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Recent problems solved by 'stanbon'

stanbon answered: 57314 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 , 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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Rational-functions/392841: im trying to solve tis problem and find the least common multiple of each pair of polynomials, please help! 2x^2-18 and 5x^3+30x^2+45x 1 solutions Answer 278864 by stanbon(57387)   on 2011-01-10 18:20:59 (Show Source): You can put this solution on YOUR website! find the least common multiple of each pair of polynomials, please help! --- Factor each expression 2x^2-18 = 2(x^2-9) = 2(x-3)(x+3) ---------------------------- 5x^3+30x^2+45x = 5x(x^2+6x+9)= 5x(x+3)^2 ---- The lcm must have each of the factors in their highest power: --- lcm = 2*5*x(x-3)(x+3)^2 ============================ Cheers, Stan H.

Evaluation_Word_Problems/392823: simplify the expression (d^-6)^7÷2 and write your answer using a possitive exponent 1 solutions Answer 278861 by stanbon(57387)   on 2011-01-10 18:11:31 (Show Source): You can put this solution on YOUR website! simplify the expression (d^-6)^7÷2 and write your answer using a possitive exponent -------------------- (d^-6)^7÷2 --- (d^-42)/2 --- (1/d^42)/2 --- = 1/(2d^42) ================= Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/392820: Laura is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.75 . See the figure below. Laura has 51 miles remaining after 33 minutes of driving. How many miles were remaining after 15 minutes of driving? 1 solutions Answer 278855 by stanbon(57387)   on 2011-01-10 17:58:36 (Show Source): You can put this solution on YOUR website! Laura is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.75 . See the figure below. --- Write the linear function as remaining distance = -0.75(drive time) + (intercept) ------- Laura has 51 miles remaining after 33 minutes of driving. That gives you the following: 51 = -0.75(33) + intercept intercept = 75.75 --- Equation is rd = -0.75t + 75.75 ------------------------------------ How many miles were remaining after 15 minutes of driving? rd(15) = -0.75*15+75.75 rd(15) = 64.5 miles ============= Cheers, Stan H.

Exponential-and-logarithmic-functions/392821: (3p+5q) + (6p-4q) 1 solutions Answer 278850 by stanbon(57387)   on 2011-01-10 17:56:02 (Show Source): You can put this solution on YOUR website! (3p+5q) + (6p-4q) -------------- Add "like" terms. --- 3p+6p + 5q-4q ----- = 9p+2q -------------- Cheers, Stan H.

Human-and-algebraic-language/392787: Step-by-Step Explanation for this problem please: Show that the equations are equal by rewriting them in the form of A(t) = ab^t: A(t) = 100e^(-0.005t) and A(t) = 100(1/2)^(t/138) 1 solutions Answer 278834 by stanbon(57387)   on 2011-01-10 17:13:56 (Show Source): You can put this solution on YOUR website! Show that the equations are equal by rewriting them in the form of A(t) = ab^t: A(t) = 100e^(-0.005t) A(t) = 100e^(-0.005)t A(t) = 100(0.995012)^t =========================== A(t) = 100(1/2)^(t/138) A(t) = 100(1/2)^(1/138)t A(t) = 100(0.994990)^t =========================== Cheers, Stan H.

Numbers_Word_Problems/392789: 10 times the square of a non-zero number is equal to 63 times that number. What is the number? 1 solutions Answer 278833 by stanbon(57387)   on 2011-01-10 17:05:27 (Show Source): You can put this solution on YOUR website! 10 times the square of a non-zero number is equal to 63 times that number. What is the number? ---- Equation: 10*x^2 = 63x ------ 10x^2-63x = 0 x(10x-63) = 0 x = 0 or x = 6.3 ================== Cheers, Stan H. =======

Polygons/392784: The measure of each interior angle of a regular polygon is 20 degrees more than 3 times the measure of each exterior angle. How many sides does the polygon have? 1 solutions Answer 278830 by stanbon(57387)   on 2011-01-10 17:00:58 (Show Source): You can put this solution on YOUR website! The measure of each interior angle of a regular polygon is 20 degrees more than 3 times the measure of each exterior angle. How many sides does the polygon have? --- Let the exterior angle be "x" Then the interior angle is "3x+20" --- These angles are supplementary: x + 3x+20 = 180 4x = 160 x = 40 (size of each exterior angle) --- The sum of the exterior angles is 360. # of exterior angles = 360/40 = 9 --- # of sides is 9. ===================== Cheers, Stan H.

Miscellaneous_Word_Problems/392782: The length of a rectangle is six times its width. If the area of the rectangle is 486yd^2 , find its perimeter 1 solutions Answer 278826 by stanbon(57387)   on 2011-01-10 16:56:18 (Show Source): You can put this solution on YOUR website! The length of a rectangle is six times its width. If the area of the rectangle is 486yd^2 , find its perimeter ------------------------------- Equations: L = 6W --- Area = LW 486 = 6W*W 6W^2 = 486 w^2 = 81 Positive solution: W = 9 yd --- L = 6W = 6*9 = 54 yd --- Perimeter = 2(L+W) P = 2(9+54) P = 2(63) P = 126 yd. ============== Cheers, Stan H.

Probability-and-statistics/392762: A researcher predicts that listening to music while solving math problems will make a particular brain area more active. To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a percentage signal change of 58. From many previous studies with this same math problems procedure (but not listening to music), it is known that the signal change in this brain area is normally distributed with a mean of 35 and a standard deviation of 10. (a) Using the .01 level, what should the researcher conclude? Solve this problem explicitly using all five steps of hypothesis testing, and illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution. (b) Then explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores). 1 solutions Answer 278823 by stanbon(57387)   on 2011-01-10 16:52:43 (Show Source): You can put this solution on YOUR website! A researcher predicts that listening to music while solving math problems will make a particular brain area more active. (that is the claim) ------------------------- To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a percentage signal change of 58. (that is the sample mean) ------------------------- From many previous studies with this same math problems procedure (but not listening to music), it is known that the signal change in this brain area is normally distributed with a mean of 35 and a standard deviation of 10. (that is the population data) --------------------------- (a) Using the .01 level, what should the researcher conclude? Solve this problem explicitly using all five steps of hypothesis testing, and illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution. ---- Ho: u = 35 Ha: u > 35 (claim) --- z(58) = (58-35)/10 = 23/10 = 2.3 --- The critical region for a right tail test with alpha = 1% is z>2.3263 ---- Conclusion: Since the test statistic is less than z = 2.3263, reject Ho. The test results support the claim. ---- Cautionary Note. Since the test statistic is barely in the reject interval more testing is required. ================================ Cheers, Stan H. (b) Then explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores).

Linear-systems/392775: 7x-(2x-12)=-8 1 solutions Answer 278816 by stanbon(57387)   on 2011-01-10 16:38:32 (Show Source): You can put this solution on YOUR website! 7x-(2x-12)=-8 -- 7x-2x+12 = -8 5x = -20 x = -4 -------------- Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/392763: jazmine has 24 candy apples and 34 nut covered candy apples.All together she made $280 dollars.what was the price of 1 candy apple 1 solutions Answer 278815 by stanbon(57387)   on 2011-01-10 16:37:04 (Show Source): You can put this solution on YOUR website! jazmine has 24 candy apples and 34 nut covered candy apples.All together she made $280 dollars.what was the price of 1 candy apple ----- Let a and b be the respective prices of the two items. ----- Value equation: 24a + 34b = 280 dollars --- You need another statement that relates a and b so you can solve a system of two equations. ======================================== Cheers, Stan H.

Matrices-and-determiminant/392769: Could someone please help? I need to a) write each linear equation as a matrix equation in the form of AX=B. then i have to B) solve the system using the inverse that is given for the coefficient matrix. here is the problem: The system is: x-6y+3z=11 2x-7y+3z=14 4x-12y+5z=25 The inverse of: 1 -1 1 0 2 -1 2 3 0 is.... 3 3 -1 -2 -2 1 -4 -5 2 Please help!! I have NO idea where to start! Thank you to whomever responds!!! 1 solutions Answer 278811 by stanbon(57387)   on 2011-01-10 16:32:56 (Show Source): You can put this solution on YOUR website! Please use Google to search for "Matrix solutions of Linear Systems". The web has good explanations and good examples. Cheers, Stan H.

Matrices-and-determiminant/392771: Please help! I need to solve the following using Cramer's Rule. The textbook doesn't do a good job of defining this, so i would be extremely grateful for any help!! solve by Cramer's Rule: 3x=7y+1 2x=3y-1 solve by Cramer's rule: x-3y+z=-2 x+2y =8 2x-y =1 Thank you for your help! 1 solutions Answer 278808 by stanbon(57387)   on 2011-01-10 16:30:40 (Show Source): You can put this solution on YOUR website! Please use Google to see how Cramer's Rule works. The web has good explanations and worked examples. --------- Cheers, Stan H.

Triangles/392773: a triangle with an angle whose measure is 90 degrees is called ? 1 solutions Answer 278805 by stanbon(57387)   on 2011-01-10 16:28:57 (Show Source): You can put this solution on YOUR website! a triangle with an angle whose measure is 90 degrees is called ? --- Ans: A right triangle. --- Cheers, Stan H.

Polynomials-and-rational-expressions/392768: i'm trying to help my daughter with homework over the phone she is trying to solve the equation x^2 + bx + c = 0 when x = -4 or 6, what are b and c haven't a clue where to start 1 solutions Answer 278804 by stanbon(57387)   on 2011-01-10 16:27:15 (Show Source): You can put this solution on YOUR website! solve the equation x^2 + bx + c = 0 when x = -4 or 6, what are b and c ----- If x = -4 you get: (-4)^2+b(-4)+c = 0 16-4b+c = 0 -4b+c = -16 ------------- If x = 6, you get: (6)^2+b(6)+c = 0 6b+c = -36 ----------- Now you have 2 equations with variables b and c. -4b+c = -16 6b+c = -36 ------------ Subtract the top equation from the lower one and solve for "b": 10b = -20 b = -2 ----- Solve for c by substituting into 6b+c = -36: 6*-2+c = -36 -12+c = -36 c = -24 ------------------ Check in the equation -4b+c = -16 -4*-2+(-24) = -16 8-24 = -16 -16 = -16 ============================ Cheers, Stan H.

decimal-numbers/392766: Which decimal has the least value: 0.6, 0.66, 0.666, 0.6666 1 solutions Answer 278794 by stanbon(57387)   on 2011-01-10 16:18:32 (Show Source): You can put this solution on YOUR website! Which decimal has the least value: 0.6, 0.66, 0.666, 0.6666 ---- Ans: 0.6 All the other numbers have 6/100 and/or 6/1000 and or 6/10000 added to 0.6 So 0.6 is the smallest of the numbers. ======================================= Cheers, Stan H.

Linear-equations/392729: Ideal waist size. According to Dr. Aaron R. Folsom of the University Of Minnesota School Of Public Health, your maximum ideal waist size is directly proportional to your hip size. For a woman with 40-inch hips, the maximum ideal waist size is 32 inches. What is the maximum ideal waist size for a woman with 35-inch hips? 1 solutions Answer 278771 by stanbon(57387)   on 2011-01-10 15:14:19 (Show Source): You can put this solution on YOUR website! maximum ideal waist size is directly proportional to your hip size. For a woman with 40-inch hips, the maximum ideal waist size is 32 inches. What is the maximum ideal waist size for a woman with 35-inch hips? ---- Equation: w = kh --- Solve for "k" using "For a woman with 40-inch hips, the maximum ideal waist size is 32 inches". --- 32 = k40 k = 4/5 ---- Equation for your problem: w = (4/5)h --- What is the maximum ideal waist size for a woman with 35-inch hips? --- w = (4/5)35 w = 4*7 w = 28 inches ======================== Cheers, Stan H.

Angles/392724: An angle is 1/7 of its compliment. Find the angle. 1 solutions Answer 278766 by stanbon(57387)   on 2011-01-10 15:09:25 (Show Source): You can put this solution on YOUR website! An angle is 1/7 of its compliment. Find the angle. angle: x complement: 90-x -------------------- Equation: x = (1/7)(90-x) 7x = 90-x 8x = 90 x = 11.25 degrees ===================== Cheers, Stan H.

Functions/392727: If the function G(x) = (x - 7)2 + 3 has the same shape as F(x) = x2 + 3, how far to the right of F(x) is G(x) shifted? 1 solutions Answer 278763 by stanbon(57387)   on 2011-01-10 15:05:00 (Show Source): You can put this solution on YOUR website! If the function G(x) = (x - 7)^2 + 3 has the same shape as F(x) = x^2 + 3, how far to the right of F(x) is G(x) shifted? --- Ans: 7 units =================== Cheers, Stan H.

Numbers_Word_Problems/392639: please help me solve this equation The difference between the squares of two odd numbers is 48. What are the numbers? i have been given a tip which is if the larger of the two numbers is x, then the smaller number is x-2. Form an equation and solve? Please would you help me solve and show me how to work it out please? 1 solutions Answer 278681 by stanbon(57387)   on 2011-01-10 08:36:12 (Show Source): You can put this solution on YOUR website! The difference between the squares of two odd numbers is 48. 1st odd: 2x-1 2nd odd: 2x+1 ------- What are the numbers? --- Form an equation and solve? (2x-1)^2 - (2x+1)^2 = 48 4x^2-4x+1-[4x^2+4x+1] = 48 ---- -8x = 48 x = -6 --- 1st: 2x-1 = -13 2nd 2x+1 = -11 ---- Check: (-13)^2-(-11)^2 = 48 169 - 121 = 48 48 = 48 ----- Note: You could also use the equation (2x+1)^2-(2x-1)^2 = 48 ----- By the way, x and x-2 do not represent 2 odd numbers. Odd numbers are always one less than or one greater than an even number. Use 2x-1 and 2x+1 to represent 2 consecutive odd numbers. ================== Cheers, Stan H.

Quadratic-relations-and-conic-sections/392641: 1) find the value of a for which the graph of y=ab^x is a horizontal line 2) find the value of b for which the graph of y=ab^x is a horizontal line. explain how you found your answers 1 solutions Answer 278675 by stanbon(57387)   on 2011-01-10 08:28:11 (Show Source): You can put this solution on YOUR website! 1) find the value of a for which the graph of y=ab^x is a horizontal line y = 0 when a = 0 ------------------------- 2) find the value of b for which the graph of y=ab^x is a horizontal line. y = 0 when b = 0 =================== Cheers, Stan H. ==================== explain how you found your answers

Linear_Equations_And_Systems_Word_Problems/392640: The sum of two numbers is 24. The second number is 3 times the first number. Write a system of equation that represent the information and solve by using the elimination method. 1 solutions Answer 278673 by stanbon(57387)   on 2011-01-10 08:24:16 (Show Source): You can put this solution on YOUR website! The sum of two numbers is 24. The second number is 3 times the first number. Write a system of equation that represent the information and solve by using the elimination method. ---------- Equations: x + y = 24 y = 3x ----- Rewrite: x+y = 24 3x-y = 0 --- Add and solve for "x": 4x = 24 x = 6 --- Substitute to solve for "y": y = 3*6 y = 18 --------------- Cheers, Stan H.

Mixture_Word_Problems/392626: Your lawn mower requires an oil and gas mixture to make it run correctly. The mixture requires 3 times as much gas as oil. Gas costs $1.43 and oil costs $.85 a gallon. How many full gallons of the mixture can be made for $20? This should be just a one variable equation... I have tried 1.43y + (1/3)(.85)y <=20 and I am not getting the correct answer? 1 solutions Answer 278671 by stanbon(57387)   on 2011-01-10 08:05:44 (Show Source): You can put this solution on YOUR website! Your lawn mower requires an oil and gas mixture to make it run correctly. The mixture requires 3 times as much gas as oil. --- g = 3o ------ Gas costs $1.43 and oil costs $.85 a gallon. Value: 1.43g + 0.85o <= 20 ---- How many full gallons of the mixture can be made for $20? ----- Substitute for "g" and solve for "o": 1.43(3o) + 0.85o <= 20 5.14o <= 20 o <= 3.89 gallons of oil --- solve for "g" (g/3) <= 3.89 g <= 11.67 gallons of gas ========================= Cheers, Stan H. ===========================

Polynomials-and-rational-expressions/392632: SIMPLIFY 2/X + 9/X-8 1 solutions Answer 278670 by stanbon(57387)   on 2011-01-10 07:58:29 (Show Source): You can put this solution on YOUR website! SIMPLIFY 2/X + 9/X-8 ---------- lcd: x(x-8) --- Rewrite each fraction with the lcd as its denominator: 2(x-8)/lcd + 9x/lcd ---- Combine the numerators over the lcd: (2x-16+9x)/lcd --- Simplify: (11x-16)/(x(x-8)) ====================== Cheers, Stan H.

Rational-functions/392631: for f(x) = x^2 + 2x, find f(-1). 1 solutions Answer 278668 by stanbon(57387)   on 2011-01-10 07:54:57 (Show Source): You can put this solution on YOUR website! for f(x) = x^2 + 2x, find f(-1). ---- f(-1) = (-1)^2+2(-1) = 1-2 = -1 ================== Cheers, Stan H.

Trigonometry-basics/392633: -2+3i 1 solutions Answer 278667 by stanbon(57387)   on 2011-01-10 07:53:13 (Show Source): You can put this solution on YOUR website! What is the question? Cheers, Stan H.

Age_Word_Problems/392630: Please help me solve this question: "A father is four times as old as his son. In four years' time their combined age will be 48 years. How old are they now?" 1 solutions Answer 278666 by stanbon(57387)   on 2011-01-10 07:52:19 (Show Source): You can put this solution on YOUR website! A father is four times as old as his son. In four years' time their combined age will be 48 years. How old are they now?" ---- Equations: f = 4s (f+4)+(s+4) = 48 ----------------------- Substitute for "f" and solve for "s": (4s+4)+(s+4) = 48 5s+8 = 48 5s = 40 s = 8 yrs old (son's age now) -------------- Solve for "f": f = 4s f = 4*8 = 32 yrs old (father's age now) ============================================== Cheers, Stan H. =========

Length-and-distance/392510: If one end point of a line segment is (-6,4), and the midpoint of the segment is (-2,7), how do you find the other end point? 1 solutions Answer 278593 by stanbon(57387)   on 2011-01-09 22:26:48 (Show Source): You can put this solution on YOUR website! If one end point of a line segment is (-6,4), and the midpoint of the segment is (-2,7), how do you find the other end point? --------------- The coordinates of the midpoint are the average of the corresponding coordinates of the endpoints. =============================================== Your Problem: Let the other endpoint be (x,y) --- Solve: (-6+x)/2 = -2 -6+x = -4 x = 2 ------------- (4+y)/2 = 7 4+y = 14 y = 10 --- Other endpoint: (2,10) ============== Cheers, Stan H.

test/392533: What I's -2/12+2/12 1 solutions Answer 278591 by stanbon(57387)   on 2011-01-09 22:19:51 (Show Source): You can put this solution on YOUR website! What I's -2/12+2/12 ---- Ans: 0 ============ Cheers, Stan H.

Expressions-with-variables/392534: x/7=3/21 find the missing variable 1 solutions Answer 278590 by stanbon(57387)   on 2011-01-09 22:17:53 (Show Source): You can put this solution on YOUR website! x/7=3/21 ------------- Multiply both sides by 21 to get: 3x = 3 Divide by 3 to get: x = 1 ================== Cheers, Stan H.

Mixture_Word_Problems/392532: An automobile radiator contains 16 quarts of a 20% solution of antifreeze. How much of the original solution must be drawn off and replaced by pure antifreeze to make a 25% antifreeze? 1 solutions Answer 278589 by stanbon(57387)   on 2011-01-09 22:16:16 (Show Source): You can put this solution on YOUR website! An automobile radiator contains 16 quarts of a 20% solution of antifreeze. How much of the original solution must be drawn off and replaced by pure antifreeze to make a 25% antifreeze? ---- Equation: alcohol - alcohol + alcohol = alcohol 0.20*16 - 0.20x + 1.00x = 0.25*16 ---- Multiply thru by 100 to get: 20*16 - 20x + 100x = 25*16 80x = 5*16 x = 5(16/80) x = 5(1/5) x = 1 quart (amt. of antifreeze that must be removed and replaced) ========================== Cheers, Stan H.