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# Recent problems solved by 'stanbon'

stanbon answered: 57239 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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 Geometry_Word_Problems/311649: Explain using words how you would set up let statements and write an equation to solve the following word problem. “The length of the skating rink is 7 less than 3 times the width. If the perimeter of the skating rink is 82 feet, find the length and width of the skating rink." You do not need to solve this problem. 1 solutions Answer 222912 by stanbon(57307)   on 2010-06-05 22:43:26 (Show Source): You can put this solution on YOUR website!“The length of the skating rink is 7 less than 3 times the width. If the perimeter of the skating rink is 82 feet, find the length and width of the skating rink." -------------------------- P = 2(L+W) 82 = 2((3W-7)+W) 41 = 4W-7 4W = 48 W = 12 feet(width) --- L = 3W-7 = 36-7 = 29 feet (length) ============================================ Cheers, Stan H.
 test/311652: Your question goes here. Write clearly! We are not mind readers, so be sure to ask a question that we can understand.1 solutions Answer 222911 by stanbon(57307)   on 2010-06-05 22:35:24 (Show Source):
 Graphs/311650: how do you graph 3x-2y=1 and y=-1/2x+2. my answer is (5/4,11/8) i just don't know how to graph it. 1 solutions Answer 222909 by stanbon(57307)   on 2010-06-05 22:29:38 (Show Source): You can put this solution on YOUR website!how do you graph 3x-2y=1 and y=-1/2x+2. my answer is (5/4,11/8) i just don't know how to graph it. ------------------ y = (3/2)x-(1/2) y = (-1/2)x+2 -------------------- Graph y = (3/2)x-(1/2) Let x = 0, then y = -1/2 giving you point (0,-1/2) Let x = 2, then y = -1+2 = 3 giving you point (2,3) Plot the two points and draw a line thru them. ================================================== Graph y = (-1/2)x+2 Let x = 0, then y = 2 giving you point (0,2) Let x = 2, then y = -1+2 = 1 giving you point (2,1) Plot the two points and draw a line thru them. ================================================== ========================================================= Cheers, Stan H.
 percentage/311646: Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost \$450? 1 solutions Answer 222907 by stanbon(57307)   on 2010-06-05 22:17:13 (Show Source): You can put this solution on YOUR website!Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost \$450? --- Let "x" be the amount he pays. ---- x = 0.80(0.85*450) ----- x = \$306.00 ================ Cheers, Stan H.
 Finance/311648: An investment company pays 9% compounded semiannually. You want to have \$13000 in the future. How much should you deposit now to have that amount 5 years from now?1 solutions Answer 222906 by stanbon(57307)   on 2010-06-05 22:12:13 (Show Source): You can put this solution on YOUR website!An investment company pays 9% compounded semiannually. You want to have \$13000 in the future. How much should you deposit now to have that amount 5 years from now? ------------- A(t) = P(1+(r/n))^(nt) --- 13000 = P(1+(0.09/2))^(2*5) 13000 = P(1.045)^10 13000 = P(1.553) P = \$8371.06 =================== Cheers, Stan H.
 Polynomials-and-rational-expressions/311647: A boxing ring is in the shape of a square, 20 feet on each side. How far apart are the fighters when they are in opposite corners of the ring?1 solutions Answer 222904 by stanbon(57307)   on 2010-06-05 22:05:57 (Show Source): You can put this solution on YOUR website!A boxing ring is in the shape of a square, 20 feet on each side. How far apart are the fighters when they are in opposite corners of the ring? ------------------------------------- Draw the picture. Draw a line from corner to opposite corner. ---- The corner to corner line is the hypotenuse of a right triangle. Use Pythagoras to find the length of the hypotenuse. ---- h^2 = 20^2 + 20^2 --- h^2 = 2*20^2 h = 20sqrt(2)feet ========================== Cheers, Stan H.
 Travel_Word_Problems/311639: Jose left the airport and traveled toward the mountains. Kayla left 2.1 hours later traveling 35 mph faster in an effort to catch up to him. After 1.2 hours Kayla finally caught up. Find Jose's average speed. 1 solutions Answer 222902 by stanbon(57307)   on 2010-06-05 22:00:03 (Show Source): You can put this solution on YOUR website!Jose left the airport and traveled toward the mountains. Kayla left 2.1 hours later traveling 35 mph faster in an effort to catch up to him. After 1.2 hours Kayla finally caught up. Find Jose's average speed ------ Jose DATA: time = 2.1+1.2 = 3.3 hrs ; rate = x mph ; distance = 3.3x miles --------------- Kayla DATA: time = 1.2 hrs ; rate = x+35 mph ; distance = 1.2(x+35) = 1.2x + 42 miles --------------------- Equation: distance = distance 3.3x = 1.2x + 42 2.1x = 42 x = 20 mph (Jose's average speed) ======================================= Cheers, Stan H.
 Quadratic_Equations/311591: 2x^2-5x=-7 need the solution set= {_____}1 solutions Answer 222848 by stanbon(57307)   on 2010-06-05 18:15:29 (Show Source): You can put this solution on YOUR website!2x^2-5x=-7 --- 2x^2-5x+7 = 0 --- 2x^2-7x+2x+7 = 0 x(2x-7)+(2x+7) = 0 (2x-7)(x+1) = 0 x = 7/2 or x = -1 need the solution set= {7/2 , -1} ==================================== Cheers, Stan H. =================
 Polynomials-and-rational-expressions/311589: Find a polynomial for the perimeter and area but do not factor. A square is pictured with y+3 on top and y on side. The perimeter= The area=1 solutions Answer 222846 by stanbon(57307)   on 2010-06-05 18:11:19 (Show Source): You can put this solution on YOUR website!Find a polynomial for the perimeter and area but do not factor. A square is pictured with y+3 on top and y on side. ----------------------------------------------- The perimeter = 2[(y+3)+y] = 3[2y+3] = 6y + 9 -------------------- The area = y(y+3) = y^2+3y ============================== Cheers, Stan H.
 Graphs/311586: Symmetry of a Graph y=x^2-9 Please Help!!!!!!!!!!!! Thanks, Stephanie Jackins1 solutions Answer 222845 by stanbon(57307)   on 2010-06-05 18:05:58 (Show Source): You can put this solution on YOUR website!Symmetry of a Graph f(x) = x^2-9 --------------------- f(-x) = (-x)^2 - 9 = x^2-9 --------------------- -f(-x) = -x^2+9 ========================== Since f(x) = f(-x) the graph is symmetric to the y axis. ---- Since f(x) is not equal to -f(-x) the graph is not symmetric to the origin. ============================================================================ Cheers, Stan H.
 Quadratic_Equations/311577: Please help me solve this quadratic equation: 1 solutions Answer 222844 by stanbon(57307)   on 2010-06-05 17:20:02 (Show Source): You can put this solution on YOUR website!solve this quadratic equation: 36x^2+84x+49=0 ------------ Factor to get: (6x+7)(6x+7) = 0 6x+7 = 0 6x = -7 x = -7/6 with multiplicity 2. ================================ Cheers, Stan H.
 Distributive-associative-commutative-properties/311581: is xz+xy = xz+yz and xz+xy = xy + xz both using the commutative property of multiplicaction?1 solutions Answer 222843 by stanbon(57307)   on 2010-06-05 17:14:56 (Show Source): You can put this solution on YOUR website!is xz+xy = xz+yz --- The terms have been cummuted under the commutative addition property. ------------------------------------------ and xz+xy = xy + xz The terms are commuted under addition and the factors of one of the terms are commuted under multiplication. ------------------------------------------ --------------------- Cheers, Stan H.
 Numbers_Word_Problems/311582: If 9 is subtracted from seven times a certain number, the result is the same as if 23 is added to three times the number. Find the number.1 solutions Answer 222841 by stanbon(57307)   on 2010-06-05 17:03:45 (Show Source): You can put this solution on YOUR website!If 9 is subtracted from seven times a certain number, the result is the same as if 23 is added to three times the number. Find the number. ------------------- Let the number be "x": Equation: 7x-9 = 3x+23 --- 4x = 32 x = 8 ----------- Cheers, Stan H.
 Quadratic_Equations/311558: How do you solve for the equation (5x+5)^2=100 ? thanks1 solutions Answer 222834 by stanbon(57307)   on 2010-06-05 14:55:21 (Show Source): You can put this solution on YOUR website!How do you solve for the equation (5x+5)^2=100 ? thanks --- You rearrange: (5x+5)^2 - 100 = 0 --- You rewrite: (5x+5)^2 - 10^2 = 0 --- You factor: (5x+5 - 10)(5x+5+10) = 0 --- You simplify: (5x-5)(5x+15) = 0 --- You solve: 5x = 5 or 5x = -15 x = 1 or x = -3 ========================== Cheers, Stan H. ==========================
 Linear-equations/311535: Can you please email me the formula and explaination of how to find the slope of a line?1 solutions Answer 222833 by stanbon(57307)   on 2010-06-05 14:51:18 (Show Source): You can put this solution on YOUR website!Can you please email me the formula and explaination of how to find the slope of a line? ------------------ If you have two points, (a,b) and (c,d) --- slope = (change in y)/(change in x) ----- So, slope = (d-b)/(c-a) =========================== Cheers, Stan H.
 Radicals/311537: find the following. assume that variables can represent any real number square root (a+5)^21 solutions Answer 222832 by stanbon(57307)   on 2010-06-05 14:48:54 (Show Source): You can put this solution on YOUR website!find the following. assume that variables can represent any real number square root (a+5)^2 = (a+5)(a+5) --- = a(a+5) + 5(a+5) --- = a^2 + 5z + 5a + 25 --- = a^2 + 10a + 25 ==================== Cheers, Stan H. ====================
 Geometry_Word_Problems/311556: The base of a triagle is 6cm greater than the height. The area is 36cm^2. Find the height and the length of the base.1 solutions Answer 222831 by stanbon(57307)   on 2010-06-05 14:44:49 (Show Source): You can put this solution on YOUR website!The base of a triangle is 6cm greater than the height. The area is 36cm^2. Find the height and the length of the base. ------------------ Area = (1/2)bh 36 = (1/2)*(h+6)h h^2 + 6h - 72 = 0 Factor: (x+12)(x-6) = 0 Positive solution: ----- h = 6 (height) h+6 = 12 (base) ================ Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/311557: find three consecutive integers sum that three times the first minus the second is one more than third 2. A number it two times the difference between eighteen and a number find the number1 solutions Answer 222830 by stanbon(57307)   on 2010-06-05 14:38:04 (Show Source): You can put this solution on YOUR website!find three consecutive integers such that three times the first minus the second is one more than third --- 1st: x 2nd: x+1 3rd: x+2 --- Equation: 3(x) - (x+1)= x+3 3x-x-1 = x+3 2x -1 = x+3 x = 4 x+1 = 5 x+2 = 6 ---------------- 2. A number is two times the difference between eighteen and a number find the number --- Let the number be "x": x = 2(18-x) x = 36 -2x 3x = 36 x = 12 =============== Cheers, Stan H.
 Equations/311440: Please help me solve this for x: 1 solutions Answer 222773 by stanbon(57307)   on 2010-06-04 21:02:20 (Show Source): You can put this solution on YOUR website!8xp=tyz --------- Divide both sides by 8p to get: x = (tyz)/(8p) =================== Cheers, Stan H.
 Linear-equations/311435: 7. Which of the following are functions? Explain your reasoning for a, b, and c. Keep the definition of a function strongly in mind as you do this problem, it is not nearly as difficult as it may look. Think about whether the relationship between f(x) and x is consistent with being a function or not and explain your reasoning. Problems b & c are multi part relations so consider all parts when deteriming if they are funcitons. a. f(x) = x 8 b. f(x) = 45 if x>2 otherwise f(x) = -4 c. f(x) = 4 if x>0 or f(x) = -4 if x<0 or f(x) = 4 or -4 if x = 0 1 solutions Answer 222772 by stanbon(57307)   on 2010-06-04 21:00:45 (Show Source): You can put this solution on YOUR website!Which of the following are functions? Explain your reasoning for a, b, and c. Keep the definition of a function strongly in mind as you do this problem, it is not nearly as difficult as it may look. Think about whether the relationship between f(x) and x is consistent with being a function or not and explain your reasoning. Problems b & c are multi part relations so consider all parts when deteriming if they are funcitons. a. f(x) = x^8 It is a function ------------------------- b. f(x) = 45 if x>2 otherwise f(x) = -4 It is a function ------------------------- c. f(x) = 4 if x>0 or f(x) = -4 if x<0 or f(x) = 4 or -4 if x = 0 No because f(0) has two values, 4 and -4 ================================================ Cheers, Stan H.
 Square-cubic-other-roots/311438: Please help me solve for x. Everything but "y" is under the square root sign: 1 solutions Answer 222770 by stanbon(57307)   on 2010-06-04 20:57:02 (Show Source): You can put this solution on YOUR website!Please help me solve for x. Everything but "y" is under the square root sign: y=sqrt[w^2+(x-z)^2] ----- y^2 = w^2 + (x-z)^2 --- (x-z)^2 = y^2-w^2 --- x-z = sqrt(y^2-w^2) x = sqrt(y^2-w^2)+z ========================= Cheers, Stan H.
 Linear-equations/311437: How do you write the following question in point-slope form? Goes through the points (4,2) parellel to y=-3/4x-51 solutions Answer 222769 by stanbon(57307)   on 2010-06-04 20:54:02 (Show Source): You can put this solution on YOUR website!How do you write the following question in point-slope form? Goes through the points (4,2) parellel to y=-3/4x-5 --- Parallel to that line means the slope must be -3/4 -------------------------------------------------- Eq. Form: y = mx + b 2 = (-3/4)*4 + b b = 2+3 b = 5 ----- Equation: y = (-3/4)x + 5 ================= Cheers, Stan H. =================
 Linear-equations/311436: 48 For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function. Explain your reasoning thoroughly. a. The time it takes you to get to work as a function the speed at which you drive b. The probability of getting into a car accident as a function of the speed at which you drive c. A person's height as a function of the person's age (from age 0 to 100) 1 solutions Answer 222768 by stanbon(57307)   on 2010-06-04 20:51:11 (Show Source): You can put this solution on YOUR website!For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function. Explain your reasoning thoroughly. a. The time it takes you to get to work as a function the speed at which you drive --- time and speed are directly related so best described by linear function. ---------------------------------------- b. The probability of getting into a car accident as a function of the speed at which you drive Increasing speed from 10 to 20 does not have the same effect on safety as increasing the speed from 55 to 65. Non-linear ----------------------------- c. A person's height as a function of the person's age (from age 0 to 100) Non-linear =============== Cheers, Stan H.
 Linear-equations/311397: Find an equation in slope-intercept form (if possible) Through (-8,1), with undefined slope1 solutions Answer 222767 by stanbon(57307)   on 2010-06-04 20:47:14 (Show Source): You can put this solution on YOUR website!Undefined slope means the line is vertical. If it passes thru (-8,1), it must pass thru all points where x = -8. ---- The equation is x = -8 ============================== Cheers, Stan H.
 Inequalities/311406: |(3x-2)/(2x-3)|=21 solutions Answer 222766 by stanbon(57307)   on 2010-06-04 20:44:31 (Show Source): You can put this solution on YOUR website!|(3x-2)/(2x-3)|=2 ----------------- (3x-2)/(2x-3) = 2 or (3x-2)/(2x-3) = -2 ----------------------------------------- 3x-2 = 4x-6 or 3x-2 = -4x+6 x = 4 or 7x = 8 x = 4 or x = 8/7 ===================== Cheers, Stan H.
 Probability-and-statistics/311421: A random sample of 10 miniature tootsie rolls was taken from a bag. Each piece was weighed n a very accurate scale. The results in grams were: 3.087,3.131,3.241,3.241,3.270,3.353,3.400,3.411,3.437,3.477 A)Construct a 90 percent confidence interval for the true mean weight. B)What sample size would be necessary to estimate the true weight with an error of +- 0.003 grams with 90 percent confidence? C)Discuss the factors which might cause variation in the weight of tootsie rolls during manufacture. (Data are from a project by MBA student Henry Scussel.) Tootsie 1 solutions Answer 222765 by stanbon(57307)   on 2010-06-04 20:41:10 (Show Source): You can put this solution on YOUR website!Answered Cheers, Stan H.
 Probability-and-statistics/311424: Need to make a circle graph of the findings: A college's complaints survey was taken and found the top five complaints to be as follows: not enough time (27) hard math questions (48) more venidng machine choices (12) high cost of books(32)and no free copying machine (8). 1 solutions Answer 222763 by stanbon(57307)   on 2010-06-04 20:40:19 (Show Source): You can put this solution on YOUR website!Need to make a circle graph of the findings: A college's complaints survey was taken and found the top five complaints to be as follows: not enough time (27) hard math questions (48) more venidng machine choices (12) high cost of books(32)and no free copying machine (8). ------------------------- Total # of complaints: 127 --- Convert each category number to approximate percentage: 27/127 = 21% --- 48/127 = 38% etc. ==== Using the %'s sketch pie-shaped segments of the circle to represent the size of the categories. ======================================== Note: It's a sketch so only need to be approximate in its representation of relative size. ======================================== Cheers, Stan H.
 Probability-and-statistics/311432: A random sample of 10 miniature tootsie rolls was taken from a bag. Each piece was weighed n a very accurate scale. The results in grams were: 3.087,3.131,3.241,3.241,3.270,3.353,3.400,3.411,3.437,3.477 A)Construct a 90 percent confidence interval for the true mean weight. B)What sample size would be necessary to estimate the true weight with an error of +- 0.003 grams with 90 percent confidence? C)Discuss the factors which might cause variation in the weight of tootsie rolls during manufacture. (Data are from a project by MBA student Henry Scussel.) Tootsie 1 solutions Answer 222758 by stanbon(57307)   on 2010-06-04 20:30:34 (Show Source): You can put this solution on YOUR website!A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.28 3.25 3.25 3.3 3.33 3.36 3.07 3.29 3.47 3.4 (a)Construct a 95 percent confidence interval for the true mean weight. x-bar: add them up and divide by 10 to get 3.3 and s = 0.1064 --- E ?: Using df=9 you get t= 2.262 E = 2.262*s/sqrt(n) = 2.262*0.1064/sqrt(10) = 0.07611 95% C.I.: 3.3-0.07611 < u < 3.3+0.0.07611 95% C.I.: 3.2239 < u < 3.3761 ------------------------------------------- (b) What sample size would be necessary to estimate the true weight with an error of ± 0.02 grams with 95 percent confidence? sqrt(n) = z*0.1064/E sqrt(n) = 1.96*0.064/0.02 n = 39.338 Rounding up: n = 40 =========================== (c) What factors might cause variation in the weight of Tootsie Rolls during manufacture? I'll leave that up to your imagination. ============================== Cheers, Stan H.
 Probability-and-statistics/311433: Catrina scored at the D9 level on a standardized reading test. About what percent of the students had scores above his score?1 solutions Answer 222756 by stanbon(57307)   on 2010-06-04 20:26:29 (Show Source): You can put this solution on YOUR website!D9 is 9 decile = 90%ile --- He has 10% above him. Cheers, Stan H.
 Geometry_Word_Problems/311420: If the diameter of a circle is 1.3 x 10-12power what is the radius?1 solutions Answer 222743 by stanbon(57307)   on 2010-06-04 19:39:29 (Show Source): You can put this solution on YOUR website!If the diameter of a circle is 1.3 x 10-12power what is the radius? ------------ r = (1/2)(1.3 x 10^-12) -------------------- 1.3x10-12 = 13x10-13 ----- So, r = (1/2)(13x10^-13) = 6.5x10^-13 ====================== Cheers, Stan H.
 Probability-and-statistics/311221: the proportion of students in private schools is around 11%. A random sample of 450 students from a wide geographic area indicated that 55 attended private schools. Estimate the true proportion of students attending private schools with 95% confidence. How does your estimate compare to 11%?1 solutions Answer 222738 by stanbon(57307)   on 2010-06-04 19:11:16 (Show Source): You can put this solution on YOUR website!the proportion of students in private schools is around 11%. A random sample of 450 students from a wide geographic area indicated that 55 attended private schools. Estimate the true proportion of students attending private schools with 95% confidence. --- p-hat = 55/450 = 0.1222 --- E = 1.96*sqrt[0.11*0.89/450] = 0.0288 =================================== 95% CI: 0.1222- 0.0288 < p < 0.1222+ 0.0288 95% CI: 0.934 < p < 0.1510 ---------------------------------- How does your estimate compare to 11%? The confidence inteval contains 11% ============================================== Cheers, Stan H.