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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 , 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 Polynomials-and-rational-expressions/511537: I need to know how to sove these problems. I sort of understand how to rewrite the problem but not solving it. what steps am I missing? 1 solutions Answer 342253 by stanbon(57387)   on 2011-10-08 16:14:16 (Show Source): You can put this solution on YOUR website!Problem missing from your post. Cheers, Stan H.
 Geometry_Word_Problems/511535: The area of a rectangle is 12 meters. If its width is 2 4/7 meters, find its length.1 solutions Answer 342252 by stanbon(57387)   on 2011-10-08 16:12:41 (Show Source): You can put this solution on YOUR website!The area of a rectangle is 12 meters square. If its width is 2 4/7 meters, find its length. ----- Area = length*width 12 m^2 = (L)(2 4/7 meters) --- Length = 12/(18/7) meters ---- Length = 14/3 = 4 2/3 meters ================================= Cheers, Stan H. ====================
 Probability-and-statistics/511531: A particular professor never dismisses class early. Let x denote the amount of time past the hour (minutes) that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 min. The density curve is shown in the following figure. (a) What is the probability that at most 4 min elapse before dismissal? (b) What is the probability that between 3 and 7 min elapse before dismissal?1 solutions Answer 342250 by stanbon(57387)   on 2011-10-08 16:03:18 (Show Source): You can put this solution on YOUR website!A particular professor never dismisses class early. Let x denote the amount of time past the hour (minutes) that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 min. The density curve is shown in the following figure. -------------------------------------- base of distribution: 10 height of distribution: 1/10 -------- (a) What is the probability that at most 4 min elapse before dismissal? P(0<= x <=4) = base* height = 4*(1/10) = 2/5 ------------------------ (b) What is the probability that between 3 and 7 min elapse before dismissal? P(3<= x <=7) = base*height = 4*(1/10) = 2/5 ================== Cheers, Stan H. ==================
 Probability-and-statistics/511455: . For the table that follows, answer the following questions: x y 1 1/3 2 2/3 3 1 4 - Would the correlation between x and y in the table above be positive or negative? - Find the missing value of y in the table. - How would the values of this table be interpreted in terms of linear regression? - If a "line of best fit" is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative? (Points : 4) 1 solutions Answer 342220 by stanbon(57387)   on 2011-10-08 12:12:10 (Show Source): You can put this solution on YOUR website!For the table that follows, answer the following questions: x y 1 1/3 2 2/3 3 1 4 4/3 -------------- Would the correlation between x and y in the table above be positive or negative?:::positive: as x increases, y increases. -------------------------- - Find the missing value of y in the table.:: 4/3 ---------------------- - How would the values of this table be interpreted in terms of linear regression? y = (1/3)x-(1/3) -------------------------- - If a "line of best fit" is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative? Ans: positive --------------------- Cheers, Stan H. =============
 Average/511427: Paul wrote five test which were marked out of a total of 200 marks. His average was 60%. Paul scored 40 out of 50 in a 6th test. What is his NEW average?1 solutions Answer 342211 by stanbon(57387)   on 2011-10-08 11:07:58 (Show Source): You can put this solution on YOUR website!Paul wrote five test which were marked out of a total of 200 marks. His average was 60%. -------------------------- Paul scored 40 out of 50 in a 6th test. What is his NEW average? ---- Old total marks: 200 Paul's total marks: 0.6*200 = 120 ------------------- New total marks: 200+50 = 250 Paul's new total marks: 120 + 40 = 160 ---- Paul's new percentage: 160/250 = 0.64 or 64% ============================================= cheers, Stan H. ==============
 Unit_Conversion_Word_Problems/511425: What is the easiest way to convert units for example 5mi in 1 hour what is this rate in minutes?1 solutions Answer 342210 by stanbon(57387)   on 2011-10-08 11:01:47 (Show Source): You can put this solution on YOUR website!What is the easiest way to convert units? Answer: Use "unit conversion fractions" Example: Since 12 inches = 1 ft you can for the fraction (12 inches/1 ft) which is a "unit conversion fraction for converting ft. to inches. --------------------------------- for example 5mi in 1 hour what is this rate in minutes? 5 mi per hour = (5 mi/1 hr)(1 hr/60 min) = (5*1)/(1*60)(mile/min) = (1/12)(mile/min) ======================= Cheers, Stan H.
 Graphs/511426: Graph the equation : f(x)= x^2-5x+6. Clearly label the x-axis, y-axis and origin. State the domain and range of the above function by predicate notation. Please help me out with this problem.1 solutions Answer 342208 by stanbon(57387)   on 2011-10-08 10:55:18 (Show Source): You can put this solution on YOUR website!Graph the equation : f(x)= x^2-5x+6. Clearly label the x-axis, y-axis and origin. ---- f(x) = (x-3)(x-2) ---- x-intercept: Let y = 0 then x = 2 or x = 3 Plot points at (2,0) and at at (3,0) The vertex occurs half-way between the x-intercepts Vertex (5/2 , -1/4) --- y-intercept: Let x = 0, then y = 6 Plot point at (0,6) --- ---------------------- State the domain and range of the above function by predicate notation. Domain: All Real Numbers Range: y >= -1/4 ======================= cheers, Stan H. ================
 Polygons/511401: Find the sum of the interior angles of a polygon with 39 sides.1 solutions Answer 342197 by stanbon(57387)   on 2011-10-08 08:27:04 (Show Source): You can put this solution on YOUR website!Find the sum of the interior angles of a polygon with 39 sides. --- Sum of the EXTERIOR angles is 360. --- Each exterior angle is 360/39 = 9.2308 degrees --- Therefore, each interior angle is 180-9.2308 = 170.7692 degrees --- So the sum of the interior angles is 39*170.7592 = 6660 degrees ==================== Cheers, Stan H.
 Numeric_Fractions/511347: what is an expression equivelent to 12/13 with a denominator of 39b?1 solutions Answer 342196 by stanbon(57387)   on 2011-10-08 08:23:49 (Show Source): You can put this solution on YOUR website!what is an expression equivelent to 12/13 with a denominator of 39b? --- Multiply numerator and denominator by 3b to get: --- (12/13)(3b/3b) = 36b/39b ============================= Cheers, Stan H. ============
 Probability-and-statistics/511397: 1. Suppose we want to determine the (binomial) probability (p) of getting 6 heads in 13 flips of a 2-sided coin. Using Table 2 in Appendix B of the text, what values of n, x, and p would we use to look up this probability, and what would be the probability? This is what I think I know: n = 11 x = 6 p = .50q = 1-p = .50 I think this is the forumula I use: 11/(11-6)6 (.50)^2(.50)^5 = I can't figure out any more or even if what I have done is correct. I need some line for line, number to number detail so I can really learn and understand this please.1 solutions Answer 342195 by stanbon(57387)   on 2011-10-08 08:17:41 (Show Source): You can put this solution on YOUR website! Suppose we want to determine the (binomial) probability (p) of getting 6 heads in 13 flips of a 2-sided coin. --- The 6 heads can show up is 13C6 = 1716 mutually exclusive ways. --- Each of those ways has probability (1/2)^6*(1/2)^7 = 1/2^13 = 1/8192 ==== Because the 1716 ways to succeed are mutually exclusive you should add all 1716 of those separate probabilities to get the final probability. ------ You could add but it's easier to just multiply 1716*(1/8192) = 0.2095 --- In general, if there are n trials, and the probability of success on each trial is "p", the probability of "k" successes is as follows: P(x = k) = nCk*p^k*q^(n-k) ============================== Cheers, stan H. ===============
 test/511334: How many gallons of water must be added to 40 gallons of 10% alcohol solution to produce an 8% alcohol solution?1 solutions Answer 342153 by stanbon(57387)   on 2011-10-07 23:00:49 (Show Source): You can put this solution on YOUR website!How many gallons of water must be added to 40 gallons of 10% alcohol solution to produce an 8% alcohol solution? ----- Equation: water + water = water x + 0.90*40 = 0.92(x+40) ---- Multiply thru by 100 to get: 100x + 90*40 = 92x + 92*40 ---- 8x = 2*40 x = 10 gallons (amt. of water to add) ======================================== cheers, stan H. ===================
 test/511341: If -3 < k < 3, which of the following must be true? a. k^2 < 3 b. |k| > 3 c. k^2 > 3 d. k^2 < 9 e. k^2 > 9 1 solutions Answer 342151 by stanbon(57387)   on 2011-10-07 22:57:14 (Show Source): You can put this solution on YOUR website!If -3 < k < 3, which of the following must be true? a. k^2 < 3-----false b. |k| > 3-----false c. k^2 > 3-----false d. k^2 < 9-----true e. k^2 > 9-----false ========================== Cheers, Stan H.
 Inequalities/511313: the depreciation for the corporate airplane from 2006 to 2009. The plane was purchased new in 2006; therefore, x = 0 represents the year 2006. X � axis (horizontal) = years starting from 0 = 2006 and increasing by 0.5 years Y � axis (vertical) = price in \$ amounts from 24,000 to 240,000 List the coordinates of two points on the graph in (x, y) form. (2.0, 216000),(3.0,204000) b) Find the slope (rate of depreciation) of this line: c) Find the linear equation of this line in slope-intercept form. d) If the rate of depreciation continues at the present rate, what will be the plane’s value in the year 2017? Show how to use the linear equation from part c) to obtain your answer. e) If the trend continued, in how many years would the plane’s value be \$48000? Show how to use the linear equation from part c) to obtain your answer. 1 solutions Answer 342149 by stanbon(57387)   on 2011-10-07 22:54:28 (Show Source): You can put this solution on YOUR website!the depreciation for the corporate airplane from 2006 to 2009. The plane was purchased new in 2006; therefore, x = 0 represents the year 2006. X � axis (horizontal) = years starting from 0 = 2006 and increasing by 0.5 years Y � axis (vertical) = price in \$ amounts from 24,000 to 240,000 List the coordinates of two points on the graph in (x, y) form. (2.0, 216000),(3.0,204000) ------------- b) Find the slope (rate of depreciation) of this line: slope = (204000-216000)/(3-2) = -12000 ----------------------------------------------- c) Find the linear equation of this line in slope-intercept form. Form: y = mx+b 216000 = -12000*2 + b b = 240000 y = -12000x + 240000 -------------------------- d) If the rate of depreciation continues at the present rate, what will be the plane’s value in the year 2017? Show how to use the linear equation from part c) to obtain your answer. --- 2017-2006 = 11 f(11) = -12000*11+240000 = \$108,000 ------------------------ e) If the trend continued, in how many years would the plane’s value be \$48000? Show how to use the linear equation from part c) to obtain your answer. --- Solve: -12000x + 240,000 = 48000 -12000x = -192000 x = 16 years ======================== ================================= Cheers, Stan H. =================================
 Probability-and-statistics/511339: 5. Using data from Boston, Massachusetts, a test of independence is run on the claim that ice cream sales per month and the number of car wrecks per month are independent. The claim is rejected. 1 solutions Answer 342147 by stanbon(57387)   on 2011-10-07 22:48:04 (Show Source): You can put this solution on YOUR website!Question missing
 test/511336: 1) If -3 < k < 3, which of the following must be true? 2) If f is a linear function and f(3) = 6 and f(5) = 12, what is the slope of the graph of f? 1 solutions Answer 342146 by stanbon(57387)   on 2011-10-07 22:47:17 (Show Source): You can put this solution on YOUR website!1) If -3 < k < 3, which of the following must be true? --- Comment: data missing ------------------------------------ 2) If f is a linear function and f(3) = 6 and f(5) = 12, what is the slope of the graph of f? --- slope = (12-6)/(5-3) = 6/2 = 3 ==================================== Cheers, Stan H. ==========
 test/511335: Which of the following cannot be possible to construct a triangle with the given side lengths? 1 solutions Answer 342145 by stanbon(57387)   on 2011-10-07 22:45:17 (Show Source): You can put this solution on YOUR website!Which of the following cannot be possible to construct a triangle with the given side lengths? ------------------------ Rule: the sum of each pair of sides must be longer than the 3rd side a. 28, 34, 39 b. 35, 120, 125 c. 40, 50, 60 d. 3,6,9----------not a triangle e. 6,7,11 =============== Cheers, Stan H. ============
 Probability-and-statistics/511222: Table 1 White Black Hispanic Asian Foreign Total Dept.1 4 0 1 1 2 8 Dept.2 2 4 1 1 0 8 Dept. 3 1 2 3 1 1 8 Dept. 4 4 0 1 1 2 8 Dept. 5 3 2 1 0 2 8 Total 14 8 7 4 7 40 Table 2 Female Male Total Black 6 2 8 White 6 8 14 Hispanic 3 4 7 Asian 2 2 4 Foreign 2 5 7 Total 19 21 40 Please refer to the conditional probability table or complete it first before attempting this assignment. The CEO has asked for a committee to be formed to approve and review promotions. Please list all your answers in percentages? From Table 1, what is the probability of choosing an African American employee? From Table 2, what is the probability of choosing an Asian female given all females? From Table 1, what is the probability of choosing a White employee from Dept. 2 and then an Hispanic employee from Dept. 3? From Table 2, what is the probability of choosing a Black male or Foreign male? From Table 1, what is the probability of choosing a Foreigner or an Hispanic both from Department 5? 1 solutions Answer 342144 by stanbon(57387)   on 2011-10-07 22:42:45 (Show Source): You can put this solution on YOUR website!Table 1 White Black Hispan Asian Foreign Total Dept.1 4 0 1 1 2 8 Dept.2 2 4 1 1 0 8 Dept.3 1 2 3 1 1 8 Dept.4 4 0 1 1 2 8 Dept.5 3 2 1 0 2 8 Total 14 8 7 4 7 40 Table 2 Female Male Total Black 6 2 8 White 6 8 14 Hispan 3 4 7 Asian 2 2 4 Foreign 2 5 7 Total 19 21 40 From Table 1, what is the probability of choosing an African American employee?:::8/40 = 20% From Table 2, what is the probability of choosing an Asian female given all females?:: 2/19 = 10.5% From Table 1, what is the probability of choosing a White employee from Dept. 2 and then an Hispanic employee from Dept. 3?:: (2+3)/40 = 20% From Table 2, what is the probability of choosing a Black male or Foreign male?::: no Foreign column listed From Table 1, what is the probability of choosing a Foreigner or an Hispanic both from Department 5?::: (2+1)/40 = 7.5% ==================== Cheers, Stan H.
 Probability-and-statistics/511145: A man claims to have extrasensory perception. As a test, a fair coin is flipped 28 times, and the man is asked to predict the outcome in advance. He gets 20 out of 28 correct. What is the probability that he would have done at least this well if he had no ESP?1 solutions Answer 342141 by stanbon(57387)   on 2011-10-07 22:29:26 (Show Source): You can put this solution on YOUR website!A man claims to have extrasensory perception. As a test, a fair coin is flipped 28 times, and the man is asked to predict the outcome in advance. He gets 20 out of 28 correct. What is the probability that he would have done at least this well if he had no ESP? ----------------------- Binomial Problem with n = 28 and p(correct) = 1/2 ------ P(20<= x <=28) = 1-P(0<= x <=19) = 1 - binomcdf(28,1/2,19) = 0.0178 ------------------- Cheers, Stan H. ===================
 Probability-and-statistics/511210: A hair salon did a survey of 360 customers regarding satisfaction with service and type of customer. a walk-in customer is one who has seen no ads and not been referred. the other customers either saw a TV ad or were referred to the salon, (but not both) Assume the sample represents the entire population of customers. Find the probaility that a customer is a. not satisfied b. not satisfied and walk-in not satisfied, given referred d. very satisfied e. very satisfied, given referred very satisfied, given referred f. very satisfied and a tv ad g. are the events satisfied and referred independant or not?1 solutions Answer 342138 by stanbon(57387)   on 2011-10-07 22:21:04 (Show Source): You can put this solution on YOUR website!No data posted.
 Probability-and-statistics/511331: There is a 35% chance that X is above what value?1 solutions Answer 342136 by stanbon(57387)   on 2011-10-07 22:18:49 (Show Source): You can put this solution on YOUR website!There is a 35% chance that X is above what value? --- Insufficient information. Cheers, Stan H. ======
 Equations/511329: This nut bread contains: 3 times as many pecans as Brazil nuts, one more walnut than Brazil nuts, 6 nuts in all How do I set this problem up? I am in pre algebra and we are simplifying algebraic equations. It is confusing to me. Thank you!1 solutions Answer 342134 by stanbon(57387)   on 2011-10-07 22:14:18 (Show Source): You can put this solution on YOUR website!This nut bread contains: 3 times as many pecans as Brazil nuts, one more walnut than Brazil nuts, 6 nuts in all ==== Let number of Brazil nuts be "x" Then number of walnuts is "x+1" And number of pecans is "3x" ---- Equation: x + x+1 + 3x = 6 5x + 1 = 6 5x = 5 x = 1 --- # of Brazil nuts = x = 1 # of walnuts is x+1 = 2 # of pecans is 3x = 3*1 = 3 ================================= Cheers, Stan H. ==============
 Equations/511327: Find the solution by using the addition method. x+6y= -4, -x-4y= 21 solutions Answer 342131 by stanbon(57387)   on 2011-10-07 22:09:21 (Show Source): You can put this solution on YOUR website!Find the solution by using the addition method. x + 6y = -4 -x- 4y = 2 ---------- Add and solve for "y": 2y = -2 y = -1 --- Solve for "x": x + 6y = -4 x + 6*-1 = -4 x -6 = -4 x = 2 ------- Solution: (2,-1) ====================== Cheers, Stan H. ======================
 test/511296: If a job can be completed by 2 workers in 10 days, then what is the number of workers needed to complete the job in 5 days? 1 solutions Answer 342112 by stanbon(57387)   on 2011-10-07 21:13:12 (Show Source): You can put this solution on YOUR website!If a job can be completed by 2 workers in 10 days, then what is the number of workers needed to complete the job in 5 days? ----- Days and # of workers are indirectly related: w = k/d --- Solve for "k" using "2 workers in 10 days": 2 = k/10 k = 20 ----- Equation: w = 20/d ----------- what is the number of workers needed to complete the job in 5 days? w = 20/5 # of workers = 4 ======================== Cheers, Stan H. ========================
 percentage/511312: the population of village is encreasing at 5% per annum,The population after 2 yrs will become 4410.what was the population in the begining i.e. before 2 yrs1 solutions Answer 342111 by stanbon(57387)   on 2011-10-07 21:09:23 (Show Source): You can put this solution on YOUR website!answered
 Mixture_Word_Problems/511304: how many milliliters of water must be added to 250 ml of 25% salt solution to reduce its concentration to 10%1 solutions Answer 342110 by stanbon(57387)   on 2011-10-07 21:08:13 (Show Source): You can put this solution on YOUR website!how many milliliters of water must be added to 250 ml of 25% salt solution to reduce its concentration to 10% ------------------ Equation: water + water = water x + 0.75*250 = 0.90(x+250) ---- Multiply thru by 100 to get: 100x + 75*250 = 90x + 90*250 10x = 15*250 x = 375 ml (amt. of pure water needed) ==================== Cheers, Stan H. ====================
 percentage/511310: the population of village is encreasing at 5% per annum,The population after 2 yrs will become 4410.what was the population in the begining i.e. before 2 yrs1 solutions Answer 342109 by stanbon(57387)   on 2011-10-07 21:03:41 (Show Source): You can put this solution on YOUR website!the population of a village is encreasing at 5% per annum,The population after 2 yrs will become 4410.what was the population in the begining i.e. before 2 yrs ------------ Let "x" be the population 2 years ago. --- Equation: (1.05)^2*x = 4410 1.1025*x = 4410 --- x = 4410/1.1025 --- x = 4000 ================ Cheers, Stan H. ================
 Equations/511309: I am in pre-algebra. My teacher gave me a worksheet with word problems, but he did not explain how to do it.Can you please help me to understand this? Thank you! Simplifying algebraic expressions... This nut bread contains: 2 walnuts, twice as many pecans as walnuts, 10 nuts in all. I am suppose to find out how many of each type of nut does the bread have.1 solutions Answer 342108 by stanbon(57387)   on 2011-10-07 20:54:21 (Show Source): You can put this solution on YOUR website!This nut bread contains: 2 walnuts, twice as many pecans as walnuts, 10 nuts in all. I am supposed to find out how many of each type of nut does the bread have. --------------------- walnuts: 2 pecans: 2*2 = 4 other nuts: 10-(2+4) = 10-6 = 4 =================================== Cheers, Stan H. =============
 Equations/511308: Please help me solve this equation: Find the equation of the line perpendicular to -3x+7y=-3 that contains the point (7,6)1 solutions Answer 342106 by stanbon(57387)   on 2011-10-07 20:50:27 (Show Source): You can put this solution on YOUR website!Please help me solve this equation: Find the equation of the line perpendicular to -3x+7y=-3 that contains the point (7,6) ------------------ Find the slope of the given line: 7y = 3x-3 y = (3/7)x - (3/7) Its slope is 3/7 ------------------------ Any perpendicular line must have slope -7/3 ------------------------- Find equation with slope = -7/3 that passes thru (7,6). ---------------- Form: y = mx + b 6 = (-7/3)(7) + b 6 = -49/3 + b b = (18/3)+(49/3) --- b = 67/3 ---- Equation: y = (-7/3)x + (67/3) ========================== Cheers, Stan H. ============ ------------
 Mixture_Word_Problems/511305: How many milliliters of orange puree must be mixed with 300 ml of 30% orange to obtain 45% orange concentrate?1 solutions Answer 342105 by stanbon(57387)   on 2011-10-07 20:42:46 (Show Source): You can put this solution on YOUR website!How many milliliters of orange puree must be mixed with 300 ml of 30% orange to obtain 45% orange concentrate? ----------------- x + 0.30*300 = 0.45(x+300) ---- Multiply thru by 100 to get: 100x + 30*300 = 45x + 45*300 55x = 15*300 x = (3/11)300 --- x = 81.82 ml (amt of 100% orange puree needed) ================ Cheers, Stan H. ================
 Rectangles/511279: What is the dimensions of a rectangle whose perimeter is 112 and the width is 3/4 the length?1 solutions Answer 342099 by stanbon(57387)   on 2011-10-07 19:14:40 (Show Source): You can put this solution on YOUR website!What is the dimensions of a rectangle whose perimeter is 112 and the width is 3/4 the length? ----------------------- Let length be L The width = (3/4)L -------- Equation: Perimeter = 2(L + (3/4)L) 112 = 2(7/4)L ----- 56 = (7/4)L ----- L = (4/7)56 --- Length = 32 Width = (3/4)32 = 24 ======================== Cheers, Stan H. ========================
 Polynomials-and-rational-expressions/511277: how do I factor: x^2-17+0 (X+/-?)(x+/-?)1 solutions Answer 342098 by stanbon(57387)   on 2011-10-07 19:09:36 (Show Source): You can put this solution on YOUR website!factor: x^2-17 --- = (x-sqrt(17))(x+sqrt(17)) =============================== Cheers, Stan H. ============