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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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 Geometry_Word_Problems/328949: Hello, I'm having a hard time figuring this out. The side of an equilateral triangle is 4 inches shorter than the side of a square. The perimeter of the square is 38 inches more than the perimeter of the triangle. Find the length of the side of the square. Thank you!1 solutions Answer 235681 by stanbon(57233)   on 2010-08-04 19:02:58 (Show Source): You can put this solution on YOUR website!The side of an equilateral triangle is 4 inches shorter than the side of a square. The perimeter of the square is 38 inches more than the perimeter of the triangle. Find the length of the side of the square. ----------- Let a side of the square be "s". Its perimeter = "4s". ----- A side of the equilateral triangle is "s-4" Its perimeter = 3(s-4) = 3s-12 ------------------------------------ Equation: Perimeter of square - Perimeter of Equilater Triangle = 38 4s - (3s-12) = 38 s = 26 inches (length of a side of the square) ================================================= Cheers, Stan H. ===============
 Radicals/328935: 1 solutions Answer 235680 by stanbon(57233)   on 2010-08-04 18:57:51 (Show Source): You can put this solution on YOUR website!(5s)^(-1/3)/(s)^(5/3) --- = 1/[(5s)^(1/3)*s^(5/3)] --- = 1/[5^(1/3)*s^2] ======================= Cheers, Stan H. =======================
 logarithm/328941: find the value of the given expression: log (2+3)1 solutions Answer 235678 by stanbon(57233)   on 2010-08-04 18:52:49 (Show Source): You can put this solution on YOUR website!find the value of the given expression: log (2+3) --- = log(5) --- = 0.6990 =============== Cheers, stan H.
 logarithm/328942: what is the characteristics of the logarithm 2520 ?1 solutions Answer 235677 by stanbon(57233)   on 2010-08-04 18:50:49 (Show Source): You can put this solution on YOUR website!what is the characteristics of the logarithm 2520 ? --- 2520 = 2.52*10^3 --- The characteristic is "3". Cheers, Stan H.
 Complex_Numbers/328943: what is the solution to the square root of -191 solutions Answer 235675 by stanbon(57233)   on 2010-08-04 18:47:11 (Show Source): You can put this solution on YOUR website!what is the solution to the square root of -19 --- = isqrt(19) ============== Cheers, Stan H.
 Radicals/328944: simplify the expession by using the properties of rational exponents. express final solution using positive exponents only 1 solutions Answer 235674 by stanbon(57233)   on 2010-08-04 18:44:39 (Show Source): You can put this solution on YOUR website! (a)^(4n)(b)^(3n)/(c)^n)^(1/n) ---------- = [a(ab)^(3n)]/c --- = (a/c)(ab)^(3n) =================== Cheers, Stan H. ================
 Probability-and-statistics/327560: Members of the general adult population volunteer an average of 4.2 hours per week. A random sample of 20 female college students and 18 male college students produced the results given in the table below. At the .01 level of significance, is there sufficient evidence to conclude that a difference exists between the mean number of volunteer hours per week for male and female college students? Females Males Sample size 20 18 Sample mean 3.8 2.5 Sample variance 3.5 2.2 1 solutions Answer 235673 by stanbon(57233)   on 2010-08-04 18:35:21 (Show Source): You can put this solution on YOUR website!Members of the general adult population volunteer an average of 4.2 hours per week. A random sample of 20 female college students and 18 male college students produced the results given in the table below. At the .01 level of significance, is there sufficient evidence to conclude that a difference exists between the mean number of volunteer hours per week for male and female college students? Females Males Sample size 20 18 Sample mean 3.8 2.5 Sample variance 3.5 2.2 ------------------------------ Ho: u(male)-u(woman) = 0 Ho: u(male)-u(woman) is not 0 I ran a 2-Sample T test and got the following: test statistic: t = 2.3845 p-value + 0.0226 df = 35.47 --- Conclusion: Reject Ho at 5% significance level. ==================== Cheers, Stan H.
 test/328906: Combine like terms 8a+5 (-a)+(-3)1 solutions Answer 235642 by stanbon(57233)   on 2010-08-04 17:16:17 (Show Source): You can put this solution on YOUR website! Combine like terms 8a+5 (-a)+(-3) --- = 7a +2 ============= Cheers, Stan H. =============
 Probability-and-statistics/328778: In a 5-card poker game a player is dealt 5 cards. How many poker hands are possible for an ordinary 52-card deck?1 solutions Answer 235582 by stanbon(57233)   on 2010-08-04 13:52:17 (Show Source): You can put this solution on YOUR website!In a 5-card poker game a player is dealt 5 cards. How many poker hands are possible for an ordinary 52-card deck? -------------------- 52C5 = 2598960 hands ========================= Cheers, Stan H.
 Probability-and-statistics/328788: A rifleman can achieve a "marksman" award if he passes a test. He is allowed to fire six shots at a target's bull's eye.If he hits the bull;s eye with at least 5 of his 6 shots he wins a set. He becomes a marksman only if he can repeat the feat 3 times straight,that is,if he can wins three straight sets. If his probability is 0.8 of hitting a bull's eye on any one shot, find the probabilities of his: a) winning a set, and b)becoming a marksman 1 solutions Answer 235581 by stanbon(57233)   on 2010-08-04 13:50:37 (Show Source): You can put this solution on YOUR website!A rifleman can achieve a "marksman" award if he passes a test. He is allowed to fire six shots at a target's bull's eye. If he hits the bullseye with at least 5 of his 6 shots he wins a set. --- P(win a set) = 1 - binomcdf(6,0.8,4) = 6554 -------------------------------------------- He becomes a marksman only if he can repeat the feat 3 times straight,that is,if he can wins three straight sets. If his probability is 0.8 of hitting a bull's eye on any one shot, find the probabilities of his: a) winning a set, and b)becoming a marksman --- P(be marksman) = 0.6554^3 = 0.2815 ====================================== Cheers, Stan H. ---------------------
 Mixture_Word_Problems/328751: Can someone please walk me through this? The daily requirements of a balanced diet for an animal are shown in the nutritional pyramid. The number of grams per cup of nutrients in three food mixes are shown in the table. How many cups of each mix should be used to meet the daily requirements for protein, carbohydrates, and essential fatty acids in the animal's diet? To answer this problem, write a system of three equations and solve it using Cramer's rule. Assume a = 5, b = 10 and c = 19 Pyramid (top to bottom) Vitamins Minerals Essential Fatty Acids a grams Carbohydrates b grams Quality Protein c grams Grams per cup Mix A Protein 4 Carbohydrates 2 Fatty Acids 1 Mix B Protein 8 Carbohydrates 3 Fatty Acids 2 Mix C Protein 3 Carbohydrates 3 Fatty Acids 1 ___ cup(s) mix A ___ cup(s) mix B ___ cup(s) mix C Thank you, Jerry1 solutions Answer 235543 by stanbon(57233)   on 2010-08-04 10:07:23 (Show Source): You can put this solution on YOUR website!The daily requirements of a balanced diet for an animal are shown in the nutritional pyramid. The number of grams per cup of nutrients in three food mixes are shown in the table. How many cups of each mix should be used to meet the daily requirements for protein, carbohydrates, and essential fatty acids in the animal's diet? To answer this problem, write a system of three equations and solve it using Cramer's rule. Assume a = 5, b = 10 and c = 19 Pyramid (top to bottom) Vitamins Minerals Essential Fatty Acids a=5 grams Carbohydrates b=10 grams Quality Protein c=19 grams Grams per cup Mix A Protein 4 Carbohydrates 2 Fatty Acids 1 Mix B Protein 8 Carbohydrates 3 Fatty Acids 2 Mix C Protein 3 Carbohydrates 3 Fatty Acids 1 --- Acid equation: A + 2B + C = 5 Carbo equatin:2A + 3B +3C = 10 Protin equatio:4A + 8B + 3C = 19 -------------------------------------- Used a TI-84 to get the following: A = 2 cups B = 1 cups C = 1 cups ============================ Cheers, Stan H. ============= ___ cup(s) mix A ___ cup(s) mix B ___ cup(s) mix C
 Rate-of-work-word-problems/328756: If Lynn can tyoe a page in P minutes, what piece of the page can she type in 5 minutes?1 solutions Answer 235542 by stanbon(57233)   on 2010-08-04 09:56:18 (Show Source): You can put this solution on YOUR website!If Lynn can type a page in P minutes, what piece of the page can she type in 5 minutes? x/5 = 1/P --- x = (5/p) of a page ===================== Cheers, Stan H. =============
 Probability-and-statistics/328619: If many random samples of 64 students who took the second midterm examination in Math 10 are taken, what is the 95th percentile of the average time to completion for these samples? Explain what this number means.1 solutions Answer 235540 by stanbon(57233)   on 2010-08-04 09:53:27 (Show Source): You can put this solution on YOUR website!If many random samples of 64 students who took the second midterm examination in Math 10 are taken, what is the 95th percentile of the average time to completion for these samples? --- Find the z-value with a left tail of 0.95 invNorm(0.95) = 1.645 ----- Find the corresponding exam score using x = zs+u x = 1.645*s + u --- Comment: You need to be given s and u. ----------------- Explain what this number means. 95% of the sample means are less than 1.645s+u =================================================== Cheers, Stan H. ============
 Probability-and-statistics/328698: Population A consists of all values of invoices of a certain company. The mean of population A is \$350 and the standard deviation is \$100. Population B consists of all samples of 16 values drawn from population A. The mean of population B is? 1 solutions Answer 235539 by stanbon(57233)   on 2010-08-04 09:46:50 (Show Source): You can put this solution on YOUR website! Population A consists of all values of invoices of a certain company. The mean of population A is \$350 and the standard deviation is \$100. Population B consists of all samples of 16 values drawn from population A. The mean of population B is? ----------- The Central Limit Theorem says u = 350 =============== Cheers, Stan H.
 Mixture_Word_Problems/328754: how many gallons each of 25% alcohol and 35% alcohol should be mixed to get 10 gallons of 32% alcohol?1 solutions Answer 235538 by stanbon(57233)   on 2010-08-04 09:43:46 (Show Source): You can put this solution on YOUR website!how many gallons each of 25% alcohol and 35% alcohol should be mixed to get 10 gallons of 32% alcohol? ------------ Equation: alcohol + alcohol = alcohol 0.25 x + 0.35(10-x) = 0.32*10 ================================== Multiply thru by 100 to get: 25x + 35*10 - 35x = 32*10 -10x = -3*10 x = 3 gallons (amt. of 25% alcohol needed in the mixture) ----------- 10-x = 7 gallons (amt. of 35% alcohol needed in the mixture) ========================== Cheers, Stan H. ================
 Probability-and-statistics/328696: A home security system is designed to have a 90% reliability rate. Suppose that nine homes equipped with this system experience an attempted burglary. The probability that eight or fewer alarms are triggered is?1 solutions Answer 235536 by stanbon(57233)   on 2010-08-04 09:40:19 (Show Source): You can put this solution on YOUR website!A home security system is designed to have a 90% reliability rate. Suppose that nine homes equipped with this system experience an attempted burglary. The probability that eight or fewer alarms are triggered is? --- Binomial with n = 9 and p = 0.9 ---------------- Using a TI-84 I get: P(x<= 8) = binomcdf(9,0.9,8) = 0.6126 ============= Cheers, stan H.
 Money_Word_Problems/328730: The cost for manufacturing a CD varies inversely with the number of CDs made. If the cost is \$2.50 per CD when 10,000 are made, then what is the cost per CD when 100,000 are made?1 solutions Answer 235506 by stanbon(57233)   on 2010-08-04 08:32:32 (Show Source): You can put this solution on YOUR website! The cost for manufacturing a CD varies inversely with the number of CDs made. If the cost is \$2.50 per CD when 10,000 are made, then what is the cost per CD when 100,000 are made? ------------------ c = k/n -- Find "k" using c=2.5 when n = 10,000 2.5 = k/10000 k = 25000 ----- Equation: c = 25000/n ----- Solve for "c" when n = 100,000 c = 25000/100000 c = \$0.25 ================ cheers, Stan H. ================
 Quadratic_Equations/328728: Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function. f(x)=-2(x+5)^2+41 solutions Answer 235502 by stanbon(57233)   on 2010-08-04 08:28:07 (Show Source): You can put this solution on YOUR website! Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function. ----- f(x)=-2(x+5)^2+4 vertex: (-5,4) ---- line: x = -5 ---- max at (-5,4) ---- ====== Cheers, Stan H. ======
 Linear-equations/328717: a gun is fired straight upward. the bullet leaves the gun at 100 feet per second (time t=0) after 2 seconds the velocity of the bullet is 36 feet per second there is a linear equation that gives the velocity v in terms of the time t. find the equation and find the velocity after 3 seconds1 solutions Answer 235499 by stanbon(57233)   on 2010-08-04 08:24:44 (Show Source): You can put this solution on YOUR website! a gun is fired straight upward. the bullet leaves the gun at 100 feet per second (time t=0) after 2 seconds the velocity of the bullet is 36 feet per second there is a linear equation that gives the velocity v in terms of the time t. ----------------------- You have two points relating time and velocity: (0,100) and (2,36) slope = (36-100)/(2-0) = -32 --- intercept = 100 --------------------- Equation: velocity = -32(time) + 100 ------------- Find the velocity after 3 seconds. v(3) = -32(3) + 100 v(3) = -96+100 v(3) = 4 ft/sec ==================== cheers, stan H. ==============
 Age_Word_Problems/328720: aljohn is ten years older than eden. four years hence he will be twice the age of eden. how old are both of them now?1 solutions Answer 235497 by stanbon(57233)   on 2010-08-04 08:17:15 (Show Source): You can put this solution on YOUR website! aljohn is ten years older than eden. four years hence he will be twice the age of eden. how old are both of them now? ---- Equations: a = e + 10 (a+4)= 2(e+4) ------------------- Substitute for "a" and solve for "e": (e+10+4) = 2(e+4) e+14 = 2e+8 e = 6 (eden's age now) ---- Since a = e+10, a = 16 (aljon's age now) ======================== Cheers, Stan H. ==============
 Age_Word_Problems/328722: aljohn is ten years older than eden. four years hence he will be twice the age of eden. how old the both of them now?1 solutions Answer 235496 by stanbon(57233)   on 2010-08-04 08:13:55 (Show Source): You can put this solution on YOUR website!duplicate
 Polynomials-and-rational-expressions/328723: Will you please show me how to factor 8ac + 12ad + 10bc + 15bd Thank you1 solutions Answer 235495 by stanbon(57233)   on 2010-08-04 08:13:05 (Show Source): You can put this solution on YOUR website!factor 8ac + 12ad + 10bc + 15bd --- Rearrange: 8ac+10bc + 12ad+15bd --- Factor the 1st 2 and the last 2 terms separately: 2c(4a+5b) + 3d(5a+5b) --- Factor again: (4a+5b)(2c+3d) ================= Cheers, Stan H. ============
 Linear-systems/328724: what would de answer be for this system of equation, using substitution or elimination? 3x-2y=5 -6x+4y=7 1 solutions Answer 235494 by stanbon(57233)   on 2010-08-04 08:10:02 (Show Source): You can put this solution on YOUR website!what would the answer be for this system of equation, using substitution or elimination? 3x-2y=5 -6x+4y=7 ----- Multiply the 1st equation by 2 to get: 6x-4y = 10 -6x+4y = 7 ------------------ Add the equations to get: 0 = 17 --- That is a contradiction. There is no solution for the system of equations. If you graphed the two equations you would see that the lines are parallel; they have no point in common. ========================= Cheers, Stan H.
 Probability-and-statistics/328699: For a normal curve, if the mean is 20 minutes and the standard deviation is 5 minutes, then the area between 22 and 25 minutes is:1 solutions Answer 235493 by stanbon(57233)   on 2010-08-04 08:06:46 (Show Source): You can put this solution on YOUR website! For a normal curve, if the mean is 20 minutes and the standard deviation is 5 minutes, then the area between 22 and 25 minutes is: Using a TI-84 I get: normalcdf(22,25,20,5) = 0.1859 Cheers, stan H.
 Probability-and-statistics/328701: Let z be a z-score that is unknown but identifiable by position and area. If the area to the right of z is 0.9306, then the value of z is?1 solutions Answer 235491 by stanbon(57233)   on 2010-08-04 08:03:35 (Show Source): You can put this solution on YOUR website!Let z be a z-score that is unknown but identifiable by position and area. If the area to the right of z is 0.9306, then the value of z is? ---- Using a TI-84 I get: invNorm(1-0.9306) = -1.4803 ============ Cheers, Stan H.
 Expressions-with-variables/328587: Chemistry. The decay rate of krypton-85 is 6.3% per year. What is its half-life?1 solutions Answer 235412 by stanbon(57233)   on 2010-08-03 20:45:26 (Show Source): You can put this solution on YOUR website!The decay rate of krypton-85 is 6.3% per year. What is its half-life? ====================== If it decays 6.3% each year 93.7% is preserved each year. ---------- A(t) = Ao*(1-0.063)^t --- (1/2)Ao = Ao(0.937)^t ----------- 0.937^t = 0.5 --- Take the log and solve for "t": t = [log(0.5)]/[log(0.937)] --- t = 10.65 years ====================== Cheers, Stan H.
 Polynomials-and-rational-expressions/328602: how can you determine if a polynormial is the difference of two squares? can you give an example of this problem1 solutions Answer 235410 by stanbon(57233)   on 2010-08-03 20:36:06 (Show Source): You can put this solution on YOUR website! how can you determine if a polynomial is the difference of two squares? can you give an example of this problem -------- x^2-4 --- 16x^2-25 ---- (abc)^2-(mnp)^2 ========================= Cheers, Stan H.
 Graphs/328604: For each line, use the given conditions to write an equation in the point-slope form and slope-intercept form. 1. Slope = 4, passing through (1,3) 2. Slope = 8, passing through (4,-1) 3. Slope = -5, p[assing through (-4,-2) 4. Slope = -2, passing through (0,-3)1 solutions Answer 235409 by stanbon(57233)   on 2010-08-03 20:34:17 (Show Source): You can put this solution on YOUR website!For each line, use the given conditions to write an equation in the point-slope form and slope-intercept form (y = mx+b). --- Solve for "b" on each of these problems: ---- 1. Slope = 4, passing through (1,3) 3 = 4*1+b b = -1 Equation: y = 4x-1 -------------------------- 2. Slope = 8, passing through (4,-1) -1 = 8*4 + b b = -33 Equation: y = 8x-33 -------------------------- 3. Slope = -5, p[assing through (-4,-2) -2 = -5*-4 + b b = -22 Equation: y = -5x-22 ========================= 4. Slope = -2, passing through (0,-3) -3 = -2*0 + b b = -3 Equation: y = -2x -3 ========================= Cheers, Stan H. ===========
 Graphs/328603: Dtermine whether each relation is a function. In addition, provide reasons for identifying a relation as a function. 1. {(3,4),(5,9),(9,9),(2,3)} 2. {(0,0),(0,1),(1,4),(2,4)} 3. {(2,1),(4,5),(8,4),(1,0)} 4. {(8,3),(8,0),(7,7),(4,7)}1 solutions Answer 235408 by stanbon(57233)   on 2010-08-03 20:29:41 (Show Source): You can put this solution on YOUR website!Dtermine whether each relation is a function. In addition, provide reasons for identifying a relation as a function. 1. {(3,4),(5,9),(9,9),(2,3)}::: is a function ----- 2. {(0,0),(0,1),(1,4),(2,4)}::: is not because x=0 is matched with 2 y-values ----- 3. {(2,1),(4,5),(8,4),(1,0)}::: is a function -------- 4. {(8,3),(8,0),(7,7),(4,7)}::: is not because x=8 is matched with 2 y-values --- Criteria: each value of x has just one corresponding value of y ==================== Cheers, Stan H.
 Probability-and-statistics/328414: In a large hotel it is known that99% of all guests return room keys when checking out.If 250 engineers check out after a large conference,what is the probability that not more than three will fail to return their keys?1 solutions Answer 235406 by stanbon(57233)   on 2010-08-03 20:25:38 (Show Source): You can put this solution on YOUR website!In a large hotel it is known that 99% of all guests return room keys when checking out.If 250 engineers check out after a large conference,what is the probability that not more than three will fail to return their keys? ------------------------ Prob a person does not return his key = 0.01 ------------------------ P(0<= x <=3) = binomcdf(250,0.01,3) = 0.7581 ================================================ Cheers, Stan H. ===========