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Recent problems solved by 'stanbon'

stanbon answered: 57178 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 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

Probability-and-statistics/719387: The J.O. Supply Company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. 100 calculators are selected at random. What is the expected number of defectives? What is the standard deviation? What is the probability that 3 or more calculators will be defective? 1 solutions Answer 441335 by stanbon(57246)   on 2013-02-26 18:54:36 (Show Source): You can put this solution on YOUR website! The J.O. Supply Company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. 100 calculators are selected at random. What is the expected number of defectives? E(x) = np = 100*0.10 = 10 ----------------------------------- What is the standard deviation? std = sqrt(npq) = sqrt(10*0.9) = 3 ----------------------------------- What is the probability that 3 or more calculators will be defective? P(3 or more) = 1 - P(0<= x <=2) = 1 - binomcdf(100,0.1,2) = 0.9900 ---------------------- Cheers, Stan H. ======================

Probability-and-statistics/719371: A box contains two aces and a king Two cards are drawn from the box: A K A a. Without replacement of the first card drawn- i. Diagram the two draws ii. What is the probability of having an ace and a king after the two draws? b. With replacement of the first card drawn- i. Diagram the two draws ii. What is the probability of having an ace and a king after the two draws? 1 solutions Answer 441332 by stanbon(57246)   on 2013-02-26 18:48:35 (Show Source): You can put this solution on YOUR website! A box contains two aces and a king Two cards are drawn from the box: A K A a. Without replacement of the first card drawn- i. Diagram the two draws AA' ; AK ;A'K ; -------------------------- ii. What is the probability of having an ace and a king after the two draws? Ans: 2/3 ------------------------------ b. With replacement of the first card drawn- i. Diagram the two draws AA ; A'A' ; A'A ; AA' ; AK ; A'k ; KK ------------------------------ ii. What is the probability of having an ace and a king after the two draws? With replacement the probability after 2 draws is the same as the probability before the two draws. ===================== Cheers, Stan H. ================

Probability-and-statistics/719361: In a game, $3 is bet on the roll of a 7 sided die. If 3, 4, 5, 6 is rolled, the player wins $2. a. What is the expected winnings from the game? b. Is the game fair? Explain why or why not. 1 solutions Answer 441329 by stanbon(57246)   on 2013-02-26 18:34:06 (Show Source): You can put this solution on YOUR website! In a game, $3 is bet on the roll of a 7 sided die. If 3, 4, 5, 6 is rolled, the player wins $2. a. What is the expected winnings from the game? Random # values: -3.......2 Probabilities::: 3/7......4/7 --- Expected winnings: (-9 + 8)/7 = -1/7 dollars ------- b. Is the game fair? Explain why or why not. Not fair as you can expect to lose 1/7 = $0.1428 cents each time you play. ================== Cheers, Stan H.

Equations/719358: i need to see exactly how to foil (3+2h*0.839)^2=33 1 solutions Answer 441327 by stanbon(57246)   on 2013-02-26 18:26:08 (Show Source): You can put this solution on YOUR website! i need to see exactly how to solve (3+2h*0.839)^2=33 ------ 3+2h*0.839 = sqrt(33) ----- 1.678h = sqrt(33)-3 --- h = (sqrt(33)+3)/1.678 ---- h = 5.211 ============== Cheers, Stan H.

Rational-functions/719354: inequality 1x+1y equal to or greater than 5 1 solutions Answer 441325 by stanbon(57246)   on 2013-02-26 18:21:04 (Show Source): You can put this solution on YOUR website! 1x+1y equal to or greater than 5 ---- If you want to graph the inequality: 1st: Graph y = -x+5 Draw a line thru (0,5),(5,0) --- 2nd: Graph the inequality: Shade the half-plane ABOVE the boundary line because you want y to get GREATER than -x+5. --------- ------------------- Cheers, Stan H. =============

Probability-and-statistics/719316: a diamond can be classified as either gem quality or industrial grade. 87% of diamonds are industrial grade. What is the probability that 2 randomly selected diamonds with be industrial grade? 1 solutions Answer 441310 by stanbon(57246)   on 2013-02-26 17:25:05 (Show Source): You can put this solution on YOUR website! a diamond can be classified as either gem quality or industrial grade. 87% of diamonds are industrial grade. What is the probability that 2 randomly selected diamonds with be industrial grade? ------------------------ The selection results are independent. --- P(2 industrial) = 0.87^2 = 0.7569 ===================================== Cheers, Stan H.

Trigonometry-basics/719291: Hello. I have the following trigonometric question to answer but im stuck. Please note the B in the equation is Beta. Solve the following for between 0 and 360 degrees: . I have done the following: 3-2sinB + 12sinB - 8sin^2B = 2, which then goes to -8sin^2B + 10sinB +1 = 0 Is my next step to transform this into a quadratic equation? and then work out both sections individually as equalling zero? Any advice would be great. Thanks! 1 solutions Answer 441296 by stanbon(57246)   on 2013-02-26 16:49:12 (Show Source): You can put this solution on YOUR website! Solve the following for B between 0 and 360 degrees: (1+4 sin B)(3-2 sin B)=2 ----- Let x = sin(B) ----- (1+4x)(3-2x) = 2 3 + 10x - 8x^2 = 2 --- 8x^2 -10x - 1 = 0 ----- x = [10 +- sqrt(100-4*8*-1)]/16 ---- x = [10 +- sqrt(132)]/16 ---- Usable solution: x = -0.0931 ----- Solve for "B" sin(B) = -0.0931 B = sin^-1(-0.0931) = 354.66 degrees or B = 185.34 degrees ============================================================= Cheers, Stan H. ==================

Equations/719287: my sister is three years older than i am . the sum of our age is 29. how old am i ? 1 solutions Answer 441293 by stanbon(57246)   on 2013-02-26 16:30:56 (Show Source): You can put this solution on YOUR website! my sister is three years older than i am . the sum of our age is 29. how old am i ? ------ Equation: s = i + 3 s + i = 29 ----- Substitute and solve for "i": i + 3 + i = 29 2i = 26 i = 13 yrs -------------- Cheers, Stan H.

Expressions-with-variables/719285: graphing, substitution, elimination 3 x + 2y= 12 3 x + 2y= 6 Helpppppppppppppppp pleaseeeeeeee explain so i can understand this.thanks 1 solutions Answer 441291 by stanbon(57246)   on 2013-02-26 16:28:29 (Show Source): You can put this solution on YOUR website! 3 x + 2y= 12 3 x + 2y= 6 ----- That is obviously a contradiction. There is no solution. ---- If you graph the two equation you will get parallel lines. ---- If you apply elimination to solve the system you will get 0 = 6, which is a contradiction. ------------------------ Cheers, Stan H.

Travel_Word_Problems/719288: If you travel for 2 hours at a rate of 15 mph, and you travel for 6 hours at a rate of 5 mph, what is your average speed and how do you solve it? 1 solutions Answer 441290 by stanbon(57246)   on 2013-02-26 16:25:22 (Show Source): You can put this solution on YOUR website! If you travel for 2 hours at a rate of 15 mph, and you travel for 6 hours at a rate of 5 mph, what is your average speed and how do you solve it? -------------- average speed = (total distance)/(total time) ------- average = (2*15+6*5)/(2+6) = 60/8 = 7.5 mph ======================== Cheers, Stan H.

Equations/719289: 6x-3=11 1 solutions Answer 441289 by stanbon(57246)   on 2013-02-26 16:22:14 (Show Source): You can put this solution on YOUR website! 6x-3=11 ---- 6x = 14 x = 7/3 ============ Cheers, Stan H. ============

test/719226: How do you find the value of w in (w,-3) and (-5,-23w-1) 1 solutions Answer 441256 by stanbon(57246)   on 2013-02-26 14:47:49 (Show Source): You can put this solution on YOUR website! How do you find the value of w in (w,-3) and (-5,-23w-1) --------------------- insufficient information

Miscellaneous_Word_Problems/719221: The coffee variety Arabica yields about 900 kg of coffee beans per hectare, while Robusta yields about 1100 kg per hectare. Suppose that a plantation has a hectares of Arabica and r hectares of Robusta. Write an equation relating a and r if the plantation yields 40000 kg of coffee. Do not enter any commas or units in your answer. 1 solutions Answer 441255 by stanbon(57246)   on 2013-02-26 14:45:37 (Show Source): You can put this solution on YOUR website! The coffee variety Arabica yields about 900 kg of coffee beans per hectare, while Robusta yields about 1100 kg per hectare. Suppose that a plantation has a hectares of Arabica and r hectares of Robusta. Write an equation relating a and r if the plantation yields 40000 kg of coffee. Do not enter any commas or units in your answer. ---------- Weight of beans Eq: 900a + 1100r = 40,000 ========================================== Cheers, Stan H.

Inequalities/719218: Hi It would be very nice to have explanations too. Thanks, Richard 1 solutions Answer 441254 by stanbon(57246)   on 2013-02-26 14:42:10 (Show Source): You can put this solution on YOUR website! (-(x-1)^2(2-x))/((3-x)(5x-1)^2) >= 0 ---- 1st: Solve the EQUALITY: -(x-1)^2(2-x) = 0 x = 1 or x = 2 --------- 2nd: Note value that x cannot take: x = 3 or x = 1/5 -------------------------- 3rd: Solve the INEQUALITY: Draw a number line and plot x = 1/5, x = 1, x = 2, x = 3 ----------------------------------- Test a value in each of the resulting 5 number line intervals to find solution intervals: (-(x-1)^2(2-x))/((3-x)(5x-1)^2) > 0 If x=0 you get: [-(-1)^2(2)]/[(3*(-1)^2] = -2/3 is not > 0 ------ If x=1/2 you get: [-(-1/2)^2(3/2)]/[(5/2)(3/2)^2] = (-3/8)/+ is not > 0 ------------ If x = 3/2 the result is not > 0 -------------------- If x = 5/2 the result IS > 0 -------- If x = 10 the result is not > 0 --- Conclusion: Solution: x = 1 or values in the interval [2,3) ================================ ======================== Cheers, Stan H. =========================

Quadratic_Equations/719217: How do you put y= -8x^2+ 3 into vertex form? 1 solutions Answer 441248 by stanbon(57246)   on 2013-02-26 14:19:09 (Show Source): You can put this solution on YOUR website! put y= -8x^2+ 3 into vertex form? ---- y = -8(x^2) + 3 ------- y = -8(x-0)^2 + 3 --------------------------- vertex: (0,3) ==================== Cheers, Stan H.

Money_Word_Problems/719215: Phyllis invested 27000 dollars, a portion earning a simple interest rate of 4 percent per year and the rest earning a rate of 7 percent per year. After one year the total interest earned on these investments was 1530 dollars. How much money did she invest at each rate? 1 solutions Answer 441246 by stanbon(57246)   on 2013-02-26 14:15:28 (Show Source): You can put this solution on YOUR website! Phyllis invested 27000 dollars, a portion earning a simple interest rate of 4 percent per year and the rest earning a rate of 7 percent per year. After one year the total interest earned on these investments was 1530 dollars. How much money did she invest at each rate? --------------------------- Equation: Quantity Equation: x + y = 27000 Interest Equation:4x +7y = 153000 ----------------------------------- Modify to eliminate: 4x + 4y = 4*27000 4x + 7y = 153000 ------- 3y = 45000 y = $15000 (amt invested at 4% x = 27000-15000 (amt. invested at 7% ---------------------------------------- Cheers, Stan H.

test/719213: a car rental company charges 60.00 per day plus 0.40 per mile to rent a car. If the car is rented for two days how many miles can be driven on a 200.00 budget 1 solutions Answer 441243 by stanbon(57246)   on 2013-02-26 14:07:36 (Show Source): You can put this solution on YOUR website! a car rental company charges 60.00 per day plus 0.40 per mile to rent a car. If the car is rented for two days how many miles can be driven on a 200.00 budget ---------- money for miles: 200-2*60 = $80 ---- # of miles: 80/0.40 = 8000/40 = 200 miles --------------------- Cheers, Stan H. =====================

Equations/719170: Tell whetber the relationships between the x and y values is linear. If it is write an esquation for tbe relationship between the values 1 solutions Answer 441223 by stanbon(57246)   on 2013-02-26 12:18:18 (Show Source): You can put this solution on YOUR website! insufficient information

Probability-and-statistics/719122: In a survey, 85% of the voters support a particular referendum. If 40 voters are chosen at random, and X is the number of voters that support this referendum, find the standard deviation X. Draw a graph showing the probability distribution for the sample space for tossing four coins. On a Saturday evening, 34% of the people in Chicago go out to dinner, 18% see a movie, 13% have a party, and 35% stay home. Seventeen people are randomly selected. Can the probability that exactly 4 of them stay home be computed using binomial model? Please help with questions. Need ASAP. Thank you in advance. 1 solutions Answer 441222 by stanbon(57246)   on 2013-02-26 12:13:29 (Show Source): You can put this solution on YOUR website! In a survey, 85% of the voters support a particular referendum. If 40 voters are chosen at random, and X is the number of voters that support this referendum, find the standard deviation X. ------- std = sqrt(npq) = sqrt(40*0.85*0.15) = 2.26 ---------------------------------------------------- Draw a graph showing the probability distribution for the sample space for tossing four coins. 4 heads::: 4C4/16 = 1/16 3 heads::: 4C3/16 = 4/16 2 heads::: 4C2/16 = 6/16 1 head:::: 4C1/16 = 4/16 0 heads::: 4C0/16 = 1/16 ========================= On a Saturday evening, 34% of the people in Chicago go out to dinner, 18% see a movie, 13% have a party, and 35% stay home. Seventeen people are randomly selected. Can the probability that exactly 4 of them stay home be computed using binomial model? ----- Binomial?? No The probability for each of the 17 is not the same. ==================================================== Cheers, Stan H.

Probability-and-statistics/719175: "A new Corvette weighs 3273 pounds. A manufacturer s scale that is accurate to the nearest 10 pounds gives the weight as 3250 pounds, while the U.S. Department of Transportation uses a scale that is accurate to the nearest 0.1 pound and obtains a weight of 3298.2 pounds" 1 solutions Answer 441217 by stanbon(57246)   on 2013-02-26 11:59:20 (Show Source): You can put this solution on YOUR website! A new Corvette weighs 3273 pounds. A manufacturer s scale that is accurate to the nearest 10 pounds gives the weight as 3250 pounds, while the U.S. Department of Transportation uses a scale that is accurate to the nearest 0.1 pound and obtains a weight of 3298.2 pounds. ------------------------- What is the question? ======================== Cheers, Stan H. ========================

Functions/719176: what is the domain and range for a function whose graph opens upward with vertex [o,-5] 1 solutions Answer 441215 by stanbon(57246)   on 2013-02-26 11:56:31 (Show Source): You can put this solution on YOUR website! what is the domain and range for a function whose graph opens upward with vertex (0,-5) ------ Sounds like a parabola. If so, domain is "all Real Numbers". ----- range is [5,+oo) =================== Cheers, Stan H. ===================

Money_Word_Problems/719174: £600 is put in a bank. After a year the money has increased by 8%. How much is now in the bank? 1 solutions Answer 441214 by stanbon(57246)   on 2013-02-26 11:52:51 (Show Source): You can put this solution on YOUR website! £600 is put in a bank. After a year the money has increased by 8%. How much is now in the bank? -------- Ans: 1.08*600 = 648 ---------------------- Cheers, Stan H. ======================

Age_Word_Problems/719105: the sum of the ages of father and his son his is 40 years. if they both live on till the son becomes as old as father is now , the sum of thier ages will be 96 years. find thier present ages 1 solutions Answer 441198 by stanbon(57246)   on 2013-02-26 08:04:54 (Show Source): You can put this solution on YOUR website! the sum of the ages of father and his son his is 40 years. if they both live on till the son becomes as old as father is now , the sum of thier ages will be 96 years. find thier present ages ----- Equations: f + s = 40 Note: Father's age now is 40-s Son's age will be "as old as father is now" = s + (40-s) = 40 ---------------------------------- 40 + (f + (40-s)) = 96 ----------------- Substitute for f and solve for "s": 40 + (40-s) + (40-s) = 96 120 - 2s = 96 2s = 24 s = 12 yrs (son's age now) ---- f = 40-s = 28 yrs (father's age now) ===================== Cheers, Stan H.

Age_Word_Problems/719104: John's age plus 7 will equal his brother's age of 19. How old is John? 1 solutions Answer 441197 by stanbon(57246)   on 2013-02-26 07:39:42 (Show Source): You can put this solution on YOUR website! John's age plus 7 will equal his brother's age of 19. How old is John? ----- Equation: j + 7 = 19 j = 12 yrs (John's age now) ================= Cheers, Stan H. ===============

Miscellaneous_Word_Problems/719100: The number of fish on a fish farm increases by 10 percent each month . If there were 350 fish calculate to the nearest 100 how may fish there would be after 12 month 1 solutions Answer 441196 by stanbon(57246)   on 2013-02-26 07:37:33 (Show Source): You can put this solution on YOUR website! The number of fish on a fish farm increases by 10 percent each month . If there were 350 fish calculate to the nearest 100 how may fish there would be after 12 months. -------- A(12) = 350*1.1^12 = 1098.45 or 1100 to the nearest 100. Cheers, Stan H. ================

Money_Word_Problems/718978: someone has 20% more money than you. They have 50 cents more than you do. How much money do you have? 1 solutions Answer 441140 by stanbon(57246)   on 2013-02-25 21:24:01 (Show Source): You can put this solution on YOUR website! someone has 20% more money than you. They have 50 cents more than you do. How much money do you have? ------ Equations: a = 1.20u a = u + 50 ------ 1.20u = u+50 0.20u = 50 u = $2.50 (amt. of money you have) ------------------------ Cheers, Stan H.

Graphs/718980: are the two equations -6+y=2x and 2y-4x=12 dependent? 1 solutions Answer 441138 by stanbon(57246)   on 2013-02-25 21:21:12 (Show Source): You can put this solution on YOUR website! are the two equations -6+y=2x and 2y-4x=12 dependent? ------- Solve each for "y": y = 2x + 6 y = 2x + 6 ------- Yes; they are dependent =========================== Cheers, Stan H.

Functions/718979: Please help me! Evaluate the function for the given value of x f(x)=3x+12;-5 g(x)=2.25x;100 1 solutions Answer 441137 by stanbon(57246)   on 2013-02-25 21:19:29 (Show Source): You can put this solution on YOUR website! Evaluate the function for the given value of x f(x)=3x+12;-5 f(-5) = 3(-5)+12 = -15+12 = -3 --------------------------------------- g(x)=2.25x;100 g(100) = 2.25*100 = 225 ============================ Cheers, Stan H. ============================

Probability-and-statistics/718977: A factory worker can package 75 games in 15 mins. How many games can he package per minute 1 solutions Answer 441136 by stanbon(57246)   on 2013-02-25 21:17:01 (Show Source): You can put this solution on YOUR website! A factory worker can package 75 games in 15 mins. How many games can he package per minute ---- games/time = games/time ----- g/1 min = 75/15 ---- g = 5 games per min ============================= Cheers, Stan H.

Percentage-and-ratio-word-problems/718973: If there are 60 students for every 9 adults on school field trips, how many adults should there be for 80 students? 1 solutions Answer 441135 by stanbon(57246)   on 2013-02-25 21:14:46 (Show Source): You can put this solution on YOUR website! If there are 60 students for every 9 adults on school field trips, how many adults should there be for 80 students? ---- Use a proportion: adults/students = adults/students --------------------------------- a/80 = 9/60 ----- a = (80*9)/60 a = 12 (# of adults for 80 students) ====================================== Cheers, Stan H. ==================

Probability-and-statistics/718942: normal distribution with a mean of 61 and standard deviation of 5, how to calculate the standard score equivalents for x x z t 66 1 solutions Answer 441127 by stanbon(57246)   on 2013-02-25 20:26:28 (Show Source): You can put this solution on YOUR website! normal distribution with a mean of 61 and standard deviation of 5, how to calculate the standard score equivalents for x x z t 66 ----- Not sure what you mean be repeating the x value. -------- z(66) = (66-61)/5 = 5/5 = 1 ----- t(66) = is the same as z(66) ==================== Cheers, Stan H.