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# Recent problems solved by 'Earlsdon'

Earlsdon answered: 6288 problems
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 Proofs/97605: I want to know the next four letters of this pattern: T,F,S,N,E,T1 solutions Answer 71002 by Earlsdon(6294)   on 2007-09-11 21:01:38 (Show Source): You can put this solution on YOUR website!Here's a guess! T, F, S, N, E. T, F, S, N, T, What do they mean...my guess is they are the initial letters of the odd integers beginning with 3. T = 3 F = 5 S = 7 N = 9 E = 11 T = 13 F = 15 S = 17 N = 19 T = 21
 Finance/97502: This question is from textbook Heres the question: A farmer wants to buy 100 animals for \$100.00 (must buy at least one of them) Horses-\$5.00 Cows-\$3.00 Chicks-.50 How many horses,cows and chicks does the farmer need to have 100 and 100.00?1 solutions Answer 70951 by Earlsdon(6294)   on 2007-09-11 18:28:20 (Show Source): You can put this solution on YOUR website!This problem involves diophantine equations, where you have more unknowns than equations. The solutions, however, are limited by the fact that the unknowns must be integers, i.e. whole cows, whole horses, etc. We can set up two equations as follows: H = number of horses, C = number of cows, and ch = number of chicks. From the problem description, we can write: H+C+ch = 100 The total number of animals is 100. (\$5)H+(\$3)C+(\$0.50)ch = \$100 The total amount the farmer spends. The two equations are: 1) H+C+ch = 100 2) 5H+3C+0.5ch = 100 Multiply this equation by 2 and subtract equation 1) from the result. 1) H+C+ch = 100 2a) 10H+6C+ch = 200 -------------------- 3) 9H+5C = 100 Subtract 9H from both sides. 3a) 5C = 100-9H Now divide both sides by 5. 3b) C = 20-(9/5)H Now C can only be an integer if H is a multiple of 5. Let's try H = 5. 3c) C = 20-(9/5)(5) C = 20 - 9 C = 11 This is one possibility. Now let's try H = 10 3d) C = 20 - (9/5)(10) C = 20 - 18 C = 2 This is another possibility. H cannot be greater than 10 otherwise you would end up with C being a non-integer or a negative number. So, if C = 11 when H = 5, then ch = 100-11-5 = 84 - the number of chicks. Let's check this solution. H+C+ch = 100 5+11+84 = 100 and... 5(\$5) + 11(\$3) + 84(\$0.50) = \$25 + \$33 + \$42 = \$100 This is a valid solution! Now if C = 2 when H = 10, then ch = 100-2-10 = 88 - the number of chicks. Let's check this solution. H+C+ch = 100 10+2+88 = 100 and... 10(\$5)+2(\$3)+88(\$0.50) = \$50+\$6+\$44 = \$100 This solution is also valid! The two solutions are: 1) 5 horses, 11 cows, and 84 chicks. 2) 10 horses, 2 cows, and 88 chicks.
 Miscellaneous_Word_Problems/97428: iN YOUR ECONOMICS CLASS YOU HAVE SCORES OF 68, 82, 87, AND 89 ON THE FIRST FOUR OF FIVE TEST. TO GET A GRADE OF B THE AVERQAGE OF THE FIRST FIVE TEST SCORES MUST BE GREATER THAN OR EQUAL TO 80 AND LESS THAN 90. SOLVE AN INEQUALITY TO FIND THE RANGE OF THE SCORES THAT YOU NEED ON THE TEST TO GET A B1 solutions Answer 70905 by Earlsdon(6294)   on 2007-09-11 11:40:55 (Show Source): You can put this solution on YOUR website!To find the average score (A) of the first five tests, you'll add the scores and divide by 5. where x is the score on the fifth test. Now you need this average (A) to be at least 80 () but less than 90 (). You can write the inequality thus: To solve this, you'll simplify the numerator. Now you'll multiply everything by 5. Simplify. Now you'll subtract 326 from everything. Simplify. Read this as: x is at least 74 but less than 124. The range of scores needed to get a B average is at least 74 but less than 124.
 Miscellaneous_Word_Problems/97186: The fifth, fifteenth & fiftieth parts of a number together make 43. Find the number.1 solutions Answer 70768 by Earlsdon(6294)   on 2007-09-10 12:10:56 (Show Source): You can put this solution on YOUR website!Let n be the required number. From the problem description, you can write: Add the fractions, the LCD is 150. Simplify. Multiply both sides by 150. Divide both sides by 43.
 Distributive-associative-commutative-properties/97039: How do you factor x^3+8?1 solutions Answer 70625 by Earlsdon(6294)   on 2007-09-09 14:45:13 (Show Source): You can put this solution on YOUR website!Factor: Do you recognise this as the sum of two cubes? ...but of course! The sum of two cubes can be factored thus: In your problem, A = x and B = 2, so... and we're done! Let's check the solution by multiplying the two factors, using FOIL. Simplify by combining like-terms.
 Travel_Word_Problems/96972: A bike race consists of two segments whose total length is 90 km. The first segment is covered at 10 kph and takes 2 hours longer to complete than the second segment, which is covered at 25 kph. How long is each segment? I have tried setting it up as t/25 = (t+2)/10 but for some reason I can't figure out the algebra. Thanks!1 solutions Answer 70600 by Earlsdon(6294)   on 2007-09-09 11:41:04 (Show Source): You can put this solution on YOUR website!From your equation, it appears that you assumed that the two segments were the same distance, but there is nothing in the problem to support this assumption. So, back to basics: and... We know that: and... and we also know that: So we can write: aagh...to many variables! Let's replace with and replace with , so now we have: and Solve this for ...but, of course, , so... Good, now we have one variable , so let's solve for it. and... hrs. Now we can find and km and... km Check: Total distance is = 90km
 Exponents/96847: how do you answer this question? (2^4)(2^3) I tink the answer may be negative exponent law = 1/2^11 solutions Answer 70470 by Earlsdon(6294)   on 2007-09-08 11:52:22 (Show Source): You can put this solution on YOUR website!Simplify: When multiplying quantities with exponents, if the bases are the same (base is 2 in this case) then you add the exponents: =
 Geometric_formulas/96851: The ideal male body weight, w (in pounds), can be determined from a man's height, h (in inches) using the formula w = 110 + 5(h-60). Solve the formula for h and write a reason for each step. Use the results to find the height of a man with an ideal weight of 135 pounds.1 solutions Answer 70469 by Earlsdon(6294)   on 2007-09-08 11:46:24 (Show Source): You can put this solution on YOUR website!Solve for h. Isolate the variable term by subtracting 110 from both sides. Divide both sides by 5 to further isolate the variable term. Finally, add 60 to both sides to solve. This can be simplified further to get: If w = 135 pounds, then the height is: inches.
 Equations/96482: Write the verbal sentence as an inequality. Then solve the ineqaulity A number divided by 2 is at most 10 Can someone help with this equation?1 solutions Answer 70250 by Earlsdon(6294)   on 2007-09-06 10:31:13 (Show Source): You can put this solution on YOUR website!Let n be the number, and "at most 10" is written as "less-than-or-equal-to 10", so you can write: To solve for n, multiply both sides by 2.
 Finance/96338: This question is from textbook prentice hall mathematics algebra 1 three friends were born in consecutive years. the sum of their birth years is 5961. find the year in which each person was born. i need help solving this problem.1 solutions Answer 70126 by Earlsdon(6294)   on 2007-09-05 18:14:41 (Show Source): You can put this solution on YOUR website!Let x = the year of birth of the youngest, then x+1 will be the year of birth of the next oldest and x+2 will be the year of birth of the eldest friend. So we need to find x. x+(x+1)+(x+2) = 5961 3x+3 = 5961 Subtract 3 from both sides. 3x = 5958 Divide both sides by 3. x = 1986 x+1 = 1987 x+2 = 1988 Check: 1986+1987+1988 = 5961
 Linear-systems/96328: This question is from textbook You travel 575 miles in 8 hours. Part of the trip is made at 60mph and part of the trip is made at 80mph. Find the time traveled at each rate. This is the question. I have that distance =rate * time and 575=r*8. I also have that r=(60T+80t)/2 and T+t=8 but when i try to solve it I get a negative time. Thanks for trying to help.1 solutions Answer 70122 by Earlsdon(6294)   on 2007-09-05 17:58:56 (Show Source): You can put this solution on YOUR website!You are taking the right approach! Let's see how it goes: and... We are given that: or and we have to find: and but we also know that: or Let's put in some values. or Now, since we can write: Solve this for substitute Solve this for hours. hours. Check: The total trip distance. = 575
 percentage/96265: If you have a 5% solution and a 50 % solution how much of each solution do you need to make 20ml of 30% solution?1 solutions Answer 70083 by Earlsdon(6294)   on 2007-09-05 14:43:19 (Show Source): You can put this solution on YOUR website!Let x = the number of ml of the 5% solution required, then 20-x = the number of ml of the 50% solution needed. The sum of these will equal 20 ml of 30% solution. From these facts, we can write the necessary equation to find x, after converting the percentages to their decimal equivalents. x(0.05)+(20-x)(0.5) = 20(0.3) Simplify and solve for x. 0.05x+10-0.5x = 6 -0.45x+10 = 6 -0.45x = -4 x = 8.89 So you would need 8.89 ml of the 5% solution and 20-x = 11.11 ml of the 50% solution to obtain 20 ml of 30% solution.
 Expressions-with-variables/96119: if 1=2n what's its property?1 solutions Answer 69974 by Earlsdon(6294)   on 2007-09-04 19:37:27 (Show Source): You can put this solution on YOUR website!If 1 = 2n, then n must be the multiplicative inverse of 2!
 Sequences-and-series/96045: I want to neqotiate an allowance with my parents propose that I make 1 cent the first week 2 cents the 2nd week 4 cents the 3rd week and 8 cents the 4th week, etc how much will I make after 52 weeks which happens to be total weeks for a year How much will I make the last week1 solutions Answer 69948 by Earlsdon(6294)   on 2007-09-04 16:05:50 (Show Source): You can put this solution on YOUR website!This is a case of a geometrical progression and can be repesented as... +...+ The sum of this progression is cents So, at the end of the year (52 weeks) you would have a total of: \$45,035,996,273,704.95 On the 52nd week, you would get: cents, which amounts to \$22,517,998,136,852.48
 Graphs/96028: A moving company charges a certain flat rate per day, plus a per-mile charge. It charged your brother \$52.90 for a one-day move of 20 miles. Your sister used the same company and was charged \$81.70 for a one-day move of 60 miles. What would you predict to pay for a one-day move of 85 miles?1 solutions Answer 69941 by Earlsdon(6294)   on 2007-09-04 15:44:09 (Show Source): You can put this solution on YOUR website!First, I would calculate the flat-rate cost (C) and the cost per mile (x). This can be done as follows: Write the equation for the cost of the brother's move of \$52.90 for a 20-mile move... 1) ...and the sister's move. 2) Now you have two equations with two unknowns (C and x). Rewrite these as: 1a) and... 2a) But the flat rate, C, is the same in both cases, so equation 1a) is equal to 2a). Simplify and solve for x, the cost per mile. Add 60x to both sides. Now subtract \$52.90 from both sides. Finally, divide both sides by 40 to get x. So the cost per mile is 72 cents. Now that we have that, we can go back to either equation 1a) or 2a) to find the value of C, the flat-rate cost. Let's use equation 1a) and we;ll substitute x = \$0.72: Simplify. ...and this (\$38.50) is the flat-rate cost. Now we can work out the cost for a one-day move of 85 miles by using 1) but substituting C = \$38.50 and x = \$0.72 per mile.. = The cost of a one-day move of 85 miles is \$99.70
 Polynomials-and-rational-expressions/95844: I need help to solve this equation 1/y+5 - 8/y-5 = 11/y^2-251 solutions Answer 69811 by Earlsdon(6294)   on 2007-09-03 16:16:33 (Show Source): You can put this solution on YOUR website!Solve for y: Add the two fractions on the left side. The LCD is Multiply both sides by and simplify. Add 45 to both sides. Divide both sides by -7. Check: Substitute y = -8 in original equation. Evaluate. OK!
 Equations/95640: 3/7x +2 =4/7x-5 I have tried this over and over again - i keep coming up with -49, but the answer should be 7. I cannot figure it out. I learned that you should multiply everything by the LCD to make everything a whole number first. 1 solutions Answer 69672 by Earlsdon(6294)   on 2007-09-02 11:53:42 (Show Source): You can put this solution on YOUR website!I have worked your problem two different ways and find that the answer that you give (x = 7) is just not possible. In the first place, to remove any ambiguity on the problem statement, please use parentheses! Why? Because... 3/7x can be interpreted to mean either: or Whereas, (3/7)x can be interpreted only as In the second place, the only way that I can get the answer that you give, (x = 7) is if the problem starts with , so... Multiply through by the LCD of 7. Simplify. Add 3x to both sides. Add 35 to both sides. Finally, divide both sides by 7. or Please check the original problem for a possible missing negative sign!
 Equations/95641: I am having trouble. Can someone please help me. Solve: -3(x+1)=2(x-8)+31 solutions Answer 69668 by Earlsdon(6294)   on 2007-09-02 11:24:23 (Show Source): You can put this solution on YOUR website!Solve for x: -3(x+1) = 2(x-8)+3 First, apply the "distributive property" to both sides of the equation. -3x-3 = 2x-16+3 Simplify. -3x-3 = 2x-13 Add 3x to both sides. -3 = 5x-13 Add 13 to both sides. 10 = 5x Finally, divide both sides by 5. 2 = x or x = 2 Check: Substitute x = 2 in the original equation. -3(2+1) = 2(2-8)+3 Simplify. -6-3 = 4-16+3 Evaluate. -9 = 7-16 -9 = -9 It checks!
 Functions/94994: Ok, My son came home from school today with Math homework. He is in Algebra 1 and they have requested he have a TI-83. I intend to buy this for him but I haven't yet and he has homework tonight. The teacher only explained how to do the problem on the calulator not on paper. I know it can be done on paper but I really do not remember how to do it. I looked in his math book and the book only goes to Chapter 12 and the worksheet is for Chapter 13. I can't figure out how to solve these problems and I'm hoping for some help. He only has to do certain problems so I'm going to send you one of the ones he doesn't have to do. The question reads as follows: Solve ecah equation if the domain is {-2, -1, 1, 3, 4}. The question is as follows: y=4 - 5x If you could just show me how to work these I can help him with the ones he has to turn in tomorrow. Thank you.1 solutions Answer 69127 by Earlsdon(6294)   on 2007-08-28 22:46:45 (Show Source): You can put this solution on YOUR website!Ok, you can start by recalling that the "domain" of a function is the set of all possible values of the independent variable. In your function x is the independent variable (y is the dependent variable). So you can answer the problem by assigning to x in your function, each of the given values of the domain, then solve for the corresponding value of y. Let x = -2 The first of the given values in the domain. This is the value of y that corresponds to the domain value of -2. Now you repeat this process for each of the remaining given values of the domain. Let x = -1 The second value in the set. Let x = 1 The third value. You proceed in this fashion until you have used all five values of the given set. Let x = 3. You should be able to finish these.
 Equations/94750: I have an algebra question for you, to which I require assistance, as I am not quite certain what it is they want me to do. It is a written question. An alloy contains 60% by weight of copper, the remainder being zinc. How much copper must be mixed with 50kg of this alloy to give an alloy containing 75% copper? I have done some nuber crunching and all I got was 60% of 50kg = 30kg and 75% of 50kg = 37.5kg and or 60x+40y=50 75x+25y=50 /5 60x+40y=50 /4 15x+5y=10 15x+10y=12.5 15x+5y=10 anyhow X = .5kg and Y = .5kg but it just does not look right, would you please be able to show me the correct way to sort this out. It would be greatly appreciated. Thank you.1 solutions Answer 68992 by Earlsdon(6294)   on 2007-08-27 23:13:06 (Show Source): You can put this solution on YOUR website!First, let's concentrate on the amount of copper (Cu) in the starting alloy and the resulting alloy. The amount of copper in the starting alloy is: 60% of 50 kg or (0.6)(50). To this we want to add x kg of Cu to make (50+x) kg of an alloy, 75% of which is Cu. So we set up the equation: (0.6)(50) + x = (0.75)(50+x) Simplify and solve for x. 30+x = 37.5+0.75x Subtract 0.75x from both sides. 30+0.25x = 37.5 Subtract 30 from both sides. 0.25x = 7.5 Finally, divide both sides by 0.25 x = 30 You would need to add 30kg of Cu to the 50kg of the starting alloy to obtain 80kg (50kg + 30kg) of the resulting alloy containing 75% Cu. Check: 50(0.6)+30 = (50+30)(0.75) 30+30 = (80)(0.75) 60 = 60
 Polynomials-and-rational-expressions/94670: I know what I am supposed to do, and if I could find the LCD, I could solve the problem, but for the life of me, I am drawing a blank on how to factor (n^4 -1)1 solutions Answer 68949 by Earlsdon(6294)   on 2007-08-27 18:20:44 (Show Source): You can put this solution on YOUR website!Factor: Notice that , so now you can write: The difference of two squares can be factored: Applying this to your problem: but again, we have the difference of two squares in the second factor, so... we would normally stop here, because the factors of involve the imaginary number If you are interested though: but don't use this if you have not yet come to imaginary numbers.
 Geometric_formulas/94561: Find the volume of a cone with a radius of 10ft. and a height of 18 ft.1 solutions Answer 68882 by Earlsdon(6294)   on 2007-08-26 23:38:53 (Show Source): You can put this solution on YOUR website!The volume of a right circular cone is given by: where r = 10ft. and h = 18ft. If you use as an approximation, you get: cu.ft.
 Exponents/94556: This is a table so it's tricky typing out in words... There are 4 rows and 4 columns, and I need to fill in the blanks. The first column is labeled POWER. The first row in the first column says 2^5. The fourth row in the first column says r^8. The second column is labeled BASE. The second row in the the second column says 3. The third column is labeled EXPONENT. The second row in the third column says 4. The fourth column is labeled STANDARD FORM. The third row in the fourth column says 125. phew... Okay, if you understood that, and if I'm correct, the entire first row should read: 2^5, 2, 5, 32. The second row should read: 3^4, 3, 4, 81. I have no idea about the third row. The last row should read: r^8, r, 8, r^8? I'm really sorry that was so long and confusing, but I just can't get that third row! 1 solutions Answer 68881 by Earlsdon(6294)   on 2007-08-26 23:33:53 (Show Source): You can put this solution on YOUR website!Here's where "a picture is worth a thousand word" n'est-ce pas? Anyway, I get the picture! (lol) You are correct for rows 1, 2, and 4. The third row is shown below: : Base = 2 Exponent = 5 : Base = 3 Exponent = 4 : Base = 5 Exponent = 3 : Base = r Exponent = 8
 Complex_Numbers/94510: I am desperate to know if I am doing this correctly. Would you please let me know how I am going? Thank you so much. a=2, b=3, c=-4, d=-1, e=0 – – (2/3) (2/3) - (-4/-1) (-4/-1) (-4/-1) 2/3*2/3 – 4*4*4 (2*3) (3*2)/3*3 – 64 6*6/9 – 64 36/9 - 64 4 – 64 = - 60 1 solutions Answer 68829 by Earlsdon(6294)   on 2007-08-26 19:35:30 (Show Source): You can put this solution on YOUR website!Subtract: = =
 Linear-equations/94429: graph the equation y = 2x - 3 on a coordinate plane1 solutions Answer 68756 by Earlsdon(6294)   on 2007-08-26 10:27:46 (Show Source): You can put this solution on YOUR website!Graph y = 2x-3 on a coordinate plane. This is quite easy to do on your own coordinate graph paper. This is a linear equation (you can tell this because the highest power of the independent variable, x, is 1) and since you need only two points to define a straight line, you would just assign a value to x and solve for the corresponding value of y to give you one point (x, y) then do this again with a different value of x to get the second point. Plot these two points on your graph paper and draw the straight through them. Let's pick x = 0 for the first point. Plugging this into your equation, we can solve for the corresponding value of y, the dependent variable. For x = 0 y = 2(0)-3 y = -3 The coordinates of the first point are (0, -3) and... For x = 3 y = 2(3)-3 y = 6-3 y = 3 The coordinates of the second point are (3, 3) The graph appears below:
 Polynomials-and-rational-expressions/94367: what is the x-intercept of 2x-5y=201 solutions Answer 68723 by Earlsdon(6294)   on 2007-08-25 18:23:35 (Show Source): You can put this solution on YOUR website!Find the x-intercept: The x-intercept is where the graph of this linear equation intersects (crosses) the x-axis. At this point, y is zero, so by setting y = 0 in the equation and solving for x, you will get the value of x where the line crosses the x-axis, also known as the x-intercept. So we'll set y = 0. Divide both sides by 2. This is the x-intercept! This is clear from the graph of the linear equation.
 Radicals/94371: 2/(3+sqrt5) please help i forgot how to deal with the denominator1 solutions Answer 68720 by Earlsdon(6294)   on 2007-08-25 18:14:06 (Show Source): You can put this solution on YOUR website!Simplify? We don't like to see radicals in the denominator, so... Multiply the numerator and the denominator by conjugate of the denominator which is (). Simplify the denominator. Simplify some more. Cancel a 2 in the top & bottom.
 Graphs/94341: I am a little confused. Can I get someone to help me please. I worked out the problem I am just not sure if it is correct. Rewrite as a function of x. 4-x-10y=11 Thank you.1 solutions Answer 68666 by Earlsdon(6294)   on 2007-08-25 12:51:10 (Show Source): You can put this solution on YOUR website!Rewrite as a function of x: First, solve this for y. Divide both sides by 10. or Now, to write this as a function of x in function form, just replace the y with f(x)