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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, >>Next

 Graphs/333452: It is a piecewise function question: it is asking to graph: Suppose that the function is defined , for all real numbers, as follows. f(x)= [-4 when x does not equal 0 [ -5 when x does equal 01 solutions Answer 238949 by stanbon(57295)   on 2010-08-20 17:32:35 (Show Source): You can put this solution on YOUR website!It is a piecewise function question: it is asking to graph: Suppose that the function is defined , for all real numbers, as follows. f(x)= [-4 when x does not equal 0 [ -5 when x does equal 0 ==== Plot the point (0,-5). Draw the line y = -4 and put an open circle at (0,-4). ======================= Cheers, Stan H. ===========
 Miscellaneous_Word_Problems/333450: The graph of y=-11x^2+154x-535 is a parabola that opens in the direction____. It has vertex____, y-intercept___, and real roots. 1. up,(7,4), 154,2 2. down,(7,4),-535,2 3. down,(7,4),-535,1 4. down,(-7,4),154,1 5.None of the above1 solutions Answer 238948 by stanbon(57295)   on 2010-08-20 17:28:35 (Show Source): You can put this solution on YOUR website!The graph of y=-11x^2+154x-535 is a parabola that opens in the direction down_. It has vertex ?, vertex at x = -b/2a = -154/(2*-11) = 7 f(7) = 4 So, vertex at (7,4) -------------- y-intercept ?, y-intercept = -535 ------------------------ and real roots, ? b^2-4ac = 154^2-4*-11*-535 = 176 Since the discriminant is positive there are 2 Real Number roots. ===================================== 1. up,(7,4), 154,2 2. down,(7,4),-535,2 3. down,(7,4),-535,1 4. down,(-7,4),154,1 5.None of the above ========================= Cheers, Stan H. =========================
 test/333451: If 1. on a scale equals 16 oz. Then how would 3 oz. appear on the scale?1 solutions Answer 238945 by stanbon(57295)   on 2010-08-20 17:14:19 (Show Source): You can put this solution on YOUR website!If 1. on a scale equals 16 oz. Then how would 3 oz. appear on the scale? --- Use a proportion: x/3oz = 1/16oz --- x = (3/16) ================= Cheers, Stan H. ==============
 Probability-and-statistics/333440: Is each question a direct variation.If it is, find the constant of variation. y+8=-x1 solutions Answer 238934 by stanbon(57295)   on 2010-08-20 16:53:43 (Show Source): You can put this solution on YOUR website!duplicate
 Probability-and-statistics/333441: is it a direct variation. if it is what is the costant of variation. y+8=-x1 solutions Answer 238933 by stanbon(57295)   on 2010-08-20 16:51:54 (Show Source): You can put this solution on YOUR website!is it a direct variation. if it is what is the costant of variation. y+8=-x -------------------- y = -x-8 --- Direct variation with constant of variation = -1 =================== Cheers, Stan H.
 Rational-functions/333392: I am attempting to solve the problem: 4x/3+6/4+(3x-2)/2 I have attempted to solve it below, but get stuck pretty quick... 4x/3+6/4+(3x-2)/2 -----> from the original problem i think you must use GCF on 6/4 which would change it to 3/2 4x/3+3/2+(3x-2)/2 -----> from here i am not sure wether to factor out the -2/2 or if i need to solve it as a quadriatic.... then from there find the LCD.... If somone could help I would be very greatful Thank you in advance Becca1 solutions Answer 238900 by stanbon(57295)   on 2010-08-20 12:49:54 (Show Source): You can put this solution on YOUR website!solve the problem: 4x/3+6/4+(3x-2)/2 ------------------- You do not have an equation, so there is no "solution". ------------------- The least common denominator is 12. Convert each fraction, as follows: --------------------- (4*4x)/12 + (3*6)/12 + (6(3x-2))/12 ----- Combine the numerators over the lcd: (16x+18+18x-12)/12 ----- (34x+6)/12 ----- Reduce: (17x+3)/6 =================================== Cheers, Stan H. ============
 Trigonometry-basics/333386: Find the remaining parts of a triangle with β=50^0 , b=5, and c=6 1 solutions Answer 238898 by stanbon(57295)   on 2010-08-20 12:32:29 (Show Source): You can put this solution on YOUR website!Find the remaining parts of a triangle with β=50^0 , b=5, and c=6 --- Using the Law of Sines, solve for angle C: --- sin(C)/6 = sin(50)/5 --- sin(C) = (6/5)sin(50) -- sin(C) = 0.9193 --- C = arcsin(0.9193) --- C = 66.82 degrees ---------------- Then A = 1-(50+66.82) A = 63.18 degrees -------------------- Now, using Law of Sines, solve for "a" and for "b". ==================== Cheers, Stan H. ====================
 Rational-functions/333334: how can i calculate the range of f(x)=x/(x^2-4)?1 solutions Answer 238858 by stanbon(57295)   on 2010-08-20 07:52:29 (Show Source): You can put this solution on YOUR website!how can i calculate the range of f(x)=x/(x^2-4)? --------- f(x) = x/(x^2-4) ------ You know that x^2-4 is >=4 ------- You know that x ranges thru all Real Number Values ------- So the quotient is "All Real Numbers". -------------- --------------- Cheers, Stan H.
 Radicals/333337: is 1/square root of 3, a surd???????????????1 solutions Answer 238856 by stanbon(57295)   on 2010-08-20 07:46:59 (Show Source): You can put this solution on YOUR website!A surd is an irrational number. --- 1/sqrt(3) is an irrational number. --- 1/sqrt(3) is a surd. ========================= Cheers, Stan H.
 test/333342: can you please explain this to me ok r/3=x/x1 solutions Answer 238855 by stanbon(57295)   on 2010-08-20 07:43:27 (Show Source): You can put this solution on YOUR website!can you please explain this to me ok r/3=x/x ----- If the "x" in the right side is not zero, the right side is equal to "1". --- Solve: r/3 = 1 --- Multiply both sides by 3 to solve for "r": r = 3 ============ Cheers, Stan H.
 Mixture_Word_Problems/333345: A chemist has 35% NaCl solution and 50% NaCl solution. How many liters of each should he mix to get 10L of NaCl solution with 40% base concentration?1 solutions Answer 238853 by stanbon(57295)   on 2010-08-20 07:41:24 (Show Source): You can put this solution on YOUR website!A chemist has 35% NaCl solution and 50% NaCl solution. How many liters of each should he mix to get 10L of NaCl solution with 40% base concentration? --------------- Equations: Quantity: x + y = 10L Quality: 0.35x + 0.50y = 0.40*10 ------------------------------------- Multiply thru 1st by 25 Multiply thru 2nd by 100 ------------------------------- Quantity: 35x + 35y = 35*10 Quality: 35x + 50y = 40*10 --------------------------------- Subtract Quantity from Quality to get: 15y = 5*10 y = 3 1/3 L (amt of 50% NaCl needed in the mixture) --- Solve for "x": x = 10- 3 1/3 = 6 2/3 L (amt of 35% NaCl needed in the mixture) =============== Cheers, Stan H.
 Probability-and-statistics/333315: 35 employees who completed two years college were asked to take basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8 respectively. In a random sample of 50 employees who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6 respectively. Estimate with 90% confidence the difference in mean scores between the two groups of employees.1 solutions Answer 238851 by stanbon(57295)   on 2010-08-20 07:34:20 (Show Source): You can put this solution on YOUR website!35 employees who completed two years college were asked to take basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8 respectively. In a random sample of 50 employees who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6 respectively. Estimate with 90% confidence the difference in mean scores between the two groups of employees. ------- I ran a 2-Smple T interval on a TI-84 and got the following: 90% CI: -1.978 < u1-u2 < 7.9778 with df = 78.7865 ====================== Cheers, Stan H.
 Probability-and-statistics/333340: Suppose a survey of 890 families with 5 children was done. a. what is the probability of observing children to be all boys or all girls? b. what is the expected number of families having 3 boys and 2 girls?1 solutions Answer 238849 by stanbon(57295)   on 2010-08-20 07:22:01 (Show Source): You can put this solution on YOUR website!Suppose a survey of 890 families with 5 children was done. a. what is the probability of observing children to be all boys or all girls? P(all are boys) = (1/2)^890 P(all are girls) = (1/2)^890 --- P(are are boys OR all are girs) = 2*(1/2)^890 = (1/2)^889 --------------------------------------------------------------- b. what is the expected number of families having 3 boys and 2 girls? P(2 girls in fam. of 5) = 5C2*(1/2)^2*(1/2)^3 = 10*(1/32) = 5/16 ======================= Cheers, Stan H.
 Geometry_Word_Problems/333233: Use the pattern to identify the next two terms or figures. 3, -6, 18, -72, 360 1 solutions Answer 238752 by stanbon(57295)   on 2010-08-19 19:17:38 (Show Source): You can put this solution on YOUR website!Use the pattern to identify the next two terms or figures. 3, -6, 18, -72, 360 ------------------------------ -6 = -2*3 18 = -3*-6 -72= -4*18 360 = -5*72 ------ Then -6*360 = -2160 And -7*-2160 = 15120 ========================== Cheers, Stan H. =============
 Probability-and-statistics/333209: You have a Normal Distribution with mean = 70 and standard deviation = 4. If you make one selection from this population, what is the probability that you get: a. a measurement of 72? b. a measurement between 71.5 and 72.5? Thanks for the help!1 solutions Answer 238749 by stanbon(57295)   on 2010-08-19 19:13:17 (Show Source): You can put this solution on YOUR website!You have a Normal Distribution with mean = 70 and standard deviation = 4. If you make one selection from this population, what is the probability that you get: a. a measurement of 72? P(x=72) = 0 Note: In a continuous distribution the probability of any single value is zero. ----------------------------- b. a measurement between 71.5 and 72.5? z(71.5) = (71.5-70)/4 = 1.5/4 = 0.3750 --- z(72.5) = (72.5-70)/4 = 2.5/4 = 0.6250 ----- P(71.5 <= x <=72.5) = P(0.3750<= z <= 0.6250) = 0.0878 ============================= Cheers, Stan H. ===============
 Probability-and-statistics/333211: You are measuring the response of a new automobile braking system and are determining skid distance during panic braking. You are willing to accept an error of 2 feet. You choose to work at the 5% level of significance. From historical data, you know that the range of data for all skidding stops is about 24 feet Thank you! 1 solutions Answer 238747 by stanbon(57295)   on 2010-08-19 19:07:56 (Show Source): You can put this solution on YOUR website!You are measuring the response of a new automobile braking system and are determining skid distance during panic braking. You are willing to accept an error of 2 feet. You choose to work at the 5% level of significance. From historical data, you know that the range of data for all skidding stops is about 24 feet --------------------- Since the range is 24 ft, 6*sigma = 24. Therefore the standard deviation = 4 ---------------------------- Sample size = [z*s/E]^2 = [1.96*4/2]^2 = 15.36 Rounding up, n = 16. =========================== Cheers, Stan H.
 Probability-and-statistics/333206: Consider a die, which has the face of the 1-spot and the 5-spot, painted red. The remaining faces of the die are white. You roll this die 12 times. It either lands with a white face up, or a red face up. a. What is the probability of getting exactly 7 red faces in these 12 rolls? b. What is the probability of getting at least 4 white faces in 12 rolls? Statics homework is kicking my butt, help would be greatly appreciated. Thanks again. 1 solutions Answer 238744 by stanbon(57295)   on 2010-08-19 19:02:38 (Show Source): You can put this solution on YOUR website! Consider a die, which has the face of the 1-spot and the 5-spot, painted red. The remaining faces of the die are white. You roll this die 12 times. It either lands with a white face up, or a red face up. P(red on each throw) = 2/6 = 1/3 P(white on each throw) = 4/6 = 2/3 ------------------------------------------- The following are binomial problems with n = 12: a. What is the probability of getting exactly 7 red faces in these 12 rolls? P(x = 7) = 12C7*(1/3)^7*(2/3)^5 = binompdf(12,1/3,7) = 0.0477 ------------------------ b. What is the probability of getting at least 4 white faces in 12 rolls? P(4<= x <=12) = 1 - binomcdf(12,1/3,3) = 0.6069 =================================================== Cheers, Stan H.
 Travel_Word_Problems/333208: An express train travels 315 kilometers in 3 hours what is the train,s average rate of speed1 solutions Answer 238732 by stanbon(57295)   on 2010-08-19 18:15:03 (Show Source): You can put this solution on YOUR website!An express train travels 315 kilometers in 3 hours what is the train,s average rate of speed ------------ Rate = distance/time ---- Rate = 315/3 = 105 km/hr ============================ Cheers, Stan H.
 expressions/333203: I really need help with this please. I am returning to school after many years and I don't know where to start with this problem. If you could please show me how to do this type of problem it would be a big help. Thank you. Simplify: 4a-{6b-2[2a-(3-b)]} I know the basic PEMDAS rules but the brackets and 3-b are confusing me.1 solutions Answer 238731 by stanbon(57295)   on 2010-08-19 18:13:02 (Show Source): You can put this solution on YOUR website!Simplify: 4a-{6b-2[2a-(3-b)]} --- Work from the inside to the outside taking one step at a time. ----------------------- 4a-{6b-2[2a-(3-b)]} --- = 4a-{6b-2[2a-3+b]} ---- = 4a-{6b-4a+6-2b} --- = 4a-{4b-4a+6} --- = 4a-4b+4a-6 --- = 8a-4b-6 ================ Cheers, Stan H. ============
 Probability-and-statistics/333201: Calculate the number of ways 6 numbers can be chosen from a list of 54. The order is not important. If this were a lottery, then 1 over this number represents the probability of winning. I cant figure out this problem help would be greatly appreciated. Thank you. 1 solutions Answer 238726 by stanbon(57295)   on 2010-08-19 18:00:27 (Show Source): You can put this solution on YOUR website!Calculate the number of ways 6 numbers can be chosen from a list of 54. The order is not important. If this were a lottery, then 1 over this number represents the probability of winning. I cant figure out this problem help would be greatly appreciated. Thank you =================== Groups of objects are called combinations. Your Answer: 54C6 = 54!/[(54-6)!*6!] = [54*53*52*51*50*49)/(1*2*3*4*5*6) = 25,827,165 ========== Probability of winning the lottery = 1/[54C6] ========== Cheers, Stan H.
 Mixture_Word_Problems/331082: What quantity of 75 per cent acid solution must be mixed with a 30 per cent solution to produce 810 mL of a 50 per cent solution? 1 solutions Answer 237354 by stanbon(57295)   on 2010-08-11 21:39:18 (Show Source): You can put this solution on YOUR website!What quantity of 75 per cent acid solution must be mixed with a 30 per cent solution to produce 810 mL of a 50 per cent solution? ---------------- acid + acid = acid 0.75x + 0.30(810-x) = 0.50*810 --- Multiply thru by 100 to get: 75x + 30*910 - 30x = 50*810 45x = 20*810 x = (4/9)(810) x = 4*90 x = 360 mL (amt. of 75% solution needed for the mixture) ============================ Cheers, Stan H.
 Linear-equations/331086: Could you please tell me if this equation has a solution or not. -8x - 3y = 6 y = -7x + 11 thank you1 solutions Answer 237352 by stanbon(57295)   on 2010-08-11 21:35:11 (Show Source): You can put this solution on YOUR website!Could you please tell me if this equation has a solution or not. -8x - 3y = 6 y = -7x + 11 -------------- Rearrange: 3y=-8x-6 y = (-8/3)y - 2 --- y = -7x+11 -------------------- The system has a solution because the two equations have different slopes. So the lines must meet at a single point. ======================================== cheers, Stan H.
 Graphs/331091: Solve and graph the solution set. |r + 5| + 3 is less than or equal to 3.1 solutions Answer 237351 by stanbon(57295)   on 2010-08-11 21:30:28 (Show Source): You can put this solution on YOUR website!Solve and graph the solution set. |r + 5| + 3 is less than or equal to 3. --- |r+5| <= 0 --- Note: absolute expressions are never < 0 --- So, |r+5| = 0 r = -5 ============= Cheers, Stan H. =============
 Equations/331095: How can I solve the equation (y-11)- (y+6) = 8y 1 solutions Answer 237350 by stanbon(57295)   on 2010-08-11 21:27:46 (Show Source): You can put this solution on YOUR website! solve the equation (y-11)- (y+6) = 8y y-11-y-6 = 8y -17 = 8y y = -17/8 =============== Cheers, Stan H.
 Expressions-with-variables/331098: how do you write an expresion for the number of hours in 5 days1 solutions Answer 237349 by stanbon(57295)   on 2010-08-11 21:26:24 (Show Source): You can put this solution on YOUR website!how do you write an expresion for the number of hours in 5 days -------------------- # of hours = 5*24 = 120 ============================= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/331096: A solid rectangular door will measure 76 2/3 inches long and 41 1/4 inches wide; and will be 1 3/8 inch thick. How many cubic inches of wood will be needed for the door? Give solution exactly as a mixed number. Include correct units with your answer.1 solutions Answer 237348 by stanbon(57295)   on 2010-08-11 21:25:13 (Show Source): You can put this solution on YOUR website!A solid rectangular door will measure 76 2/3 inches long and 41 1/4 inches wide; and will be 1 3/8 inch thick. How many cubic inches of wood will be needed for the door? Give solution exactly as a mixed number. Include correct units with your answer. --------------------------------- (76 2/3)(41 1/4)(1 3/8) = 69575/16 = 4348 7/16 ==================================================== Cheers, Stan H.
 test/331097: Write an equation to solve the problem. The sides of a triangle are in the ratio 3 : 4 : 6. What is the length of each side if the perimeter is 104 cm? 1 solutions Answer 237347 by stanbon(57295)   on 2010-08-11 21:21:23 (Show Source): You can put this solution on YOUR website!Write an equation to solve the problem. The sides of a triangle are in the ratio 3 : 4 : 6. What is the length of each side if the perimeter is 104 cm? -------------------- Equation: 3x+4x+6x = 104 13x = 104 x = 104/13 ------------------- 3x = 3[104/13] --- 4x = 4[104/13] --- 6x = 6[104/13] ==================== Cheers, Stan H. ===========
 Linear-equations/331053: Twice the greater of two consecutive odd integers is 13 less than three times the lesser. Find the integers.1 solutions Answer 237331 by stanbon(57295)   on 2010-08-11 20:10:23 (Show Source): You can put this solution on YOUR website!Twice the greater of two consecutive odd integers is 13 less than three times the lesser. Find the integers. ---- Lesser: 2x+1 Greater:2x+3 ------------------ Equation: 2(2x+3) = 3(2x+1)-13 4x+6 = 6x+3-13 2x = 16 x = 8 ----------------- Lesser: 2x+1 = 17 Greater: 2x+3 = 19 ==================== Cheers, Stan H.
 Linear-equations/331046: Could you please Simplify (-5t^3r^3)^4 If you could answer asap that would be great! thankyou!1 solutions Answer 237328 by stanbon(57295)   on 2010-08-11 20:01:46 (Show Source): You can put this solution on YOUR website!Simplify (-5t^3r^3)^4 -------------------- = 625t^12r^9 ================ Cheers, Stan H.
 Polynomials-and-rational-expressions/331047: Solve 9x^2-81=0 1 solutions Answer 237327 by stanbon(57295)   on 2010-08-11 19:59:55 (Show Source): You can put this solution on YOUR website! Solve 9x^2-81=0 ---------------- 9(x^2-9) = 0 Divide by 9 to get: (x^2-9) = 0 Factor: (x-3)(x+3) = 0 x = 3 or x = -3 ---------------- Cheers, Stan H.
 Probability-and-statistics/330976: 1. The speed of automobiles on a section of I-95 is normally distributed with a population mean of 67 miles per hour and a population standard deviation of 6 miles per hour. A random sample of 50 cars is to be selected for a speed study. A) What is the shape, mean, and standard deviation of the sampling distribution of the sample mean for samples of size 50? B) What is the probability that a sample mean will be 69 miles per hour or more? C) What is the probability that the sample mean will be between 65 and 68 miles per hour? 1 solutions Answer 237325 by stanbon(57295)   on 2010-08-11 19:57:36 (Show Source): You can put this solution on YOUR website!The speed of automobiles on a section of I-95 is normally distributed with a population mean of 67 miles per hour and a population standard deviation of 6 miles per hour. A random sample of 50 cars is to be selected for a speed study. ----------------------------- A) What is the shape, mean, and standard deviation of the sampling distribution Shape is normal; mean of the sample means = 67 mph ; std of the sample means = 6/(sqrt(50)) = (6/5)sqrt(2) ============================================== B) What is the probability that a sample mean will be 69 miles per hour or more? --- t(69) = (69-67)/[6/sqrt(50)] = 2.357 --- P(xbar >= 69) = P(t >= 2.357 when df = 49) = 0.0112 ============================================== C) What is the probability that the sample mean will be between 65 and 68 miles per hour? --- P(65 < xbar < 68) = P(-2.357 < t < 1.1785 when df = 49) = 0.8666 ==================== Cheers, Stan H. ====================