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# Recent problems solved by 'josmiceli'

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 Probability-and-statistics/720606: By using an appropriate average find out the average rate of motion in the case of a person who rides the first mile at the rate of 10 miles per hour, the next mile at the rate of 8 miles per hour and the third at the rate of 6 miles per hour.1 solutions Answer 441906 by josmiceli(9819)   on 2013-03-01 05:00:01 (Show Source): You can put this solution on YOUR website!Average speed is always ( total distance / total time ) Total distance = mi -------------- -------------- Ave speed = Ave speed = Ave speed = Ave speed = Ave speed = mi/hr check: close enough
 Linear-equations/720605: Kabir age is 20 years hence will be 3 time his age 12 years ago. Find Kabir present age.1 solutions Answer 441905 by josmiceli(9819)   on 2013-03-01 04:45:37 (Show Source): You can put this solution on YOUR website!Let = his age now = his age 20 years hence = his age 12 years ago given: He is 28 now ----------- check: In 20 years he is 48 12 years ago he was 16 OK
 Linear-equations/720611: write each equation in slope intercept form, and then find the slope and y intercept 2x-y=-151 solutions Answer 441904 by josmiceli(9819)   on 2013-03-01 04:40:03 (Show Source): You can put this solution on YOUR website! Subtract from both sides Multiply both sides by
 Numeric_Fractions/720630: cows+hens=48 there less are 146 how many hens.1 solutions Answer 441903 by josmiceli(9819)   on 2013-03-01 04:37:24 (Show Source): You can put this solution on YOUR website!They have 146 legs? Let = number of cows Let = number of hens given: (1) (2) Subtract (1) from (2) (2) (1) and, since (1) (1) (1) There are 25 cows and 23 hens check: (2) (2) OK
 Angles/720629: How can I know what the value of x is in this question: Find the value of x in one angle, and the value of x + 20 in the other. But these two are complementary angles, how can I know so that the sum of x+x+20 totals to 90 degrees? And the 2 x's must be the same number? Please answer my question and put a solution and explanation.1 solutions Answer 441902 by josmiceli(9819)   on 2013-03-01 04:28:37 (Show Source): You can put this solution on YOUR website!You have 2 angles that add up to 90 degrees The angles are and Add the angles So, the angles are 35 degrees and 55 degrees
 Linear-equations/720609: 1. write each equation in slope-interceprt form, and them find the slope and y-intercept 3x+y=0 1 solutions Answer 441901 by josmiceli(9819)   on 2013-03-01 04:23:52 (Show Source): You can put this solution on YOUR website! The slope intercept form looks like: where is the slope Subtract from both sides This is in the slope-intercept form Note that and Here's a plot of the equation:
 Linear-equations/720612: write the equation of the line that passes through each pair of points in slope intercept form (3,4),(4,6)1 solutions Answer 441900 by josmiceli(9819)   on 2013-03-01 04:18:08 (Show Source): You can put this solution on YOUR website!Use the point-slope formula ------------- check: (3,4) OK (4,6) OK
 Age_Word_Problems/720620: if today a father is four times as old as his son and five years ago he was five times as old as his son, find their present age 1 solutions Answer 441899 by josmiceli(9819)   on 2013-03-01 04:12:56 (Show Source): You can put this solution on YOUR website!Let = Father's age now Let = Son's age now given: (1) (2) ---------------------- (2) (2) By substitution: (2) and (1) (1) (1) The Father is 80 The Son is 20 -------------- check: 5 years ago, the Father was 5 years ago, the Son was OK
 Travel_Word_Problems/720607: A JOGGER STARTS FROM ONE END OF A 15 MILE NATURE TRAIL AT 8:00 AM ONE HOUR LATER A CYCLIST STARTS FROM THE OTHER END OF THE TRAIL AND RIDES TOWARD THE JOGGER IF THE RATE OF THE JOGGER IS 6MPH AND THE RATE OF THE CYCLIST IS 9MPH AT WHAT TIME WILL THE TWO MEET? THANK YOU1 solutions Answer 441898 by josmiceli(9819)   on 2013-03-01 04:04:18 (Show Source): You can put this solution on YOUR website!You can think of the jogger as standing still and the cyclist approaching at the sum of their speeds ----------- The jogger cuts down the distance between them by mi So now the cyclist only has to travel mi ----------- Let = the time in hrs it takes the cyclist to meet the jogger hrs min The two will meet at 8:36 AM ----------- check: jogger's equation: mi Cyclist's equation: must = 9 mi OK
 Mixture_Word_Problems/720623: Gus has on hand 5% alcohol solution and a 20% alcohol solution. He needs 30 liters of 10% alcohol solution. How many liters of each solution should he mix together to obtain the mixture he needs?1 solutions Answer 441897 by josmiceli(9819)   on 2013-03-01 03:50:39 (Show Source): You can put this solution on YOUR website!Let = liters of 5% solution needed Let = liters of 20% solution needed ----------- (1) (2) --------------------------- (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) 20 liters of 5% solution are needed 10 liters of 20% solution are needed check answer: (2) (2) (2) (2) OK
 Mixture_Word_Problems/720619: How many liters of water must be added to 8 liters of a 40% salt solution to obtain a 10% salt solution?1 solutions Answer 441896 by josmiceli(9819)   on 2013-03-01 03:41:53 (Show Source): You can put this solution on YOUR website!Let = liters of water to be added liters of salt in 40% solution ----------- 24 liters of water must be added check: OK
 Surface-area/720548: I am trying to find the perimeter of a back yard that has a length of 18x+2 and a width of 14x+1 but cannot figure out what the variable is for. Can you please help? Thank you1 solutions Answer 441882 by josmiceli(9819)   on 2013-02-28 23:56:35 (Show Source): You can put this solution on YOUR website!You don't have to know that. There is no reason for it. Just add the 2 long sides and the 2 short sides
 Money_Word_Problems/720588: how much money would you have to accumulate in an investment in order the the yearly interest paid (simple) is equal to \$70000 in the investment pays 5.9%1 solutions Answer 441881 by josmiceli(9819)   on 2013-02-28 23:51:40 (Show Source): You can put this solution on YOUR website!Let = amount in investment The investment is \$1,186,440.60
 Money_Word_Problems/720571: An engine repair cost a truck owner \$1,406 in parts and labor. If the parts were \$670 and the mechanic charged \$46 per hour, how many hours did the repair take? 1 solutions Answer 441880 by josmiceli(9819)   on 2013-02-28 23:46:56 (Show Source): You can put this solution on YOUR website!\$1,406 in parts and labor Let = hours of labor The repair took 16 hrs
 percentage/720585: If you know 70% is 235 how do you find the other 30%1 solutions Answer 441879 by josmiceli(9819)   on 2013-02-28 23:41:06 (Show Source): You can put this solution on YOUR website!One way is the subtract 70% of 235 from 235
 Travel_Word_Problems/720576: Charles was racing his remote control car this past weekend. The track is 1/4 mile long. His car averages 10 mph. How long did it take him to complete 20 laps around the track?1 solutions Answer 441878 by josmiceli(9819)   on 2013-02-28 23:32:06 (Show Source): You can put this solution on YOUR website! hrs This is the time to complete 1 lap It takes a half hour to complete 20 laps
 Miscellaneous_Word_Problems/720584: Find an equation for the graph (-2,4) and (0,-2)1 solutions Answer 441877 by josmiceli(9819)   on 2013-02-28 23:27:36 (Show Source): You can put this solution on YOUR website!( -2,4 ) ( 0,-2 ) Use the general point-slope formula --------------- check: ( -2,4 ) ---------- ( 0,-2 ) OK
 Word_Problems_With_Coins/720582: The total value of the quarters and dimes in a coin bank is \$8.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would be \$8.60. Find the number of quarters in the bank.1 solutions Answer 441876 by josmiceli(9819)   on 2013-02-28 23:18:03 (Show Source): You can put this solution on YOUR website!Let = the number of dimes Let = the number of quarters given: (1) ( in cents ) (2) ----------------------- Rewrite the equations (1) (2) --------------------- Multiply both sides of (1) by and both sides of (2) by then subtract (2) from (1) ------------------------------ (1) (2) and (1) (1) (1) (1) (1) The number of dimes in the bank is 24 The number of quarters in the bank is 26 check: (2) (2) (2) (2) OK
 Age_Word_Problems/720491: If Jack adds his current age to the age he will be next year on this date, the sum is 17 years. How old will Jack be 6 years from today?1 solutions Answer 441854 by josmiceli(9819)   on 2013-02-28 21:30:02 (Show Source): You can put this solution on YOUR website!Let = his current age = his age 1 year from now given: and Jack will be 14 in 6 years
 Linear_Equations_And_Systems_Word_Problems/720504: The largest box of popcorn in the world held a volume of 880 ft3 of popcorn. It took about six hours to fill the box. Find the rate per minute.1 solutions Answer 441851 by josmiceli(9819)   on 2013-02-28 21:24:51 (Show Source): You can put this solution on YOUR website!In just units: ( ft3 / hr ) x ( hr / min ) = ft3 / min The rate per minute is 2.444 ft3/min
 Travel_Word_Problems/720508: Will you please help me answer this question none of my friends or parents know what to do, I could really use your help. Here is the question: flying with the wind a plane went 135 mph. Flying into the same wind the plane only went 93 mph. Find the speed of the wind and the speed of the plane in still air.1 solutions Answer 441846 by josmiceli(9819)   on 2013-02-28 21:15:48 (Show Source): You can put this solution on YOUR website!Let = the speed of the plane in still air Let = the speed of the wind = the plane's speed flying with the wind = the plane's speed flying into the wind ------------------------------------------- given: (1) mi/hr 92) mi/hr Now add the equations Plug this value back into (1) or (2) (1) (1) The speed of the plane in still air is 114 mi/hr The speed of the wind is 21 mi/hr
 test/720496: 235 is 15% of what?1 solutions Answer 441840 by josmiceli(9819)   on 2013-02-28 20:55:54 (Show Source):
 logarithm/720493: 7log(base7)4=x i can get to 7^x=4^7 but i'm lost after that! (not allowed to use calculators)1 solutions Answer 441839 by josmiceli(9819)   on 2013-02-28 20:53:58 (Show Source): You can put this solution on YOUR website! Raise both sides to the 7th power take the log of both sides
 Rational-functions/720469: 6. A ball is thrown vertically upward with an initial velocity of 48 feet per second. The ball started from a height of 8 feet off the ground. a. At what time will the rocket reach the maximum height? ______________ b. What is the maximum height the ball will reach? _______________ d. Where will the ball be after three seconds? _____________ e. What is the equation for the axis of symmetry? ________________________ 1 solutions Answer 441834 by josmiceli(9819)   on 2013-02-28 20:25:04 (Show Source): You can put this solution on YOUR website!The effect of gravity pulling down is ft/sec2 The effect of upward initial velocity is ft/sec The hight off the ground adds ft --------------------------------- The equation is (a) The maximum height is at for a parabola ( which this is ), when the form of the equation is So, at t = 1.5 sec, the height is a maximum ------------------- (b) Plug back into the equation to find The max height is 44 ft -------------------- (d) In 3 sec, the ball will be In 3 sec, the ball will be 8 ft off the ground again --------------------- (e) The axis of symmetry is a vertical line, and every point on that line has the same x-value, so the equation for this line is Here's the plot of the equation:
 Rate-of-work-word-problems/720385: heather can rake all the leaves in the yard in 4 hours, Beth can do it in 6. How long would it take them to do the yard together?1 solutions Answer 441806 by josmiceli(9819)   on 2013-02-28 18:12:24 (Show Source): You can put this solution on YOUR website!Add their rates of raking Heather's rate: ( 1 yard ) / ( 4 hrs ) Beth's rate ( 1 yard ) / ( 6 hrs ) Rate raking together: ( 1 yard ) / ( t hrs ) ----------------- Multiply both sides y hrs Together, they can rake the yard in 2 hrs 24 min ---------------- check: OK
 Linear_Equations_And_Systems_Word_Problems/720374: its costs \$120 to manufacture 2 bicycles and \$160 to manufacture 4 bicycles. if the number of bicycles is the x- coordinate, and the amount of money is the y- coordinate, draw a graph of the line that would represent the relation between the number of bicycles and the cost to manufacture them assume it is a linear relationship1 solutions Answer 441803 by josmiceli(9819)   on 2013-02-28 18:00:32 (Show Source): You can put this solution on YOUR website!Plot on the vertical axis Plot on the horizontal axis You are given the points ( 2,120 ) ( 4,160 ) ------- ----------------- check: Does the line go through ( 2,120) ? Does the line go through (4,160) ? OK
 Radicals/720371: Please help us solve: 9^(2x+3)=2187 Keep getting negative number. Thanks Pat1 solutions Answer 441793 by josmiceli(9819)   on 2013-02-28 17:46:41 (Show Source): You can put this solution on YOUR website! The exponents must be the same on both sides ----------- check: OK
 Volume/720366: How to find at least two new dimensions of the new box that's 4"by12"by8" that both have volumes 20% more than 384. Please help, so lost.1 solutions Answer 441786 by josmiceli(9819)   on 2013-02-28 17:34:52 (Show Source): You can put this solution on YOUR website!That's a confusing question. So, I guess they want 2 different boxes whose volumes are 20% more than the given box ------------------- I think the thing to realize here is that if you multiply any one of the 3 dimensions of the original box by , you will get a volume that is 20% larger, so 4 x 12 x 9.6 is a possible box ------------------------- 4 x 14.4 x 8 is a possible box ------------------------- 4.8 x 12 x 8 is a possible box -------------------------- Note all 3 give volume = 460.8 in3
 Trigonometry-basics/720359: find the exact value of: cos pi/3 + sin pi/2 question 2: 4cos60(degrees) + 3tan pi/3 1 solutions Answer 441782 by josmiceli(9819)   on 2013-02-28 17:21:49 (Show Source): You can put this solution on YOUR website!I tend to convert radians to degrees so I can visualize the angle. degrees radians = degrees ---------------------------------- radians = degrees radians = degrees --------------------------------- (1) I'll do the conversions to degrees: (2)
 Radicals/720022: A bird leaves its nest in NY. it flies 6 km due east and 3 km due north how far is the bird from its nest. I dont know if this is a radical the unit we were studying is radical applications. Thank you1 solutions Answer 441630 by josmiceli(9819)   on 2013-02-27 22:01:05 (Show Source): You can put this solution on YOUR website!The bird's path form a right triangle Use the Pythagorean theorem The bird is 6.7082 km from it's nest
 Money_Word_Problems/720024: Jordan invested \$600 in a savings account. The interest rate is 6% per year. Find the simple interest earned in 3 years. Then find the total of principal plus interest1 solutions Answer 441628 by josmiceli(9819)   on 2013-02-27 21:56:22 (Show Source): You can put this solution on YOUR website! In 3 yrs \$108 in interest is earned Principle + interest = \$708