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# Recent problems solved by 'stanbon'

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 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899, >>Next

 Distributive-associative-commutative-properties/673450: Simplify the expression and justify the steps? -36 ÷ (-12)1 solutions Answer 418670 by stanbon(57953)   on 2012-10-29 18:23:24 (Show Source): You can put this solution on YOUR website!Simplify the expression and justify the steps? -36 ÷ (-12) ---- = 3 ===== Cheers, Stan H.
 Distributive-associative-commutative-properties/673451: simplifying the expression and justifying the steps? 27rst + 27tsr1 solutions Answer 418666 by stanbon(57953)   on 2012-10-29 18:21:34 (Show Source): You can put this solution on YOUR website!27rst + 27tsr ------ = 54rst =========== Cheers, Stan H. ===========
 Distributive-associative-commutative-properties/673449: Simplifying the expression and justifying the steps? (3^3 - 3^3)(1 - 2^2)1 solutions Answer 418665 by stanbon(57953)   on 2012-10-29 18:19:45 (Show Source): You can put this solution on YOUR website!Simplifying the expression and justifying the steps? (3^3 - 3^3)(1 - 2^2) ----- (27-27)(1-4) ---- 0*(-3) ---- = 0 ========== Cheers, Stan H.
 test/673444: 2x+15=27-4x1 solutions Answer 418664 by stanbon(57953)   on 2012-10-29 18:17:56 (Show Source): You can put this solution on YOUR website!2x+15=27-4x ---- 6x = 12 x = 2 --------------- Cheers, Stan H.
 Equations/673441: How do I factor (x-3)^2-2251 solutions Answer 418663 by stanbon(57953)   on 2012-10-29 18:16:29 (Show Source): You can put this solution on YOUR website!factor (x-3)^2-225 ---- You have the difference of squares: --- = (x-3)^2 - 15^2 ------------------- Factor: [(x-3)-15] ----- = (x-18)(x+12) =============== Cheers, Stan H. ===============
 Geometry_Word_Problems/673436: If you have a 108 square feet then enclose it by sqaure what is the length and width? 1 solutions Answer 418662 by stanbon(57953)   on 2012-10-29 18:13:38 (Show Source): You can put this solution on YOUR website!If you have a 108 square feet then enclose it by square what is the length and width? ---- Length = Width = sqrt(108) = sqrt(36*3) = 6sqrt(3)ft. ==================== Cheers, Stan H. ====================
 Quadratic-relations-and-conic-sections/673437: Which of the following equations is of an ellipse with x-intercepts at (1, 0) and (-1, 0), y-intercepts at (0, 3) and (0, -3), and center at (0, 0)? 1 solutions Answer 418661 by stanbon(57953)   on 2012-10-29 18:09:18 (Show Source): You can put this solution on YOUR website!Option answers not posted.
 Percentage-and-ratio-word-problems/673418: Before Christmas an item was marked up 20%. What percent will the new price have to be marked down in order to sell for the original price?1 solutions Answer 418660 by stanbon(57953)   on 2012-10-29 18:08:07 (Show Source): You can put this solution on YOUR website!Before Christmas an item was marked up 20%. What percent will the new price have to be marked down in order to sell for the original price? ----- Let original price be "x". ---- After mark up the price was 1.2x ------- Equation to get back to original price: k(1.2x) = x k = 1/1.2 k = 10/12 k = 0.8333 = ----- It will have to be marked down 100-0.8333 = 16 2/3% =========================== Cheers, Stan H. ===========================
 Geometry_proofs/673399: Do midpoints ALWAYS separate congruent lines? such as: (segment)AG where X is the mid point, would (segment)AX be congruent to (segment)XG? 1 solutions Answer 418647 by stanbon(57953)   on 2012-10-29 17:08:46 (Show Source): You can put this solution on YOUR website!Yes. The midpoint separates congruent line segments. Cheers, Stan H. ===============
 Geometry_proofs/673397: given that <1 and <5 are supplementary. prove that m is parallel to n1 solutions Answer 418644 by stanbon(57953)   on 2012-10-29 17:06:38 (Show Source): You can put this solution on YOUR website!insufficient information
 test/673394: The air show has 5 more biplanes and gliders. Together there are 23 flying machines. How many biplanes are there?1 solutions Answer 418641 by stanbon(57953)   on 2012-10-29 17:01:12 (Show Source): You can put this solution on YOUR website!The air show has 5 more biplanes then gliders. Together there are 23 flying machines. How many biplanes are there? ---- Let # of gliders be "x". Then # of biplanes is "x+5". ----- Equation: x + x+5 = 23 2x = 18 x = 9 (# of gliders) x+5 = 14 (3 of biplanes) --------- Cheers, Stan H.
 Age_Word_Problems/673393: Three friends drove west into Illinois. Kyle drove half as far as jamaal. Conner drove 4 times as far as Kyle. Altogether they drove 357 miles. How far did each drive?1 solutions Answer 418638 by stanbon(57953)   on 2012-10-29 16:56:20 (Show Source): You can put this solution on YOUR website!Three friends drove west into Illinois. Kyle drove half as far as jamaal. Conner drove 4 times as far as Kyle. Altogether they drove 357 miles. How far did each drive? ------ Assume Jamaal drove "2x" miles Then Connor drove "8x" miles And Kyle drove "x" miles ------------------------------- Equation: x + 2x 8x = 357 x = 32.45 (Kyle"s distance) 2x = 64.9 (Jamaaal's distance) 8x = 259.64 miles (Connor's distance) ---- Cheers, Stan H. ===========
 test/673390: Stephanienn1@yahoo.com 1 solutions Answer 418636 by stanbon(57953)   on 2012-10-29 16:48:36 (Show Source):
 Evaluation_Word_Problems/673389: George earns \$30 plus tips each day. Write an expression to show his total day pay. If George receives \$8 in tips yesterday, how much did he earn in all?"1 solutions Answer 418635 by stanbon(57953)   on 2012-10-29 16:47:36 (Show Source): You can put this solution on YOUR website!George earns \$30 plus tips each day. Write an expression to show his total day pay. If George receives \$8 in tips yesterday, how much did he earn in all?" ---- total day pay = 30 + 8 = 38 dollars ------------------------- Cheers, Stan H. --------
 Probability-and-statistics/673195: the amount of chemical W used to manufacture certain detergents vary, depending on the concentration and use of the required detergent. company records show that the amounts used are normally distributed. futher, they indicate that the chances of any detergent having at least 2.4grams of this chemical are 2.28% while the chances of having less than 1.4grams are 30.85% a) determine the probability of a detergent having i)more than 1.2grams but not exceeding 2.6grams of the chemical ii)either less than 0.4grams, exactly 0.8grams or more than 2.8grams1 solutions Answer 418621 by stanbon(57953)   on 2012-10-29 16:00:32 (Show Source): You can put this solution on YOUR website!the chances of any detergent having at least 2.4grams of this chemical are 2.28% while the chances of having less than 1.4grams are 30.85% --------- The z-value with a right tail of 2.28% is z = invNorm(0.9772) = 1.9991 The z-value with a left tail of 30.85% is z = invNorm(0.3085) = 0.5001 Equations based on x = z*s + u 2.4 = 1.9991*s + u 1.4 = 0.5001*s + u ------- Subtract to solve for "s": 1 = 1.499s s = 0.667 ---- Solve for "u": 2.4 = 1.9991*0.667 + u u = 1.0666 a) determine the probability of a detergent having i)more than 1.2grams but not exceeding 2.6grams of the chemical z(1.2) = (1.2-1.0666)/0.667 = 0.1999 z(2.6) = (2.6-1.0666)/0.667 = 2.2990 ----- P(1.2 < x < 2.6) = P(0.1999 < z < 2.2990) = 0.4100 --------------------------------------------------------- ii) either less than 0.4grams z(0.4) = (0.4-1.0666)/0.667 = -0.999 P(x < 0.4) = P(z < -0.999) = normalcdf(-100,-0.999) = 0.1589 ---------------- exactly 0.8grams P(x = 0.8) = 0 Why?:: The probability of ANY particular value in a continuous distribution is zero. ------------------------- more than 2.8grams z(2.8) = (2.8-1.0666)/0.667 = 2.5987 P(x > 2.8) = P(z > 2.5987) = normalcdf(2.5987,100) = 0.0047 =============================================================== cheers, Stan H. =======================
 Probability-and-statistics/673338: A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 35, how many individuals were in the sample1 solutions Answer 418610 by stanbon(57953)   on 2012-10-29 15:32:35 (Show Source): You can put this solution on YOUR website!A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 35, how many individuals were in the sample ------- Ans: n = 36 ============ Cheers, Stan H.
 Functions/673251: Verify that the function f -1 (x)= x-1/2 is the inverse of f(x)= 2x+1 by showing that f (f-1(x))=f-1(f(x))=x. 1 solutions Answer 418549 by stanbon(57953)   on 2012-10-29 11:30:48 (Show Source): You can put this solution on YOUR website!Verify that the function f -1 (x)= (x-1)/2 is the inverse of f(x)= 2x+1 by showing that f (f-1(x))=f-1(f(x)) = x. ------ f^-1[f(x)] = f^-1[2x+1] = (2x+1-1)/2 = 2x/2 = x ---------------- f[f^-1(x)] = f[(x-1)/2] = 2[(x-1)/2]+1 = x-1+1 = x =========================== cheers, Stan H. ============
 Triangles/673252: what are my dimensions for a 90 degree triangle with a length of 11' 8" 1 solutions Answer 418548 by stanbon(57953)   on 2012-10-29 11:25:02 (Show Source): You can put this solution on YOUR website!insufficient information
 Quadratic_Equations/673245: Find the length of the shorter leg of a right triangle if the longer leg is 12 feet more than the shorter leg and the hypotenuse is 12 feet less than twice the shorter leg. 1 solutions Answer 418547 by stanbon(57953)   on 2012-10-29 11:23:39 (Show Source): You can put this solution on YOUR website!Find the length of the shorter leg of a right triangle if the longer leg is 12 feet more than the shorter leg and the hypotenuse is 12 feet less than twice the shorter leg. ---- Let the shorter leg be "x". Other leg: "x+12" Hypotenuse: "2x-12" ------- Equation: (2x-12)^2 = x^2 + (x+12)^2 ------- 4x^2 - 48x + 144 = 2x^2 + 24x + 144 ------ 2x^2 - 72x = 0 2x(x-36) = 0 Positive solution: x = 36 (shorter leg) x+12 = 48 (longer leg) 2x-12 = 60 (hypotenuse) ---------------------- Cheers, Stan H.
 Radicals/673234: Multiply the radical expressions. a.) √3 × √15 b.) √8 × √12 1 solutions Answer 418537 by stanbon(57953)   on 2012-10-29 10:59:02 (Show Source): You can put this solution on YOUR website! Multiply the radical expressions. a.) √3 × √15 ----- = sqrt(45) = sqrt(9*5) = sqrt(9)*sqrt(5) = 3sqrt(5) -------------------------- b.) √8 × √12 = 2sqrt(2) * 2sqrt(3) = 4sqrt(6) =============================================== Cheers, Stan H.
 Money_Word_Problems/673235: the bank loaned out \$17,000, part of it at the rate of 8% per year and the rest at 18% per year. If the interest received in one year totaled \$2000, how much was loaned at 8%?1 solutions Answer 418534 by stanbon(57953)   on 2012-10-29 10:56:34 (Show Source): You can put this solution on YOUR website!answered
 logarithm/673239: given, ln(3y+2)=5ln(x-1)-ln(2-x)-x 1)determine the range of x and y. 2)find y explicitly as a function of x. thanks. 1 solutions Answer 418531 by stanbon(57953)   on 2012-10-29 10:55:01 (Show Source): You can put this solution on YOUR website!ln(3y+2)=5ln(x-1)-ln(2-x)-x 1)determine the range of x and y. Those anti-logs must ALL be positive. y has to be > -2/3 x has to be greater than 1 but less than 2 ---- Domain: All Real Numbers greater than 1 but less than 2 Range: All Real Numbers greater than -2/3 ---- 2)find y explicitly as a function of x. ln(3y+2) = ln[(x-1)^5/(2-x)] - x ----- That looks like a mess but here goes: --- 3y+2 = 10^[ln[(x-1)^5/(2-x)] - x] ---- y = [10^[ln[(x-1)^5/(2-x)] - x]- 2]/3 ============================================= Cheers, Stan H. ================
 Money_Word_Problems/673237: the bank loaned out \$17,000, part of it at the rate of 8% per year and the rest at 18% per year. If the interest received in one year totaled \$2000, how much was loaned at 8%? How much of the \$17,000 did the bank loan out at 8%?1 solutions Answer 418527 by stanbon(57953)   on 2012-10-29 10:42:00 (Show Source): You can put this solution on YOUR website!the bank loaned out \$17,000, part of it at the rate of 8% per year and the rest at 18% per year. If the interest received in one year totaled \$2000, how much was loaned at 8%? How much of the \$17,000 did the bank loan out at 8%? ------- Quantity Eq::: x + y = 17000 Interest Eq:::0.08x + 0.18y = 2000 ---------------------------------- Multiply thru 1st by 8 Multiply thru 2nd by 100 ------ 8x + 8y = 8*17000 8x +18y = 100*2000 ------ 10y = 64000 y = \$6400 (amt. invested at 18% ---- Solve for "x" using x + y = 17000 x = 17000-6400 = \$10,600 (amt. invested at 8%) ------ Cheers, Stan H. =================
 Travel_Word_Problems/673238: An airplane pilot requests a change in altitude from 32,000 feet to 36,000 feet to aviod bad weather. What is the percentage gain in altitude? 1 solutions Answer 418526 by stanbon(57953)   on 2012-10-29 10:34:10 (Show Source): You can put this solution on YOUR website!An airplane pilot requests a change in altitude from 32,000 feet to 36,000 feet to aviod bad weather. What is the percentage gain in altitude? --------------------------- Quantity Gain: 36000-32000 = 4000 ---- Percent Gain: 4000/32000 = 1/8 = 12.5% ============== Cheers, Stan H. ==============
 Linear-systems/673232: I need help. The directions are solve each system. If the system has in infinate solution set, specify it and give three solutions. If the system has no solution, say so. The prolem is: d = 2 - 6c (1/2)d - c = 11 solutions Answer 418525 by stanbon(57953)   on 2012-10-29 10:29:43 (Show Source): You can put this solution on YOUR website!The prolem is: d = 2 - 6c (1/2)d - c = 1 ----- Substitute for "d" and solve for "c": (1/2)(2-6c) - c = 1 ---- 1 - 3c - c = 1 -4c = 0 c = 0 -------- Solve for "d" using d = 2 - 6c d = 2 - 6*0 d = 2 =============== Cheers, Stan H. ===============
 Evaluation_Word_Problems/673226: A) Find an equation in the form ax^2+bx+c=0 that can be used to determine the first year in which the population of US prisons was approximately 1216 people. P=2x^2+18x+332 Do Not Solve Yet B)Now factorthe equation to solve it and specify the first year in which the population was approximately 1216 thousand people. Any help would be very much appreciated. Thank you.1 solutions Answer 418523 by stanbon(57953)   on 2012-10-29 09:58:56 (Show Source): You can put this solution on YOUR website!A) Find an equation in the form ax^2+bx+c=0 that can be used to determine the first year in which the population of US prisons was approximately 1216 people. P(x) = 2x^2+18x+332 --- Solve: 2x^2+18x+332-1216 = 0 2x^2 + 18x - 884 = 0 Do Not Solve Yet --------------------- B)Now factor the equation to solve it and specify the first year in which the population was approximately 1216 thousand people. x^2 + 9x - 442 = 0 (x-17)(x+26) = 0 --- Positive solution: x = 17 years ================== Cheers, Stan H. ==================
 expressions/673217: Pleas Solve 4/(x+3) + 3/(2x-1) =1 4(2x-1)/(x+3)(2x-1) + 3(x+3)/(x+3)(2x-1)1 solutions Answer 418522 by stanbon(57953)   on 2012-10-29 09:51:17 (Show Source): You can put this solution on YOUR website!4/(x+3) + 3/(2x-1) =1 Multiply thru by (x+3)(2x-1) to get: 4(2x-1) + 3(x+3) = (x+3)(2x-1) 8x-4+3x+9 = 2x^2+5x-3 2x^2 -6x -8 = 0 x^2 -3x -4 = 0 Factor: (x-4)(x+1) = 0 x = 4 or x = -1 ============================= 4(2x-1)/(x+3)(2x-1) + 3(x+3)/(x+3)(2x-1) ---- The denominators are the same, so just add the numerators over the common denominator. --- = [8x-4+3x+9]/[(x+3)(2x-1)] --- = [12x+5] / [(x+3)(2x-1)] ================= Cheers, Stan H. ===================
 Functions/673214: how do i state the domain of: g(x)=x^2-1/x^2+1 and then: l(x)=|5-4x|? Does y=4/2x+3 define y as a function of x? I believe it does because there is an x in the equation. However i dont kow how to show my work for that. Finally how do i write a cost function for this equation: a car rental charges \$65, per day plus .45 cents per miles?1 solutions Answer 418521 by stanbon(57953)   on 2012-10-29 09:09:30 (Show Source): You can put this solution on YOUR website!how do i state the domain of: g(x)= (x^2-1)/(x^2+1) ---- That denominator cannot be zero. But, no matter what value "x" takes THAT denominator will not be zero. So the domain is "All Real Numbers". ---------------------------------------- and then: L(x)=|5-4x| Domain is "All Real Numbers" ---------------------------------------- Does y=4/(2x+3) define y as a function of x? Ans: Yes, because for each value of "x" there is only one value of "y". ---------------------------------------- Finally how do i write a cost function for this equation: a car rental charges \$65, per day plus .45 cents per miles? --- Let Let "d" be the numberf of days ; let "m" be the number of miles. --- C(d,m) = 65d + 0.45m ======================== Cheers, Stan H. =========================
 Graphs/673203: Graph each line from the given information; then find the equation in general form for each line. Through (1,2) and parallel to 4x+y-1=0 (draw both lines, then find the equation.)1 solutions Answer 418519 by stanbon(57953)   on 2012-10-29 09:01:36 (Show Source): You can put this solution on YOUR website!Through (1,2) and parallel to 4x+y-1=0 --------------------- Find the slope of the given line: y = -4x+1 slope = -4 ---- All lines parallel to it must have slope = -4 ---- Form: y = mx + b Solve for "b": 2 = -4*1 + b b = 6 ------ Equation of your line: y = -4x + 6 ======================= Cheers, Stan H. =======================
 Linear_Equations_And_Systems_Word_Problems/673212: Suppose the cost to produce 10 units of a product is \$20 and the cost to produce 20 units is \$70. Find the equation of the line, then find the cost to produce 35 units. I'm using excel and your help is greatly appreciated.1 solutions Answer 418518 by stanbon(57953)   on 2012-10-29 08:56:34 (Show Source): You can put this solution on YOUR website!Suppose the cost to produce 10 units of a product is \$20 and the cost to produce 20 units is \$70. Find the equation of the line, then find the cost to produce 35 units. ----- You have 2 points:: (10,20) and (20,70) --- slope = (70-20)/(20-10) = 50/10 = 5 ------- Form:: y = mx + b Solve for "b": 20 = 5*10 + b b = -30 ---- Equation: y = 5x - 30 =================== Cheers, Stan H. ===================
 logarithm/673206: can you please solve log 4.6 -log 1.6 and then find the antilog1 solutions Answer 418517 by stanbon(57953)   on 2012-10-29 08:50:42 (Show Source): You can put this solution on YOUR website!solve log 4.6 -log 1.6 and then find the antilog ---- log(4.6)-log(1.6) = log[4.6/1.6]l = log[2.875] = 0.4586 --- anti-log(0.4586) = 10^0.4586 = 2.875 =========================== Cheers, Stan H.