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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 , 57180..57209 , 57210..57239, >>Next

 Rectangles/238377: Let's say you have a rectangle and you would like to find the area of it in square units. The width is 7 units but the length us (2x-5) units. What do you do to find the area? It is a TAKS question and I would really appreciate your help, thank you. 1 solutions Answer 175159 by stanbon(57290)   on 2009-11-12 21:55:55 (Show Source): You can put this solution on YOUR website!Let's say you have a rectangle and you would like to find the area of it in square units. The width is 7 units but the length us (2x-5) units. What do you do to find the area? Area = width*length Area = 7*(2x-5) Area = 14x-35 sq.units ============================ Cheers, Stan H.
 Polynomials-and-rational-expressions/238374: A student opens a mathematics book to two facing pages. The product of the page numbers is 1482. Find the page numbers.1 solutions Answer 175158 by stanbon(57290)   on 2009-11-12 21:53:05 (Show Source): You can put this solution on YOUR website!A student opens a mathematics book to two facing pages. The product of the page numbers is 1482. Find the page numbers. ------------------- Solve x(x+1) = 1482 for x Ans: x = 38 x+1= 39 ==================== Cheers, Stan H.
 Expressions-with-variables/238345: please help me solve a/b=c solve for b and h-4/j=k solve for j1 solutions Answer 175157 by stanbon(57290)   on 2009-11-12 21:48:00 (Show Source): You can put this solution on YOUR website!please help me solve a/b=c solve for b --- Invert both sides to get: b/a = 1/c Multiply both sides by a to get: b = a/c --------------------- h-4/j=k solve for j --- Invert both sides to get: j/(h-4) = 1/k Multiply both sides by h-4 j = (h-4)/k ============================= Cheers, Stan H.
 Square-cubic-other-roots/238367: how to get the answer for a square root of 35 and round to nearest thousandths how does it get rounded1 solutions Answer 175156 by stanbon(57290)   on 2009-11-12 21:44:01 (Show Source): You can put this solution on YOUR website!sqrt(35) = 5.916079783... Rounded to thousandths = 5.916 --------------------------------------- Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/238368: How do I solve this question? If 2k + 3y = k and 4x =7y, which of the following represents the value of y in terms of k?1 solutions Answer 175155 by stanbon(57290)   on 2009-11-12 21:41:34 (Show Source): You can put this solution on YOUR website!You did not list the optional answers. Cheers, Stan H.
 Matrices-and-determiminant/238372: How can i use cramers rule to solve linear system?1 solutions Answer 175154 by stanbon(57290)   on 2009-11-12 21:39:56 (Show Source): You can put this solution on YOUR website!That is a long topic to explain. May I suggest you use Google to search for "linear systems Cramer Method" Cheers, Stan H.
 Probability-and-statistics/238363: a student takes a 20 question multiple choice exam with 5 choices for each question and guesses on each question. find the probability of guessing at least 15 out of the 20 correctly. 1 solutions Answer 175153 by stanbon(57290)   on 2009-11-12 21:38:13 (Show Source): You can put this solution on YOUR website!a student takes a 20 question multiple choice exam with 5 choices for each question and guesses on each question. find the probability of guessing at least 15 out of the 20 correctly. ----------------------- It is a binomial problem with n=20, p=1/5 ; 15<= x <=20 -------------------------- Prob = 1 - binomcdf(20,1/5,14) = 0.0000001803 ==================================================== Cheers, Stan H.
 Linear-systems/238366: Solve this system by the addition method: x/4 + y/3 =5 x - y =6 1 solutions Answer 175152 by stanbon(57290)   on 2009-11-12 21:18:56 (Show Source): You can put this solution on YOUR website!Solve this system by the addition method: x/4 + y/3 =5 x - y =6 -------------------- Multiply thru the 1st equation by 12 Multiply thru the 2nd equation by -3 ----------------------------------------- 3x + 4y = 60 -3x+ 3y =-18 ------------------- Add and solve for "y": 7y = 42 y = 6 ------------------------------ Substitute into x-y=6 to solve for "x": x - 6 = 6 x = 12 --------------------------------------- Cheers, Stan H.
 Complex_Numbers/238358: Please help me solve this equation (-5-2i)(3+7i)1 solutions Answer 175151 by stanbon(57290)   on 2009-11-12 21:15:16 (Show Source): You can put this solution on YOUR website!What equation? Cheers, Stan H.
 Miscellaneous_Word_Problems/238346: i'm doing optimization problems in class and i have no clue where to even start with these problems...thanks A computer company determines the profit equation (in millions of dollars) is given by P=x^3-48x^2+720x-1000, where x is the number of thousands of units of software sold and x is greater than or equal to 0 and less than or equal to 401 solutions Answer 175148 by stanbon(57290)   on 2009-11-12 21:09:00 (Show Source): You can put this solution on YOUR website!A computer company determines the profit equation (in millions of dollars) is given by P=x^3-48x^2+720x-1000, where x is the number of thousands of units of software sold and x is greater than or equal to 0 and less than or equal to 40 ------------------ You could graph it and see where the high and the low points are in that interval. --------------------------- Or, if you are studying calculus you could take the 1st derivative, and the 2nd derivative and determine the local and absolute max/min values on [0,40] --------------------------- Cheers, Stan H.
 Equations/238359: Thank you for helping with that last question. I have another. Please help! 15-w/4=28 Answer is -521 solutions Answer 175146 by stanbon(57290)   on 2009-11-12 20:58:05 (Show Source): You can put this solution on YOUR website!15-w/4=28 --- Subtract 15 from both sides to get: -w/4 = 13 Multiply both sides by -4 to get: w = -4*13 w = - 52 ================ Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/238357: The product of two consecutive odd intergers is 1 less than four times their sum. Find the two intergers.1 solutions Answer 175145 by stanbon(57290)   on 2009-11-12 20:55:28 (Show Source): You can put this solution on YOUR website!The product of two consecutive odd integers is 1 less than four times their sum. Find the two integers. --- 1st: 2x-1 2nd: 2x+1 ----------------- Equation: (2x-1)(2x+1) = 4[(2x-1)+(2x+1)]-1 ---------------------------------- 4x^2-1 = 4[4x]-1 4x^2 = 16x x^2-x = 0 x(x-1) = 0 x = 0 or x = 1 ------------------------ If x = 0 1st: 2x-1 = -1 2nd: 2x+1 = 1 ------------------- If x = 1 1st: 2x-1 = 1 2nd: 2x+1 = 3 ======================== Cheers, Stan H.
 Equations/238354: 10(2x)=?1 solutions Answer 175144 by stanbon(57290)   on 2009-11-12 20:50:21 (Show Source): You can put this solution on YOUR website!Ans: 20x Cheers, Stan H.
 Functions/238355: In 2002, the price of mailing a letter was \$.34 for the first ounce and \$.21 for each ounce after the first ounce. Write a rule to describe the function.1 solutions Answer 175143 by stanbon(57290)   on 2009-11-12 20:49:20 (Show Source): You can put this solution on YOUR website!In 2002, the price of mailing a letter was \$.34 for the first ounce and \$.21 for each ounce after the first ounce. Write a rule to describe the function. --------------------------------------- Price = 0.34 + 0.21(x-1) where x is the weight of the item in ounces. ============================================================== Cheers, Stan H.
 Mixture_Word_Problems/238350: a 2004 Pontiac Montana has an engine coolant system capacity of 10.01 liter. If the system is currently filled with a mixture that is 30% antifreeze, how much of it should be drained and replaced with pure antifreeze so that they system is filled with a mixture that is 50% antifreeze?1 solutions Answer 175141 by stanbon(57290)   on 2009-11-12 20:47:02 (Show Source): You can put this solution on YOUR website!Pontiac Montana has an engine coolant system capacity of 10.01 liter. If the system is currently filled with a mixture that is 30% antifreeze, how much of it should be drained and replaced with pure antifreeze so that they system is filled with a mixture that is 50% antifreeze? ----------------------- Let "x" be the amount that should be drained and replaced. ------------------------------ Equation: 0.30*10.01 - 0.30x + 1.00x = 0.50*10.01 --- Multiply thru by 100 to get: 30*10.01 + 70x = 50*10.01 70x = 20*10.1 x = 2.89 liters (amount that should be drained and replaced) ================================================================ Cheers, Stan H.
 Probability-and-statistics/238196: what is the probability of your 13th birthday falling on friday the 13th1 solutions Answer 175128 by stanbon(57290)   on 2009-11-12 19:42:47 (Show Source): You can put this solution on YOUR website!what is the probability of your 13th birthday falling on friday the 13th ------------------------- The events are independent. P(born on 13th of a month) = 12/365 P(born on a friday) = 1/7 -------------------------------- P(born on friday the 13) = (1/7)(12/365) = 12/2555 = 0.0047 ========================= Cheers, Stan H.
 Probability-and-statistics/238064: Carlos, Mary, Rick and Yolanda are students in a class of 17. 4 students in the class are to be selected at random to present a report. What is the probability that Carlos, Mary, Rick and Yolanda are selected in that order?1 solutions Answer 175117 by stanbon(57290)   on 2009-11-12 19:17:57 (Show Source): You can put this solution on YOUR website!Carlos, Mary, Rick and Yolanda are students in a class of 17. 4 students in the class are to be selected at random to present a report. What is the probability that Carlos, Mary, Rick and Yolanda are selected in that order? --------------------------------------------------------------------- # of ways to succeed: 1 # of possible outcomes: 17P4 = 17*16*15*14 = 57120 ------------------------------------------ Probability = 1/57120 = 0.000017507... Cheers, Stan H.
 Linear-equations/238270: The directions are Solve each system by elimination. Check your answers. The first problem is x-y+z=-1 x+y+3z=-3 2x-y+2z=0 I've tried this like 15 times and cannot figure it out. Most of the time I would check what I got and it would be 1 instead of -1 or 3 instead of -3... I know how to do them I think. But I just can't get it.1 solutions Answer 175100 by stanbon(57290)   on 2009-11-12 18:40:14 (Show Source): You can put this solution on YOUR website!Solve each system by elimination. Check your answers. The first problem is x-y+z=-1 x+y+3z=-3 2x-y+2z=0 --------------------- Subtract 1st from the 2nd; Subtract 2 times the 1st from the 3rd. ----------- x-y+z=-1 0x+2y+2z=-2 0x+y+0z=2 ----------------- Solve the 3rd Eq. for y: y = 2 -------------------------- Substitute y=2 into the 2nd equation and solve for "z": 2*2 + 2z = -2 2Z = -6 z = -3 ------------ Substitute into x-y+z=-1 and solve for "x" x - 2 - 3 = -1 x = 4 =================================== Solution: x = 4 y = 2 z = -3 00000000000000000000000000000000000 Cheers, Stan H.
 test/238265: A store sells turkey sandwiches for \$5.00 and ham sandwiches for \$4.00. The store sells 5 more turkey sandwiches than double the amount of ham sandwiches and the total sales are \$1089.00. How many of each are sold?1 solutions Answer 175092 by stanbon(57290)   on 2009-11-12 18:17:34 (Show Source): You can put this solution on YOUR website!A store sells turkey sandwiches for \$5.00 and ham sandwiches for \$4.00. The store sells 5 more turkey sandwiches than double the amount of ham sandwiches and the total sales are \$1089.00. How many of each are sold? --------------------------------------- Quantity Equation: t = 2h + 5 Value Equation:::: 5t + 4h = 1089 ----------------------------------------- Substitute for t in the value equation and solve for "h: 5(2h+5) + 4h = 1089 14h = 1064 h = 76 (# of ham sandwiches sold) ----- Substitute into the Quantity Eq to solve for "y": t = 2*76 + 5 = 157 (# of turkey sandwiches sold) ================================================ Cheers, Stan H.
 Money_Word_Problems/238264: a triangle has a perimeter of 54 inches. find the length of the three sides if one side is 10 inches longer than the smallest and the third side is twice the smallest.1 solutions Answer 175086 by stanbon(57290)   on 2009-11-12 18:02:46 (Show Source): You can put this solution on YOUR website!a triangle has a perimeter of 54 inches. find the length of the three sides if one side is 10 inches longer than the smallest and the third side is twice the smallest. ---------------------- Let the smallest be "x". The 2nd side is "x+10" The 3rd side is "2x" ---------------------------- Equation: x + x+10 + 2x = 54 4x + 10 = 54 4x = 44 x = 11 --------------- smallest = 11 inches 2nd = 11+10 = 21 inches 3rd = 2x = 22 inches =================================== Cheers, Stan H.
 Probability-and-statistics/238197: A 3-card hand is drawn from a standard deck of 52 playing cards. Find the probability that the hand contains the given cards. no clubs 1 solutions Answer 175082 by stanbon(57290)   on 2009-11-12 17:57:53 (Show Source): You can put this solution on YOUR website!A 3-card hand is drawn from a standard deck of 52 playing cards. Find the probability that the hand contains the given cards. no clubs ------------------------------- # of ways to pick 3 that are not clubs : 39C3 ---------------- # of ways to pick 3 with no restriction: 52C3 -------------------------------------------------- Probability (no clubs) = 39C3/52C3 = 9139/22100 = 0.4135 ================================================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/237943: Solve the polynomial equation by factoring and using the zero product principle. I have solved simpiler versions but I'm having a hard time understanding how to attack this one. X^3-2X^2-X+2=01 solutions Answer 174900 by stanbon(57290)   on 2009-11-11 21:15:52 (Show Source): You can put this solution on YOUR website!X^3-2X^2-X+2=0 --- Factor the 1st two and the last two terms separately. ---- x^2(x-2)-(x-2) = 0 (x-2)(x^2-1) = 0 (x-2)(x-1)(x+1) = 0 x = 2 or x = 1 or x = -1 ============================= Cheers, Stan H.
 Matrices-and-determiminant/237895: Write the augmented matrix for the system of equations and solve the system using Gauss-Jordan Elimination. 10x+8y+20Z=6,000 10x+20y+40Z=11,000 100X+20y+200z=36,900 Help PLEASE :)1 solutions Answer 174899 by stanbon(57290)   on 2009-11-11 21:12:36 (Show Source): You can put this solution on YOUR website!Write the augmented matrix for the system of equations and solve the system using Gauss-Jordan Elimination. ---------------------------------- 10x+8y+20Z=6,000 10x+20y+40Z=11,000 100X+20y+200z=36,900 -------------------- Subtract 1st from 2nd and Subtract 10 times 1st from 3rd to get: 10x+8y+20Z=6,000 0x+12y+20z = 5000 0x-60y+0z = -23100 --------------------- Solve the 3rd equation for "y" y = 385 ------------- Substitute into the 2nd and solve for "z" 12*385 + 20z = 5000 z = 19 ------------------- Substitute into the 1st and solve for "x" 10x + 8*385 + 20*19 = 6000 x = 254 ================= Cheers, Stan H.
 Polynomials-and-rational-expressions/237877: Need to solve the following 8y^2=14y-5 (hint set equal to 0 first)1 solutions Answer 174893 by stanbon(57290)   on 2009-11-11 20:46:13 (Show Source): You can put this solution on YOUR website!to solve the following 8y^2=14y-5 8y^2 - 14y + 5 = 0 --- Think of two numbers whose product is 5*8=40 and whose sum is -14. --------------- They are -10 and -4 --------------- Rewrite the problem: 8y^2 - 10y - 4y + 5 = 0 --- Factor the 1st two and the last two terms seperately: 2y(4y-5) - (4y-5) = 0 Factor again: (4y-5)(2y-1) = 0 y = 5/4 or y = 1/2 ============================ Cheers, Stan H.
 Exponents-negative-and-fractional/237889: What Is The Multiplicative Inverse Of Negative 71 solutions Answer 174892 by stanbon(57290)   on 2009-11-11 20:37:24 (Show Source): You can put this solution on YOUR website!What Is The Multiplicative Inverse Of Negative 7 -------------- The multiplicative Inverse of ANY number except zero, is 1 over the number. ------------ Your Problem: MI = 1/(-7) = -1/7 ======================= Cheers, Stan H.
 Proportions/237859: the amount of gold is measured in karats(K), where 24K represents pure gold. the mark 14K on a chain indicates that the ratio between the mass of the gold in the chain and the mass of the chain is 14:24. If a gold ring is marked 18K and it weighs 0.04 oz, what is the value of the gold in the ring if pure gold is valued at \$300 per oz?1 solutions Answer 174890 by stanbon(57290)   on 2009-11-11 20:28:11 (Show Source): You can put this solution on YOUR website!18:24 is the same as 0.75 or 3/4 ----------------------------- the ring is 3/4 * 0.04 = 0.03 oz. of gold. --- value of the ring is 0.03*300 = \$9 ==================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/237903: Please help!! Multiply and Simplify 64c^2 * 2c-6 ----------- ---- 2c^2-12c+18 8c Subtract and simplify if possible 7-y - 8y-9 --- ---- y-9 9-y1 solutions Answer 174881 by stanbon(57290)   on 2009-11-11 19:57:41 (Show Source): You can put this solution on YOUR website!Multiply and Simplify 64c^2 * 2c-6 ----------- ---- 2c^2-12c+18 8c ------------------------------------ Reduce where you can: 8c/(2(c^2-6c+9) * 2(c-3)/1 ------ Reduce again: 8c/(c^2-6c+9) * (c-3)/1 ------ Factor: 8c/(c-3)^2 * (c-3)/1 ---------- Reduce again: 8c/(c-3) ================================== Subtract and simplify if possible 7-y 8y-9 --- - ---- y-9 9-y ------------------ Adjust the 2nd denominator sign. (7-y)/(y-9) + (8y-9)/(y-9) ---- [8y-y-9+7)/(y-9) ---- [7y-2]/[y-9] ================== Cheers, Stan H.
 Probability-and-statistics/237830: Ten quarters dated 1990-1999 are tossed. What is the probability of the following a) tails occurring on 1991 quarter only (b) tails on all 10 quarters (c) exactly 4 tails (d) at least 3 tails 1 solutions Answer 174877 by stanbon(57290)   on 2009-11-11 19:34:59 (Show Source): You can put this solution on YOUR website!Ten quarters dated 1990-1999 are tossed. What is the probability of the following a) tails occurring on 1991 quarter only # of ways to succeed: 1 # of possible outcomes 2^10 = 1024 P(tail on 1991 only) = 1/1024 ------------------------------------------- (b) tails on all 10 quarters (1/2)^10 = 1/1024 ------------------------ c) exactly 4 tails 10C4*(1/2)^4*(1/2)^6 = 210/1024 --------------------------------- (d) at least 3 tails 1 - binomcdf(10,0.4,2) = 0.9453 ====================================== Cheers, Stan H.
 Probability-and-statistics/237881: A box contains 65 balls numbered from 1 to 65. If 10 balls are drawn with replacement, what is the probability that at least two of them have the same number?1 solutions Answer 174869 by stanbon(57290)   on 2009-11-11 19:27:30 (Show Source): You can put this solution on YOUR website!A box contains 65 balls numbered from 1 to 65. If 10 balls are drawn with replacement, what is the probability that at least two of them have the same number? ----------- # of ways to pick a number: 65 probability of picking any particular number: (1/65) ------------ With replacement means the draw results are independent. This is a binomial problem with n=10, p=1/65, 2<= x <= 65 ---- Ans P(2 <= x <= 65) = 1-[P(x=0)+P(x=1)] = 1 - 10C0(1/65)^0(64/65)^65 + 10C1(1/65)^1*(64/65)^64] = 1 - 0.99019 = 0.0.00981 ================================ Cheers, Stan H.
 Polynomials-and-rational-expressions/237856: Need to factor this problem completely 27a^3+81 solutions Answer 174858 by stanbon(57290)   on 2009-11-11 18:18:14 (Show Source): You can put this solution on YOUR website!Need to factor this problem completely 27a^3+8 ------------ (3a)^2 + (2)^3 = (3a+2)((3a)^2-(3a)(2)+(2)^2) --- = (3a+2)(9a^2 - 6a + 4) ================================== Cheers, Stan H.
 Travel_Word_Problems/237843: Nicole jogged for a distance and then turned around and walked back to her starting point. While jogging she averaged 7.2 miles per hour, and while walking she averaged 2.4 miles per hour. If the total time spent jogging and walking was 4 hours, find (a) how long she jogged; (b) the total distance she traveled.1 solutions Answer 174854 by stanbon(57290)   on 2009-11-11 18:14:45 (Show Source): You can put this solution on YOUR website!Nicole jogged for a distance and then turned around and walked back to her starting point. While jogging she averaged 7.2 miles per hour, and while walking she averaged 2.4 miles per hour. If the total time spent jogging and walking was 4 hours, find (a) how long she jogged; (b) the total distance she traveled. ------------------------------------ Jogging DATA: rate = 7.2 mph ; distance = x miles ; time = d/r = x/7.2 hrs -------------------------- Walking DATA: rate = 2.4 mph ; distance = x miles ; time = d/r = x/2.4 hrs ----------------------------- Equation: time + time = 4 hrs x/7.2 + x/2.4 = 4 hrs. 2.4x + 7.2x = 7.2*2.4*4 ------------ 9.6x = 69.12 x = 7.2 miles ------------ Jog time = x/7.2 = 7.2/7.2 = 1 hr Total distance traveled = 2x = 2*7.2 = 14.4 miles ========================== Cheers, Stan H.