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# Recent problems solved by 'Mathtut'

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 Geometry_proofs/178817: This question is from textbook Geometry 1 solutions Answer 133778 by Mathtut(3670)   on 2009-01-27 18:41:48 (Show Source): You can put this solution on YOUR website!oooopppppssssssss for the problem ...thanks Mathtut
 Expressions-with-variables/178814: x-y=4 x-2y=101 solutions Answer 133777 by Mathtut(3670)   on 2009-01-27 18:40:40 (Show Source): You can put this solution on YOUR website!x-y=4.......eq 1 x-2y=10.....eq 2 : subtract all terms in eq 2 from terms in equation 1: : x terms will be eliminated because x-x=0. We are left with -y+2y=4-10 : : take y's found value and plug it back into either eq 1 or 2 . I chose eq 1 : x-(-6)=4 : x+6=4 : :
 Polynomials-and-rational-expressions/178811: This question is from textbook Algebra and Trigonometry Structure and Method book 2 I have been working on this math problem and I can't seem to get the answer. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Equations Containing Radicals Solve. If an equation has no real solution, say so. √(x ) + √3 = √(x+3)1 solutions Answer 133775 by Mathtut(3670)   on 2009-01-27 18:35:00 (Show Source): You can put this solution on YOUR website! : squared both sides : : : :
 Rational-functions/178801: (x-1)(2x-4) ----------- x+4 times (x+1)(x+4) ---------- 2x-4 Can you please help with this problem? i need to simplify it and find the restrictions if any. Thank you so much. 1 solutions Answer 133772 by Mathtut(3670)   on 2009-01-27 18:18:36 (Show Source): You can put this solution on YOUR website! : =
 Miscellaneous_Word_Problems/178802: This question is from textbook 1 solutions Answer 133770 by Mathtut(3670)   on 2009-01-27 18:09:19 (Show Source): You can put this solution on YOUR website!ooooooooops you forgot the problem....thanks Mathtut
 Linear-equations/178798: If a line passes through (5, 2) and has a slope of 2/3, then what is the value of y on this line when x = 8, x=11 and x= 12?1 solutions Answer 133769 by Mathtut(3670)   on 2009-01-27 18:07:49 (Show Source): You can put this solution on YOUR website!use point slope formula : y-2=(2/3)(x-5) : y-2=2/3x-10 : y=(2/3)x-8 : so for x=8: y=2/3(8)-8=16/3-24/3=-8/3 : x=11: y=2/3(11)-8=22/3-24/3=-2/3 : x=12: y=2/3(12)-8=8-8=0
 Miscellaneous_Word_Problems/178795: Tickets for a concert were sold to adults for \$3 and to students for \$2. If the total receipts were \$824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?1 solutions Answer 133768 by Mathtut(3670)   on 2009-01-27 18:02:57 (Show Source): You can put this solution on YOUR website!let the number of adult and student tickets be a and s respectively : a=2s..........eq 1 3a+2s=824.....eq 2 : take a's value in eq 1 and plug that into eq 2 : 3(2s)+2s=824 : 8s=824 : number of student tickets sold : number of adult tickets sold
 Equations/178780: A bicycle rider travels 18 miles in the same amount of time that it takes a jogger to travel 10 miles. If the bicyclist goes 9.6 miles per hour faster than the jogger, how fast does each person travel?1 solutions Answer 133767 by Mathtut(3670)   on 2009-01-27 17:58:54 (Show Source): You can put this solution on YOUR website!A bicycle rider travels 18 miles in the same amount of time that it takes a jogger to travel 10 miles. If the bicyclist goes 9.6 miles per hour faster than the jogger, how fast does each person travel? : distance = rate * time : let r be the rate of the jogger...therefore rate of the bike rider is r+9.6 times are equal : bike:18=(r+9.6)t...eq 1 jogger:10=rt.......eq 2 : rewrite eq 2 to t=10/r and plug that into eq 1 : 18=(r+9.6)(10/r) : 18r=10(r+9.6)......multiplied both sides by r : 18r=10r+96 : 8r=96 : mph-speed of jogger : mph-speed of bike rider
 Linear-equations/178784: How to solve C= 2.85n + 30.52 to a) Find and interpret the C-intercept for the line? b) Find and interpret the n-intercept for the line? c) Graph the line for n ranging from 0 through 20? Can you please offer me some helpful information on how to solve equations such as these? Thank you, kelloggdmk1 solutions Answer 133764 by Mathtut(3670)   on 2009-01-27 17:48:15 (Show Source): You can put this solution on YOUR website!a) it would correctly be the C intercept not the n intercept : remember the slope intercept equation y=mx+b......where m is the slope and b is the y intercept. This is the same thing only its C instead of y. : so the C-intercept is 30.52. We cannot really interpret it without more information which you probably didnt give us. If you want it interpreted email me the rest of the problem. : for n=0 to 20 you just plug the values in for n and solve for C : example: n=0, C=30.52...so (0,30.52) : n=1, C=2.85(1)+30.52=33.37...so (1,33.37) : you'll find for every increase in n by 1 that the C will increase by 2.85 : so n=2 is 33.37+2.85=36.22 ...n=3 is 36.22+2.85 : and so it continues to 20 : here is the graph:
 Radicals/178787: 30) If f(x) = -3x2 – 4x + 5, evaluate for f(0) and f(2) 1 solutions Answer 133761 by Mathtut(3670)   on 2009-01-27 17:32:34 (Show Source): You can put this solution on YOUR website!f(x) = -3x2 – 4x + 5, evaluate for f(0) and f(2 : :
 Bodies-in-space/178740: a cone-shaped container has a height of 12 inches. if the radius of the circular base of the cone is 3 inches, what is the measure of the space inside the conte to the nearest cubic inch?1 solutions Answer 133760 by Mathtut(3670)   on 2009-01-27 17:29:57 (Show Source): You can put this solution on YOUR website! : : ..if then V=113.04 cu inches
 Equations/178776: A small company has \$24,000 to invest. It invested some of the money in a bank that paid 8% annual simple interest. The rest of the money was invested in stocks that paid dividends equivalent to 11% annual simple interest. t the end of 1 year, the combined income form these investments was \$2,340. How much was originally invested in stocks?1 solutions Answer 133759 by Mathtut(3670)   on 2009-01-27 17:22:28 (Show Source): You can put this solution on YOUR website!let x and y be the amount of money invested at 8 and 11%, respectively : x+y=24000.........eq 1 .08x+.11y=2340....eq 2 : rewrite eq 1 to x=24000-y and plug that value into eq 2 : .08(24000-y)+.11y=2340 : 1920-08y+.11y=2340 : .03y=420 : \$invested at 11% : \$invested at 8%
 Equations/178775: EZ car rental charges a weekly rate of \$189 plus \$0.07 permile.write an equation that can be used to determined the cost, of renting the car for one week and driving.1 solutions Answer 133758 by Mathtut(3670)   on 2009-01-27 17:17:17 (Show Source): You can put this solution on YOUR website!C(m)=.07m+189.......m is the amount of miles driven for the week. C is the Cost of driving the car per week as a funtion of miles.
 Equations/178768: -7+4r=-15 what is the answer with showing work -5x+13=-17 what is the answer with showing work 1 solutions Answer 133756 by Mathtut(3670)   on 2009-01-27 17:15:01 (Show Source): You can put this solution on YOUR website!-7+4r=-15 : 4r=-8.....added 7 to both sides : divided both sides by 4 to isolate the variable r : -5x+13=-17 : -5x=-30.....subtracted 13 from both sides : divided both sides by -5 to isolate the variable x
 Equations/178766: -7+4r=-15 what is the answer with showing work 1 solutions Answer 133755 by Mathtut(3670)   on 2009-01-27 17:12:31 (Show Source): You can put this solution on YOUR website!-7+4r=-15 : 4r=-8.....added 7 to both sides : divided both sides by 4 to isolate the variable r
 Graphs/178778: Find the value of b so that the graph of bx + 5y = 10 and has a slope of 31 solutions Answer 133753 by Mathtut(3670)   on 2009-01-27 17:11:11 (Show Source): You can put this solution on YOUR website!write this in slope intercept form y=mx+b : 5y=bx+10 : y=(b/5)x+2 : so m=slope=( b/5)=3 is what we are looking for :
 Rational-functions/178781: 7x-28 ------ x^2-16 can you help me simplify the equation and then show the restrictions?1 solutions Answer 133752 by Mathtut(3670)   on 2009-01-27 17:09:14 (Show Source): You can put this solution on YOUR website! : : : : restrictions are x can be all real numbers except for -4. -4 would put a zero in the denominator and that would make this undefined, therefore it is not allowed.
 Equations/178779: Two cranes, operating together, can unload a cargo ship in 4 hours. If it takes one crane twice as long as the other to unload the ship, how long would it take each crane to unload the ship by itself?1 solutions Answer 133751 by Mathtut(3670)   on 2009-01-27 17:05:55 (Show Source): You can put this solution on YOUR website!let y and x be the time crane 1 and crane 2, respectively, take to unload the ship by themselves. y=2x : crane 1 does 1/2x of the job per hour : crane 2 does 1/x of the job per hour : (1/x+1/2x)(4)=1job : ((2+1)/2x)4=1 : 12/2x=1 : 2x=12= : hours-time for crane 2 to do the job : y=2xhours-time for crane 1 to do the job
 Miscellaneous_Word_Problems/178755: The police use the formula v=4.9√L to estimatethe speed of a car v based on the length L of its skid marks on dry pavement. a. What is a reasonable estimate for a car's speed if its skid marks measure 220 feet? b. What would be the length of your skid marks if you drove with the speed of 65 mph?1 solutions Answer 133734 by Mathtut(3670)   on 2009-01-27 15:10:16 (Show Source): You can put this solution on YOUR website! : a)mph : b) : : feet
 Complex_Numbers/178760: (-1 + [SQRT(3)]i)3 A) 2 + 2[SQRT(3)]i B) -2 - 2[SQRT(3)]i C) 0 D) -8 E) -8 + 8[SQRT(3)]i F) 8 1 solutions Answer 133732 by Mathtut(3670)   on 2009-01-27 15:03:20 (Show Source): You can put this solution on YOUR website!answer is F) it is equal to 8 : :
 Equations/178765: i need help writing an expression that is equivalent to (x+2)(x+5)1 solutions Answer 133731 by Mathtut(3670)   on 2009-01-27 14:55:38 (Show Source): You can put this solution on YOUR website!just multiply out the terms using FOIL-first terms ,outside terms, inside terms,followed by last terms : so you would have
 Complex_Numbers/178759: -i4 A) -1 B) 1 C) i D) -i 1 solutions Answer 133730 by Mathtut(3670)   on 2009-01-27 14:45:57 (Show Source): You can put this solution on YOUR website! : remember =-1 so we have -(-1)(-1)=-1 : so A is the answer
 Linear-equations/178762: I need help with nonlinear functions, a few examples and some imputs to evaluate1 solutions Answer 133729 by Mathtut(3670)   on 2009-01-27 14:43:50 (Show Source): You can put this solution on YOUR website!there are many is a parabola : is another. : for inputs just put in any value for x that you choose and solve for y. : remember in a function for every value of x there is 1 and only 1 value of y. : :
 Linear-equations/178757: This question is from textbook Introduction and Intermediate algebra why is the line x=4 a vertical line?1 solutions Answer 133728 by Mathtut(3670)   on 2009-01-27 13:45:11 (Show Source): You can put this solution on YOUR website!because for every value of y the value of x is 4.....this creates a vertical line at x=4
 Exponential-and-logarithmic-functions/178752: Solve for x; y=3^x1 solutions Answer 133727 by Mathtut(3670)   on 2009-01-27 13:21:02 (Show Source):
 Probability-and-statistics/178749: The 5 participants in a 200-meter dash had the following finishing times (in seconds): 30,27,30,27,26 Assuming that these times constitute an entire population, find the standard deviation of the population. Round your answer to at least two decimal places. 1 solutions Answer 133726 by Mathtut(3670)   on 2009-01-27 13:15:45 (Show Source): You can put this solution on YOUR website!S= where X is each term, M is the mean and n is the number of terms. : mean is 28 : S=1.87 : population S : pS== : pS=1.67
 Word_Problems_With_Coins/178751: Wendy has 52 coins consisting of nickels and pennies. The value of the coins is \$1.20, then how many of each type does she have?1 solutions Answer 133725 by Mathtut(3670)   on 2009-01-27 13:06:24 (Show Source): You can put this solution on YOUR website!let n and p be the number of nickles and pennies : n+p=52...........eq 1 .05n+.01p=1.2....eq 2 : rewrite eq 1 to n=52-p and plug that value into eq 2 : .05(52-p)+.01p=1.2 : 2.6-.05p+.01p=1.2 : -.04p=-1.4 : number of pennies : number of nickels
 Inequalities/178743: the solution to the inequality (1/2x)- 15 > 11 is ( , ). 1 solutions Answer 133724 by Mathtut(3670)   on 2009-01-27 12:45:56 (Show Source): You can put this solution on YOUR website!(1/2x)- 15 > 11 : (1/2)x>26.....added 15 to both sides : x>52.......multiplied both sides by 2 : (52,infinity)
 Inequalities/178744: the solution to the inequality -10<3-x<-5 is ( , ) negative 10 is less than 3 subtract x less than or equal to -51 solutions Answer 133723 by Mathtut(3670)   on 2009-01-27 12:43:02 (Show Source): You can put this solution on YOUR website!-10<3-x<-5 : -13<-x<-8 : 13>x>8......reversed signs when we divided by a negative 1 : (8,13)
 Probability-and-statistics/178747: The 5 participants in a 200-meter dash had the following finishing times (in seconds): 30,27,30,27,26 Assuming that these times constitute an entire population, find the standard deviation of the population. Round your answer to at least two decimal places. 1 solutions Answer 133722 by Mathtut(3670)   on 2009-01-27 12:35:08 (Show Source): You can put this solution on YOUR website!mean is 28 : S=1.87S= where X is each term, M is the mean and n is the number of terms. : mean is 28 : S=1.87 : population S : pS== : pS=1.67
 Probability-and-statistics/178741: The following are the P/E ratios (price of stock divided by projected earnings per share) for 20 banks. 20,22,22,19,22,50,24,15,34,43,22,20,17,38,18,21,21,23,18,23 Find 20th and 75th percentiles for these ratios.1 solutions Answer 133720 by Mathtut(3670)   on 2009-01-27 12:26:46 (Show Source): You can put this solution on YOUR website!I think people shy away from percentiles because the math world cant get their act together on one definition:...there are really 3 ways of looking at percentiles .: : There is no universally accepted definition of a percentile. Using the 65th percentile as an example, the 65th percentile can be defined as the lowest score that is greater than 65% of the scores. Lets call this "Definition 1". The 65th percentile can also be defined as the smallest score that is greater than or equal to 65% of the scores. This we will call "Definition 2". Unfortunately, these two definitions can lead to dramatically different results, especially when there is relatively little data. Moreover, neither of these definitions is explicit about how to handle rounding. For instance, what score is required to be higher than 65% of the scores when the total number of scores is 50? This is tricky because 65% of 50 is 32.5. How do we find the lowest number that is less than 32.5% of the scores? A third way to compute percentiles is a weighted average of the percentiles computed according to the first two definitions. This third definition handles rounding more gracefully than the other two and has the advantage that it allows the median to be defined conveniently as the 50th percentile. : I will use the 3rd method but give answers to the other 2 : first line this up in ascending order: : 20,22,22,19,22,50,24,15,34,43,22,20,17,38,18,21,21,23,18,23 : : 15,17,18,18,19,20,20,21,21,22,22,22,22,23,23,24,34,38,43,50 : The first step is to compute the rank (R) of the 20th and 75th percentiles. This is done using the following formula: R=P/100(N+1) where P is the desired percentile and N is the number of terms. In our cases P=20 and 75 and N=20 : so in our case for the 20 percentile: R=20/100(20+1)=4.2 .......................75 percentile: R=75/100(20+1)=15.75 If R were an integer, the P the percentile would be the number with rank R. When R is not an integer, we compute the Pth percentile by interpolation as follows: Define IR as the integer portion of R (the number to the left of the decimal point). For our problems IR = 4 and 15 Define FR as the fractional portion of R. In our problems FR= .2 and .75 Find the scores with Rank IR and with Rank IR+1. For our problems this would be the 4th and 5th terms for 20th percentile and 15 and 16th for the 75th percentile. For P=20 this would be 18 and 19. for P=75 it would be 23 and 24 Interpolate by multiplying the difference between the scores by FR and add the result to the lower score. So for P=20 you would take .2(19-18)+18=. For P=75 it would be .75(24-23)+23= : 15,17,18,18,19,20,20,21,21,22,22,22,22,23,23,24,34,38,43,50 : Therefore, the 20th percentile is 18.2 and the 75th percentile is 23.75. If we had used the first definition (the smallest score greater than 20% and 75% of the scores) the 20th percentile would have been 19(5th term) and for the 75 percentile would have been 24(16th term). If we had used the second definition ( the smallest score greater than or equal to 25% of the scores) the 20th percentile would have been 18(4th term) and the 75 percentile would have been 23(15th term). : As you can see these definitions need to be standardized so everyone is on the same page. : hope that helps