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# Recent problems solved by 'stanbon'

stanbon answered: 57151 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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 Geometry_Word_Problems/672248: if the measure of the one of the base angles of an isosceles triangle is 62 degrees find the measure of the vertex angle1 solutions Answer 417843 by stanbon(57219)   on 2012-10-26 08:33:20 (Show Source): You can put this solution on YOUR website!if the measure of the one of the base angles of an isosceles triangle is 62 degrees find the measure of the vertex angle ------- If one of the base angles is 62 degrees so is the other one. --- Vertex angle = 180-2(62) = 56 degrees ================= Cheers, Stan H. =================
 test/672124: Write the equation in slope intercept form that is parallel to y=2x+5 & contains the point 3,-81 solutions Answer 417810 by stanbon(57219)   on 2012-10-25 21:36:21 (Show Source): You can put this solution on YOUR website!Write the equation in slope intercept form that is parallel to y=2x+5 & contains the point 3,-8 ----- The given line has slope = 2. Any line parallel to it must have slope = 2. ---- Form: y = mx + b You have y = -8 when x = 3 and m = 2 ---- Solve for "b": -8 = 2*3 + b b = -14 -------- Equation: y = 2x -14 ------------------- Cheers, Stan H. ===================
 Travel_Word_Problems/672110: Cheryl and Judy trudged at 4 mph until their packs got too heavy. Then they dropped their packs and continued at the brisk pace of 6 mph. If the total trip of 56 miles took 12 hours, how long did they trudge? How long did they walk briskly.1 solutions Answer 417808 by stanbon(57219)   on 2012-10-25 21:32:46 (Show Source): You can put this solution on YOUR website!Cheryl and Judy trudged at 4 mph until their packs got too heavy. Then they dropped their packs and continued at the brisk pace of 6 mph. If the total trip of 56 miles took 12 hours, how long did they trudge? How long did they walk briskly. ----- Trudge DATA: rate = 4 mph ; distance = x miles ; time = x/4 hrs ---------------------- Brisk Pace DATA: rate = 6 mph ; distance = 56-x miles ; time = (56-x)/6 hrs --------- Equation: time + time = 12 hrs. x/4 + (56-x)/6 = 12 6x +4(56-x) = 24*12 ---- 6x + 224 - 4x = 24*12 2x = 64 x = 32 miles (trudge distance) 56-x = 24 miles (brisk pace distance) ========================================== Cheers, Stan H. ====================
 Money_Word_Problems/672094: An overseas call is charged at one rate(a fixed amount) for the first minute and at a different rate for each additional minute. if a 7 minute call costs \$10, and a 4 minute call costs \$6.40, find the rate.1 solutions Answer 417804 by stanbon(57219)   on 2012-10-25 21:01:33 (Show Source): You can put this solution on YOUR website!An overseas call is charged at one rate(a fixed amount) for the first minute and at a different rate for each additional minute. if a 7 minute call costs \$10, and a 4 minute call costs \$6.40, find the rate. ------- Let fixed amount be "x" and additional rate be "y": Equation: x + 6y = 1000 cents x + 3y = 640 cents ----- Subtract and solve for "y": 3y = 360 y = \$1.20 (added minutes rate) ---- solve for "x": x + 3*120 = 640 x + 360 = 640 x = \$2.80 (1st minute rate) =================================== Cheers, Stan H. ==================
 Equations/672087: I can't seem to get this one at all... -11+10(p+10)=4-5(2p+11)1 solutions Answer 417803 by stanbon(57219)   on 2012-10-25 20:55:51 (Show Source): You can put this solution on YOUR website!-11+10(p+10)=4-5(2p+11) ----- -11 + 10p + 100 = 4 -10p - 55 ------ 20p + 89 = -51 ---- 20p = -140 ---- p = -7 =============== Cheers, Stan H. ===============
 Rational-functions/672074: How would you define what a rational exponent is? Is there such a thing as an irrational exponent? Explain. 1 solutions Answer 417799 by stanbon(57219)   on 2012-10-25 20:44:18 (Show Source): You can put this solution on YOUR website!How would you define what a rational exponent is? Is there such a thing as an irrational exponent? Explain. ------- Rational : any number which can be expressed in the form a/b where a and b are integers and b is not zero. ----------------------------------- Yes there are irrational exponents: Example: 2^(sqrt(3)) = 3.32199....... -------------------------- Cheers, Stan H.
 Linear-equations/672071: How do you solve Linear equation? Example problem 3(x+6)=5(x-4) Thank you. 1 solutions Answer 417794 by stanbon(57219)   on 2012-10-25 20:37:13 (Show Source): You can put this solution on YOUR website!3(x+6)=5(x-4) 3x + 18 = 5x - 20 2x = 38 x = 19 ============ Cheers, Stan H. ============
 Percentage-and-ratio-word-problems/672062: Kristina needs to mix a 10% glucose solution with a 50% glucose solution to create 200 millileters of a 34% solution. How many millileters of each solution must Kristina use? Answer: Kristina must mix millileters of 10% solution millileters of 50% solution.1 solutions Answer 417793 by stanbon(57219)   on 2012-10-25 20:33:43 (Show Source): You can put this solution on YOUR website! Kristina needs to mix a 10% glucose solution with a 50% glucose solution to create 200 millileters of a 34% solution. How many millileters of each solution must Kristina use? ------ Equation: gluc + gluc = gluc 0.10x + 0.50(200-x) = 0.34*200 ----- 10x + 50*200 - 50x = 34*200 -40x = -16*200 --- x = 80 ml (amt. of 10% solution needed) ---- 200-x = 120 ml (amt. of 50% solution needed) ====================== Cheers, Stan H. ====================
 decimal-numbers/672054: Please help solve: 6.1e+1.07=91 solutions Answer 417792 by stanbon(57219)   on 2012-10-25 20:16:24 (Show Source): You can put this solution on YOUR website!6.1e+1.07=9 ----- Multiply thru by 100 to get: 610e + 107 = 900 ---- 610e = 793 ---- e = 1.3 ============= Cheers, Stan H. =============
 Money_Word_Problems/672055: Tickets for the homecoming dance cost \$20 for a single ticket or \$35 for a couple. Ticket sales totaled \$2280, and 128 people attended. How many tickets of each type were sold? 1 solutions Answer 417787 by stanbon(57219)   on 2012-10-25 20:12:44 (Show Source): You can put this solution on YOUR website!Tickets for the homecoming dance cost \$20 for a single ticket or \$35 for a couple. Ticket sales totaled \$2280, and 128 people attended. How many tickets of each type were sold? ------- Quantity Eq.::: s + 2d = 128 Value Eq::::: 20s +35d = 2280 -------------------------------- 20s + 40d = 20*128 20s + 35d = 2280 -------------------- Subtract and solve for "d": 5d = 280 d = 56 (# of double tickets sold) ----- Solve for "s": s + 2*56 = 128 s + 112 = 128 s = 16 (# of single tickets sold) =================================== Cheers, Stan H. ============
 Numeric_Fractions/672050: 1 1/4 multiplied by 30 dont understand how to work out 1 solutions Answer 417786 by stanbon(57219)   on 2012-10-25 19:57:19 (Show Source): You can put this solution on YOUR website!1 1/4 multiplied by 30 --------------------- (5/4)30 = (5/2)15 = 75/2 = 37 1/2 ====================================== Cheers, Stan H.
 Finance/672047: Workout Plus offers a membership for \$30 each month plus a \$100 start up fee. Fit works offers a membership for \$50 each month plus a \$20 start up fee. After how many months will memberships to both gyms cost the same amount? 1 solutions Answer 417785 by stanbon(57219)   on 2012-10-25 19:54:28 (Show Source): You can put this solution on YOUR website!Workout Plus offers a membership for \$30 each month plus a \$100 start up fee. Fit works offers a membership for \$50 each month plus a \$20 start up fee. After how many months will memberships to both gyms cost the same amount? --------------------------- W(x) = 100 + 30x F(x) = 20 + 50x ------- Equal Cost: Solve: 100+30x = 20+50x 20x = 80 x = 4 months (equal at 4 months) ================ Cheers, Stan H.
 Polynomials-and-rational-expressions/672042: How can I factor this: (7x^4-4x^2+x) - (7x^3+8x^2+9x) + (2x^2-x) 1 solutions Answer 417781 by stanbon(57219)   on 2012-10-25 19:48:35 (Show Source): You can put this solution on YOUR website!(7x^4-4x^2+x) - (7x^3+8x^2+9x) + (2x^2-x) ----- 7x^4 - 4x^2 + x - 7x^3 - 8x^2 - 9x + 2x^2 - x --------------------- = 7x^4 - 7x^3 - 10x^2 - 9x ------------------- = x[7x^3 - 7x^2 - 10x - 9] ============================ Cheers, Stan H. ==============
 expressions/672043: 4/x=6/(3x+2)1 solutions Answer 417776 by stanbon(57219)   on 2012-10-25 19:42:34 (Show Source): You can put this solution on YOUR website!4/x=6/(3x+2) ---- Cross-multiply to get: 12x+8 = 6x --- 6x = -8 x = -4/3 ====================== Cheers, Stan H.
 Trigonometry-basics/672037: determine the number of possible solutions for each triangle. A= 42 degrees, a=22, b=121 solutions Answer 417775 by stanbon(57219)   on 2012-10-25 19:37:50 (Show Source): You can put this solution on YOUR website!determine the number of possible solutions for each triangle. A= 42 degrees, a=22, b=12 ------ sin(B)/12 = sin(42)/22 ------ sin(B) = (12/22)sin(42) = 0.3857 --- B = 22.69 degrees of B = 157.31 degrees --------- Possibly 2 solutions. ================ Cheers, Stan H.
 Subset/671734: calulate the number of possible subsets for the following {2,4,6,8}1 solutions Answer 417596 by stanbon(57219)   on 2012-10-25 09:43:53 (Show Source): You can put this solution on YOUR website!calulate the number of possible subsets for the following {2,4,6,8} ------ Each element is either in or not in each subset. ----- # of subsets = 2^4 = 16 ============================= Cheers, Stan H.
 Probability-and-statistics/671768: Fifteen (15) widgets are randomly taken from an assembly line and measured for quality control. The widgets have an average weight of 38.5 grams with a standard deviation of 3.5 grams. What is the margin of error of the widgets on the assembly line? 1 solutions Answer 417595 by stanbon(57219)   on 2012-10-25 09:40:37 (Show Source): You can put this solution on YOUR website!Fifteen (15) widgets are randomly taken from an assembly line and measured for quality control. The widgets have an average weight of 38.5 grams with a standard deviation of 3.5 grams. What is the margin of error of the widgets on the assembly line? -------- Note: Standard error is the word used to describe the standard deviation. Margin of error should have some level of confidence associated with it. Your problem statement does not. ---- ME = z*s where z relates to a level of confidence. ================ Cheers, Stan H.
 Probability-and-statistics/671770: you roll a blue number cube and a green number cube. find p a number greater than 2 on the blue cube and an odd number on the green cube 1 solutions Answer 417590 by stanbon(57219)   on 2012-10-25 09:34:11 (Show Source): You can put this solution on YOUR website!you roll a blue number cube and a green number cube. find p a number greater than 2 on the blue cube and an odd number on the green cube ------- Note: The events are independent. --------------------- Assuming both cubes are numbered 1 to 6 you get: P(3<= x <=6)*P(odd number) = (4/6)(3/6) = 1/3 ================= Cheers, Stan H.
 Rational-functions/671771: Can you find the following product and write the result in standard form a+bi (-1+i)(-1-i) thank you1 solutions Answer 417589 by stanbon(57219)   on 2012-10-25 09:30:34 (Show Source): You can put this solution on YOUR website!(-1+i)(-1-i) ----- = 1+1 = 2 + 0i ============= Cheers, Stan H.
 Polynomials-and-rational-expressions/671773: Find all real and imaginary zeros of the following polynomial equation: m(x)= x^3-81 solutions Answer 417588 by stanbon(57219)   on 2012-10-25 09:28:22 (Show Source): You can put this solution on YOUR website!Find all real and imaginary zeros of the following polynomial equation: m(x)= x^3-8 ----- x^3-8 = 0 (x-2)(x^2+2x+4) = 0 ----- Solve the quadratic: x = [-2+-sqrt(4-8)]/2 x = [-2 +- sqrt(-4)]/2 x = [-2 +- 2i]/2 --- x = -1+i or x = -1-i or x = 2 ================================= Cheers, Stan H. ==============
 Numeric_Fractions/671636: What is the pattern in the numbers 1,4,10,20,35,56,84? I have tried to multiply numerous number but, I alas can't get it. 1 solutions Answer 417497 by stanbon(57219)   on 2012-10-24 21:54:28 (Show Source): You can put this solution on YOUR website!What is the pattern in the numbers 1,4,10,20,35,56,84? I have tried to multiply numerous number but, I alas can't get it. ------ I ran a Cubic Regression Program on the data and got the following equation: y = (15/90)x^3 + (1/2)x^2 : (1/3)x ------- I would not expect you could ever do that manually. Cheers, Stan H.
 Linear-equations/671625: At 68 degrees F, a certain species of cricket chirps 24 times per minute.At 40 degrees F, the same cricket chirps 86 A. express the number of chirps (y) as a linear function of the farenheit temperature (X)( hint: find the slope first). B. Interpet the slope in a sentence for this linear function. C. If the temperature is 60 degrees F how many times will the cricket chirp per min? D. If you count the number of cricket chirps in one half minute and hear 40 chirps,what is the temperature?times per min.1 solutions Answer 417495 by stanbon(57219)   on 2012-10-24 21:37:36 (Show Source): You can put this solution on YOUR website!At 68 degrees F, a certain species of cricket chirps 24 times per minute.At 40 degrees F, the same cricket chirps 86 ----- Points: (68,24) and (40,86) ----------------------------------- A. express the number of chirps (y) as a linear function of the farenheit temperature (X)( hint: find the slope first). slope = (86-24)/(40-68) = 62/-28 = -(31/14) ---- Form: y = mx + b substitute for y,x,m ; Solve for "b": 24 = (-31/14)68 + b b = 174.57 ------ Equation: y = (-31/14)x + 174.57 ------------------------------- B. Interpet the slope in a sentence for this linear function. When the temperature decreases 31, the # of chirps increases 14 =================================================================== C. If the temperature is 60 degrees F how many times will the cricket chirp per min? Solve f(60) =================== D. If you count the number of cricket chirps in one half minute and hear 40 chirps,what is the temperature?times per min. # per minute would be 80 ---- solve 80 = (-31/14)x + 174.57 for "x". ========================================= cheers, Stan H.
 Probability-and-statistics/671419: A standard poker deck of cards contains 52 cards, of which four are sevens. Suppose two cards are drawn sequentially, so that one random circumstance is the result of the first card drawn and the second random circumstance is the result of the second card drawn. Find the probability that the first card is a seven and the second card is not a seven. (Round your answer to four decimal places.)1 solutions Answer 417487 by stanbon(57219)   on 2012-10-24 21:21:02 (Show Source): You can put this solution on YOUR website!A standard poker deck of cards contains 52 cards, of which four are sevens. Suppose two cards are drawn sequentially, so that one random circumstance is the result of the first card drawn and the second random circumstance is the result of the second card drawn. Find the probability that the first card is a seven and the second card is not a seven. ----------------------------- # of ways to succeed: 4C2 = 6 # of possible outcomes: 52C2 = 1326 ----- P(2 7's) = 6/1326 = 0.0045 =============================== Cheers, Stan H. ===============================
 Probability-and-statistics/671442: 10% of Americans are left handed. a) If 6 people are selected at random, what is the probability that more than 3 of them are left-handed? b) Suppose a group of 600 mathematicians get together for a conference. What is the probability that more than 80 of them are left-handed? (Use the normal approximation to the binomial)1 solutions Answer 417483 by stanbon(57219)   on 2012-10-24 21:16:06 (Show Source): You can put this solution on YOUR website!10% of Americans are left handed. a) If 6 people are selected at random, what is the probability that more than 3 of them are left-handed? Binomial Problem with n = 6 ; p(left) = 0.10 P(4<= x <=6) = 1 - binomcdf(6,0.10,3) = 0.0013 ------------------------------------------------------ b) Suppose a group of 600 mathematicians get together for a conference. What is the probability that more than 80 of them are left-handed? (Use the normal approximation to the binomial) ------ mean = np = 600*0.10 = 60 std = sqrt(npq) = 7.35 ----------- P(81<= x <= 600) = 1 - P(x < 80.5) ------------------- z(80.5) = (80.5-60)/7.35 = 2.79 ----- 1 - P(z < 2.79) = 0.0026 =========================== Cheers, Stan H.
 Probability-and-statistics/671569: a bag contains 6 red balls and 6 blues balls. 2 balls are selected random. find the probability of selecting 2 red balls1 solutions Answer 417473 by stanbon(57219)   on 2012-10-24 20:49:36 (Show Source): You can put this solution on YOUR website!a bag contains 6 red balls and 6 blues balls. 2 balls are selected random. find the probability of selecting 2 red balls ----- # of ways to succeed: 6C2 = 15 ways ------------------------------------ # of possible pairs: 12C2 = 66 -------- P(2 red) = 15/66 = 5/22 ========================= Cheers, Stan H. ===========================
 Probability-and-statistics/671598: An oil company is interested in estimating the true proportion of female truck drivers based in five southern states. A statistician hired by the oil company must determine the sample size needed in order to make the estimate accurate to within 2% of the true proportion with 95% confidence. What is the minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy? Use the appropriate table in your book.1 solutions Answer 417471 by stanbon(57219)   on 2012-10-24 20:44:10 (Show Source): You can put this solution on YOUR website!An oil company is interested in estimating the true proportion of female truck drivers based in five southern states. A statistician hired by the oil company must determine the sample size needed in order to make the estimate accurate to within 2% of the true proportion with 95% confidence. What is the minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy? ------------ n = [z/E]^2*pq ---- Since no p estimate is available the "least biased" estimate is p = 1/2 =================== n = [1.96/0.02]^2(1/2)(1/2) ---- n = 2401 ================= Cheers, Stan H. ==============
 Probability-and-statistics/671516: What percentage of the grapefruits in this orchard are larger than 6.75 inches? z(6.75) = (6.75 - 6.85)/0.8 = -0.125 P(x>6.75) + P(z>-0.125) = 1 solutions Answer 417463 by stanbon(57219)   on 2012-10-24 20:15:04 (Show Source): You can put this solution on YOUR website!What percentage of the grapefruits in this orchard are larger than 6.75 inches? z(6.75) = (6.75 - 6.85)/0.8 = -0.125 P(x>6.75) + P(z>-0.125) = 0.0096 = 0.96% ======================= Cheers, Stan H. --------
 Probability-and-statistics/671523: compute the probability of randomly selecting a ace or heart. 1 solutions Answer 417461 by stanbon(57219)   on 2012-10-24 19:49:13 (Show Source): You can put this solution on YOUR website!compute the probability of randomly selecting a ace or heart. --------- P(A or H) = P(A) + p(H) - P(A AND H) ----- = (4 + 13 - 1)/52 = 16/52 = 4/13 =================== Cheers, Stan H. ===================
 Probability-and-statistics/671543: HELP PLEASE! Let two cards be dealt successively, with replacement, from a standard 52-card deck. Find P(first is a diamond, second is a heart) as a decimal to 3 places. 1 solutions Answer 417459 by stanbon(57219)   on 2012-10-24 19:44:55 (Show Source): You can put this solution on YOUR website!Let two cards be dealt successively, with replacement, from a standard 52-card deck. Find P(first is a diamond, second is a heart) as a decimal to 3 places. ------- "With replacement" means the events are independent. ------------------------------------------------------ P(D and H) = P(D)*P(H) = (1/4)(1/4) = 1/16 --------------------------------------------- Cheers, Stan H.
 Probability-and-statistics/671544: PLEASE HELP AND EXPLAIN!!!!! Three men and four women are waiting to be interviewed for jobs and selected in random order. Find P(second interviewed is a woman) as a decimal to 3 places. Thanks. 1 solutions Answer 417458 by stanbon(57219)   on 2012-10-24 19:39:14 (Show Source): You can put this solution on YOUR website!Three men and four women are waiting to be interviewed for jobs and selected in random order. Find P(second interviewed is a woman) as a decimal to 3 places. ----- Number of possible pairs: 3*4 = 12 ---- Number of pairs where the 2nd person selected is a woman: 6 ----- P(2nd intereviewed is a woman) = 6/12 = 1/2 =============================================== If you are looking for "the 1st interviewed is a man and 2nd is a woman" the answer is 3/12 = 1/4 ==================================== Cheers, Stan H.
 test/671532: Add first finding the LCD.simplify if possible. 1/6+3/401 solutions Answer 417455 by stanbon(57219)   on 2012-10-24 19:28:21 (Show Source): You can put this solution on YOUR website!1/6+3/40 ------ LCD: 120 ----- (20/120) + (9/120) ----- = 29/120 ============== Cheers, Stan H.