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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, >>Next

 Exponents-negative-and-fractional/434013: evaluate the following expresion 6^-3 as a fraction1 solutions Answer 300787 by stanbon(57224)   on 2011-04-10 21:44:26 (Show Source): You can put this solution on YOUR website!evaluate the following expresion 6^-3 as a fraction ------- 6^(-3) = (1/6)^3 = 1/216 ============================= Cheers, Stan H. ============
 Geometry_Word_Problems/434006: Jamal sees a tree on the shore directly across a lake and wonders what the distance is across the lake to the tree. He turns 90 degrees to the right and walks in a straight line for 100 meters. Jamal turns to face the tree and finds the angle between his line of sight and his path measures 25 degrees. Which of the following is closest to the distance, in meters, from Jamal's intial position on the tree? (note: sin-25 degrees=0.42, cos degrees=0.91, tan 25 degrees=0.47) a)42 b)47 c)91 d)213 e)2381 solutions Answer 300786 by stanbon(57224)   on 2011-04-10 21:42:46 (Show Source): You can put this solution on YOUR website!Jamal sees a tree on the shore directly across a lake and wonders what the distance is across the lake to the tree. He turns 90 degrees to the right and walks in a straight line for 100 meters. Jamal turns to face the tree and finds the angle between his line of sight and his path measures 25 degrees. Which of the following is closest to the distance, in meters, from Jamal's intial position on the tree? ----------------------- Draw the picture. You have a right triangle with base = 100 m, and angle opposite the distance across the lake equal to 25 degrees. --- Let dist. across lake be "x": tan(25 degree) = x/100 x = 100*tan(25 degrees) x = 100*0.4663 x = 46.63 meters --------------------- Cheers, Stan H. =============== a)42 b)47 c)91 d)213 e)238
 Angles/434009: Draw 2 supplementary angles. One angle is x-15 degrees and one is 2x degrees. What is the value of x in degrees?1 solutions Answer 300779 by stanbon(57224)   on 2011-04-10 21:35:23 (Show Source): You can put this solution on YOUR website!Draw 2 supplementary angles. One angle is x-15 degrees and one is 2x degrees. What is the value of x in degrees? --- If the 2 angles are supplementary their sum is 180 degrees. ----- Equation: 2x + (x-15) = 180 3x = 195 x = 63 degrees ==================== Cheers, Stan H.
 Surface-area/433996: one face of a cubed-shape package has an area of 7 and five sixth inches.what is the closest total suface area of the package1 solutions Answer 300764 by stanbon(57224)   on 2011-04-10 21:02:49 (Show Source): You can put this solution on YOUR website!one face of a cubed-shape package has an area of 7 and five sixth sq in. What is the closest total suface area of the package ----- There are six faces on a cube. Total area = 6(7 5/6)) = 6(47/6) = 47 sq. in ============== Cheers, Stan H.
 Expressions-with-variables/433994: Hello. May I have some assistance. I have a test and am having trouble with some. here it is. Solve by substitution method. 8x+6y=-2 and -6x+y=51 must be typed as an ordered pair. thank you1 solutions Answer 300762 by stanbon(57224)   on 2011-04-10 20:59:18 (Show Source): You can put this solution on YOUR website!Solve by substitution method. 8x+6y=-2 -6x+y=51 ----- Solve the 2nd equation for "y": y = 6x+51 ----- Substitute into the 1st and solve for "x": 8x+6(6x+51) = -2 8x+36x+306 = -2 44x = -308 x = -7 ----- Solve for "y": y = 6x+51 y = 6*-7+51 y = -42+51 y = 9 ----------------- Ans: (-7,9) =============== cheers, Stan H. ===========
 Miscellaneous_Word_Problems/433991: what is the sum of the 2 solutions of the equation x^2-3x-28=0? a) 7, b) 3, c)0, d)-4, e)-281 solutions Answer 300759 by stanbon(57224)   on 2011-04-10 20:55:03 (Show Source): You can put this solution on YOUR website!what is the sum of the 2 solutions of the equation x^2-3x-28=0? --- The sum of the 2 answers to any quadratic equation is 2(-b/(2a)) = -b/a --- Your Problem: The sum is 3/1 = 3 ----------------------- cheers, Stan H. ========================= a) 7, b) 3, c)0, d)-4, e)-28
 Triangles/433988: the Monongahela incline, in Pittsburgh, PA is 635 feet long with a vertical rise of 369.39 feet. Determine the incline of the Monongahela incline. 1 solutions Answer 300757 by stanbon(57224)   on 2011-04-10 20:52:40 (Show Source): You can put this solution on YOUR website!the Monongahela incline, in Pittsburgh, PA is 635 feet long with a vertical rise of 369.39 feet. Determine the incline of the Monongahela incline. ----- If you are looking for the angle, invtan(369.39/635) = 30.187 degrees ------------------- Cheers, Stan H. ============
 Equations/433984: what is the exact value of the solution to this equation? 32.4=(68.4)r^121 solutions Answer 300756 by stanbon(57224)   on 2011-04-10 20:50:24 (Show Source): You can put this solution on YOUR website!what is the exact value of the solution to this equation? 32.4=(68.4)r^12 --- Divide to get: r^12 = 32.4/68.4 = 0.473684 Take the 12th root to get: r = 0.939531... Cheers, Stan H. =========
 Probability-and-statistics/433985: Copykwik has a four photocopy machines: A B C and D The probability that a given machine will break down ona particular day is P(A)= 1/50 P(B)= 1/60 P(C)= 1/75 P(D)= 1/40 assuming independence, what is the probability on a particular da that. a. All four machines break down? b. None of the machines will break down? 1 solutions Answer 300753 by stanbon(57224)   on 2011-04-10 20:47:17 (Show Source): You can put this solution on YOUR website!Copykwik has a four photocopy machines: A B C and D The probability that a given machine will break down ona particular day is P(A)= 1/50 P(B)= 1/60 P(C)= 1/75 P(D)= 1/40 assuming independence, what is the probability on a particular da that. a. All four machines break down? Multiply all those probabilities to get the answer to "A". ------------------------------------------------- b. None of the machines will break down? Subtract the answer of "A" from 1 to get the answer to "B". =================================================== Cheers, Stan H. ===========
 sets-and-operations/433982: How do I find the intersection: Given U {10,11,12,13,14,15,16,18,19,20} A{12,14,16,18,20} B{11,13,14,15,18,19,20} Find A intersect B1 solutions Answer 300752 by stanbon(57224)   on 2011-04-10 20:44:57 (Show Source): You can put this solution on YOUR website!How do I find the intersection: Given U {10,11,12,13,14,15,16,18,19,20} A{12,14,16,18,20} B{11,13,14,15,18,19,20} Find A intersect B ------- The intersection of Park Ave and 1st St. is the part of the road that is on Park and also on 1st. ---- Similarly: A intersect B = {14,18,20} because each of those is in both A and B. ====================== Cheers, Stan H.
 Probability-and-statistics/433974: A pair of dice is rolled. What are the odds against rolling a sum of 5? Thank you for your help!1 solutions Answer 300749 by stanbon(57224)   on 2011-04-10 20:41:52 (Show Source): You can put this solution on YOUR website!A pair of dice is rolled. What are the odds against rolling a sum of 5? ------------------------ To get a sum of 5 roll:1,4;2,3;3,2; or 4,1 So there are 4 of 36 ways to succeed. Then there are 32 way to fail. ----- odds against rolling sum of 5 = (32/36)/(4/36) = 8/1 = 8:1 --------------------- Cheers, Stan H.
 Numbers_Word_Problems/433978: which of the following is the same as five less than a number d is -401 solutions Answer 300746 by stanbon(57224)   on 2011-04-10 20:36:53 (Show Source): You can put this solution on YOUR website!Answer options not listed.
 expressions/433977: How do you solve -4(6+3x)=-46.1 solutions Answer 300745 by stanbon(57224)   on 2011-04-10 20:35:34 (Show Source): You can put this solution on YOUR website!solve -4(6+3x)=-46 -24-3x = -46 3x = -24+46 3x = 22 x = 7 1/3 ============== Cheers, Stan H. ==================
 Miscellaneous_Word_Problems/433971: Tracy is trying to find a wrench to fit a bolt. The 3/8-inch wrench is too large, and the 5/16-inch wrench is too small. Which of the following could be the size of the wrench that will fit the bolt exactly? a)1/4-inch, b) 9/32-inch, c) 11/32-inch, d) 25/64, e) 13/32-inch1 solutions Answer 300744 by stanbon(57224)   on 2011-04-10 20:33:23 (Show Source): You can put this solution on YOUR website!Tracy is trying to find a wrench to fit a bolt. The 3/8-inch wrench is too large, and the 5/16-inch wrench is too small. --- Let x be the proper size: 5/16< x < 3/8 --- Changing to various denominators: ------------------------- 5/16< x < 6/16 ------------------------ (5/4)/4 < x < (3/2)/4 ------------------------ 10/32< x < 12/32 -------------------------- 20/64< x < 24/64 ------------------------ Which of the following could be the size of the wrench that will fit the bolt exactly? a) 1/4-inch::::no b) 9/32-inch:::no c) 11/32-inch::yes d) 25/64-inch::no e) 13/32-inch::no ====================== Cheers, Stan H.
 logarithm/433968: Express as a single logarithm and, if possible, simplify. (((logb 3x + 6(logb x - logb y) ))))1 solutions Answer 300743 by stanbon(57224)   on 2011-04-10 20:23:52 (Show Source): You can put this solution on YOUR website!logb 3x + 6(logb x - logb y) ------ logb(3x) + 6logb(x)-6logb(y) ------ = logb(3x) + logb(x^6) - logb(y^6) ------ = logb[3x*x^6/y^6] --- = logb[3x^7/y^6] ============================ Cheers, Stan H. =================
 Polynomials-and-rational-expressions/433942: I am having trouble with this problem. Given the polynomial function f(x). find the rational zeros. then the other zeros and factor f(x) into linear factors: f(x)= x^3 + 5^2 +25x + 1251 solutions Answer 300737 by stanbon(57224)   on 2011-04-10 19:33:34 (Show Source): You can put this solution on YOUR website!Given the polynomial function f(x). find the rational zeros. then the other zeros and factor f(x) into linear factors: f(x)= x^3 + 5x^2 +25x + 125 ------------------------------ x^3 + 5x^2 +25x + 125 = 0 ------ I graphed it and found a zero at x = -5 --- To find the other solutiions use synthetic division: -5)....1....5....25....125 ........1....0....25....|..0 Quotient: x^2+25 Solve that quadratic: x^2+25 = 0 (x+5i)(x-5i) = 0 x = -5i or x = -5i or x = -5 ================================================== Cheers, Stan H. =================
 Equations/433939: Evaluate the discriminant of each equation.How many real and imaginary solutions does it have. 1.4x^2-4x+1=0 2.x^2-6x+7=01 solutions Answer 300736 by stanbon(57224)   on 2011-04-10 19:18:32 (Show Source): You can put this solution on YOUR website!Evaluate the discriminant of each equation.How many real and imaginary solutions does it have. 1.4x^2-4x+1=0 b^2-4ac = 16-4*4*1 = 0 So, the equation has 2 equal Real Number solutions. --------------------------------- 2.x^2-6x+7=0 b^2-4ac = 36-4*1*7 = 8 Since the determinant is positive there are 2 unequal Real Number solutions. =================================== Cheers, Stan H.
 Square-cubic-other-roots/433940: 7 divided by fifth root 1281 solutions Answer 300734 by stanbon(57224)   on 2011-04-10 19:12:42 (Show Source): You can put this solution on YOUR website! 7 divided by fifth root 128 --- Ans: 7/(128)^(1/5) ========================== Cheers, Stan H.
 Numbers_Word_Problems/433937: I need some help with algebra translating verbal expression into an algebraic expression. The sum of three and a number is added to twenty-four. 1 solutions Answer 300731 by stanbon(57224)   on 2011-04-10 19:07:53 (Show Source): You can put this solution on YOUR website!The sum of three and a number is added to twenty-four. ---------------------- Let the number be "x": Then, 24+(3+x) is the expression. ---------------------------------- Cheers, Stan H. ==========
 Average/433921: I took a test with 18 questions and recieved an 82 i know that eaah prblem is worth qbout 5.5 or 5.6 pts. How many questions did I miss to receive this grade? thanks, I have tried to figure it out but sometimes my chemo-brain doesn't work.1 solutions Answer 300729 by stanbon(57224)   on 2011-04-10 19:02:32 (Show Source): You can put this solution on YOUR website! I took a test with 18 questions and recieved an 82 i know that eaah prblem is worth qbout 5.5 or 5.6 pts. How many questions did I miss to receive this grade? thanks, I have tried to figure it out but sometimes my chemo-brain doesn't work. ------ The score of 82 is based on a test with 100 questions. --- Solve: x/18 = 82/100 --- x = 18(82/100) --- x = 14.76 ------------------------------ You got between 14 and 15 questions right. ---------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/433919: 1. Find the zeros of the polynomial function and state the multiplicity of each: f(x) = -5x^2 (x-9)(x+3)^31 solutions Answer 300726 by stanbon(57224)   on 2011-04-10 18:35:51 (Show Source): You can put this solution on YOUR website!Find the zeros of the polynomial function and state the multiplicity of each: f(x) = -5x^2 (x-9)(x+3)^3 ---- Let y = 0 and solve for "x": -5x^2 (x-9)(x+3)^3 = 0 --- -5x^2 = 0 or x-9 = 0 or (x+3)^3 = 0 ---- So: x = 0 with multiplicity 2 or x = 9 with multiplicity 1 or x = -3 with multiplicity 3 ============================== Cheers, Stan H. ==========
 Finance/433915: you invested 7000 in two accounts paying 2% and 3% annual interest.if the total interest earned for the year was 170 how much was invested at each rate1 solutions Answer 300724 by stanbon(57224)   on 2011-04-10 18:32:21 (Show Source): You can put this solution on YOUR website!you invested 7000 in two accounts paying 2% and 3% annual interest.if the total interest earned for the year was 170 how much was invested at each rate ------------------------------- Equations: Quantity: x + y = 7000 Interest:0.02x+0.03y = 170 ------ Multiply 1st by 2 Multiply 2nd by 100 ----------------------- 2x + 2y = 2*7000 2x + 3y = 17000 -------------------- Subtract and solve for "Y"; y = \$3000 (amt. invested at 2%) --- Solve for "x": x+y = 7000 x+3000 = 7000 x = \$4000 (amt. invested at 3%) ------------------- Cheers, Stan H. ===========
 Numbers_Word_Problems/433911: HEY! can you help me figure out this digit problem?? Im stuck at the end result and need some help...Thanks!! The value of a certain two-digit number is 9 times the sum of its digits. If the digits are reversed, the resulting number is 63 less than the original number. Find the original number.1 solutions Answer 300723 by stanbon(57224)   on 2011-04-10 18:21:48 (Show Source): You can put this solution on YOUR website!The value of a certain two-digit number is 9 times the sum of its digits. If the digits are reversed, the resulting number is 63 less than the original number. Find the original number. ---------------- Equations: 10t+u = 9(t+u) 10u+t = (10t+u)-63 ------------------------- Rearrange: t = 8u 9u-9t = -63 ------------------- t = 8u u-t = -7 ---- Substitute for "t" ans solve for "u": u-8u = -7 -7u = -7 u = 1 --- Solve for "t": t = 8*1 t = 8 --- Original Number: 10t+u = 81 =============================== Cheers, Stan H. ============
 Geometry_proofs/433909: Dada la correspondencia entre el triangulo ABC y el triangulo DEF tal que angulo A congruente con angulo D, El angulo C congruente con angulo F y el segmento AC congruente con segmento DF, demuestre que el triangulo ABC congruente con el triangulo DEF Translation Given the correspondence between the triangle ABC and the triangle DEF such that angle to consistent with angulo (d), (c) consistent with angle F angle and the segment congruent AC with segment DF, show that the triangle ABC congruent with the triangle DEF 1 solutions Answer 300721 by stanbon(57224)   on 2011-04-10 18:13:07 (Show Source): You can put this solution on YOUR website!Translation Given the correspondence between the triangle ABC and the triangle DEF such that angle to consistent with angulo (d), (c) consistent with angle F angle and the segment congruent AC with segment DF, show that the triangle ABC congruent with the triangle DEF ---------------- They are congruent by the angle-side-angle Theorem =========================== Cheers, Stan H. ================
 test/433875: HELP NEEDED..! Identify the slope-intercept form of the equation of a line which contains the points (–2, –1) and (3, 4).1 solutions Answer 300720 by stanbon(57224)   on 2011-04-10 18:10:13 (Show Source): You can put this solution on YOUR website!Identify the slope-intercept form of the equation of a line which contains the points (–2, –1) and (3, 4). ----------------------------- slope = (4--1)/(3--2) = 5/5 = 1 ---- Form: y = mx+b 4 = 1*3+b b =1 --- Equation: y = x+1 ========= Cheers, Stan H. =========
 test/433872: PLEASE HELP ME..! Find the value of x in the matrix equation. {{3x+2y, -6x-3y}} = {{6,-6}} 1 solutions Answer 300713 by stanbon(57224)   on 2011-04-10 17:11:43 (Show Source): You can put this solution on YOUR website!Find the value of x in the matrix equation. {{3x+2y, -6x-3y}} = {{6,-6}} ----------------------- 3x+2y = 6 -6x-3y = -6 ---------------- Multiply the 1st equation by 2: 6x+4y = 12 -6x-3y = -6 ---- Add and solve for "y": y = 6 ------------- Solve for "x": 3x+2y = 6 3x+2*6 = 6 3x = -6 x = -2 ============= Cheers, Stan H. =============
 Rational-functions/433867: multiply (2 sqrt 6 - 4 sqrt 5) (3 sqrt 6 + 6 sqrt 5) please help, Thank You1 solutions Answer 300712 by stanbon(57224)   on 2011-04-10 17:00:38 (Show Source): You can put this solution on YOUR website!(2 sqrt 6 - 4 sqrt 5) (3 sqrt 6 + 6 sqrt 5) ------ Use FOIL: F: 6*6 = 36 O: 12sqrt(30) I: -12sqrt(30) L: -24*5 = -120 --- Combine to get the answer: Ans: -84 =================== Cheers, Stan H. ==========
 Quadratic_Equations/433863: I need a little help if anyone has a few moments. I need to write a quadratic equation with these two answers: x=1 or x=6 Any help would be great. I just seem to be getting these wrong. 1 solutions Answer 300711 by stanbon(57224)   on 2011-04-10 16:48:42 (Show Source): You can put this solution on YOUR website!I need to write a quadratic equation with these two answers: x=1 or x=6 ---- If x=1 is a solution, x-1 is a factor. If x=6 is a solution, x-6 is a factor. ---- Your equation: f(x) = (x-1)(x-6) f(x) = x^2 -7x+6 ============= Cheers, Stan H.
 Probability-and-statistics/433823: i have a bike lock locked on my bike and i wanted to find out my combination. that way i can lock it onto something so nobody steals it. It has FOUR slots with six numbers on each. what are all of the possible outcomes of it?1 solutions Answer 300695 by stanbon(57224)   on 2011-04-10 15:48:22 (Show Source): You can put this solution on YOUR website!i have a bike lock lock on my bike and i wanted to find out my combination. that way i can lock it onto something so nobody steals it. It has FOUR slots with six numbers on each. what are all of the possible outcomes of it? --------------------- If it had 1 slot the # of possibles would be 6 If it had 2 slots the # of possibles would be 6^2 etc. Can you figure it for FOUR slots? Cheers, Stan H.
 test/433820: a world globe is a sphere. the formula for the volume of a sphere is V=4pier^3/3 and the formula for surface area is SA=4pier^2. Part A. Write an expression for the ratio of the surface area of a sphere to its volume. Part B. Simplify the expression.1 solutions Answer 300694 by stanbon(57224)   on 2011-04-10 15:43:33 (Show Source): You can put this solution on YOUR website!a world globe is a sphere. the formula for the volume of a sphere is V=4pier^3/3 and the formula for surface area is SA=4pier^2. -------------------------- Part A. Write an expression for the ratio of the surface area of a sphere to its volume. S:V = (4(pi)r^2):((4/3)(pi)r^3) -------- Part B. Simplify the expression. S:V = 3/r ================= Cheers, Stan H. ============
 Linear-equations/433816: need help graphing y = 3/4x + 21 solutions Answer 300691 by stanbon(57224)   on 2011-04-10 15:38:02 (Show Source): You can put this solution on YOUR website!need help graphing y = 3/4x + 2 ----- Plot two points: Let x = 0, then y = 2 Let x = 4, then y = 3 ------------------------ Plot (0,2), (4/3) and draw a line thru them. ----------------------- Cheers, Stan H. ===========