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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

 Probability-and-statistics/530010: Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost. Less than 11 pounds1 solutions Answer 349850 by stanbon(57246)   on 2011-11-11 10:33:43 (Show Source): You can put this solution on YOUR website!Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost. Less than 11 pounds ---- 6 sigma = (12-6) = 6 -- sigma = 6 === u = (12+6)/2 = 9 ------ z(11) = (11-9)/6 = 1/3 --- P(x < 11) = P(z < 1/3) = 0.6306 ================== Cheers, Stan H. ===========
 Probability-and-statistics/530013: Which of the following numbers represents the smallest amount? 0.309 1.000 0.999 0.333 11.00 1 solutions Answer 349849 by stanbon(57246)   on 2011-11-11 10:30:02 (Show Source): You can put this solution on YOUR website!Which of the following numbers represents the smallest amount? 0.309 1.000 0.999 0.333 11.00 --- Ans: 0.309 ============
 Money_Word_Problems/529847: 5. Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, R(x), and cost, C(x), are in thousands of dollars and x in thousands of units for R(x) = 100x-x2 C(x) = 1/3 x^3-6x^2+89x+100 1 solutions Answer 349775 by stanbon(57246)   on 2011-11-10 21:22:42 (Show Source): You can put this solution on YOUR website!Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, R(x), and cost, C(x), are in thousands of dollars and x in thousands of units for R(x) = 100x-x2 C(x) = 1/3 x^3-6x^2+89x+100 ---------- Profit = Revenue - Cost --- P(x) = 100x-x^2-[(1/3)x^3-6x^2+89x+100] ---- P(x) = (-1/3)x^3+5x^2+11x-100 --- P'(x) = -x^2+10x+11 --- P''(x) = -2x+10 ---- Solve: -x^2+10x+11 = 0 x^2-10x-11 = 0 (x-11)(x+1) = 0 x = -1 or x = 11 --- P''(-1) = -2(-1)+10 = 12 (minimum at (-1,f(-1))) P''(11) = -2(11)+10 = -12 (maximum at (11,f(11)) --- Graph of P(x): ================= Cheers, Stan H. ===========
 absolute-value/529848: I need a method for graphing this equation (parenthesis stand for absolute value signs): y =(x-4)-3 If someone could explain this to me thoroughly, that would help a lot. Thanks!1 solutions Answer 349767 by stanbon(57246)   on 2011-11-10 20:57:43 (Show Source): You can put this solution on YOUR website!I need a method for graphing this equation (parenthesis stand for absolute value signs): y =(x-4)-3 If someone could explain this to me thoroughly, that would help a lot. Thanks! ----------- y = |x-4|-3 --- y = |x-4| is a "V" with bottom point at (4,0) and opening up. ---- The "-3" in the equation causes all the y-values to be "3" lower, so the bottom of the "V" is at (4,-3). -------------------- -------------- Cheers, Stan H. =======
 Polynomials-and-rational-expressions/529844: how would i write a polynomial equation with rational coefficients in standard form with the given solutions of so far I've gotten then I'm not sure what to do after that.1 solutions Answer 349766 by stanbon(57246)   on 2011-11-10 20:53:16 (Show Source): You can put this solution on YOUR website!write a polynomial equation with rational coefficients in standard form with the given solutions of ---- If it is going to have rational coefficients it must also have as solutions -sqrt(3) and -2i. --- So you have: f(x) = (x-sqrt(3))(x+sqrt(3))(x-2i)(x+2i) --- f(x) = (x^2-3)(x^2+4) --- f(x) = x^4+x^2-12 ===================== cheers, Stan H.
 Complex_Numbers/529836: Evaluate the expression (sqrt(-5))/(sqrt(-1)sqrt(-7)) and write the result in the form a+bi. The real number a= The real number b=1 solutions Answer 349764 by stanbon(57246)   on 2011-11-10 20:47:57 (Show Source): You can put this solution on YOUR website!Evaluate the expression (sqrt(-5))/(sqrt(-1)sqrt(-7)) and write the result in the form a+bi. -------------------- (sqrt(-5))/(sqrt(-1)sqrt(-7)) --- = sqrt(-5)/(i*sqrt(7)i) ----- = sqrt(5)i/(-sqrt(7)) --- = sqrt(35)i/(-7) --- = 0 -(1/7)sqrt(35)i ------------------------ The real number a= 0 The real number b= (-1/7)sqrt(35) ====================================== Cheers, Stan H. =================
 Trigonometry-basics/529744: Please help me solve this equation: x^3+2x^2+3x+6=01 solutions Answer 349760 by stanbon(57246)   on 2011-11-10 20:15:28 (Show Source): You can put this solution on YOUR website!Please help me solve this equation: x^3+2x^2+3x+6 = 0 Factor: x^2(x+2)+3(x+2) = 0 Factor: (x+2)(x^2+3) = 0 --- x = -2 or x = sqrt(3)i or x = -sqrt(3)i ============================================ Cheers, Stan H. ================
 Age_Word_Problems/529805: Mickey is 5 years older than Minnie. Three more than four times Minnie's age is 2 less than 3 times Mickey's age. How old is each person?1 solutions Answer 349758 by stanbon(57246)   on 2011-11-10 20:11:14 (Show Source): You can put this solution on YOUR website!Mickey is 5 years older than Minnie. Three more than four times Minnie's age is 2 less than 3 times Mickey's age. How old is each person? ---- Equations: k = n + 5 4n+3 = 3k-2 ------------ Substitute for "k" and solve for "n": 4n+3 = 3(n+5)-2 4n+3 = 3n+13 n = 10 (Minnie's age now) --- solve for "k": k = n + 5 k = 15 (Mickey's age now) =============================== Cheers, Stan H. ===============
 Mixture_Word_Problems/529818: A tank contains 20 gallons of antifreeze solution.  When it is full, it contains 15% antifreeze.  How many gallons must be replaced by an 80% antifreeze solution to get 20 1 solutions Answer 349757 by stanbon(57246)   on 2011-11-10 20:07:51 (Show Source): You can put this solution on YOUR website!A tank contains 20 gallons of antifreeze solution. When it is full, it contains 15% antifreeze. How many gallons must be replaced by an 80% antifreeze solution to get 20 ---- Equation: alcohol - alcohol + alcohol = alcohol 0.15*20 - 0.15x + 0.80x = ?*20 ------------- You post does not state the % of alcohol in the final solution. ============== cheers, Stan H.
 Equations/529813: Could you please help me with this problem? I came up with 42/91 but I don't know if that is right because I don't know if I did them in the right order. 2 1/3 / 1 1/6 * 3 1/4 / 1 1/31 solutions Answer 349755 by stanbon(57246)   on 2011-11-10 20:04:23 (Show Source): You can put this solution on YOUR website!I came up with 42/91 but I don't know if that is right because I don't know if I did them in the right order. 2 1/3 / 1 1/6 * 3 1/4 / 1 1/3 --- [(7/3)/(7/6)] ---- = (6/3)*(39/16) ---- = (1/2)(39/16) --- = (39/32) ============ Cheers, Stan H. ===============
 test/529817: Through (4,2) parrallel to y=-3/4x-51 solutions Answer 349753 by stanbon(57246)   on 2011-11-10 19:55:19 (Show Source): You can put this solution on YOUR website!Through (4,2) parallel to y=-3/4x-5 --- Slope must be -3/4 and y = 2 when x = 4 Form y = mx + b Solve for "b": 2 = (-3/4)4+b b = 5 ---- Equation; y = (-3/4)x + 5 ================== Cheers, Stan H. =========
 Probability-and-statistics/529717: How many different ways can 4 aces be dealt to one person, order matters.1 solutions Answer 349726 by stanbon(57246)   on 2011-11-10 19:13:54 (Show Source): You can put this solution on YOUR website!1st card: 4 choices 2nd card: 3 choices 3rd card: 2 choices 4th card: 1 choice ---- Total = 4! = 24 ways ========================== Cheers, Stan H. =============
 Probability-and-statistics/529437: The sitting height (from seat to top of head) of drivers must be considered in the design of a new car model. Men have sitting heights that are normally distributed with a mean of 36.0 inches and a standard deviation of 1.4 inches. Engineers have provided plans that can accommodate men with sitting heights up to 38.8 heights, but taller men cannot fit. If a man is randomly selected, find the probability that he has a sitting height less than 38.8 inches. Is it possible for a customer paying by check to spend more than \$185? Explain. 1 solutions Answer 349639 by stanbon(57246)   on 2011-11-10 13:31:26 (Show Source): You can put this solution on YOUR website!The sitting height (from seat to top of head) of drivers must be considered in the design of a new car model. Men have sitting heights that are normally distributed with a mean of 36.0 inches and a standard deviation of 1.4 inches. Engineers have provided plans that can accommodate men with sitting heights up to 38.8 heights, but taller men cannot fit. If a man is randomly selected, find the probability that he has a sitting height less than 38.8 inches. --- z(38.8) = (38.8-36)/1.4 = 2 ---- P(x < 38.8) = P(z < 2) = normalcdf(-100,2) = 0.9772 ===================== Cheers, Stan H. =====================
 Probability-and-statistics/529494: telephone answering devices. Seventy-seven percent of U>S> homes have a telephone answering device. In a random sample of 290 home, what is the probability that more than 50 do not have an answering device?1 solutions Answer 349637 by stanbon(57246)   on 2011-11-10 13:23:24 (Show Source): You can put this solution on YOUR website!telephone answering devices. Seventy-seven percent of U>S> homes have a telephone answering device. In a random sample of 290 home, what is the probability that more than 50 do not have an answering device? ---- 23% do not have answering device. Binomial Problem with n = 290 and p(not) = 0.23 --- P(51<= x <=290) = 1 - P(0<= x <= 50) = 0.9898 ============================ Cheers, Stan H.
 Probability-and-statistics/529602: If two cards are drawn from a standard 52 card deck without replacement, in how many different ways is it possible to obtain a heart on the first draw and an ace on the second?1 solutions Answer 349636 by stanbon(57246)   on 2011-11-10 13:18:28 (Show Source): You can put this solution on YOUR website!If two cards are drawn from a standard 52 card deck without replacement, in how many different ways is it possible to obtain a heart on the first draw and an ace on the second? ------- # of ways to succeed: 12*4 ways to pick a heart, not the ace of hearts, followed by an ace = 48 --- # of ways to succeed; 1 way to pick ace of hearts followed by ace = 1*3 = 3 --- Total ways to succeed: 51 ----- Total # of random pairs: 52C2 = 1326 ----- Probability = 51/1326 = 0.0385 ================================ Cheers, Stan H. ==============
 Probability-and-statistics/529522: a couple plans to have three children until they get a girl but they agree they will not have more than three children eveen if they have all boys. Assume the probablity of having a girl is 45%. what is the probability of having three children.1 solutions Answer 349633 by stanbon(57246)   on 2011-11-10 13:08:33 (Show Source): You can put this solution on YOUR website!To have 3 children they would need to have 2 boys then the 3rd child. ---- P(bb*) = (1/2)(1/2)*1 = 1/4 ======================= Cheers, Stan H. ===========
 Probability-and-statistics/529575: a multiple choice test consists of 4 questions, each of which has four possible answers. In how many ways could the test be answered? 1 solutions Answer 349631 by stanbon(57246)   on 2011-11-10 13:03:09 (Show Source): You can put this solution on YOUR website!a multiple choice test consists of 4 questions, each of which has four possible answers. In how many ways could the test be answered? ---- 1st question: 4 ways 2nd question: 4 ways 3rd question: 4 ways 4th question: 4 ways --- Total ways = 4^4 = 256 ways ============================== Cheers, Stan H. ==========
 Probability-and-statistics/529615: State the null hypothesis Ho and the alternative hypothesis Ha that would be used for a hypothesis test of the following: The mean age of the students enrolled in evening classes at a certain college is greater than 26 years. 1 solutions Answer 349630 by stanbon(57246)   on 2011-11-10 13:00:11 (Show Source): You can put this solution on YOUR website!State the null hypothesis Ho and the alternative hypothesis Ha that would be used for a hypothesis test of the following: The mean age of the students enrolled in evening classes at a certain college is greater than 26 years. ----- Rule: Ho must ALWAYS include equality. --- Ho: u <= 26 Ha: u > 26 (claim) ------ Cheers, Stan H.
 Triangles/529470: the measure of the angles of a triangle are in the ratio of 1:2:6 find the measure of each angle1 solutions Answer 349602 by stanbon(57246)   on 2011-11-10 07:05:15 (Show Source): You can put this solution on YOUR website!the measure of the angles of a triangle are in the ratio of 1:2:6 find the measure of each angle --------- Equation: x + 2x + 6x = 180 9x = 180 x = 20 degrees 2x = 40 degrees 6x = 120 degrees --- Cheers, Stan H. =============
 Linear-systems/529465: Determine whether the point (0, -8) is a solution of the system -3x + 9y = 72 9x + 3y = 24 by substituting the point into each equation. 1 solutions Answer 349601 by stanbon(57246)   on 2011-11-10 07:03:10 (Show Source): You can put this solution on YOUR website!Determine whether the point (0, -8) is a solution of the system -3x + 9y = 72 9x + 3y = 24 by substituting the point into each equation. ---- -3*0 + 9*-8 = 72:::::::false 9*0 + 3*-8 = 24:::::::false =================== It is not a solution. =================== Cheers, Stan H.
 Mixture_Word_Problems/529466: Eric needs to fill up his gas tank which holds 21 liters and is currently a third empty how many liters of gas will it take to fill the tank?1 solutions Answer 349599 by stanbon(57246)   on 2011-11-10 07:00:16 (Show Source): You can put this solution on YOUR website!Eric needs to fill up his gas tank which holds 21 liters and is currently a third empty how many liters of gas will it take to fill the tank? --- Ans: (1/3)21 = 7 gallons (amt. he needs to fill the tank) ========== Cheers, Stan H.
 Travel_Word_Problems/529459: A train is moving at the speed of 90 km/h. What is the speed of the train in m/s?1 solutions Answer 349598 by stanbon(57246)   on 2011-11-10 06:58:19 (Show Source): You can put this solution on YOUR website!A train is moving at the speed of 90 km/h. What is the speed of the train in m/s? --------- 90 (km/h)(1000 m/1 km)(1hr/3600 sec) = (90*1000*1)/(1*1*3600)(meters/sec) --- = 25 (meters/sec) ===================== Cheers, Stan H. ==========
 Probability-and-statistics/528866: A botanist is studying a new hybrid Kentucky blue grass seed. It is known that these grass seeds have a 95% probability of germinating. If six seeds were planted what is the probability that exactly four seeds will germinate? or at least five will germinate? or at most one will not germinate?1 solutions Answer 349571 by stanbon(57246)   on 2011-11-09 22:09:16 (Show Source): You can put this solution on YOUR website!A botanist is studying a new hybrid Kentucky blue grass seed. It is known that these grass seeds have a 95% probability of germinating. If six seeds were planted what is the probability:: --- Binomial Problems with n = 6 and p(germinate) = 0.95 ; p(not germ) = 0.05 ------------------- P(that exactly four seeds will germinate) = 6C4*0.95^4*0.05^2 = 0.0305 ---------------------- P(at least five will germinate) = 1 - binomcdf(6,0.45,4) = 0.9672 ----------------------- P(at most one will not germinate) = 1 - P(all will germinate) = 1 - 0.95^6 = 0.2649 ======================== Cheers, Stan H. ========================
 Probability-and-statistics/529155: m/-11+1=-10 what is m1 solutions Answer 349569 by stanbon(57246)   on 2011-11-09 21:56:16 (Show Source): You can put this solution on YOUR website!m/-11+1=-10 what is m ---- (m/-11) + 1 = -10 --- (m/-11) = -11 --- m = (-11)(-11) --- m = 121 ============== cheers, Stan H.
 Probability-and-statistics/529165: Traffic researchers determined that at a particular stop light, there is a 45% chance that drivers will come to a complete stop on a red light, and a 55% chance they will drive through the light without doing so. What is the probability that 4 of the first 12 drivers that arrive at the light during a period of observation will completely stop?1 solutions Answer 349568 by stanbon(57246)   on 2011-11-09 21:54:16 (Show Source): You can put this solution on YOUR website!Traffic researchers determined that at a particular stop light, there is a 45% chance that drivers will come to a complete stop on a red light, and a 55% chance they will drive through the light without doing so. What is the probability that 4 of the first 12 drivers that arrive at the light during a period of observation will completely stop? ----------- Binomial Problem with n = 12 and p(stop)= 0.45 ------ P(x = 4) = 12C4*0.45^4*0.55^8 = 0.1700 ------------------- Cheers, Stan H. ==============
 Probability-and-statistics/529179: For the following, would you calculate simple probability, conditional probability, or binomial probability? a) The probability of picking a second winning number in a lottery. b) The probability of selecting three correct answers in a multiple choice test of 10 questions by guessing. c) The probability of your bus being late on the day of an important test in statistics. d) The probability of selecting nine correct answers on a test with 15 true / false questions. e) The probability of getting three broken eggs in the same carton of a dozen eggs.1 solutions Answer 349565 by stanbon(57246)   on 2011-11-09 21:50:22 (Show Source): You can put this solution on YOUR website!For the following, would you calculate simple probability, conditional probability, or binomial probability? a) The probability of picking a second winning number in a lottery.::conditional b) The probability of selecting three correct answers in a multiple choice test of 10 questions by guessing.::binomial c) The probability of your bus being late on the day of an important test in statistics.:::simple prob d) The probability of selecting nine correct answers on a test with 15 true / false questions.:: binomial e) The probability of getting three broken eggs in the same carton of a dozen eggs.:::binomial ==================== Cheers, Stan H. ====================
 Probability-and-statistics/529199: A bag contains lottery balls that are numbered 1 throught 15. If you draw two numbers without replacement, what is the probability that you will draw two even numbers?1 solutions Answer 349563 by stanbon(57246)   on 2011-11-09 21:47:02 (Show Source): You can put this solution on YOUR website!A bag contains lottery balls that are numbered 1 throught 15. If you draw two numbers without replacement, what is the probability that you will draw two even numbers? ----- There are 8 "even" balls. # of ways to succeed: 8C2 = 28 # of ways to draw a pair randomly: 15C2 = 105 --- P(draw 2 even) = 28/105 =========================== Cheers, Stan H. =========
 Probability-and-statistics/529348: A box contains 7 red balls and 7 blue balls. If we choose three random balls, how many ways can we choose exactly 1 red ball?1 solutions Answer 349561 by stanbon(57246)   on 2011-11-09 21:44:25 (Show Source): You can put this solution on YOUR website!A box contains 7 red balls and 7 blue balls. If we choose three random balls, how many ways can we choose exactly 1 red ball? ---- # of ways to select 1 red ball: 7 # of ways to select 2 blue: 7C2 = 21 ---- # of ways when select 3 to select 1 red: 7*21 = 147 ========================================================== Cheers, Stan H. ===========
 Probability-and-statistics/529304: a department store has 22 major departments, only 4 of which can be featured in the next sales flyer. Find the number of ways this can be done if: a) order of appearance in the flyer is not important b)order of appearance in the flyer is important1 solutions Answer 349560 by stanbon(57246)   on 2011-11-09 21:41:53 (Show Source): You can put this solution on YOUR website!a department store has 22 major departments, only 4 of which can be featured in the next sales flyer. Find the number of ways this can be done if: a) order of appearance in the flyer is not important:: # of ways to select 4::: 22C4 = 7315 ---------------------------------------------- b)order of appearance in the flyer is important select 4 then put them in order: 7315*4! = 175,560 ================= Cheers, Stan H.
 real-numbers/529336: if the answer is m=0 does that make it all real numbers or no solutions? how?1 solutions Answer 349552 by stanbon(57246)   on 2011-11-09 21:23:37 (Show Source): You can put this solution on YOUR website!if the answer is m=0 does that make it all real numbers or no solutions? how? --- If m = 0 the equation is y = k where k is some Real Number. ----- The graph will be a horizontal line thru all points where y = k. --- The domain is All Real Numbers. The range is {k} ================== Cheers, Stan H. =============