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Recent problems solved by 'josmiceli'

josmiceli answered: 9642 problems
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logarithm/281174: solve 1/4 = 4with the exponent k + 5 1 solutions Answer 204263 by josmiceli(9645)   on 2010-03-15 17:08:20 (Show Source): You can put this solution on YOUR website! check: OK

Miscellaneous_Word_Problems/281171: Find three consecutive odd integers such that four times the sum of the last two is two greater than ten times the first. 1 solutions Answer 204259 by josmiceli(9645)   on 2010-03-15 17:03:06 (Show Source): You can put this solution on YOUR website! The consecutive odd integers are: given: The numbers are 11,13, and 15 check: OK

Average/281164: Helping my son, 7th grade. We need help please. Q- average for five quizzes is 86. To have an average of 88 or more for six quizzes, what is the lowest score to get on the sixth quiz? Thanks. 1 solutions Answer 204257 by josmiceli(9645)   on 2010-03-15 16:52:52 (Show Source): You can put this solution on YOUR website! Let = lowest score to get on 6th quiz The average is: (sum of scores on quizzes)/(number of quizzes) = average grade For the 1st quizzes, the average is (Sum of scores on 5 quizzes)/5 = Sum of scores on 5 quizzes = 5*86 Sum of scores on 5 quizzes = 430 and, after taking the 6th quiz: Multiply both sides by Must get at least a 98 to average 88 for 6 quizzes check: OK

Exponential-and-logarithmic-functions/281085: what is the sqare root of 64b^48? 1 solutions Answer 204206 by josmiceli(9645)   on 2010-03-15 14:12:02 (Show Source): You can put this solution on YOUR website! As a general rule, I can say that Suppose the problem was The square root is since( )x() = Your problem is , so

Travel_Word_Problems/280838: Train A & B are traveling in the same direction on parallel track. Train A is traveling 80 miles per hour and train B is traveling 90 miles per hour. Train A passes station at 3:10 pm If train B passes same station at 3:22 pm what time will train B catch up to train A 1 solutions Answer 204088 by josmiceli(9645)   on 2010-03-14 21:24:57 (Show Source): You can put this solution on YOUR website! I have a stopwatch. I'll start it when the 2nd train, train B, passes the station Train A passed the station 12 min ago at 3:10 How far did train A get in 12/60 hr? That is his headstart mi Now write equations for each train, with time = for both, since I'll stop the stopwatch when they meet Also note that Substituting: (1) (2) Substituting again: hr B will catch A in 1 hour 36 min, or at 3:22 + 1:36 = 4:58 PM check: OK

Travel_Word_Problems/280471: On her camping trip Li spent as much time hiking as she did rafting. She traveled 2.5 mph when she was rafting and 3mph when she was hiking. If she went 3 miles more hiking than she did rafting, how far did she hike? Thank you. 1 solutions Answer 203851 by josmiceli(9645)   on 2010-03-13 20:44:32 (Show Source): You can put this solution on YOUR website! Let her time for hiking in hours = and also her time for rafting = Let distance hiking in miles = Let distance rafting in miles = ----------------------------------- given: --------------------- By substitution: By substitution again: And, since She hiked 18 miles

Exponential-and-logarithmic-functions/280462: This one looked easy but it's got me confused please help and thank you. Use the laws of logarithms to express log base2 6 - log base 2 3 + 2 log base 2 sqrt8 as a single logarithm then evaluate. I got this far log base 2^6 - log base2^3 +2 log base 2 sqrt 8 =log base 2 6/3 sqrt8^2??? help 1 solutions Answer 203850 by josmiceli(9645)   on 2010-03-13 20:34:09 (Show Source): You can put this solution on YOUR website! The 1st 2 terms are: So far I have

Miscellaneous_Word_Problems/280051: From an original group of boys and girls, twenty girls leave. There are then left two boys for each girl. After this, sixty boys leave. There are then two girls for each boy.The number of girls in the original group was: (A) 81 (B) 72 (C) 68 (D) 60 (E) 50 1 solutions Answer 203587 by josmiceli(9645)   on 2010-03-12 13:26:52 (Show Source): You can put this solution on YOUR website! Let = original number of girls Let = original number of boys given: Initially, there are: in the group 20 girls leave in the group (1) Then boys leave in the group (2) (1) and (2) are 2 equations with 2 unknowns, so it's solvable (1) (1) (1) (2) (2) (2) Multiply both sides of (1) by and add equations (1) (2) The number of girls in the original group was 60 check answer: (1) (2) (2) OK

Complex_Numbers/280121: Maple syrup worth $6.00 a gallon and corn syrup worth .80 cents a gallon are used to make a mixture worth $2.36 a gallon. How many gallons of each kind of syrup are needed to make 50 gallons of the mixture? 1 solutions Answer 203561 by josmiceli(9645)   on 2010-03-12 11:21:39 (Show Source): You can put this solution on YOUR website! Let = galloons of maple syrup needed Let = gallons of corn syrup needed given: gal (in cents) By substitution: and, since 15 gallons of maple syrup and 35 gallons of corn syrup are needed check: OK

real-numbers/280060: Two trains, one traveling 10 km/h faster than the other, leave the same station at the same time, one traveling east and one traveling west. At the end of 6 hours, they are 540 km apart. How far does each train travel? 1 solutions Answer 203559 by josmiceli(9645)   on 2010-03-12 11:11:19 (Show Source): You can put this solution on YOUR website! It's the same problem if you think of 1 train as being stationary, and the other moving at their added speeds In hrs: km/hr is their added speeds Their speeds are and In hrs, 1st train goes km and the 2nd train goes km check: OK

Travel_Word_Problems/280067: whta is the speed of a car that travels 60 miles in 20 minutes 1 solutions Answer 203555 by josmiceli(9645)   on 2010-03-12 11:01:13 (Show Source): You can put this solution on YOUR website! (60 miles/20 min)x(60 min/1 hr) = 180 mi/hr

Linear_Equations_And_Systems_Word_Problems/280112: The Brooklyn Bridge was built 54 years before the Golden Gate Bridge. In 1983 the Golden Gate Bridge was 23/50 the age of the Brooklyn Bridge. What year was each bridge built? 1 solutions Answer 203551 by josmiceli(9645)   on 2010-03-12 10:57:17 (Show Source): You can put this solution on YOUR website! Let = the year the Brooklyn Bridge was built Then = the year the Golden Gate was built given: the Brooklyn Bridge was built in 1883 the Golden Gate Bridge was built in 1937 check answer: OK

real-numbers/280061: A car traveling at a rate of 30 km/h left Gander. A second car left Gander 1 hour later. At what rate must the second car travel to catch up with the first in 3 hours? 1 solutions Answer 203535 by josmiceli(9645)   on 2010-03-12 10:20:41 (Show Source): You can put this solution on YOUR website! Start a stopwatch when the 2nd car leaves Gander When I start the stopwatch, the 1st car has a mile head start When I stop the stopwatch, they both will have driven for the same time, which is hrs 1st car: mi 2nd car: mi and The 2nd car must drive 40 mi/hr to catch the 1st car

Finance/280077: I just need to set this up: I invested X at 10%, and 2X at 12%, for a total interest of 2890. What is X? 1 solutions Answer 203529 by josmiceli(9645)   on 2010-03-12 10:09:18 (Show Source): You can put this solution on YOUR website!

Human-and-algebraic-language/280101: Sherie is goin gto buy a microwave in a city with an 8% sales tax. She has at most $594 to spend. In what price range should she look? 1 solutions Answer 203525 by josmiceli(9645)   on 2010-03-12 10:06:04 (Show Source): You can put this solution on YOUR website! Let the price before tax = The highest price she can afford is $550 before tax

Finance/280100: John put $40 into his investment club every month for a year at a 7% annual interest rate. Interest is calculated once at the end of the year. How much money was in his account at the end of the year? 1 solutions Answer 203522 by josmiceli(9645)   on 2010-03-12 10:02:08 (Show Source): You can put this solution on YOUR website! There are months in a year, so $513.60 was in the account at the end of the year

Equations/280103: There are 480 dishes that need to be rinsed. John can rinse them in 80 minutes by himself. It will take his friend Bob 120 minutes to rinse these dishes. How long will it take them if they rinse these 480 dishes together? 1 solutions Answer 203521 by josmiceli(9645)   on 2010-03-12 09:58:25 (Show Source): You can put this solution on YOUR website! The number does not need to enter the calculations Just call washing that many dishes 1 job In words: (John's rate of working) + (Bob's rate of working) = rate of working together John's rate = 1 job/80 min Bob's rate = 1 job/120 min Multiply both sides by It will take them 48 minutes working together

Equations/280104: There is a sales tax of $22 on an item that costs $275 before tax. A second item costs $87.50 before tax. What is the sales tax on the second item? 1 solutions Answer 203519 by josmiceli(9645)   on 2010-03-12 09:48:58 (Show Source): You can put this solution on YOUR website! The sales tax will be the same percent rate for both items. For the 1st item, $22 is what percent of $275? = 8% For the 2nd item, $7 is the sales tax

Linear-systems/280099: train A is traveling at 60 mph and train B at 80 mph. train A passes the station at 810 and train B at 825 at what time will train B catch train A? 1 solutions Answer 203518 by josmiceli(9645)   on 2010-03-12 09:44:23 (Show Source): You can put this solution on YOUR website! Train A has a 15 minute head start over B if you consider the station as the starting point. In that time, A has gone miles. Assume I have a stopwatch. I'll start it when B reaches the station If I stop it when B catches A, both trains will have been moving for the same length of time, which I'll call given: mi/hr mi/hr mi ---------------- Now I can write equations for both trains By substitution, hr Train B will catch train A in 45 min, or at 8:25 + 45 = 9:05 check answer: mi and mi OK

Rational-functions/280098: can you help me with this problem? I don't understand it. (-5+2i)-(9+3i) 1 solutions Answer 203515 by josmiceli(9645)   on 2010-03-12 09:18:43 (Show Source): You can put this solution on YOUR website! You are asked to subtract 2 complex numbers. You have to subtract the real parts separately from the imaginary parts. I don't know how far you are with imaginary numbers, but subtract them like this: Now subtract the real parts The answer is:

Travel_Word_Problems/280092: The separate sections of rail on a railroad track are 30 ft. long. As the train passes over the point where the sections are joined, there is an audible click. By what fraction must the number of clicks in a minute be multiplied to find the speed of the train in miles per hour? 1 solutions Answer 203514 by josmiceli(9645)   on 2010-03-12 09:13:20 (Show Source): You can put this solution on YOUR website! There are ft in a mile You will hear clicks/mile If the train's speed was mile/min, that is miles/hr So, clicks/min means the train's speed is miles/hr Therefore, x clicks/min gives the train's speed in miles/hr

Systems-of-equations/280070: what is the sum of the roots of this equation. ax^2+bx+c=0 im not sure what they mean by this. 1 solutions Answer 203504 by josmiceli(9645)   on 2010-03-12 08:32:23 (Show Source): You can put this solution on YOUR website! The roots are the values of that make the equation true. The quadratic formula for the roots is: So, the 2 roots are: ------------------ Another way to do it is: Call the roots and , then

Miscellaneous_Word_Problems/280081: A piece of string 15 inches long is cut into four pieces. If each successive piece is half as long as the preceding piece, then the length of the first piece, in inches, is: (A) 6 (B) 7 (C) 8 (D) 9 (E) 10 1 solutions Answer 203502 by josmiceli(9645)   on 2010-03-12 08:18:02 (Show Source): You can put this solution on YOUR website! The lengths are: , , , (C) 8 in

Miscellaneous_Word_Problems/280080: Sales of cassette tapes of music decreased by 7% per year for 3 years. The percent that best approximates the total percent that sales of cassette tapes of music decreased during this time period is: (A) 80.4% (B) 79% (C) 34.3% (D) 21% (E) 19.6% 1 solutions Answer 203501 by josmiceli(9645)   on 2010-03-12 08:08:44 (Show Source): You can put this solution on YOUR website! Let = sales 3 years ago After 1st year: After 2nd year: After 3rd year: Cassette sales decreased by (E) 19.6%

logarithm/279976: log 28 1 solutions Answer 203465 by josmiceli(9645)   on 2010-03-11 22:11:13 (Show Source): You can put this solution on YOUR website!

Percentage-and-ratio-word-problems/279975: An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost? 1 solutions Answer 203463 by josmiceli(9645)   on 2010-03-11 22:06:31 (Show Source): You can put this solution on YOUR website! Let = original price After the 1st discount, it cost After the 2nd discount, it costs The original cost was $400

Surface-area/279972: how do you find the area when they only give you the diameter? 1 solutions Answer 203459 by josmiceli(9645)   on 2010-03-11 21:44:17 (Show Source): You can put this solution on YOUR website! Let = radius Le = diameter Area = diameter = 2 x radius radius = diameter/2 Area =

Linear_Equations_And_Systems_Word_Problems/279961: A patch of measuring 6 feet by 6 feet requires 2 ounces of fertilizer. How many pounds should be used on a lawn that measures 30 feet by 75 feet? 1 solutions Answer 203457 by josmiceli(9645)   on 2010-03-11 21:40:21 (Show Source): You can put this solution on YOUR website! ft2 This is the factor to multiply 2 ounces by ounces needed To find pounds of fertilizer needed, divide by pounds 7 pounds and 13 ounces are needed

Linear_Equations_And_Systems_Word_Problems/279960: juan donates 10% of his salary to his church. he earns 3500 per month. he used to earn $3200, an he gave the same dollar amount. what percent of his income does he donate to the church when he earned $3,200? 1 solutions Answer 203454 by josmiceli(9645)   on 2010-03-11 21:32:40 (Show Source): You can put this solution on YOUR website! When he earned $3200, he also donated $350 He donated 10.9% of his income

Mixture_Word_Problems/279858: A 10% salt solution is mixed with an 18% salt solution to obtain a 32 oz 15% solution. How many ounces of each are needed? 1 solutions Answer 203402 by josmiceli(9645)   on 2010-03-11 18:51:03 (Show Source): You can put this solution on YOUR website! Let = ounces of 10% solution needed Let = ounces of 18% solution needed given: (1) ounces (2) (2) ------------------- Multiply both sides of (2) by (2) Multiply both sides of (1) by and subtract from (2) (2) (1) and, since 12 ounces of 10% solution and 20 ounces of 18% solution are needed check: (2) OK

Money_Word_Problems/279764: I get paid monthly. I want to know how to figure out how much I earn hourly. Thank you. 1 solutions Answer 203351 by josmiceli(9645)   on 2010-03-11 14:35:30 (Show Source): You can put this solution on YOUR website! There are 4 weeks in a month, and most people work 5 days/week and 40 hours/day days/month of work Let = monthly pay in dollars (x/1 month ) x (1 month/4 weeks) x (1 week/5 days) x (1 day/40 hours) = x/(4 x 5 x 40) = x/800 Hourly, you earn (monthly pay)/800 If you earned $4,000/month, you make = $5/hr