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Recent problems solved by 'stanbon'

stanbon answered: 57135 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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>Next

Probability-and-statistics/732322: A business has 10 locations and wishes to rank the top 3 locations as 1st, 2nd, or 3rd. How many different ways can this be done? 1 solutions Answer 447767 by stanbon(57203)   on 2013-03-31 18:29:52 (Show Source): You can put this solution on YOUR website! A business has 10 locations and wishes to rank the top 3 locations as 1st, 2nd, or 3rd. How many different ways can this be done? ---- Select 1 of the 3 as 1st: 3 ways Select 1l of the remaining 2 as 2nd: 2 ways The remaining one is 3rd: 1 way ---- # of choices: 3*2*1 = 6 ======================= Cheers, Stan H. =======================

Probability-and-statistics/732287: You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a queen. Express your answer as a simplified fraction. A) 2/13 B) 1/663 C) 13/102 D) 4/663 1 solutions Answer 447760 by stanbon(57203)   on 2013-03-31 18:22:03 (Show Source): You can put this solution on YOUR website! You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a queen. Express your answer as a simplified fraction. ----- P(K and Q) = (4/52)(4/51) = 16/2652 = 4/663 ====================== Cheers, Stan H. ====================== A) 2/13 B) 1/663 C) 13/102 D) 4/663

Probability-and-statistics/732300: In given case, find the probability of x successes in n Bernoulli trials with success probability p for each trial X=4 n=5 p=.55 1 solutions Answer 447757 by stanbon(57203)   on 2013-03-31 18:15:34 (Show Source): You can put this solution on YOUR website! In given case, find the probability of x successes in n Bernoulli trials with success probability p for each trial X=4 n=5 p=.55 -------- P(x = 4) = 5C4*0.55*4*0.45 = binompdf(5,0.55,4) = 0.2059 ================= Cheers, Stan H. =================

�t�e�s�t/732211: If sec a = 13/5 where a lies between 0° and 90° then the value of 2 sin a - 3 cos a / 4 sin a - 9 cos a is please send me step by step 1 solutions Answer 447692 by stanbon(57203)   on 2013-03-31 12:32:16 (Show Source): You can put this solution on YOUR website! If sec a = 13/5 where a lies between 0° and 90° then the value of 2 sin a - 3 cos a / 4 sin a - 9 cos a is please send me step by step ------- sec = 13/5 = r/x, so r = 13 and x = 5 --- Find "y": x^2 + y^2 = r^2 y^2 = r^2-x^2 y = sqrt[13^2-5^2] = 12 ------ sin(a) = y/r = 12/13 cos(a) = x/r = 5/13 ------- 2 sin a - 3 cos a / 4 sin a - 9 cos a --- [2(12/13)-3(5/13)]/[4(12/13)-9(5/13)] ------- = [9-3]/13 ------- = 6/13 ================== Cheers, Stan H. =============

Age_Word_Problems/732173: Seven years ago, my father's age was five times mine. Right now, his age is the sum of our ages 7 years ago. How old am I? 1 solutions Answer 447666 by stanbon(57203)   on 2013-03-31 11:29:43 (Show Source): You can put this solution on YOUR website! Seven years ago, my father's age was five times mine. Right now, his age is the sum of our ages 7 years ago. How old am I? ------ Equations: f-7 = 5(m-5) f = (f-7)+(m-7) ------ Rearrange: f-5m = -18 m = 14 (My age now) --- f - 5*14 = -18 f = 62 (father's age now) ============= Cheers, Stan H. =====================

Travel_Word_Problems/732175: you drive 104 miles along a scenic highway and then take a 34-mile bike ride. your driving rate is 4 times your cycling rate. suppose you have no more than a total of 4 hours for driving and cycling. Let x represent your cycling rate in miles per hour. Use a rational inequality to determine the possible values of x. 1 solutions Answer 447648 by stanbon(57203)   on 2013-03-31 11:01:23 (Show Source): You can put this solution on YOUR website! you drive 104 miles along a scenic highway and then take a 34-mile bike ride. your driving rate is 4 times your cycling rate. suppose you have no more than a total of 4 hours for driving and cycling. Let x represent your cycling rate in miles per hour. Use a rational inequality to determine the possible values of x. ---- Driving DATA: distance = 104 miles ; rate = 4x mph ; time = d/r = 104/(4x) hrs. ------ Cycling DATA: distance = 34 miles ; rate = x mph ; time = d/r = 34/x hrs. ----------- Inequality: 104/(4x) + 34/x <= 4 hrs ----- Multiply thru by 4x to get: ------ 104 + 34*4 <= 16x 26 + 34 <= 4x 60 <= 4x x >= 15 mph (cycling rate) ---------------- Cheers, Stan H. ================

Polynomials-and-rational-expressions/732181: simplify this expression(12)/(7d)-(3)/(14d) 1 solutions Answer 447643 by stanbon(57203)   on 2013-03-31 10:48:46 (Show Source): You can put this solution on YOUR website! simplify this expression (12)/(7d)-(3)/(14d) ------ least common denominator: 14d ----- Rewrite with the lcd of each fraction: [12*2)/14d) - (3/14d) ---- Combine the numerators over the lcd: = [24 + 3]/(14d) ---- = 27/14d --- Cheers, Stan H. ==========

Triangles/732180: A triangle has two sides that measure 4 ft and 3 ft. Which could be the measure of the third side? A. 5 ft B. 7 ft C. 10 ft D. 12 ft A triangle has two sides that measure 12 meters and 3 meters. Which could be the measure of the third side? A. 17 m B. 15 m C. 10 m D. 9 m 1 solutions Answer 447639 by stanbon(57203)   on 2013-03-31 10:41:57 (Show Source): You can put this solution on YOUR website! A triangle has two sides that measure 4 ft and 3 ft. Which could be the measure of the third side? ----- 4-3 < 3rd side < 4+3 1 < 3rd side < 7 --- Ans: A ================ A. 5 ft B. 7 ft C. 10 ft D. 12 ft A triangle has two sides that measure 12 meters and 3 meters. Which could be the measure of the third side? 12-3 < 3rd side < 12+3 Ans: C ============== A. 17 m B. 15 m C. 10 m D. 9 m ----- Cheers, Stan H.

Triangles/732176: A triangle has two sides that measure 23 ft and 30 ft. Which could be the measure of the third side? A. 5 ft B. 7 ft C. 10 ft D. 53 ft 1 solutions Answer 447636 by stanbon(57203)   on 2013-03-31 10:37:12 (Show Source): You can put this solution on YOUR website! A triangle has two sides that measure 23 ft and 30 ft. Which could be the measure of the third side? ----- Ans: 30-23 < 3rd side < 23+30 7 < 3rd side < 40 ---- Ans: C ---------------- Cheers, Stan H. ================== A. 5 ft B. 7 ft C. 10 ft D. 53 ft

Linear-equations/732012: what equation is is used; "put equation in slope-intercept form by solving for y" problem is 3y = 4x 1 solutions Answer 447434 by stanbon(57203)   on 2013-03-30 12:39:57 (Show Source): You can put this solution on YOUR website! what equation is is used; "put equation in slope-intercept form by solving for y" problem is 3y = 4x ---- y" normally designates the 2nd derivative. If that is what you mean, If y = (4/3)x then y' = 4/3 and y" = 0 ================ Cheers, Stan H. ================

Money_Word_Problems/732004: Hi! Can anyone help me discern the solution and answer for this problem: "The supply equation for a calculator is y=m^2+ square root of 'm', where 100y calculators are supplied when m dollars is the price per calculator. find the instantaneous rate of change of the supply with respect to the price when the price is $1,600." Thanks! :) 1 solutions Answer 447433 by stanbon(57203)   on 2013-03-30 12:35:54 (Show Source): You can put this solution on YOUR website! "The supply equation for a calculator is y=m^2+ square root of 'm', where 100y calculators are supplied when m dollars is the price per calculator. find the instantaneous rate of change of the supply with respect to the price when the price is $1,600." ----- The instantaneous rate of change = the derivative is y'(m) = 2m+(1/(sqrt(m)) --- y'(1600) = 2*1600+(1/40) = 3200.03 ================== Cheers, Stan H. ==================

Rational-functions/732010: Please solve and show all work. It would be greatly appreciated if you explained it too. Thanks. Divide: 4x^2 - 15 / 2x - 5 1 solutions Answer 447430 by stanbon(57203)   on 2013-03-30 12:28:12 (Show Source): You can put this solution on YOUR website! Please solve and show all work. It would be greatly appreciated if you explained it too. Thanks. Divide: 4x^2 - 15 / 2x - 5 ---- Set it up like a long-division problem --- Divide the 4x^2 by 2x to get 2x (that is the 1st term of the quotient) --- Multiply 2x(2x-5) = 4x^2-10x ---- Subtract that from 4x^2-15 to get: 10x-15 ---- Divide that by 2x to get 5 (that is the 2nd term of the quotient ----------- Multiply 5*(2x-5) = get 10x-25 --- Subtract that from 10x-15 to get: 10 (that is the remainder) Answer: Quotient: 2x+5 Remainder: 10 ======================= cheers, Stan H. =========================

Probability-and-statistics/732007: The owner of an antique store estimates that there is a 40% chance she will make $2000 when she sells an antique china cabinet, a 50% chance she will make $750 when she sells the cabinet, and 10% chance she will break even when she sells the cabinet. Determine the expected amount she will make when she sells the cabinet. 1 solutions Answer 447429 by stanbon(57203)   on 2013-03-30 12:19:56 (Show Source): You can put this solution on YOUR website! The owner of an antique store estimates that there is a 40% chance she will make $2000 when she sells an antique china cabinet, a 50% chance she will make $750 when she sells the cabinet, and 10% chance she will break even when she sells the cabinet. Determine the expected amount she will make when she sells the cabinet. ------------- E(x) = 0.4*2000+0.5*750+0.1*0 = 80 + 37.5 = $117.50 ==================== Cheers, Stan H. ====================

Probability-and-statistics/731998: assume that a person spins the pointer and is awarded the amount indicated by the pointer.If it cost $2.00 to play the game. A)Determine the expectations of a person who plays the game. B)the fair price to play the game. The spinner has 1/2$10 1/4$1 1/4$5 1 solutions Answer 447425 by stanbon(57203)   on 2013-03-30 12:07:11 (Show Source): You can put this solution on YOUR website! assume that a person spins the pointer and is awarded the amount indicated by the pointer.If it cost $2.00 to play the game. A)Determine the expectations of a person who plays the game. B)the fair price to play the game. The spinner has 1/2$10 1/4$1 1/4$5 ===== Expected winnings: (1/2)*8 + (1/4)(-1) + (1/4)3 --- = 4 - 1/4 + 3/4 ---- = $3.50 (Can expect to win $3.50 each time the game is played) ----- Fair price = cost + expected value = 2+3.50 = $5.50 ------------- Cheers, Stan H.

Age_Word_Problems/731977: The sum of Nora's age and her grandmas age is 65. Four time law Nora's age is 10 less than her grandmas age. Fund Nora's present age and her grandmas present age. 1 solutions Answer 447417 by stanbon(57203)   on 2013-03-30 10:42:55 (Show Source): You can put this solution on YOUR website! The sum of Nora's age and her grandmas age is 65. Four time law Nora's age is 10 less than her grandmas age. Fund Nora's present age and her grandmas present age. ------ Equations: n + g = 65 4n = g-10 ----- Rearrange: n + g = 65 4n- g =-10 ---- Add and solve for "n": 5n = 55 Nora's age = 11 years ---- solve for "g": n + g = 65 11 + g = 65 grandma's age is 54 ========================== Cheers, Stan H. ==========================

Age_Word_Problems/731976: a daughters age is 32 years younger than her farther. In 4 years, the farther will be 5 times as old as hid daughter. How old is each now? 1 solutions Answer 447416 by stanbon(57203)   on 2013-03-30 10:34:33 (Show Source): You can put this solution on YOUR website! a daughters age is 32 years younger than her father. In 4 years, the father will be 5 times as old as his daughter. How old is each now? ----- Equations: d = f-32 (f+4) = 5(d+4) ----- Substitute for "d" and solve for "f": f+4 = 5(f-32+4) f+4 = 5(f-28) f+4 = 5f-140 4f = 144 father's age = 144/4 = 36 ----- Solve for "d": daughter's age = 36-32 = 4 ============ cheers, Stan H. ==============

Linear-systems/731973: 2(2x-1)>4x-6u Can you solve this for me 1 solutions Answer 447414 by stanbon(57203)   on 2013-03-30 10:29:29 (Show Source): You can put this solution on YOUR website! 2(2x-1)>4x-6u ---- 4x-2 > 4x-6u ----- -6u < -2 ---- u > 1/3 and x can be any number. ============= Cheers, Stan H.

Expressions-with-variables/731975: Twice the difference between a number, n, and thirty-one is three times the number. How do I translate n solve this problem? 1 solutions Answer 447412 by stanbon(57203)   on 2013-03-30 10:26:10 (Show Source): You can put this solution on YOUR website! Twice the difference between a number, n, and thirty-one is three times the number. --- Equation: 2(n-31) = 3n 2n-62 = 3n n = -62 -------------- Cheers, Stan H. ==============

Probability-and-statistics/731974: The expected value of a carnival game is -$6.50, and the cost to play the game is $10.00. Determine the fair price to play the game. 1 solutions Answer 447411 by stanbon(57203)   on 2013-03-30 10:23:56 (Show Source): You can put this solution on YOUR website! The expected value of a carnival game is -$6.50, and the cost to play the game is $10.00. Determine the fair price to play the game. fair price = cost + expected value fair price = 10.00 + (-6.50) fair price = $3.50 ------------ Cheers, Stan H. ============

Quadratic_Equations/731923: Multiply every term in the equation 2x^2 + 10x + 12 = 0 by a number other than 0 that has not been used in this discussion thread already, and solve for x by factoring. These numbers can not be used: 0, 1, 4, 6, 1 solutions Answer 447377 by stanbon(57203)   on 2013-03-29 23:29:24 (Show Source): You can put this solution on YOUR website! Multiply every term in the equation 2x^2 + 10x + 12 = 0 by a number other than 0 that has not been used in this discussion thread already, and solve for x by factoring. These numbers can not be used: 0, 1, 4, 6, ------ Multiply through by 1/2 to get: x^2 + 5x + 6 = 0 Factor: (x+3)(x+2) = 0 x = -3 or x = -2 ==================== Cheers, Stan H.

absolute-value/731914: Can someone solve this a simple way? 1.)-5|x-5|-15 < 0 2.)-4+2|x-37|=20 1 solutions Answer 447368 by stanbon(57203)   on 2013-03-29 23:22:41 (Show Source): You can put this solution on YOUR website! 1.)-5|x-5|-15 < 0 ---- -5|x-5| < 15 |x-5| > -3 ---- Since |x-5| is never negative, you have |x-5| >= 0 --- x-5 >= 0 or x-5 <= 0 --- x >= 5 or x <= 5 ---- Conclusion: x is all possible Real Number values. =========================== 2.)-4+2|x-37|=20 --- 2|x-37| = 24 |x-37| = 12 x-37 = 12 or x-37 = -12 x = 49 or x = 25 ======================= Cheers, Stan H. =======================

Polynomials-and-rational-expressions/731916: show me how to factor the trinomial 7x^2 + 27x -4 1 solutions Answer 447366 by stanbon(57203)   on 2013-03-29 23:09:02 (Show Source): You can put this solution on YOUR website! factor the trinomial 7x^2 + 27x -4 ----- 7x^2+28x-x-4 ----- 7x(x+4)-(x+4) ----- = (x+4)(7x-1) ===================== Cheers, Stan H. ===============

absolute-value/731903: Can someone let me know what is 1+x divided by 1-x greater than equal to to 1 And i need something clearified. When solving absolute values of inequalities when plotting the graph when do u shade in the circle on the graph and when do u plot above the line with th arrows instead of on the line.Thanks!! 1 solutions Answer 447363 by stanbon(57203)   on 2013-03-29 22:23:13 (Show Source): You can put this solution on YOUR website! Can someone let me know what is 1+x divided by 1-x greater than equal to to 1 ---------------------- (1+x)/(1-x) >= 1 --- (1+x) >= 1-x 2x >= 0 x >= 0 =============================== And i need something clearified. When solving absolute values of inequalities when plotting the graph when do u shade in the circle on the graph and when do u plot above the line with th arrows instead of on the line. --- If x > 4 the point x = 4 is circled but not shaded, Then an arrow is drawn to the right from x = 4. ---- If x >=4 the x = 4 is circled and shaded. Then an arraw is drawn to the right from x = 4. ============= Cheers, Stan H.

Angles/731908: If <1 and <2 form a linear pair and m<1 is one-fifth m<2, what is the measure of each angle? 1 solutions Answer 447360 by stanbon(57203)   on 2013-03-29 22:06:56 (Show Source): You can put this solution on YOUR website! If <1 and <2 form a linear pair and m<1 is one-fifth m<2, what is the measure of each angle? ---- Equations: a + b = 180 a = (1/5)b ---- Substitute and solve for "b": (1/5)b + b = 180 --- (6/5)b = 180 b = 150 a = (1/5)b = 30 ------------------------ cheers, Stan H.

absolute-value/731905: Solve please.How is this done. 1.) x-4 divided by x+2 greater than equal to 4 1 solutions Answer 447358 by stanbon(57203)   on 2013-03-29 22:02:14 (Show Source): You can put this solution on YOUR website! x-4 divided by x+2 greater than equal to 4 ----- (x-4)/(x+2)>= 4 ---- Multiply both sides by x+2 to get: (x-4) >= 4x+8 --- 3x <= -12 -- x <= -4 ------------- Cheers, Stan H. ============-

Polynomials-and-rational-expressions/731898: Factor by grouping. 4a2 + 7ab - 2b2 1 solutions Answer 447357 by stanbon(57203)   on 2013-03-29 21:50:57 (Show Source): You can put this solution on YOUR website! Factor by grouping. 4a2 + 7ab - 2b2 ----- 4a^2 + 8ab-ab - 2b^2 ------ = 4a(a+2b)-b(a+2b) ---- = (a+2b)(4a-b) ====================== Cheers, Stan H. ================

Linear-equations/731900: find the x-axis intercept of the graph of: y=x^2 - 3x + 3 1 solutions Answer 447354 by stanbon(57203)   on 2013-03-29 21:46:34 (Show Source): You can put this solution on YOUR website! find the x-axis intercept of the graph of: y=x^2 - 3x + 3 ---- Solve x^2 - 3x + 3 = 0 --- Use Quadratic Formula: x = [3 +- sqrt(9-4*1*3)]/2 ---- x = [3 +- sqrt(-3)]/2 ---- Note: The root values are complex. There are no x-intercepts. Cheers, Stan H. ================

Inequalities/731901: I am stuck on a question on one of my tests. . Solve the inequality: |3 - 3x/4| >= 9 . I know the equation will be an inequality, but I've tried several times and I haven't been right. Could I have some help understanding how to tackle this, and all the steps involved? 1 solutions Answer 447352 by stanbon(57203)   on 2013-03-29 21:41:47 (Show Source): You can put this solution on YOUR website! Solve the inequality: |3 - 3x/4| >= 9 -------- 3-(3/4)x >= 9 or 3-(3/4)x <= -9 ----- -(3/4)x >= 6 or -(3/4)x <= -12 ---- x <= -8 or x >= 16 ========================= Cheers, Stan H. ==============

absolute-value/731896: What is |3x+2|greater than equal to 4 x(x-1)(x-2)greater than 0 1 solutions Answer 447350 by stanbon(57203)   on 2013-03-29 21:17:17 (Show Source): You can put this solution on YOUR website! What is |3x+2|greater than equal to 4 ---- 3x+2 <= -4 or 3x+2 >= 4 3x <= -6 or 3x >= 2 x <= -2 or x >= 2/3 ============================ x(x-1)(x-2)greater than 0 Draw a number line. Plot points at 0,1,2 ---- Test a value in each interval: Test x = -10 to get -*-*- > 0 ; false Test x = 0.5 to get +*-*- > 0 ; true Test x = 1.5 to get +*+*- > 0 ; false Test x = 10 to get +*+*+ > 0 ; true ---- Solutions: (0,1)U(2,+oo) =============================== cheers, Stan H. Test x =

Circles/731894: how long is arc acb if the radius of a circle is 6? round your answer to two decimal places? 1 solutions Answer 447348 by stanbon(57203)   on 2013-03-29 21:07:44 (Show Source): You can put this solution on YOUR website! how long is arc acb if the radius of a circle is 6? round your answer to two decimal places? ---- You have to know the size of the subtended angle. Cheers, Stan H. ======================= Cheers, Stan H.

logarithm/731889: Solve the exponential equation. Express the solution in terms of natural logarithms. Then use a calculator to obtain a decimal approximation for the solution. e^x = 22.8 1 solutions Answer 447347 by stanbon(57203)   on 2013-03-29 21:04:34 (Show Source): You can put this solution on YOUR website! Solve the exponential equation. Express the solution in terms of natural logarithms. Then use a calculator to obtain a decimal approximation for the solution. e^x = 22.8 ------ base = e exponent = log = x result = 22.8 ------ ln(22.8) = x --- x = 3.1268 =================== Cheers, Stan H.