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Recent problems solved by 'stanbon'

stanbon answered: 57911 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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Quadratic_Equations/544834: Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions. 8x2 + 2x + 4 = 0 (Points : 10) Two different irrational solutions Two different imaginary solutions Exactly one rational solution Two different rational solutions 1 solutions Answer 355242 by stanbon(57984)   on 2011-12-09 20:34:03 (Show Source): You can put this solution on YOUR website! Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions. 8x2 + 2x + 4 = 0 ---- b^2-4ac = 2^2-4*8*4 < 0 -------------- Ans: Two different imaginary solutions ======== Cheers, Stan H. ========

Surface-area/544830: For the right rectangular prism (or box) shown, the dimensions are = 12 in, w = 4 in,and h = 3 in. How long is a diagonal of the box? 1 solutions Answer 355241 by stanbon(57984)   on 2011-12-09 20:31:08 (Show Source): You can put this solution on YOUR website! For the right rectangular prism (or box) shown, the dimensions are = 12 in, w = 4 in,and h = 3 in. How long is a diagonal of the box? ------- diagonal of the base = sqrt[12^2+4^2] = sqrt(160) ------- Diagonal of the box = sqrt[160 + 3^2] = sqrt(169) = 13 inches ============================================================ Cheers, Stan H. ============

Probability-and-statistics/544813: I am having trouble just understanding the standard normal distribution table, can you please show me how to use it.I really don't want you to work it I really need to know the correct way of finding it myself. 1 solutions Answer 355236 by stanbon(57984)   on 2011-12-09 19:45:18 (Show Source): You can put this solution on YOUR website! Use Google to search "standard normal distribution table". That will lead you to tables and examples. Cheers, Stan H. ==========

Functions/544814: what is the slope intercept form of x/3+y/5=1 1 solutions Answer 355233 by stanbon(57984)   on 2011-12-09 19:41:23 (Show Source): You can put this solution on YOUR website! what is the slope intercept form of x/3+y/5=1 ---- Multiply thru by 15 to get: 5x + 3y = 15 --- Solve for "y": 3y = -5x+15 y = (-5/3)x = 5 =================== Cheers, Stan H. ===============

Triangles/544812: The second angle in a triangle is 24 degrees larger then the first. And the third angle is 69 degrees larger than the second. What are the measures of all three angles? I tried adding together 69 and 24 and subtracting it from 180 but then I realized that wasn't correct. I don't really know how to do problems like this. 1 solutions Answer 355229 by stanbon(57984)   on 2011-12-09 19:28:40 (Show Source): You can put this solution on YOUR website! The second angle in a triangle is 24 degrees larger then the first. And the third angle is 69 degrees larger than the second. What are the measures of all three angles? ---------- Let 1st be "x": Then 2nd is "x+24": And 3rd is "x+24+69" ----- Equation: x + x+24 + x + 93 = 180 3x = 180-117 3x = 63 x = 21 degrees x+24 = 45 degrees x+93 = 114 degrees ======================== Cheers, Stan H. ===============

Polynomials-and-rational-expressions/544811: The monthly text plan varies inversely as the number of text messages sent. If I send 450 messages for 80 cents a message, what is an inverse variation equation I can use that relates the per message rate and the number of text messages? 1 solutions Answer 355228 by stanbon(57984)   on 2011-12-09 19:24:05 (Show Source): You can put this solution on YOUR website! The monthly text plan varies inversely as the number of text messages sent. p = k/n Solve for "k" using "If I send 450 messages for 80 cents a message, what is an inverse variation equation?" ---- 80 = k/450 k = 36000 --- Equation: plan = 36000/(number of message) ===================================== Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/544803: Determine a system of three linear equations in three variables having the solution (1,-1,2)and describle two ways by which you could verify this solution to your system. 1 solutions Answer 355227 by stanbon(57984)   on 2011-12-09 19:20:26 (Show Source): You can put this solution on YOUR website! Determine a system of three linear equations in three variables having the solution (1,-1,2)and describe two ways by which you could verify this solution to your system. ---- Let x = 1 ; y = -1 ; z = 2 ---- 2x + 3y +z = 1 x - y - z = 0 3x + 2y +4z = 9 ========================== Cheers, Stan H. ==========

absolute-value/544807: How big is the solution set for an equation that cannot be solved? 1 solutions Answer 355226 by stanbon(57984)   on 2011-12-09 19:17:43 (Show Source): You can put this solution on YOUR website! Ans: The null set.

Polynomials-and-rational-expressions/544808: how do you put 4x^2-3 in factored form ? 1 solutions Answer 355225 by stanbon(57984)   on 2011-12-09 19:16:02 (Show Source): You can put this solution on YOUR website! put 4x^2-3 in factored form ---- You can treat the problem as a difference of squares and factor as follows: --- = (2x-sqrt(3))(2x+sqrt(3)) ============================= Cheers, Stan H. ===========

Triangles/544805: Find the altitude of an equilateral triangle, if each side of the triangle has a length of 14 meters. 1 solutions Answer 355223 by stanbon(57984)   on 2011-12-09 19:08:06 (Show Source): You can put this solution on YOUR website! Find the altitude of an equilateral triangle, if each side of the triangle has a length of 14 meters. --- Draw the triangle. Draw in the altitude. Mark the length of the side and (1/2) the base. --- Solve for the altitude. 14^2 = h^2 + 7^2 h^2 = 147 h = 12.12 meters ==================== Cheers, Stan H. =============

Permutations/544804: how many permutations are in the number 2713? I am looking for all choices thanks! 1 solutions Answer 355222 by stanbon(57984)   on 2011-12-09 19:04:53 (Show Source): You can put this solution on YOUR website! If you mean "how many ways can you permute that number" the answer is 4! = 24 ============== Cheers, Stan H.

absolute-value/544806: What is the solution set for an equation in which all numbers work? 1 solutions Answer 355221 by stanbon(57984)   on 2011-12-09 19:02:53 (Show Source): You can put this solution on YOUR website! Ans: All Real Numbers

test/544801: how long will it take danette to travel 90 miles if she drives at an average speed of 50 mph for 25 miles and at an average speed of 65 mph the rest of the way? 1 solutions Answer 355220 by stanbon(57984)   on 2011-12-09 19:00:36 (Show Source): You can put this solution on YOUR website! how long will it take danette to travel 90 miles if she drives at an average speed of 50 mph for 25 miles and at an average speed of 65 mph the rest of the way? ---------------------------------- time = 25/50 + (90-25)/65 --- time = (1/2) + 65/65 --- time = 1.5 hours ======================= Cheers, Stan H. ======================

Probability-and-statistics/544100: 1.How many bit strings of length 6 have: (a) Exactly three 0s? (b) The same number of 0s as 1s? (d) At least three 1s? 2.What is the probability that a positive integer m in the range 1= m= 100, which is selected randomly, is divisible by 4? . 1 solutions Answer 355211 by stanbon(57984)   on 2011-12-09 17:13:01 (Show Source): You can put this solution on YOUR website! To double an investment of $12,000 compounded continuously at 2.5% interest, how much time will it take? ----------------- A(t) = Ao*e^(rt) ---- 24000 = 12000*e^(0.025t) e^(0.025t) = 2 0.025t = ln(2) t = 27.73 years ==================== Cheers, Stan H. ====================

Probability-and-statistics/544597: If you are not prepaired for a test and you have 3 true or false questions what is the probablity of getting 2 out of the 3 correct? 1 solutions Answer 355162 by stanbon(57984)   on 2011-12-09 09:45:08 (Show Source): You can put this solution on YOUR website! If you are not prepaired for a test and you have 3 true or false questions what is the probablity of getting 2 out of the 3 correct? ----- Binomial Problem with n = 3 and p(correct) = 1/2 --- P(x = 2 or 3) = P(2) + P(3) = 3C2(1/2)^3 + 3C3(1/2)^2 ---- = (3+1)(1/2)^3 ---- = 4/8 --- = 1/2 ============ Cheers, Stan H. ==============

Linear-systems/544461: okay so it says solve linear system using substitution 4x + 3y = -5 x = y - 3 1 solutions Answer 355097 by stanbon(57984)   on 2011-12-08 22:19:22 (Show Source): You can put this solution on YOUR website! using substitution 4x + 3y = -5 x = y - 3 ------ Substitute for "x" and solve for "y": 4(y-3) + 3y = -5 4y-12+3y = -5 7y = 7 y = 1 ---- Solve for "x": x = y-3 x = 1-3 x = -2 -------- Cheers, Stan H. ============

�t�e�s�t/544458: The temperature of air in a room that began at 55 degrees F is increasing by 8 degrees F. Write a function that describes the temperature of the air over time. Graph the function to show the temperatures over the first 5 hours. 1 solutions Answer 355095 by stanbon(57984)   on 2011-12-08 22:14:25 (Show Source): You can put this solution on YOUR website! The temperature of air in a room that began at 55 degrees F is increasing by 8 degrees F. Write a function that describes the temperature of the air over time. Graph the function to show the temperatures over the first 5 hours. ---- T(t) = 55+8t where t is number of hours. ---- T(5) = 55+8*5 = 95 degrees ----- Cheers, Stan H. =============

Geometry_Word_Problems/544078: how to find the angle in a quadrilateral that has 4 angles with the numbers 85, 69, (6x+22), and (x+37) please help 6th grader 1 solutions Answer 355023 by stanbon(57984)   on 2011-12-08 14:06:59 (Show Source): You can put this solution on YOUR website! how to find the angle in a quadrilateral that has 4 angles with the numbers 85, 69, (6x+22), and (x+37) please help 6th grader ---- The sum of the four angles is 360 degrees ---- Equation: 85 + 69 + 6x+22 + x+37 = 360 degrees --- 213 + 7x = 360 7x = 147 x = 21 ----- Angle: 6x+22 = 6*21+22 == 126+22 = 148 degrees Angle: x+37 = 21+37 = 58 degrees =================================== Cheers, Stan H. ==============================

Percentage-and-ratio-word-problems/544071: 25 litres of salt solution contain 6% salt. How many litres of water must be added so as to get a resultant solution containing 5% salt. 1 solutions Answer 355022 by stanbon(57984)   on 2011-12-08 14:01:22 (Show Source): You can put this solution on YOUR website! 25 litres of salt solution contain 6% salt. How many litres of water must be added so as to get a resultant solution containing 5% salt. ------- Equation: water + water = water 0.94*25 + x = 0.95(25+x) ------- Multiply thru by 100 to get: 94*25 + 100x = 95*25+95x 5x = 25 x = 5 liters (amt. of water needed) ================== Cheers, Stan H. ==================

Rational-functions/544072: Please help! I have been trying. I have to graph with inverse of radical 2 (exponent 4 sqrt x) Thank you 1 solutions Answer 355020 by stanbon(57984)   on 2011-12-08 13:52:36 (Show Source): You can put this solution on YOUR website! confusing

Mixture_Word_Problems/544062: Please help me with the following word problem (I am pretty certain that it has to do with system of equations): A mechanic has 351 gallons of gasoline and 18 gallons of oil to make gas/oil mixtures. He wants one mixture to be 6% oil and the other mixture to be 2.5% oil. If he wants to use all of the gas and oil, how many gallons of gas and oil are in each of the resulting mixtures? I have tried putting it into two equations .06x+.025y=18 and .94x+.975y=351 and then using the substitution method to solve for x and y. Yet my answers only become true for the first equation 1 solutions Answer 355018 by stanbon(57984)   on 2011-12-08 13:42:42 (Show Source): You can put this solution on YOUR website! A mechanic has 351 gallons of gasoline and 18 gallons of oil to make gas/oil mixtures. ------------- He wants one mixture to be 6% oil and the other mixture to be 2.5% oil. ------- If he wants to use all of the gas and oil, how many gallons of gas and oil are in each of the resulting mixtures? I have tried putting it into two equations .06x+.025y=18 and .94x+.975y=351 and then using the substitution method to solve for x and y. Yet my answers only become true for the first equation ----- .06x+.025y=18 .94x+.975y=351 --- I used a Matrix method on a TI-84 and got: x = 250.71 gallons y = 118.29 gallons ========================= Cheers, Stan H. ===================

Graphs/544065: Axia College Material Appendix F Ticket Sales Living in or near a metropolitan area has some advantages. Entertainment opportunities are almost endless in a major city. Events occur almost every night, from sporting events to the symphony. Tickets to these events are not available long and can often be modeled by quadratic equations. Application Practice Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting. 1. Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale). a. Does the graph of this equation open up or down? How did you determine this? The graph will open down because the coefficient of x^2 is negative. b. Describe what happens to the tickets sales as time passes. Over time the ticket sales will increase reach a peak then decrease c. Use the quadratic equation to determine the last day that tickets will be sold. Day 25 Note. Write your answer in terms of the number of days after ticket sales begin. d. Will tickets peak or be at a low during the middle of the sale? How do you know? The ticket sales will peak during the middle of the sale because the graph opens down looking like an upside down u. e. After how many days will the peak or low occur? After about 12 days the ticket sales will peak f. How many tickets will be sold on the day when the peak or low occurs? g. What is the point of the vertex? How does this number relate to your answers in parts e. and f? h. How many solutions are there to the equation ? How do you know? i. What do the solutions represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? 1 solutions Answer 355015 by stanbon(57984)   on 2011-12-08 13:34:17 (Show Source): You can put this solution on YOUR website! Most of your questions are answered in your post. Those not answered are missing required information. Cheers, Stan H.

Graphs/544057: If f and g are linear functions such that g(f(x)) = 2x+ 6 and the graph of y = f(g(x)) passes through the origin what is the value of f(g(2011))? 1 solutions Answer 355005 by stanbon(57984)   on 2011-12-08 13:11:12 (Show Source): You can put this solution on YOUR website! If f and g are linear functions such that g(f(x)) = 2x+ 6 and the graph of y = f(g(x)) passes through the origin what is the value of f(g(2011))? ---- If g(f(x)) = 2x+6 then f(g(x)) is its inverse So f(g(x)) = (x-6)/2 = (x/2)-3 ------------------------------- f(g(2011)) = (2011/2)-3 = 1005.5-3 = 1002.5 ------------------------------- Cheers, Stan H.

Polynomials-and-rational-expressions/544042: Simplify: 1 solutions Answer 355003 by stanbon(57984)   on 2011-12-08 13:02:49 (Show Source): You can put this solution on YOUR website! x-(y/((x/y)+(y/x)) ----- x - [y/(x^2+y^2)/(xy)) ---- x - [(xy^2)/(x^2+y^2)] ---- = [(x^2+xy^2)-(xy^2]/(x^2+y^2) ---- = [x^2/(x^2+y^2)] ====================== Cheers, Stan H. ======================

Rate-of-work-word-problems/544051: it will take 3/4 of a can of paint to paint a room.you have one can that is 1/3 full. how much more is required? 1 solutions Answer 355002 by stanbon(57984)   on 2011-12-08 12:57:13 (Show Source): You can put this solution on YOUR website! it will take 3/4 of a can of paint to paint a room.you have one can that is 1/3 full. how much more is required? ----- Ans: (3/4)-(1/3) = (9-4)/12 = 5/12 of a can is required. ================ Cheers, Stan H. ================

Trigonometry-basics/544049: Cos^2(x)-5cos(x)+4=0 1 solutions Answer 355001 by stanbon(57984)   on 2011-12-08 12:54:50 (Show Source): You can put this solution on YOUR website! Cos^2(x)-5cos(x)+4=0 ---- Quadratic in cos(x): Factor: (cos(x)-4)(cos(x)-1) = 0 ------ cos(x) = 4 or cos(x) = 1 ---- Only cos(x) = 1 is legitimate --- x = 0 =============== Cheers, Stan H.

Complex_Numbers/544045: find the fourth roots of giving your answers in the form a+bi where a and b are real numbers. I have gotten to this point,Z^4=16(COS 5/3 PIE+i SIN 5/3 PIE) i am not sure if am right. 1 solutions Answer 354999 by stanbon(57984)   on 2011-12-08 12:50:28 (Show Source): You can put this solution on YOUR website! find the fourth roots of giving your answers in the form a+bi where a and b are real numbers. ------------------------- z^4 = -8+8sqrt(3)i --- r = sqrt[8^2 (8sqrt(3))^2] = sqrt[64 + 64*3] = 2^4 ------- theta = tan^-1(8sqrt(3)/(-8)) = -60 degrees or 120 degrees ----------------------------------- since cos(-60) = cos(60) and since sin(-60) = -sin(60), z^4 = 2^4(cos(120)+isin(120)) ---- 4th Roots: z = 2(cos((120+360n)/4) + isin((120+360n)/4))/4 n= 0: z = 2(cis(30) = 2(cos(30)+isin(30)) = 2(sqrt(3)/2 + i/2) = sqrt(3)+i ------------------------ n= 1: z = 2(cis(120))= 2(cos(120)+isin(120)) = 2(-sqrt(3)/2+i/2)= -sqrt(3)+i ------------------------ n= 2: z = 2(cis(210)) = 2(cos(210)+isin(210)) = -sqrt(3)-i ------------------------ n= 3: z = 2(cis(300)) = sqrt(3)-i ===================================== Cheers, Stan H. ================ z = 2(cos(30)+ isin(30))

Complex_Numbers/543998: 3-3i/4i 1 solutions Answer 354993 by stanbon(57984)   on 2011-12-08 11:01:27 (Show Source): You can put this solution on YOUR website! (3-3i)/4i ---- Multiply numerator and denominator by -4i to get: ---- [-4i(3-3i)]/[4i*(-4i)] ----- = [-12-12i]/16 ----- = (-3/4)(1-i) ==================== Cheers, Stan H. ====================

Inequalities/543947: I am trying to help my daughter with her homework and it has been quite a while for me. Thanks for your help. Solve with answer in interval notation 3x + 5(x - 4) + 7 < 5(x -1) + 2x 1 solutions Answer 354992 by stanbon(57984)   on 2011-12-08 10:56:30 (Show Source): You can put this solution on YOUR website! Solve with answer in interval notation 3x + 5(x - 4) + 7 < 5(x -1) + 2x ---------------- 3x+5x-20+7 < 5x-5+2x ----- 8x-13 < 7x-5 ----- x < 8 ============== Interval notation: (-oo , -8) ================================= Cheers, Stan H. ==============

test/543941: its dividing polynomials if its possible work would be nice (6t^3+5t^2+9)/(2t+3) 1 solutions Answer 354981 by stanbon(57984)   on 2011-12-08 09:11:53 (Show Source): You can put this solution on YOUR website! (6t^3+5t^2+9)/(2t+3) ---- (2t+3))6t^3+5t^2+9 ------- 1st piece of the quotient: 3t^2 --- Multiply: 3t^2(2t+3) = 6t^3+9t^2 --- Subtract from 6t^3+5t^2+9 to get: -4t^2+9 --- 2nd piece of the quotient: -2t -------- Multiply: -2t(2t+3) = -4t^2-6t ----- Subtract from 4t^2+9 to get: -6t-9 ---- 3rd piece of the quotient: -3 ------- Multiply -3(2t+3) = -6t-9 ------- Subtract from -6t-9 to get: 0 =========================== Final Answer: 3t^2-2t-3 =============================== Cheers, Stan H. ============= ----

Numbers_Word_Problems/543931: What is the largest number you can obtain by multiplying two real numbers whose sum is 9? 1 solutions Answer 354979 by stanbon(57984)   on 2011-12-08 09:03:58 (Show Source): You can put this solution on YOUR website! What is the largest number you can obtain by multiplying two real numbers whose sum is 9? ----- Equations: x + y = 9 -- Product = xy = x(9-x) ---- P = -x^2+9x --- Max occurs when x = -b/(2a) = -9/(2*-1) = 4.5 ---- Solve for "y": y = 9-x = 4.5 ---- Maximum product = 4.5^2 = 20.25 ====================================== Cheers, Stan H. ================