29:38 (Show Source): You can put this solution on YOUR website!You originally has dollars given: You originally had \$136.36
 Exponential-and-logarithmic-functions/529392: 4log5(x+3)-log5(x-18)-log5(x-1)1 solutions Answer 349584 by josmiceli(9817)   on 2011-11-09 23:21:50 (Show Source): You can put this solution on YOUR website! I'm not sure if it can be simplified beyond this
 Numbers_Word_Problems/529346: find 3 consecutive odd integers such that the sum of four times the smallest integer and three times the largest integer is 159.1 solutions Answer 349564 by josmiceli(9817)   on 2011-11-09 21:50:15 (Show Source): You can put this solution on YOUR website!Let the consecutive odd integers be , , and given: The numbers are 21, 23, and 25
 Age_Word_Problems/529334: Mrs Sabado is 6 times as old as her daughter May. Next year her age will be equal to the square of her daughter's age. Find the present age.1 solutions Answer 349558 by josmiceli(9817)   on 2011-11-09 21:41:22 (Show Source): You can put this solution on YOUR website!Let = Mrs. Sabado's age now Let = May's age now given: (1) (2) ---------------------- (2) Substitute (1) into (2) (2) (2) (2) Either or If , (1) (1) ------------ If , then (1) (1) This says they are both newborns, which is impossible, so 24 is Mrs. Sabado's age now 4 is May's age now check: (2) (2) (2) (2) OK
 Distributive-associative-commutative-properties/529323: what is the distributive property of algebra1 solutions Answer 349548 by josmiceli(9817)   on 2011-11-09 21:18:17 (Show Source):
 Inequalities/529309: Need assistance with this, i cant figure it out. It's driving me mad. Thank you. Lena is choosing between two exercise routines. In routine #1, she burns 25 calories walking. She then runs at a rate that burns 18 calories per minute. In routine #2, she burns 49 calories walking. She then runs at a rate that burns 14 calories per  minute. For what amount of time spent running will routine #1 burn fewer calories than routine#2? Use t for the number of minutes spent running, and solve your inequality for t.1 solutions Answer 349543 by josmiceli(9817)   on 2011-11-09 21:14:36 (Show Source): You can put this solution on YOUR website!Let = minutes spent running given: Routine #1 Calories burnt = Routine #2 Calories burnt = ------------------------ Let calories burnt = The question is: for what values of is Subtract from both sides Subtract from both sides or, what is the same, So, for all values of minutes spent running, The calories burnt using routine #1 are less than the calories burnt using #2 Here's a plot of routine #1 and #2: The bottom line is routine #1. You can see that when as it should, and they meet at
 Money_Word_Problems/529293: Cliff had a total of \$100,000 to invest. He put some of the money in Bank A that paid 4% interest and the rest in Bank B which paid 5% interest. After a year, the amount of interest he earned was \$4850. How much money did Cliff invest in Bank A? Also provide a step by step procedure on how to get the answer.1 solutions Answer 349538 by josmiceli(9817)   on 2011-11-09 20:51:27 (Show Source): You can put this solution on YOUR website!Let = amount invested @ 4% Let = amount invested @ 5% given: (1) (2) -------------------- (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) Cliff invested \$15,000 in bank A check answer: (2) (2) (2) (2) OK
 logarithm/529226: how do I evaluate this: log2 120 − log2 12 − log2 401 solutions Answer 349527 by josmiceli(9817)   on 2011-11-09 19:48:06 (Show Source): You can put this solution on YOUR website! If I set this expression equal to , then The answer is:
 Money_Word_Problems/529205: John invested \$8000 for one year, part at 8% interest and the rest at 10%. If John earned \$700 in interest, how much is in each account?1 solutions Answer 349524 by josmiceli(9817)   on 2011-11-09 19:31:33 (Show Source): You can put this solution on YOUR website!Let = amount invested @ 8% Let = amount invested @ 10% given: (1) (2) ----------------- (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) \$5,000 is the amount invested @ 8% \$3,000 is the amount invested @ 10% check answer: (2) (2) (2) (2) OK
 Expressions-with-variables/529203: can you please explain how to solve this problem.I'm trying to help my 5th grader understand. thanks=) 8+n if n=12,and 7xn if n=81 solutions Answer 349517 by josmiceli(9817)   on 2011-11-09 19:13:34 (Show Source): You can put this solution on YOUR website! given: Replace with -------------- given: Replace with --------------
 Angles/529201: the angels of an acute triangle are 2x, x, and x+10 what are the measurement of each angel1 solutions Answer 349514 by josmiceli(9817)   on 2011-11-09 19:09:00 (Show Source): You can put this solution on YOUR website!The sum of the angles of a triangle are 180 degrees The angles are 42.5, 52.5, and 85 degrees
 Miscellaneous_Word_Problems/528674: One morning martin drove 80 miles in 2 hours. After lunch he covered 100 miles more in 3 hours. What was his average rate of speed in miles per hour for the 5 hours of driving?1 solutions Answer 349389 by josmiceli(9817)   on 2011-11-09 03:34:09 (Show Source): You can put this solution on YOUR website!Average speed is always ( total distance ) / ( total time ) The average speed is 36 mi/hr
 Rate-of-work-word-problems/528667: One computer takes 21 minutes longer than a second computer to do the job. Working together these computers can do the same job in 10 minutes. How long would it take each computer working alone to do the same job?1 solutions Answer 349388 by josmiceli(9817)   on 2011-11-09 03:31:07 (Show Source): You can put this solution on YOUR website!Add their rate of doing jobs to get their rate together. Let = the time in minutes for the 2nd computer to finish the job. Then is the time for the 1st computer to do the job is the 1st computer's rate is the 2nd computer's rate is their rate working together Multiply both sides by Complete the square ( ignore the negative square root ) It will take the 1st computer 35 min It will take the 2nd computer 14 min check: Multiply both sides by OK
 Numbers_Word_Problems/528694: One number is ten more than other. If the sum of twice the smaller number and three times the larger number is 55, find the two numbers.1 solutions Answer 349387 by josmiceli(9817)   on 2011-11-09 03:06:07 (Show Source): You can put this solution on YOUR website!You can call the numbers and given: check: OK
 Polynomials-and-rational-expressions/528696: This question is driving me up the wall. It has to be answered only in fractions and not in decimals. Two thirds of two is what part of three or put another way, 2/3 of 2 is x (what) part of 3. I'm not sure, but the answer is 4/9, but how is the problem solved (step by step) to arrive at the figure of say 4/9 or whatever?. I'm 80+ and still doing ok, no Alzheimer yet..ha-ha, many thanks for any help. 1 solutions Answer 349386 by josmiceli(9817)   on 2011-11-09 03:00:39 (Show Source): You can put this solution on YOUR website!1st I'll find What part of is this? The way the problem is stated is just a little different from usual, and can throw you off.
 Evaluation_Word_Problems/528695: A twelve foot board is cut into two pieces. One piece is two feet longer than the other piece. How long is each piece.1 solutions Answer 349385 by josmiceli(9817)   on 2011-11-09 02:31:02 (Show Source): You can put this solution on YOUR website!Let the pieces be and ft in length given: The pieces are 5 ft and 7 ft long
 Permutations/528682: I am having a really hard time trying to figure out this question please help,all I know so far is that I should use permutation, but I don't know how: Question: A class consists of 60 ladies and 40 men. In how many ways can a president, vice president, treasurer and secretary be chosen if the treasurer must be a lady, the secretary must be a man and the student may not hold more than one office? Thank you1 solutions Answer 349384 by josmiceli(9817)   on 2011-11-09 02:27:51 (Show Source): You can put this solution on YOUR website!I'll take shot at it, but you might want to get a 2nd opinion Since the treasurer must be a lady, there are 60 different ways that office can be filled Since the Secretary must be a man, there are 40 ways that office can be filled. There are different ways that the 2 offices can be held ------------------------- Once the Treasurer and Secretary offices have been filled, there are people left to fill President and Vice-President There are different ways to fill these 2 offices ( M or F doesn't matter ) ------------------------- The 4 offices can then be filled in different ways. ( I lost calculator, you can finish )
 Equations/528541: In a fifth-grade class of 16 students, one-half of the students showed up early, one-fourth of the students showed up on time and one-eighth showed up late. How many students were absent?1 solutions Answer 349322 by josmiceli(9817)   on 2011-11-08 20:25:00 (Show Source): You can put this solution on YOUR website! 1/8 of the students were absent 2 students were absent
 Evaluation_Word_Problems/528539: The class average on a test is exactly 83. take away the best score and the average is 82. There are 16 students in the class, what is the best score? x/16=83-x/16???1 solutions Answer 349319 by josmiceli(9817)   on 2011-11-08 20:20:17 (Show Source): You can put this solution on YOUR website!Let = sum of scores of all 16 students in class Let = the highest score of the 16 students With all the students in class: (1) With highest score taken away: (2) ------------------ This is 2 equations and 2 unknowns, so it's solvable (1) (2) Substitute (1) into (2) (2) (2) Can't find my calculator- you can finish
 Travel_Word_Problems/528170: A man rode a bicycle for 12 miles and then hiked and additional 8 miles. The total time for the trip was 5 hours. If his rate when riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?1 solutions Answer 349174 by josmiceli(9817)   on 2011-11-08 12:06:59 (Show Source): You can put this solution on YOUR website!Let = rate walking Let = rate biking given: mi/hr hrs -------------------- biking: walking: ------------------- By substitution: By substitution again: Substitution again: Completing the square: ( can't use the negative root ) and His speed biking was 12 mi/hr His speed walking was 2 mi/hr
 Mixture_Word_Problems/528169: A 50 milliliter solution of acid and water contains 25% acid. How much water do you need to add in order to make a 10% acid solution?1 solutions Answer 349163 by josmiceli(9817)   on 2011-11-08 11:43:02 (Show Source): You can put this solution on YOUR website!Let = ml of water needed given: ml of acid in 25% solution --------------- 75 ml of water is needed
 Probability-and-statistics/528157: in a certain population, 30% of the women are married and 40% of the men are married. what percent of the total population in married? round answer to the nearest tenth of a percent. assume that one woman is married to one man and that each couple resides in this population-1 solutions Answer 349162 by josmiceli(9817)   on 2011-11-08 11:33:28 (Show Source): You can put this solution on YOUR website!Let = number of women in population Let = number of men in population Because the married women and married men are paired with each other, I can say I am asked to find: To the nearest 1/10 of a percent, 34.3% of the population is married
 Linear-systems/528039: How do you solve for y and x ? Like my promblem says solve for y right? So they gave me the promblem 4y + 12 = -3(2x-4), could you help me with this promblem?1 solutions Answer 349139 by josmiceli(9817)   on 2011-11-08 03:59:02 (Show Source): You can put this solution on YOUR website!What they mean is: Get y all by itself on one side of the equation It doesn't really matter which side --------------------------- You do this by doing the same thing to both sides of the equation, which leaves the equation unchanged ---------------------------- Subtract from both sides Now divide both sides by This is OK, but you can finish by multiplying out Now you have
 Probability-and-statistics/527740: A card is randomly drawn from a deck of 52 playing cards. What is the probability that it is a King given that the card is Red?1 solutions Answer 349014 by josmiceli(9817)   on 2011-11-07 18:12:39 (Show Source): You can put this solution on YOUR website!Half of the deck is red: hearts and diamonds there are 2 Kings that are red, so, given that the card drawn is red, the probability that it is a King is 2/26, or 1/13
 Miscellaneous_Word_Problems/527745: Juan wants to make a trail mix that contains 40% pecans. He has a bag of trail mix that has only 25% pecans at home and another bag that contains only pecans. How much of each should he mix together to make a 16-oz bag of trail mix that contains 40% pecans?1 solutions Answer 349013 by josmiceli(9817)   on 2011-11-07 18:06:17 (Show Source): You can put this solution on YOUR website!He ends up with ounces of pecans Let = ounces of 25% mix needed Let = ounces of 100% mix needed given: (1) (2) Multiply both sides of (2) by . Then multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) 12.8 ounces of 25% mix are needed 3.2 ounces of 100% mix are needed
 Rate-of-work-word-problems/527717: SOPPOSE 4 PEOPLE CAN PAINT A HOUSE IF THEY WORKK 3 DAYS EACH. HOW LONG WOULD IT TAKE OF A CREW OF 5 PEOPLE TO PAINT THE HOUSE ?1 solutions Answer 349012 by josmiceli(9817)   on 2011-11-07 17:46:20 (Show Source): You can put this solution on YOUR website!I assume all these people work at the same rate 4 people working 3 days can paint 1 house 1 person takes 4 times as long to paint the house, so 1 person takes 12 days to paint the house 5 people will take 1/5 of that time to paint the house 5 people will take 12/5 days, or 2.4 days to paint the house