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Recent problems solved by 'stanbon'

stanbon answered: 57274 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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Probability-and-statistics/533721: what is the probability of getting a club in a standard deck of cards? What is the probability of getting a red queen? 1 solutions Answer 351133 by stanbon(57347)   on 2011-11-17 22:52:32 (Show Source): You can put this solution on YOUR website! what is the probability of getting a club in a standard deck of cards? Ans: 1/4 --------------------------- What is the probability of getting a red queen? Ans: 2/52 = 1/26 ===================== Cheers, Stan H.

Probability-and-statistics/533720: Determine the area under the standard normal curve that lies to the left of the following z value: z = 0.54 1 solutions Answer 351132 by stanbon(57347)   on 2011-11-17 22:47:36 (Show Source): You can put this solution on YOUR website! Determine the area under the standard normal curve that lies to the left of the following z value: z = 0.54 ---- invNOrm(0.54) = 0.1004 ------------------------ Cheers, Stan H. ==========

Polynomials-and-rational-expressions/533711: x^7/x^-2 1 solutions Answer 351129 by stanbon(57347)   on 2011-11-17 22:35:51 (Show Source): You can put this solution on YOUR website! x^7/x^-2 ---------- = x^(7-(-2)) ------- = x^9 ================ Cheers, Stan H.

Average/533715: what is the average of 1/4 and 1/6? 1 solutions Answer 351122 by stanbon(57347)   on 2011-11-17 22:13:49 (Show Source): You can put this solution on YOUR website! what is the average of 1/4 and 1/6 ------ Ave = [(1/4)+(1/6)]/2 = (10/24)/2 = (5/12)/2 = 5/24 --------------------------- Cheers, Stan H. ==============

Trigonometry-basics/533712: find all the solutions on the interval [0,2pi). 2tan2x-2sqrt3=0 1 solutions Answer 351120 by stanbon(57347)   on 2011-11-17 22:10:20 (Show Source): You can put this solution on YOUR website! find all the solutions on the interval [0,2pi). 2tan2x-2sqrt3=0 ---- tan(2x) - sqrt(3) = 0 ---- tan(2x) = sqrt(3) = 0 2x = tan^-1[sqrt(3)] --- 2x = pi/3 or (4/3)pi --- x = pi/6 or (2/3)pi ---- Cheers, Stan H. =========================

logarithm/533701: 4log3 (7p+5)-6=2 1 solutions Answer 351119 by stanbon(57347)   on 2011-11-17 22:05:06 (Show Source): You can put this solution on YOUR website! 4log3 (7p+5)-6=2 --- 4log3(7p+5) = 8 ----- log3(7p+5) = 2 7p+5 = 3^2 7p = 4 p = 4/7 ============ Cheers, Stan H. ============

Word_Problems_With_Coins/533696: A jar of coins contains dimes, pennies, and quarters. There are 220 pennies in the jar. There are 3 quarters for every 4 pennies, and there is 1 dime for every 3 quarters. How many dimes and quarters are in the jar? 1 solutions Answer 351114 by stanbon(57347)   on 2011-11-17 21:49:01 (Show Source): You can put this solution on YOUR website! A jar of coins contains dimes, pennies, and quarters. There are 220 pennies in the jar. There are 3 quarters for every 4 pennies, and there is 1 dime for every 3 quarters. How many dimes and quarters are in the jar? ------------------------------ Equations: p - 220 4q = 3p q = 3d ---------------- Information missing Cheers, Stan H.

Exponential-and-logarithmic-functions/533693: Find the value of the expression: 8 1 solutions Answer 351113 by stanbon(57347)   on 2011-11-17 21:38:26 (Show Source): You can put this solution on YOUR website! log (1/2)8 ----- Let x = log(1/2)8 --- Then (1/2)^x = 8 --- 2^-x = 2^3 -x = 3 x = -3 -------------- log(1/2)8 = -3 =============== Cheers, Stan H. ===============

Probability-and-statistics/533404: there are 37 members on a board A. if they elect a chairperson, 1st vp, 2nd vp, and a secretary, how many different slates of candidates are possible? B. if they form an ethics subcommittee of four members, how many different subcommittees are possible? 1 solutions Answer 351055 by stanbon(57347)   on 2011-11-17 15:30:25 (Show Source): You can put this solution on YOUR website! there are 37 members on a board A. if they elect a chairperson, 1st vp, 2nd vp, and a secretary, how many different slates of candidates are possible? Ans: 37C3 = (37*36*35)/(1*2*3) = 7770 ---------------------------------------------- B. if they form an ethics subcommittee of four members, how many different subcommittees are possible? Ans: 37C4 = (37*36*35*34)/(1*2*3*4) = 66045 ============ Cheers, Stan H. =========

Probability-and-statistics/533397: Kobe Bryant makes 80% of his free throws in his god season. What is the probability that he will make at least 6 of his next 8 free-throw attempts? Use the probability table given to solve the problem. 1 solutions Answer 351053 by stanbon(57347)   on 2011-11-17 15:25:55 (Show Source): You can put this solution on YOUR website! Kobe Bryant makes 80% of his free throws in his good season. What is the probability that he will make at least 6 of his next 8 free-throw attempts? Use the probability table given to solve the problem. -------------------- Binomial with n = 8 and p(make free throw) = 0.8 ------- P(6<= x <=8) = 1 - binomcdf(8,0.8,5) = 0.7969 ================================ Cheers, Stan H. ============

Linear-equations/533366: hi, can you tell me how to solve the following?? X*10= 810 1 solutions Answer 351036 by stanbon(57347)   on 2011-11-17 14:24:47 (Show Source): You can put this solution on YOUR website! hi, can you tell me how to solve the following?? X*10= 810 --- Divide both sides by 10 to get: x = 81 ============= Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/533362: how do i solve the rational equation of 2-(4/x^2)=-2 1 solutions Answer 351035 by stanbon(57347)   on 2011-11-17 14:22:55 (Show Source): You can put this solution on YOUR website! solve the rational equation of 2-(4/x^2)=-2 ----- Subtract 2 from both sides: -(4/x^2) = -4 ---- 4/x^2 = 4 x^2 = 16 x^2-16 = 0 (x-4)(x+4) = 0 x = 4 or x = -4 ---- Cheers, Stan H. ============

Probability-and-statistics/533365: If 9 states are considered to be in the "Northeast" of the U.S., what is the probability that a state picked at random will be in the Northeast? 1 solutions Answer 351033 by stanbon(57347)   on 2011-11-17 14:14:36 (Show Source): You can put this solution on YOUR website! If 9 states are considered to be in the "Northeast" of the U.S., what is the probability that a state picked at random will be in the Northeast? --- P(northeast) = 9/50 Cheers, Stan H.

Linear-equations/533358: P = (6,3), m = -1/3 Find the equation of the line containing the point P and having the slope m. Write the answer in slope-intercept form and Graph the line. 1 solutions Answer 351032 by stanbon(57347)   on 2011-11-17 14:12:56 (Show Source): You can put this solution on YOUR website! P = (6,3), m = -1/3 Find the equation of the line containing the point P and having the slope m. Write the answer in slope-intercept form and Graph the line. --- Form: y = mx + b You are told that y = 3 when x = 6; and m = -1/3. Solve for "b": ------ 3 = (-1/3)*3 + b 3 = -1 + b b = 4 ------ Equation: y = (-1/3)x + 4 ==================== Cheers, Stan H. ====================

Probability-and-statistics/533220: Find the shift, the new model points and the equation of the asymptote: y = log8(x - 6) - 5 Shift. ( , ) New Model Points. ( , ) and ( , ) Asymptote. x = 1 solutions Answer 351020 by stanbon(57347)   on 2011-11-17 08:53:23 (Show Source): You can put this solution on YOUR website! Find the shift, the new model points and the equation of the asymptote: y = log8(x - 6) - 5 Shift. Ans: 6 to the right -------- ( , ) New Model Points. ( , ) and ( , ) Asymptote. x = 6 ------ Cheers, Stan H.

Probability-and-statistics/533222: If four dogs are picked up from the Veterinarian and they are returned to their owners at random, what is the probability that at least one owner receives the wrong dog? Round your answer to two decimal places. 1 solutions Answer 351019 by stanbon(57347)   on 2011-11-17 08:49:05 (Show Source): You can put this solution on YOUR website! If four dogs are picked up from the Veterinarian and they are returned to their owners at random, what is the probability that at least one owner receives the wrong dog? Round your answer to two decimal places. ---- Binomial with n = 4 and p(correct dog) = 1/4 ----- P(1<= x <=4) = 1 - P(x = 0) = 1-(3/4)^4 = .6836 ====================== Cheers, Stan H.

Probability-and-statistics/533224: A box of candy contains four orange and six cherry hot sticks. If three hot sticks are chosen at random from the box, what is the probability that no more than one will be cherry? Round your answer to two decimal place. 1 solutions Answer 351018 by stanbon(57347)   on 2011-11-17 08:45:57 (Show Source): You can put this solution on YOUR website! A box of candy contains four orange and six cherry hot sticks. If three hot sticks are chosen at random from the box, what is the probability that no more than one will be cherry? Round your answer to two decimal place. ----------- Binomial with n = 3 and p(cherry) = 6/10 = 0.6 --- P(0<= x <=1) = binomcdf(3,0.6,1) = 0.3520 ================= Cheers, Stan H. =================

Divisibility_and_Prime_Numbers/533216: what is the divisibility of 13,710 1 solutions Answer 351017 by stanbon(57347)   on 2011-11-17 08:41:47 (Show Source): You can put this solution on YOUR website! what is the divisibility of 13,710 = 5*2742 = 5*2*1371 Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/533218: Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of 2150 . What was the rate charged per hour by each mechanic if the sum of the two rates was 175 per hour? 1 solutions Answer 351016 by stanbon(57347)   on 2011-11-17 08:34:45 (Show Source): You can put this solution on YOUR website! Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of 2150 . What was the rate charged per hour by each mechanic if the sum of the two rates was 175 per hour? ------ r1 + r2 = 175 10r1 + 15r2 = 2150 ----- Multiply thru 1st by 10 to get: 10r1 + 10r2 = 10*175 10r1 + 15r2 = 2150 --- Subtract and solve for r2 5r2 = 400 r2 = $80 per hr --- Solve for r1: r1 + r2 = 175 r1 + 80 = 175 r1 = $95 per hr ==================== Cheers, Stan H. ====================

Quadratic_Equations/533213: Y=-3x-6x-5 I'm experiencing difficulties with figuring out which points to use when creating a table of values. I found that the vertex is (-1,-2) and the y intercept is (0,-5), there is no x intercept. I'm unable to get the graph to open facing downward in an excel spread sheet. I'm not sure if my first point should be my vertex and what other points to use. Please help! X Y -1 -2 0 -5 The points that I have are not creating the graph that I need facing downward below the x axis. Thank you, 1 solutions Answer 351014 by stanbon(57347)   on 2011-11-17 08:22:37 (Show Source): You can put this solution on YOUR website! Y=-3x^2-6x-5 ---------------------- Vertex = ? x = -b/(2a) = 6/(-6) = -1 f(x) = -3*(-1)^2 -6*-1 -5 = -3+6-5 = -2- --- Vertex is at (-1,-2) ----------------------- y- intercept: f(0) = -5 y-intercept at (0,-5) --- Plot those two points and draw a parabola opening downward. --------------------- Cheers, Stan H. =============

Quadratic-relations-and-conic-sections/533215: without writing the equation y + x^2 = -(8x + 23) in standard form, state whether the graph of this equation is a parabola, circle, ellipse, or hyperbola. 1 solutions Answer 351013 by stanbon(57347)   on 2011-11-17 08:18:01 (Show Source): You can put this solution on YOUR website! without writing the equation y + x^2 = -(8x + 23) in standard form, state whether the graph of this equation is a parabola, circle, ellipse, or hyperbola. ---- Ans: Parabola opening downward. Cheers, Stan H.

Probability-and-statistics/533214: A conference has 13 basketball teams. At the end of the season a first, second, and third place winner is declared. How many ways can these places be chosen? 1 solutions Answer 351012 by stanbon(57347)   on 2011-11-17 08:16:18 (Show Source): You can put this solution on YOUR website! A conference has 13 basketball teams. At the end of the season a first, second, and third place winner is declared. How many ways can these places be chosen? ---------------- Ans: 13P3 = 13*12*11 ====================== Cheers, Stan H.

Functions/533206: I am not understanding these Adavanced Functions and could use some help please. f(x)=-3x-3 and g(x)=x^2+2x find (f-g)(2) 1 solutions Answer 351007 by stanbon(57347)   on 2011-11-17 07:38:09 (Show Source): You can put this solution on YOUR website! I am not understanding these Adavanced Functions and could use some help please. f(x)=-3x-3 and g(x)=x^2+2x find (f-g)(2) = f(2)-g(2) = [-3*2-3]-[2^2+2*2] = -9-0 = -9 ======================== Cheers, Stan H. ===========

logarithm/533207: Write the exponential equations in logarithmic form? x=4^y 1 solutions Answer 351006 by stanbon(57347)   on 2011-11-17 07:35:11 (Show Source): You can put this solution on YOUR website! Write the exponential equations in logarithmic form? x=4^y ----- The log is the exponent = y The base is 4 The result is x ====== log4(x) = y ================== Cheers, Stan H. ==================

Probability-and-statistics/533198: A random sample of 500 fish is taken from a lake, marked, and returned to the lake.after a suitable interval a second sample of 500 is taken and 25 of these are found to be marked. by considering the number of fish marked in the second sample, 1)Estimate the number of fish in the lake 2)By considering the confidence interval for the proportion of marked fish in the lake, obtain a 95% confidence limits for the number of fish in the lake 1 solutions Answer 351005 by stanbon(57347)   on 2011-11-17 07:29:41 (Show Source): You can put this solution on YOUR website! A random sample of 500 fish is taken from a lake, marked, and returned to the lake.after a suitable interval a second sample of 500 is taken and 25 of these are found to be marked. by considering the number of fish marked in the second sample, 1)Estimate the number of fish in the lake Let the population be "x": x/500 = 500/25 x = 20*500 x = 10,000 ------------------------- 2)By considering the confidence interval for the proportion of marked fish in the lake, obtain a 95% confidence limits for the number of fish in the lake --- p-hat = 500/10,000 = 0.05 --- ME: = 1.96*sqrt[0.05*0.95/500] = 0.0191 ----- 95% CI: 0.03 <= p <= 0.07 =================================== So, if proportion of marked fish is 0.03, # of fish = 500/0.03 = 16,667 And, if proportion of marked fish is 0.07, # of fish = 500/0.07 = 7143 ---- 95% fish population : 7143<= x <= 16,667 ================= Cheers, Stan H.

Rational-functions/533199: x varies as 1/y, if x=25, y=10 1 solutions Answer 351002 by stanbon(57347)   on 2011-11-17 07:16:34 (Show Source): You can put this solution on YOUR website! You've made two statements. What is the question?

Age_Word_Problems/533200: susan is six years older than ana. she is twice as old as ana. how old is each now? 1 solutions Answer 351001 by stanbon(57347)   on 2011-11-17 07:14:45 (Show Source): You can put this solution on YOUR website! susan is six years older than ana. she is twice as old as ana. how old is each now? --- Equations: s = a + 6 s = 2a --- Substitute for "s" and solve for "a": 2a = a + 6 a = 6 (Ana's age now) --- Solve for "s": s = a + 6 Susan = 12 (Susan's age now) ============================== Cheers, Stan H. ===============

Probability-and-statistics/533204: -3/4r>-3/4 1 solutions Answer 351000 by stanbon(57347)   on 2011-11-17 07:11:48 (Show Source): You can put this solution on YOUR website! -3/4r>-3/4 ----- Multiply both sides by -4/3 to get: r < 1 =========== Cheers, Stan H.

absolute-value/533202: Find the absolute Value |-7*1| 1 solutions Answer 350999 by stanbon(57347)   on 2011-11-17 07:10:22 (Show Source): You can put this solution on YOUR website! Find the absolute Value |-7*1| = |-7| = 7 Cheers, Stan H.

Complex_Numbers/533203: Find the number of nonzero solutions of the equation: z^2+2z̅=0. 1 solutions Answer 350998 by stanbon(57347)   on 2011-11-17 07:08:57 (Show Source): You can put this solution on YOUR website! Find the number of nonzero solutions of the equation: z^2+2z̅=0. ------ If you are just looking for the number of solutions, use the discriminant: b^2-4ac = 2^2-4*1*0 = 4 --- Since it is > 0 there are 2 solutions. ==================== If you need the solutions: Factor z^2+2z = 0 z(z+2) = 0 z = 0 or z = -2 ==================== Cheers, Stan H.

Polygons/532935: What is the measure of one exterior angle if the 14-gon is a regular figure? 1 solutions Answer 350935 by stanbon(57347)   on 2011-11-16 19:11:46 (Show Source): You can put this solution on YOUR website! What is the measure of one exterior angle if the 14-gon is a regular figure? ----- The sum of the 14 exterior angles is 360 degrees. --- Each ext. angle is 360/14 = 25.71 degrees ===================== Cheers, Stan h.