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 percentage/385942: Solve the following equation for m. Please show all of your work s= 4m-3n/211 solutions Answer 272943 by stanbon(60772)   on 2010-12-14 08:40:38 (Show Source): You can put this solution on YOUR website!s= (4m-3n)/21 --- 21s = 4m-3n ---- 21s+3n = 4m -------- m = (21s+3n)/4 ================== Cheers, Stan H.
 logarithm/385928: if b is 1.2 and t is 4. first make x the subject and work out its value in this equation b = log4x - 2log t1 solutions Answer 272940 by stanbon(60772)   on 2010-12-14 08:36:57 (Show Source): You can put this solution on YOUR website!if b is 1.2 and t is 4. first make x the subject and work out its value in this equation ------------------------ b = log4x - 2log t --- 1.2 = log4(x) - 2log(4) --- 1.2 = log4(x) - log(16) ---- 1.2 = log4(x) - 1.2041 ---- log4(x) = 2.4041 --- x = 4^2.4041 --- x = 28.016.. =============== Cheers, Stan H. ============
 Probability-and-statistics/385490: Consider the following contingency table of travelers on a cruise ship and their ages: Age 1st cruise 2nd cruise 3rd cruise 21 - 30 25 17 33 31 - 40 12 23 10 41 – 50 35 15 45 Total 72 55 88 A. If a person is selected at random, what is the probability it is his/her 2nd cruise? ____ B. If a person is selected at random, what is the probability the person is either in the age group 31-40 or 41-50? ____ C. If a person is selected at random, what is the probability the person is either 21-30 or on his/her 2nd cruise? _____ D. If two people are selected at random, what is the probability they are both on their 1st cruise? ____ If I get this answer correct, I will provide you with a DONATION. 1 solutions Answer 272937 by stanbon(60772)   on 2010-12-14 08:30:11 (Show Source): You can put this solution on YOUR website!Consider the following contingency table of travelers on a cruise ship and their ages: Age 1st cruise 2nd cruise 3rd cruise 21 - 30 25 17 33 31 - 40 12 23 10 41 – 50 35 15 45 Total 72 55 88 A. If a person is selected at random, what is the probability it is his/her 2nd cruise? (total of 2nd cruise column)/(grand total) B. If a person is selected at random, what is the probability the person is either in the age group 31-40 or 41-50? (sum of those rows)/grand total) C. If a person is selected at random, what is the probability the person is either 21-30 or on his/her 2nd cruise? (sum of 21-30 and 2nd - intersection of that row and column)/grand total D. If two people are selected at random, what is the probability they are both on their 1st cruise? 144C2/grandtotalC2 =================== Cheers, Stan H.
 Sequences-and-series/385826: Find the next 3 numbers in the following pattern: 2/3, 2/5, 6/25, 18/125,... 1 solutions Answer 272884 by stanbon(60772)   on 2010-12-13 22:13:14 (Show Source): You can put this solution on YOUR website!Find the next 3 numbers in the following pattern: 2/3, 2/5, 6/25, 18/125,... --------------------- Find the pattern: The numerators are multiplied by 3 The denominators are multiplied by 5 --- 5th term: (3/5)(18/125) --- 6th term: (3/5)^2(18/125) ---- 7th term: (3/5)^3(18/125) ============================ Cheers, Stan H.
 Inequalities/385819: 6. Write an inequality to describe all the points on the coordinate plane above y = -4. A. y < 4 B. y > -4 C. y > 4 D. y < -4 1 solutions Answer 272881 by stanbon(60772)   on 2010-12-13 21:56:32 (Show Source): You can put this solution on YOUR website!Write an inequality to describe all the points on the coordinate plane above y = -4. Ans: y > -4 ============= Cheers, Stan H.
 Mixture_Word_Problems/385787: how many pounds of 40 cent nuts and how many pounds of 25 cent nuts must you a dealer use to produce a misture of 90 pounds to sell at 31 cents per pound?1 solutions Answer 272878 by stanbon(60772)   on 2010-12-13 21:17:26 (Show Source): You can put this solution on YOUR website!how many pounds of 40 cent nuts and how many pounds of 25 cent nuts must you a dealer use to produce a misture of 90 pounds to sell at 31 cents per pound? --------- Equations: Quantity: x + y = 90 lbs Value:::40x + 25y = 31*90 cents ---------------------------------- Multiply Quantity by 40 ---- 40x + 40y = 40*90 --- Subtract from Value and solve for "y": -15y = -9*90 y = 54 lbs (amt. of 25 cent nuts needed in the mixture) --- Since x+y = 90, x = 36 lbs (amt. of 40 cent nuts needed in the mixture) ------ Cheers, Stan H.
 percentage/385788: what percentage of 600 is 750.1 solutions Answer 272876 by stanbon(60772)   on 2010-12-13 20:55:43 (Show Source): You can put this solution on YOUR website!what percentage of 600 is 750 ---- x/100 = 750/600 --- x = 100(750/600) --- x = 750/6 --- x = 125% ============== Cheers, Stan H.
 Linear-equations/385783: find the intercepts then use them to graph the equation: 1.1x-1.9y=4.181 solutions Answer 272875 by stanbon(60772)   on 2010-12-13 20:52:20 (Show Source): You can put this solution on YOUR website!find the intercepts then use them to graph the equation: 1.1x-1.9y=4.18 --- Multiply thru by 100 to get rid of the decimals. ---- 110x - 190y = 418 --- x-intercept = ? Let y = 0, then x = 418/110 = 3.8 ---- y-intercept = ? Let x = 0, then y = 418/-190 = -2.2 ======================= Plot (0,-2.2) and (3.8,0) and draw a line thru them to get: ========================== Cheers, Stan H. =========
 logarithm/385774: Rewrite the expression as a single logarithm: log(3,5) + 5log(3,2)1 solutions Answer 272873 by stanbon(60772)   on 2010-12-13 20:44:56 (Show Source): You can put this solution on YOUR website!Rewrite the expression as a single logarithm: log(3,5) + 5log(3,2) ---- log3(6)+5log3(2) -------- = log3(6)+log3(2^5) --- = log3(6)+log3(32) --- = log3[6*32] --- = log3[192] =============== Cheers, Stan H.
 Percentage-and-ratio-word-problems/385766: Of the \$50,000 that Natasha pocketed on her last real estate deal, \$20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made \$6060 on these investments in 1 year, then how much did she invest in each fund? 1 solutions Answer 272869 by stanbon(60772)   on 2010-12-13 20:39:19 (Show Source): You can put this solution on YOUR website!Of the \$50,000 that Natasha pocketed on her last real estate deal, \$20,000 went to charity. ------------------------- She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made \$6060 on these investments in 1 year, then how much did she invest in each fund? ----- Equations: Quantity Eq::: x + y = 30000 Interest Eq::: 0.16x+0.25y = 6060 --- Multiply the Quantity Eq. by 16 Multiply the Interest Eq. by 100 ---------------------------- 16x + 16y = 16*30000 16x + 25y = 606000 ------------------------ Subtract and solve for "y": 9y = 126000 ---- y = \$14000 (amt. invested at 25% --- Since x+y= 30000, x = \$16000 (amt. invested at 16%) ============== Cheers, Stan H. -------
 percentage/385768: roger has completed 78% of his 200 page thesis.how many pages has he written1 solutions Answer 272862 by stanbon(60772)   on 2010-12-13 20:18:21 (Show Source): You can put this solution on YOUR website!roger has completed 78% of his 200 page thesis.how many pages has he written ---- # of pages = 0.78*200 = 156 ============= Cheers, Stan H.
 test/385756: 8y over 4 equals 2y1 solutions Answer 272861 by stanbon(60772)   on 2010-12-13 20:15:59 (Show Source): You can put this solution on YOUR website! 8y over 4 equals 2y ---- (8y)/4 = 2y That is true for all Real Numbers. It is an identity. Cheers, Stan H.
 Probability-and-statistics/385634: a coin is flipped five times. find the number of possible sets of heads and tails that have each of the follwing a. 0 heads b. 2 heads1 solutions Answer 272829 by stanbon(60772)   on 2010-12-13 18:55:04 (Show Source): You can put this solution on YOUR website!a coin is flipped five times. find the number of possible sets of heads and tails that have each of the follwing --- Binomial Problem with n = 5 and p = 1/2 ---- a. P(0 heads) = (1/2)^5 = 1/32 ------ b. P(2 heads) = 5C2(1/2)^5 = 10/32 5/16 ============== Cheers, Stan H.
 Exponents/385695: -3x over 8 times 16x over 9 1 solutions Answer 272823 by stanbon(60772)   on 2010-12-13 18:39:04 (Show Source): You can put this solution on YOUR website! -3x over 8 times 16x over 9 -------- [-3x/8] --- Cancel any factor that is common to a numerator and a denominator. ---- = [-x/1] ---- = -(2/3)x^2 ============ Cheers, Stan H.
 logarithm/385685: ln(2x-1)=81 solutions Answer 272819 by stanbon(60772)   on 2010-12-13 18:33:44 (Show Source): You can put this solution on YOUR website!ln(2x-1)=8 ----- 2x-1 = e^8 2x = e^(8) +1 2x = 2981.96 ---- x = 1490.98 ====================== Cheers, Stan H.
 logarithm/385687: ln2+lnx=51 solutions Answer 272814 by stanbon(60772)   on 2010-12-13 18:27:11 (Show Source): You can put this solution on YOUR website!ln2+lnx=5 ---- ln[2x] = 5 --- 2x = e^5 --- 2x = 148.41 --- x = 74.205 =============== Cheers, Stan H.
 logarithm/385683: log3x+log9=01 solutions Answer 272812 by stanbon(60772)   on 2010-12-13 18:23:57 (Show Source): You can put this solution on YOUR website!log3x+log9=0 ---- log[9*3x] = 0 ---- 27x = 10^0 --- 27x = 1 x = 1/27 ========== Cheers, Stan H.
 Quadratic_Equations/385671: Twelve less than the square root of a number is the same as 4 times the number. Find the number 1 solutions Answer 272810 by stanbon(60772)   on 2010-12-13 18:19:07 (Show Source): You can put this solution on YOUR website! Twelve less than the square root of a number is the same as 4 times the number. Find the number ------------------ Equation: sqrt(x) - 12 = 4x --------- Rearrange: sqrt(x) = 4x+12 --- Square both sides to get: x = 16x^2 + 96x + 144 ---- 16x^2 + 95x + 144 = 0 -------- Positive solution: There is no positive soltion. ========================= Cheers, Stan H.
 Travel_Word_Problems/385663: if i average 20 miles per hour on the way to a show and 30 miles per hour on the way back what was the average speed for the whole trip?1 solutions Answer 272803 by stanbon(60772)   on 2010-12-13 18:10:24 (Show Source): You can put this solution on YOUR website! If i average 20 miles per hour on the way to a show and 30 miles per hour on the way back what was the average speed for the whole trip? ---- To the show: rate = 20 mph ; distance = x miles ; time = x/20 hrs. ------------------- From the show: rate = 30 mph ; distance = x miles ; time = x/30 hrs. ---- Average for the whole trip = total distance/ total time = (2x)/[x/20 + x/30] --- = (2x)/[(30x+20x)/600] --- = (2x)/[50x/600] --- = 2x[600/50x] = 2[12] = 24 mph ========== Cheers, Stan H.
 Probability-and-statistics/385625: In how many different ways can the top twelve new indie bands be ranked on a top twelve list? The top hit song for each of the twelve bands will compete to receive monetary awards of \$1000, \$500, \$250 and \$100, respectively. In how many ways can the awards be given out? 1 solutions Answer 272784 by stanbon(60772)   on 2010-12-13 17:09:59 (Show Source): You can put this solution on YOUR website!In how many different ways can the top twelve new indie bands be ranked on a top twelve list? Ans: 12! = 479,001,600 ways -------------------- The top hit song for each of the twelve bands will compete to receive monetary awards of \$1000, \$500, \$250 and \$100, respectively. In how many ways can the awards be given out? Ans: 12P4 = 12*11*10*9 ============================= Cheers, Stan H.
 Equations/385622: solve 3x-1/4=x-5/5>-21 solutions Answer 272783 by stanbon(60772)   on 2010-12-13 17:04:00 (Show Source): You can put this solution on YOUR website!You cannot have that arrangement of equality and inequality on the same line. ================ Cheers, Stan H.
 Graphs/385615: determine whether the graph of f(x)= x^3-x^2-12x/x-4 has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous1 solutions Answer 272782 by stanbon(60772)   on 2010-12-13 17:02:00 (Show Source): You can put this solution on YOUR website!determine whether the graph of f(x)= x^3-x^2-12x/x-4 ---------------------- has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous. ---------------------- There is a discontinuity at x = 4 Not sure how you categorize it. Cheers, Stan H.
 Functions/385604: given f(x)5x^3, find f^-1(x). then state whether f^-1(x) is a function1 solutions Answer 272781 by stanbon(60772)   on 2010-12-13 16:52:45 (Show Source): You can put this solution on YOUR website!given f(x)= 5x^3, find f^-1(x). 1st: Interchange x and y to get: x = 5y^3 --- 2nd: solve for "y": y^3= (x/5) --- y = cbrt(x/5) ------------------- then state whether f^-1(x) is a function Yes, it is a function. --------------------- Cheers, Stan H.
 Mixture_Word_Problems/385555: A lab technician is required to prepare 200 liters of a fungicide. The prepared solution must contain 42% fungicide. The lab technician wishes to use a solution that contains 30% fungicide with a solution that contains 50% fungicide. How much of each solution should he use. thanks1 solutions Answer 272770 by stanbon(60772)   on 2010-12-13 15:54:13 (Show Source): You can put this solution on YOUR website!A lab technician is required to prepare 200 liters of a fungicide. The prepared solution must contain 42% fungicide. The lab technician wishes to use a solution that contains 30% fungicide with a solution that contains 50% fungicide. How much of each solution should he use. Equation: fungi + fungi = fungi 0.50x + 0.30(200-x) = 0.42*200 --- Multiply thru by 100 to get: 50x + 30*200 - 30x = 42*200 20x = 12*200 x = 120 liters (amt. of 50% solution needed in the mixture) 200-x = 80 liters (amt. of 30% solution needed in the mixture) ========================= Cheers, Stan H. =============
 Graphs/385559: how can the equation of a point (0,-5) with a slope of 31 solutions Answer 272767 by stanbon(60772)   on 2010-12-13 15:42:47 (Show Source): You can put this solution on YOUR website! how can the equation of a point (0,-5) with a slope of 3 --- y-intercept = -5 slope = 3 --- Equation: y = 3x-5 ============ Cheers, Stan H.
 Travel_Word_Problems/385552: at full speed, a motor boat can travel 32 miles upstream in 8 hours, but it can travle the same distance downstram in 4 hours. What is the rate of the current in miles per hour.1 solutions Answer 272765 by stanbon(60772)   on 2010-12-13 15:41:19 (Show Source): You can put this solution on YOUR website! At full speed, a motor boat can travel 32 miles upstream in 8 hours, but it can travel the same distance downstram in 4 hours. What is the rate of the current in miles per hr. --------------------------- Upstream DATA: distance = 32 miles; time = 8 hrs ; rate = 32/8 = 4 mph ----- Downstream DATA: distance = 32 miles ; time = 4 hrs ; rate = 32/4 8 mph ----- Equation: Let boat speed = b Let current speed = c --- b-c = 4 b+c = 8 --- 2b = 12 b = 6 mph (speed of the boat in still water)\ ---- Since b + c = 8, c = 2 mph ============================= cheers, Stan H. =============================
 Sequences-and-series/385518: the sequence is 1/6,1,6,36. how do i find the explicit formula? what is the explicit formula?1 solutions Answer 272755 by stanbon(60772)   on 2010-12-13 14:50:19 (Show Source): You can put this solution on YOUR website!the sequence is 1/6,1,6,36. how do i find the explicit formula? what is the explicit formula? ----- Find the pattern for the nth term: 1---1/6 2---(1/6)*6 3---(1/6)*6^2 4---(1/6)*6^3 ---- ---- n---(1/6)*6^(n-1) ------ Explicit Formula: a(n) = (1/6)*6^(n-1) or 6^(n-2) ==================================================== Cheers, Stan H.
 Equations/385520: Write an equation that is a direct variation with a constant of variation of 2/3.1 solutions Answer 272752 by stanbon(60772)   on 2010-12-13 14:45:05 (Show Source): You can put this solution on YOUR website!Write an equation that is a direct variation with a constant of variation of 2/3. --- y = (2/3)x =============== Cheers, Stan H.
 Quadratic_Equations/385519: x^2+9x-12=0 x^2=9x=12 4x^2+36x=12x4 4x^2+36x=48 4x^2+36x+6=48+6 and this is where i get completely confused...i don't even know if I've done the problem right thus far. your suggestions please???1 solutions Answer 272750 by stanbon(60772)   on 2010-12-13 14:42:26 (Show Source): You can put this solution on YOUR website! x^2+9x-12=0 Use the quadratic formula: x = [-b +- sqrt(b^2-4ac)]/(2a) ----------------------------------- x = [-9 +- sqrt(81 - 4*1*-12)]/2 --- x = [-9 +- sqrt(129)]/2 ---- x = [-9 +- 11.36]/2 --- x = [2.36/2] or x = [-20.36/2] --- x = 1.18 or x = -10.18 ============================ cheers, Stan H.
 Functions/385510: let f(x)= 6+x and g(x)= x^2-x+1, find (f-g)(x)1 solutions Answer 272749 by stanbon(60772)   on 2010-12-13 14:36:54 (Show Source): You can put this solution on YOUR website!let f(x)= 6+x and g(x)= x^2-x+1, find (f-g)(x) ----- (f-g)(x) = f(x)-g(x) = (6+x)-(x^2-x+1) --- = -x^2+2x+5 ============== Cheers, Stan H.