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# Recent problems solved by 'nyc_function'

nyc_function answered: 2728 problems
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 Angles/323897: The measure of an angle is six more than twice the measure of its complement. Find the measures of both angles.1 solutions Answer 231783 by nyc_function(2733)   on 2010-07-19 23:52:08 (Show Source): You can put this solution on YOUR website!Let A = angle Let (90 - A) = the complement of the angle A = 2(90 - A) Can you take it from here?
 Graphs/323879: How many liters of a 40%-alcohol solution must be mixed with 10 liters of a solution that is 80% alcohol to get a solution that is 60% alcohol?1 solutions Answer 231782 by nyc_function(2733)   on 2010-07-19 23:50:19 (Show Source): You can put this solution on YOUR website!Let L = liters 0.40L + 10(0.80) = 0.60(L + 10) The above equation is all you need to find the answer.
 Geometry_Word_Problems/322449: Two angles of a triangle measure 75° and 51°. The side opposite the largest angle measures 25 inches. How long is the shortest side?1 solutions Answer 230856 by nyc_function(2733)   on 2010-07-14 16:52:11 (Show Source): You can put this solution on YOUR website!I know that this is a geometry question but it can be solved using trigonometry. We use the law of sines. The sum of the angles of a triangle is 180 degrees. To find the missing angle, add 51 + 75 and then subtract the sum from 180. This will give you 54 degrees. We now use the law of sines. Let x = the missing side we want to find sin51/x = sin75/25 x(sin75) = sin51(25) x(sin75) = 19.42864904 x = 19.42864904/sin75 x = 20.11401756 The side opposite the smallest angle is 20 inches.
 Geometry_Word_Problems/322452: The length of one side of an equilateral triangle is 10 cm. what is the altitude of the triangle?1 solutions Answer 230853 by nyc_function(2733)   on 2010-07-14 16:34:34 (Show Source): You can put this solution on YOUR website!Equilateral means all sides are the same. The bottom side can be divided into two parts of equal length: 10cm = 5cm + 5cm. Let h = height Use the Pythagorean Theorem to find h. h^2 + 5^2 = 10^2 Can you take it from here?
 Miscellaneous_Word_Problems/322473: jasmine is reading a book. She has finished 3/4 of the book and has 82 pages left to read. How many pages has she already read.1 solutions Answer 230852 by nyc_function(2733)   on 2010-07-14 16:27:28 (Show Source): You can put this solution on YOUR website!3x/4 + 82 = x 4*(3x/4) + 4*84 = 4*x 3x + 328 = 4x 328 = 4x - 3x 328 = x Now, 3/4 * 328 = 246
 Mixture_Word_Problems/322471: The owner of Nuts2U Snack Shack mixes cashews worth \$6.25 a pound with peanuts worth \$2.00 a pound to get a half-pound mixed nut bag worth \$1.70. How much of each kind of nut is included in the mixed bag?1 solutions Answer 230848 by nyc_function(2733)   on 2010-07-14 16:16:14 (Show Source): You can put this solution on YOUR website!Let c = number of cashews Let p = number of peanuts c + p = 0.5 6.25c + 2.00p = 1.70 This is your system of equations in two variables. Can you take it from here? If not, write back.
 Average/322026: The average of seven different positive integers is 7 . what is the largest possible value of any of these numbers ?1 solutions Answer 230581 by nyc_function(2733)   on 2010-07-13 15:51:42 (Show Source): You can put this solution on YOUR website!You want the other six numbers to be as small as possible. The smallest the first six might be is 1,2,3,4,5,6 and the sum of these is 21. The total of all the numbers is 7x7=49 so the largest number would be 49-21=28.
 Equations/321963: Please help me solve this problem (finding the pronumeral value) and explain the solution: 7(b-3)= -281 solutions Answer 230538 by nyc_function(2733)   on 2010-07-13 11:43:17 (Show Source): You can put this solution on YOUR website!7(b-3)= -28 7b - 21 = -28 7b = -28 + 21 7b = -7 b = -7/7 b = -1
 Functions/321994: what is the result of substituting a value for a variable in a function?1 solutions Answer 230537 by nyc_function(2733)   on 2010-07-13 11:35:45 (Show Source): You can put this solution on YOUR website!To evaluate a function, we insert a given x value, a number in the domain, and see what number we get, which is a number in a range. SAMPLE: f(x) = x + 2 Pick a number for x. Any number will do. Say, x = 3. f(3) = 3 + 2 f(3) = 5 Here, 3 is the number in the domain of the function and 5 is the range of the function. Understand?
 Functions/322023: What is the smallest integer that is NOT in the domain of the function below? f(x)= squareroot of 4-x my answer is 5 1 solutions Answer 230535 by nyc_function(2733)   on 2010-07-13 11:30:16 (Show Source): You can put this solution on YOUR website!The domain is all values that x can take on. The only problem I have with this function is that I cannot have a negative inside the square root. So I'll set the insides greater-than-or-equal-to zero, and solve. The result will be my domain: 4 - x ≥ 0 - x ≥ 0 - 4 -x ≥ -4 x ≤ -4/-1 x ≤ 4 The values for x must be less than or equal to 4. Anything else will make the square root function undefined.
 Quadratic_Equations/322027: one factor of x^3 + 1 is (x + 1). what is the other factor ?1 solutions Answer 230531 by nyc_function(2733)   on 2010-07-13 11:19:47 (Show Source): You can put this solution on YOUR website!Use the sum of cubes formula. A^3 + B^3 = (A + B)(A^2 - AB + B^2) x^3 + 1 = x^3 + 1^3 Let A = x Let B = 1 x^3 + 1 = (x + 1)(x^2 - (x)(1) + 1^2) x^3 + 1 = (x + 1)(x^2 - x + 1) The other factor is (x^2 - x + 1).
 Geometry_Word_Problems/322029: What does it mean to refer to a 20-in TV set or a 25-in TV set? Such units refer to the diagonal of the screen. A 20-in TV set also has a width of 16-in. What is its height?1 solutions Answer 230530 by nyc_function(2733)   on 2010-07-13 11:15:26 (Show Source): You can put this solution on YOUR website!The lngth of tv sets are given by the diagonal measure. The height is the side measure (from top to bottom). The width is the bottom measure (from left to right). The diagonla is 20. Th width is 16 inches. Use the Pythagorean Theorem to find the height. Let h = height 16^2 + h^2 = 20^2 256 + h^2 = 400 h^2 = 400 - 256 h^2 = 144 = h = 12 The height is 12 inches.
 Miscellaneous_Word_Problems/321998: How many batting lineups are there for nine players of a baseball team if the center fielder must bat fourth, the second baseman must bat third and the pitcher last?1 solutions Answer 230498 by nyc_function(2733)   on 2010-07-13 09:11:24 (Show Source): You can put this solution on YOUR website!9P3 = 9!/(9 - 3)! 9P3 = 362880/6! 9P3 = 362880/720 9P3 = 504 batting line ups. I hope this helps. If not, write back.
 Miscellaneous_Word_Problems/322001: Two dice are rolled together. What is the probability of rolling a prime number?1 solutions Answer 230497 by nyc_function(2733)   on 2010-07-13 09:07:49 (Show Source): You can put this solution on YOUR website!Each die has numbers 1 to 6. There are 3 prime numbers per die. The prime numbers are 2, 3 and 5 for each die. This means there are 6 prime numbers in total from a list of 12 possibilities. Let P = probability P(rolling a prime) = (what we want)/(total number of possible outcomes) P(rolling a prime) = 6/12 or 1/2
 Triangles/322002: the measure of one angle of a triangle is 115 celcius. the other two angles are congruent. what is the measure of each angle?1 solutions Answer 230496 by nyc_function(2733)   on 2010-07-13 09:01:25 (Show Source): You can put this solution on YOUR website!Celcius? You mean degrees, right? Angles are measured in degrees and radians. But in your case, we are dealing with degrees since this is not a trigonometry question. 115 + x + x = 180 115 + 2x = 180 Can you take it from here?
 Mixture_Word_Problems/322012: Angie bought some golf balls for \$24. If each ball had cost \$0.50 less, she could have purchased one more ball for the same amount of money. How many golf balls did Angie buy?1 solutions Answer 230495 by nyc_function(2733)   on 2010-07-13 08:55:58 (Show Source): You can put this solution on YOUR website! Here is another method: Let n = number of balls purchased Let p = price per ball Therefore: n * p = 24 (n + 1)(p - 0.5) = 24 Therefore: p = 24/n (n + 1)((24/n) - 0.5) = 24 24 - 0.5n + (24/n) - 0.5 = 24 -0.5n + (24/n) - 0.5 = 0 Multiply through by -2n: n^2 + n - 48 = 0 n = (-1 +/- sqrt(1^2 - 4(1)(-48))) / (2*1) n = (-1 +/- sqrt(1 + 192)) / 2 n = (-1 +/- sqrt(193)) / 2 n = -0.5 +/- sqrt(48.25) n =~ 6.47 or -7.47 Suppose she bought 6 balls, so they each cost \$4. If they had cost \$3.50, then \$24 would still not be enough to buy 7 balls. So that doesn't work. Suppose she bought 7 balls, so they each cost about \$3.43. If they had cost \$2.93, she could have bought 8 balls for \$24 (and received \$0.56 in change). Suppose she bought 8 balls, so they each cost \$3. If they had cost \$2.50, she could have bought 9 balls for \$24 (and received \$1.50 in change). Suppose she bought 9 balls, so they each cost about \$2.67. If they had cost \$2.17, she could have bought at least 11 balls for \$24. So that doesn't work. So the answer must be 7 (or 8).
 Geometry_Word_Problems/322013: The width of a rectangle is 6 feet, and the diagonal is 10 feet. What is the area of the rectangle?1 solutions Answer 230494 by nyc_function(2733)   on 2010-07-13 08:52:59 (Show Source): You can put this solution on YOUR website!Length = 6 diagnoal = 10 side = x We need to find x using the Pythagorean Theorem. x^2 + 6^2 = 10^2 x^2 + 36 = 100 x^2 = 100 - 36 x^2 = 64 = x = 8 The width is 8. Area = length times width Area = length times width Area = 6 times 8 Area = 48 square feet Done!
 Miscellaneous_Word_Problems/320928: The mathmatics department of a college has 14 male professors, 14 female proffesors, 7 male teaching assistants, and 14 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a teaching assistant or a female.1 solutions Answer 229842 by nyc_function(2733)   on 2010-07-09 08:48:08 (Show Source): You can put this solution on YOUR website!You need the formula: P(A or B) = P(A) + P(B) - P(A and B), where is P = probability. Let A = selecting a teaching assistance Let B = selecting a female P(A or B) = P(A) + P(B) - P(A and B) P(A or B) = (28/49) + (28/49) - (28/49*28/49) P(A or B) = (4/7) + (4/7) - (4/7*4/7) P(A or B) = (8/7) - (16/49) P(A or B) = 40/49
 Inequalities/320933: -5 < 9x + 8 -8x I need step by step break down so i can understand what i am doing please 1 solutions Answer 229836 by nyc_function(2733)   on 2010-07-09 08:25:05 (Show Source): You can put this solution on YOUR website!-5 < 9x + 8 -8x Treat it like a regular equation disregarding the inequality sign. On the right side, combine like terms. We can combine 9x and -8x because they both share an x. After that, subtract 8 from both sides. -5 < 9x - 8x + 8 -5 < x + 8 -5 - 8 < x -13 < x Done! But, what does the answer mean? It means that any value you choose for x must be bigger than -13 to make the original inequality question a true statement. Let me ask you some questions. Can x be -15? No, because -15 is smaller than -13. Can x be -100? No, because -100 is smaller than -13. It must be bigger than -13. Any number to the right of -13, (not including -13), on the real number can be used to replace x with. The question, however, is not asking you to replace x with a number. The correct answer is -13 < x. I just wanted to break down the answer a bit more in detail. Understand?
 Miscellaneous_Word_Problems/320930: An election ballot asks voters to select 6 city commissioners from a group of 12 candidates. In how many ways can this be done. Use the formula nCr to solve. I am stuck please help1 solutions Answer 229835 by nyc_function(2733)   on 2010-07-09 08:15:55 (Show Source): You can put this solution on YOUR website!Let n = total of city commissioners Let r = how many candidate are taken from the total This is a combination question from probability math. The formula you need is given by: nCr = n!/[(n - r)! * r!] The exclamation point (!) means factorial. What is a factorial anyway? A factorial is the product of all the positive integers from 1 to a given number. For example, 6 factorial, written 6!, means 6 x 5 x 4 x 3 x 2 x 1 = 720. What would 4! be? It is 4 x 3 x 2 x 1 = 24. Understand? ============================================ Back to your question. Let n = 12 Let r = 6 Replace every n! with 12 and every r! with 6 and then do the math. nCr = 12!/[(12 - 6)!*6!] nCr = 479001600/(720)(720) nCr = 479001600/518400 nCr = 924 There are 924 ways or combinations to select 6 city commissioners from a group of 12 candidates.
 Rectangles/320931: A rectangle has a perimeter of 38 inches. If the lengths of all sides are doubled, what will be the new perimetr?1 solutions Answer 229833 by nyc_function(2733)   on 2010-07-09 08:03:26 (Show Source): You can put this solution on YOUR website!Let p = perimeter Let x = lengths and sides The perimeter of a rectangle formula is given by P = 2L + 2W. 38 = 2(2x) + 2(2x) Can you take it from here?
 Linear_Equations_And_Systems_Word_Problems/320929: A full-price ticket for a college basketball game costs \$6.00, and a student ticket costs \$4.25. If 496 tickets were sold, and the total receipts were \$2,498.25, how many tickets were student tickets?1 solutions Answer 229831 by nyc_function(2733)   on 2010-07-09 07:59:28 (Show Source): You can put this solution on YOUR website!Let f = full-price ticket Let s = student ticket f + s = 496 6.00f + 4.25s = 2498.25 This is a system of linear equations in two variables. The two variables are f and s. I selected f and s but you can use any other two letters. You now have the two equations above. Use the substitution method to find the value of s. I assume that you know how to solve this type of problem. Can you take it from here?
 Polynomials-and-rational-expressions/320624: how to factor out 8x^3+641 solutions Answer 229619 by nyc_function(2733)   on 2010-07-07 23:08:00 (Show Source): You can put this solution on YOUR website!This is addition of cubes. Use the following formula: a^3 + b^3 = (a + b)(a^2 – ab + b^2) Write 8 as 2^3 and 64 as 4^3 to get the same exponent of 3. (2x)^3 + 4^3 = (2x + 4)((2x)^2 - (2x)(4) + 4^2) (2x)^3 + 4^3 = (2x + 4)(4x^2 - 8x + 16) So, 8x^3 + 64 in factored form looks like this: (2x + 4)(4x^2 - 8x + 16)
 Linear-equations/320622: "What is the graph of the equation c= 20t+30"1 solutions Answer 229612 by nyc_function(2733)   on 2010-07-07 22:54:18 (Show Source): You can put this solution on YOUR website!Your graph will have points in the form (t,c). STEPS: 1-select about 3 values for t (I chose t = 0...see below) 2-simplify the right side of the equation for each value selected in terms of t 3-When you find the value of t and c, plot each point (t,c) on the coordinate plane 4-Connect each point with a line ================================== Let's say that t = 0 c = 20t + 30 c = 20(0) + 30 c = 0 + 30 c = 30 Your first point to plot is (0,30). Can you find two more points and then follow the above steps? Your function is a straight line. Can you do it now?
 Percentage-and-ratio-word-problems/320617: If 4 boys can shovel a driveway in 2 hours, how many minutes will 5 boys take to do the job?1 solutions Answer 229610 by nyc_function(2733)   on 2010-07-07 22:37:43 (Show Source): You can put this solution on YOUR website! Since 4 boys can shovel a driveway in 2 hours, 1 boy can do it in 4 x 2 hours = 8 hours. Thus, 5 boys can do it in 8/5 hours. Now, each hour is 60 minutes, so 5 boys can do it in 8/5 * 60 = 60 + 36 = 96 minutes. How about now?
 Travel_Word_Problems/320599: During the first part of a trip a conoeist travels 54 miles at a certain speed. The conoeist travels 8 miles on the second part of the trip at a speed 5mph slower. Total time of the trip is 3hrs. What was the speed of each part of the trip?1 solutions Answer 229608 by nyc_function(2733)   on 2010-07-07 22:27:37 (Show Source): You can put this solution on YOUR website! Let x be the speed for the first part of the trip. So that part takes 54/x hours. So the speed for the second part of the trip is x - 5, so that part takes 8/(x-5). Therefore: (54/x) + (8/(x-5)) = 3 54(x - 5) + 8x = 3x(x - 5) 54x - 270 + 8x = 3x^2 - 15x 62x - 270 = 3x^2 - 15x 3x^2 - 15x - 62x + 270 = 0 3x^2 - 77x + 270 = 0 x = (-(-77) +/- sqrt((-77)^2 - 4(3)(270))) / (2*3) x = (77 +/- sqrt(5929 - 3240)) / 6 x = (77 +/- sqrt(2689)) / 6 x =~ 21.4759 or 4.19 If x =~ 4.19, then the speed for the first part of the trip is 4.19, and the speed for the second part of the trip is -0.81. But a negative number makes sense, so we'll discount that solution. Therefore, x =~ 21.4759, so the speed for the first part of the trip is about 21.4759, so the speed for the second part of the trip is about 16.4759.
 Square-cubic-other-roots/320591: x 3/2 = 1251 solutions Answer 229604 by nyc_function(2733)   on 2010-07-07 21:36:50 (Show Source): You can put this solution on YOUR website!Is this what you wanted to type: = 125? If so, write back.
 Problems-with-consecutive-odd-even-integers/320547: what is the product of five less than a number and ten?1 solutions Answer 229602 by nyc_function(2733)   on 2010-07-07 21:30:14 (Show Source): You can put this solution on YOUR website!Let n = the number 10 times (n - 5), which be written 10(n - 5). We now apply the distributive rule to remove the parentheses. 10(n - 5) = 10n - 50.
 Exponents/320594: Write in scientific notation: 762.20 1 solutions Answer 229601 by nyc_function(2733)   on 2010-07-07 21:25:44 (Show Source): You can put this solution on YOUR website!To Change from Standard Form to Scientific Notation: (1) Place the decimal point such that there is one non-zero digit to the left of the decimal point. (2) Count the number of decimal places the decimal has "moved" from the original number. This will be the exponent of the 10. (3) If the original number was less than 1, the exponent is negative; if the original number was greater than 1, the exponent is positive. 762.20 = 7.62 x 10^2
 Exponents/320595: Write in decimal form: 6.20 x 10^-2 1 solutions Answer 229600 by nyc_function(2733)   on 2010-07-07 21:23:07 (Show Source): You can put this solution on YOUR website! To Change from Scientific Notation to Standard Form: (1) Move the decimal point to the right for positive exponents of 10. The exponent tells you how many places to move. (2) Move the decimal point to the left for negative exponents of 10. Again, the exponent tells you how many places to move. 6.20 x 10^-2 = 0.0620
 Numbers_Word_Problems/320598: i am confused about this math question, two less than a number y is seven times y. im not sure if the number is y or a different number like x1 solutions Answer 229599 by nyc_function(2733)   on 2010-07-07 21:19:31 (Show Source): You can put this solution on YOUR website!The statement "two less than a number y is seven times y" can be written in the following way: y - 2 = 7y. You need to solve for y. y - 2 = 7y y - 7y = 2 -6y = 2 y = 2/-6 y = -2/6 y = -1/3 Done!