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# Recent problems solved by 'stanbon'

stanbon answered: 57911 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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 Probability-and-statistics/695855: bags of mixed lollies are being made by selecting: 2 different lolly pops from a choice of 4 lollypops; 3 different caramels from a choice of 6 caramels and 5 jellybeans from 10 different flavours. how many different types of mixed lolly bags can be made?1 solutions Answer 428710 by stanbon(57984)   on 2012-12-19 12:53:15 (Show Source): You can put this solution on YOUR website! bags of mixed lollies are being made by selecting: 2 different lolly pops from a choice of 4 lollypops; 3 different caramels from a choice of 6 caramels and 5 jellybeans from 10 different flavours. how many different types of mixed lolly bags can be made? --- # of ways to get 2 pops from 4: 4C2 = 6 # of ways to get 3 cara from 6: 6C3 = (6*5*4)(1*2*3) = 20 # of ways to get 5 jelly from 10: 10C5 = 252 ==== Total # of mixed bags: 6*20*252 = 30,240 ================== Cheers, Stan H. ==================
 Probability-and-statistics/695876: Ms. Swift's reading class can read an average of 170 words per minute with a standard deviation of 25 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would need to read in order to get the award? Assume the data is normally distributed.1 solutions Answer 428709 by stanbon(57984)   on 2012-12-19 12:48:49 (Show Source): You can put this solution on YOUR website!Ms. Swift's reading class can read an average of 170 words per minute with a standard deviation of 25 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would need to read in order to get the award? Assume the data is normally distributed. ------------------- Find the z-value with a left-tail of 0.97. invNorm(0.97) = 1.8808 ------- Solve for x using x = z*s + u x = 1.8808*25 + 170 x = 217 words per minute ========================= Cheers, Stan H. ===============
 Probability-and-statistics/695878: The average hourly wage of workers at a fast food restaurant is \$7.75. Assume the wages are normally distributed with a standard deviation of \$0.45. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than \$7.50 per hour?1 solutions Answer 428706 by stanbon(57984)   on 2012-12-19 12:44:44 (Show Source): You can put this solution on YOUR website!The average hourly wage of workers at a fast food restaurant is \$7.75. Assume the wages are normally distributed with a standard deviation of \$0.45. If a worker at this fast food restaurant is selected at random, what is the probability that the worker earns more than \$7.50 per hour? ------- z(7.5) = (7.5-7.75)/0.45 = -0.5556 -------- P(x > 7.50) = P(z > -0.5556) = 0.7107 ======================================= Cheers, Stan H.
 Probability-and-statistics/695879: Of the members of a Boy scout troop, 15% have received the First Aid merit badge. If 40 Boy Scouts are selected at random, use the normal distribution as an approximation to the binomial distribution to find the probability that four or more will have the First Aid merit badge. MULTIPLE CHOICE: A)86.6% B)81.3% C)36.6% D)31.3%1 solutions Answer 428704 by stanbon(57984)   on 2012-12-19 12:40:57 (Show Source): You can put this solution on YOUR website!Of the members of a Boy scout troop, 15% have received the First Aid merit badge. If 40 Boy Scouts are selected at random, use the normal distribution as an approximation to the binomial distribution to find the probability that four or more will have the First Aid merit badge. ------ u = np = 0.15*40 = 6 s = sqrt(6*0.85) = 2.258 ------------------------------- z(3.5) = (3.5-6)/[2.258] = -1.1072 ----- P(4<= x <=15) = P(-1.1072<= z <= 100) = 0.8659 ------------- Cheers, Stan H. =============== MULTIPLE CHOICE: A)86.6% B)81.3% C)36.6% D)31.3%
 Probability-and-statistics/695896: In a recent survey 80% of the citizens in the community favored the building of a municipal golf course. If you ask 15 citizens about this project find the probability that a. at least 9 favor the project b. exactly 9 favor the project c. less than 9 favor the project I cannot remember how to calculate this formula or use minitab to calculate it for me. Can you help?1 solutions Answer 428702 by stanbon(57984)   on 2012-12-19 12:32:04 (Show Source): You can put this solution on YOUR website!In a recent survey 80% of the citizens in the community favored the building of a municipal golf course. If you ask 15 citizens about this project find the probability that: Binomial Problems with n = 15 ; p(favor) = 0.80 -------------------- I use a TI-84 calculator. --------------------------------- a. at least 9 favor the project P(9<= x <=15) = 1-P(0<= x <=8) = 1 - binomcdf(15,0.8,8) = 0.9819 ------------------------------------------ b. exactly 9 favor the project P(x = 9) = binompdf(15,0.8,9) = 0.0430 ------------------------------------------ c. less than 9 favor the P(0<= x <=8) = binomcdf(15,0.8,8) = 0.0181 =================================== Cheers, Stan H. ===============
 Probability-and-statistics/695916: There are 60 tables in a restaurant, with 25% of them seating 2 people. The tables remaining seat 4 people. How many seats are there in the restaurant? 1 solutions Answer 428701 by stanbon(57984)   on 2012-12-19 12:20:33 (Show Source): You can put this solution on YOUR website!There are 60 tables in a restaurant, with 25% of them seating 2 people. The tables remaining seat 4 people. How many seats are there in the restaurant? ------ Tables Equation: t + f = 60 t = 0.25(t+f) t = 0.25t + 0.25f 0.75t = 0.25f t = (1/3)f -------- Substitute for "t" and solve for "f": (1/3)f + f = 60 (4/3)f = 60 f = 45 (# of tables that seat 4 people) --------- Solve for "t": t + f = 60 t + 45 = 60 t = 15 (# of tables that seat 2 people) ====================== Cheers, Stan H. ======================
 Trigonometry-basics/695503: A)write the equation cos(2 theta)-sin(theta)=0 in terms of sin (theta) B) Hence solve cos(2 theta)-sin(theta)=0 for 01 solutions Answer 428645 by stanbon(57984)   on 2012-12-18 21:35:26 (Show Source): You can put this solution on YOUR website!A)write the equation cos(2 theta)-sin(theta)=0 in terms of sin (theta) ---- cos(2x) - sin(x) = 0 --- 1 - 2sin^2(x) - sin(x) = 0 ---- 2sin^2(x)+sin(x) -1 = 0 Factor: (2sin(x)-1)(sin(x)+1) = 0 ----------------------- sin(x) = 1/2 or sin(x) = -1 x = 30 or 120 degrees OR x = 270 degrees ========================================== Cheers, Stan H. ==============
 Trigonometry-basics/695548: How do I find the opposite sine of -pi divided by 3 without using a calculator or the opposite sine of the positive sine of 2pi divided by 3?1 solutions Answer 428644 by stanbon(57984)   on 2012-12-18 21:17:11 (Show Source): You can put this solution on YOUR website!How do I find the opposite sine of -pi divided by 3 without using a calculator or the opposite sine of the positive sine of 2pi divided by 3? ---------- find the opposite sine of -pi divided by 3 without using a calculator sin(-pi/3) = -sin(pi/3) = -sin(60 degrees) = -1/sqrt(3) ---- sin((2/3)pi) = sin(120 degrees) = sin(30) = 1/2 --------------------- Cheers, Stan H. =====================
 Trigonometry-basics/695593: If 90 degrees is less than theta is less than 180 degrees, express cos theta in terms of tan theta.1 solutions Answer 428643 by stanbon(57984)   on 2012-12-18 21:01:02 (Show Source): You can put this solution on YOUR website!If 90 degrees is less than theta is less than 180 degrees, express cos theta in terms of tan theta. ----- cos = 1/sec = 1/sqrt(1+tan^2) ----------- Cheers, Stan H.
 Trigonometry-basics/695750: Write down the period of the graph of y = 3/(2+cos^2 2x) (that's 2 plus cosine squared 2x in case it isn't clear) and also the coordinates of a maximum value of y. Okay so I've always been confused about the period thing. The equation is 2pi/b, where the b value is the frequency, but I'm not sure how to use that. And also, to find the coordinates of the max, you take the derivative and set it equal to 0 and find the values that make that true and then test for if it's a minimum or maximum, correct?1 solutions Answer 428641 by stanbon(57984)   on 2012-12-18 20:37:23 (Show Source): You can put this solution on YOUR website!Write down the period of the graph of y = 3/(2+cos^2 2x) (that's 2 plus cosine squared 2x in case it isn't clear) and also the coordinates of a maximum value of y. Okay so I've always been confused about the period thing. The equation is 2pi/b, where the b value is the frequency, but I'm not sure how to use that. And also, to find the coordinates of the max, you take the derivative and set it equal to 0 and find the values that make that true and then test for if it's a minimum or maximum, correct? ------ The (2pi)/b for the period relates to f(x) = acos(2x+b)=c, not to y = 3/(2+cos^2 2x). ---- What you say about the derivative to find the max or min is true. Cheers, Stan H. ===============
 Trigonometry-basics/695719: what is the cos-4.5*pi?1 solutions Answer 428623 by stanbon(57984)   on 2012-12-18 19:11:10 (Show Source): You can put this solution on YOUR website!what is the cos-4.5*pi? ---------------------------- cos(-4.5pi) = cos(-4pi -0.5pi) = cos(-5pi) = 0 =========================== Cheers, Stan H. ================
 Mixture_Word_Problems/695706: a grocer mixed nuts worth \$.80 per pound with nuts worth \$.50 per pound. How many pounds of each did he use to make a mixture of 30 pounds to sell at \$.75 per pound?1 solutions Answer 428621 by stanbon(57984)   on 2012-12-18 19:02:59 (Show Source): You can put this solution on YOUR website!a grocer mixed nuts worth \$.80 per pound with nuts worth \$.50 per pound. How many pounds of each did he use to make a mixture of 30 pounds to sell at \$.75 per pound? ================== Using 2 equations: Quantity: a + b = 30 lbs Value:::80a + 50b = 75*30 ------------ Modify the equations for elimination: 8a + 8b = 8*30 8a + 5b = 3*75 ------ Subtract and solve for "b": 3b = 15 b = 5 lbs (amt of 50 cent nuts) -------- Solve for "a" using a + b = 30 a + 5 = 30 a = 25 lbs (amt. of 80 cent nuts) ============== Cheers, Stan H. ================
 Exponents-negative-and-fractional/695696: 7x+2(11-4x)<2(3-1/2x)1 solutions Answer 428611 by stanbon(57984)   on 2012-12-18 18:26:43 (Show Source): You can put this solution on YOUR website!7x+2(11-4x)<2(3-1/2x) ------------- 7x + 22 - 8x < 6 - x ----- 9-x + 22 < 6 -x -x + 31 < 6 -x 31 < 6 ----- That is a contradiction. Ans: No solution. ======================= Cheers, Stan H. =======================
 Exponents/695699: Multiply. (1/5x^4y^3)(y^2z^4)(20x^2z^3) I do not understand the steps or where to begin1 solutions Answer 428609 by stanbon(57984)   on 2012-12-18 18:13:19 (Show Source): You can put this solution on YOUR website!Multiply. (1/5x^4y^3)(y^2z^4)(20x^2z^3) ---------- [(1/5)(1)(20)][x^4*1*x^2][y^3*y^2*1][1*z^4*z^3] ---------- = (4)(x^6)(y^5)(z^7) ------ = 4x^6y^5z^7 ======================= Cheers, Stan H. ====================
 Exponents/695698: This is what I have so far before I got confused multiply (2r+3s)^2 1st step: (2r+3s)(2r+3s) 2nd step: 2r^2 9s^2 this is where I got confused: Do I multiply the 3s and 2r? If so do I get 6s^2r^2 or 5s^2r^21 solutions Answer 428608 by stanbon(57984)   on 2012-12-18 18:05:55 (Show Source): You can put this solution on YOUR website!answered
 Exponents/695689: I started this problem then I got stuck multiply (2r+3s)^2 1st step: (2r+3s)(2r+3s) 2nd step: 2r^2 9s^2 this is where I got confused: Do I multiply the 3s and 2r? If so do I get 6s^2r^2 or 5s^2r^21 solutions Answer 428607 by stanbon(57984)   on 2012-12-18 18:03:18 (Show Source): You can put this solution on YOUR website!multiply (2r+3s)^2 1st step: (2r+3s)(2r+3s) Use FOIL: F: 2r*2r = 4r^2 O: 2r*3s = 6rs I: 2r*3s = 6rs L: 3s*3s = 9s^2 -------------------- Combine those products to get: 4r^2 + 12rs + 9s^2 ============================= Cheers, Stan H. =======================
 Quadratic_Equations/695678: find b if you happen to know the maximum y-value of the function y= -4x^2 + bx -1 is 21. 1 solutions Answer 428606 by stanbon(57984)   on 2012-12-18 17:52:46 (Show Source): You can put this solution on YOUR website!find b if you happen to know the maximum y-value of the function y= -4x^2 + bx -1 is 21 ---------------- Comment: Maximum occurs where x = -b/(2a) = -b/(-8) = b/8 ----- Max = f(b/8) = -4(b/8)^2 + b(b/8) -1 = 21 ----------- -4(b^2/64) + b^2/8 = 22 ------ -b^2/16 +2(b^2/16) = 22 ------ -b^2 + 2b^2 = 16*22 --- b^2 = 16*22 --------- b = 4*sqrt(22) ===================== ====================== Cheers, Stan H. ============
 Geometry_Word_Problems/695675: The mean length of the sides of a triangular plot of land is 18 yards. What is its perimeter1 solutions Answer 428603 by stanbon(57984)   on 2012-12-18 17:33:41 (Show Source): You can put this solution on YOUR website!The mean length of the sides of a triangular plot of land is 18 yards. What is its perimeter ------ Ans: Perimeter = 3*18 = 54 yds. --------------------------------- Cheers, Stan H.
 percentage/695672: 21 is 60% of what number?1 solutions Answer 428600 by stanbon(57984)   on 2012-12-18 17:30:48 (Show Source): You can put this solution on YOUR website!21 is 60% of what number? ---- Equation: 21 = 0.60x --- x = 21/0.6 x = 210/6 x = 35 -------- Cheers, Stan H. =====================
 test/695652: Describe how the graph of y=2log3(x-4)+2 compare to parent graph. Tell if any changes in range, domain, or asymptotes 1 solutions Answer 428598 by stanbon(57984)   on 2012-12-18 17:27:18 (Show Source): You can put this solution on YOUR website! Describe how the graph of y=2log3(x-4)+2 compare to parent graph. ---- 1st: shift 4 units to the right because of x-4 2nd: Multiply all the y values by 2 3rd: Make a vertical shift of 2 ------------------------------------- Tell if any changes in range::: no change domain::: x > 4 instead of x = 0 asymptotes::: x = 4 instead of x = 0 ====================================== Cheers, Stan H.
 Angles/695650: Angle E and angle T and supplementary. If angle E is 23 degrees more than twice the complement of T, what are the two angles?1 solutions Answer 428587 by stanbon(57984)   on 2012-12-18 16:42:18 (Show Source): You can put this solution on YOUR website!Angle E and angle T and supplementary. E = 180-T --------------------- If angle E is 23 degrees more than twice the complement of T, what are the two angles? E = 2(90-T) + 23 ------- Substitute for E and solve for T: 180-T = 2(90-T)+23 180 - T = 180 - 2T + 23 T = 23 degrees --- E = 180-T = 157 degrees ============================= Cheers, Stan H. =============================
 Linear-systems/695649: I am stuck on this Linear Systems problem. Roy and Steve have the same number of coins. Roy has only dimes and Steve has only quarters. If Steve has \$1.80 more than Roy does, how many coins does each have? Thanks in advance1 solutions Answer 428584 by stanbon(57984)   on 2012-12-18 16:34:25 (Show Source): You can put this solution on YOUR website!Roy and Steve have the same number of coins. Roy has only dimes and Steve has only quarters. If Steve has \$1.80 more than Roy does, how many coins does each have? ---------- Equation: Quantity Eq:: d = q Value Eq:: 25q = 10d +180 cents ------ Substitute for "d" and solve for "q": 25d = 10d + 180 15d = 180 d = 12 (# of dimes Roy has) ------ q = 12 (# of quarters Steve has) ==================================== Cheers, Stan H. ==============
 Quadratic_Equations/695644: Please help me solve by completing the squares: 1 solutions Answer 428582 by stanbon(57984)   on 2012-12-18 16:26:23 (Show Source): You can put this solution on YOUR website!(x^2) - (6x) = (27) ----- x^2 - 6x + (6/2)^2 = 27 + (6/2)^2 -------- x^2 -6x + 9 = 27 + 9 -------- (x-3)^2 = 36 ---- x-3 = 6 or x - 3 = -3 x = 9 or x = 0 =============================== (2x^2) - (9x) + (9) = (0) ----- 2[x^2 - (9/2)x + ?] = -9 + 2? ----- 2[x^2 -(9/2)x + (9/4)^2] = -9 + 2(9/4)^2 ----- 2(x-(3/2))^2 = [-9*16 + 162]/16 ----- 2(x-(3/2))^2 = 1/2 ---- (x-(3/2))^2 = 1/4 ---- x-(3/2) = 1/2 or x-(3/2) = -1/2 ------- x = 2 or x = 1 ===================== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/695641: Please graph, label the vertex, the axis of symmetry and the x and y intercepts for G(x)=(x+6)^2-1 1 solutions Answer 428577 by stanbon(57984)   on 2012-12-18 16:12:34 (Show Source): You can put this solution on YOUR website!Please graph, label the vertex, the axis of symmetry and the x and y intercepts for G(x)=(x+6)^2-1 ----- Vertex:: (-6,-1) Axis: x = -6 ---- x-int ??? Let y = 0 (x+6)^2 = 1 x+6 = 1 or x+6 = -1 x = -5 or x = -7 =================== y-int ??? Let x = 0 y = 6^2-1 = 35 ==================== Cheers, Stan H. ====================
 Functions/695639: The Output of a function is 7 more than 3 times the input. Find the input when the output is -81 solutions Answer 428575 by stanbon(57984)   on 2012-12-18 16:08:37 (Show Source): You can put this solution on YOUR website!The Output of a function is 7 more than 3 times the input. Find the input when the output is -8 ----- Equation: y = 3x+7 --- Solve: -8 = 3x+7 3x = -15 x = -5 (that's the input) ======= Cheers, Stan H. -------
 Triangles/695634: The distance betweenn Atlanta and Cleveland is about 554 miles. The distance between Cleveland and New York City is about 399 miles. Use the Triangle Inequality Theorem to find the possible values of the distance between New York and Atlanta.1 solutions Answer 428572 by stanbon(57984)   on 2012-12-18 16:05:06 (Show Source): You can put this solution on YOUR website!the longest side is always shorter than the sum of the other two. ---------------------The distance betweenn Atlanta and Cleveland is about 554 miles. The distance between Cleveland and New York City is about 399 miles. Use the Triangle Inequality Theorem to find the possible values of the distance between New York and Atlanta. ---------------------------------- That distance is < 554+399 = 953 miles That distance is > 554-399 = 155 miles ================== Cheers, Stan H.
 Travel_Word_Problems/695613: I need the equation and step by step directions to solve this word problem. Two cars leave a garage traveling in opposite directions. One car leaves at 8am and averages 60mph. The other car leaves at 9am and averages 50mph. At what time will they be 225 miles apart?1 solutions Answer 428560 by stanbon(57984)   on 2012-12-18 14:53:34 (Show Source): You can put this solution on YOUR website!Two cars leave a garage traveling in opposite directions. One car leaves at 8am and averages 60mph. The other car leaves at 9am and averages 50mph. At what time will they be 225 miles apart? ----- Early car DATA: rate = 60 mph ; time = x hrs ; distance = 60x miles ----- Later car DATA: rate = 50 mph ; time = x-1 hrs ; distance = 50(x-1) miles ----- Equation: distance + distance = 225 miles 60x + 50(x-1) = 225 110x = 275 x = 2.5 hrs ---- Ans: 8:00 AM + 2.5 hrs = 10:30 AM =========== Cheers, Stan H.
 Equations/695526: y^3-2y^2+3y-4 y=5 can you show me the steps to get the right answer1 solutions Answer 428541 by stanbon(57984)   on 2012-12-18 09:34:08 (Show Source): You can put this solution on YOUR website!y^3-2y^2+3y-4 y=5 ---- 5^3 - 2*5^2 + 3*5 - 4 ---- = 125 - 2*25 + 15 - 4 ---- = 75 + 15 -4 --- = 90-4 ----- = 86 ============ Cheers, Stan H. ==============
 Numeric_Fractions/695495: how do i convert 2 6/17, -5 3/4, 8 2/6, 5 3/9, 12 49/50, -7 2/8,into an improper fraction, and reduce the final answer if necessary.1 solutions Answer 428539 by stanbon(57984)   on 2012-12-18 09:31:00 (Show Source): You can put this solution on YOUR website! convert 2 6/17, -5 3/4, 8 2/6, 5 3/9, 12 49/50, -7 2/8,into an improper fraction, and reduce the final answer if necessary. --------------------- 2 6/17 = (2*17+6)/17 = 40/16 -------------- -5 3/4 = -(5*4+3)/4 = -23/4 ----------------------- 8 2/6 = 8 1/3 = (8*3+1)/3 = 25/3 ------------------------ 5 3/9 = 5 1/3 = (5*3+1)/3 = 16/3 --------------------------- etc. Cheers, Stan H.
 Permutations/695160: Count the number of possible 4-letter arrangements that can be formed using the letters in the word 'Butterworth'1 solutions Answer 428535 by stanbon(57984)   on 2012-12-18 09:21:35 (Show Source): You can put this solution on YOUR website! Count the number of possible 4-letter arrangements that can be formed using the letters in the word 'Butterworth' --------------------- There are 9 different letters. Ans: 9P4 = 9!/(9-4)! = 9*8*7*6 = 3024 ============= Cheers, Stan H.
 Permutations/695170: Determine the number of ways to form 4-digit numbers by using the digits 1,2,3,4,5,6, and 7 if repetitions of digits are allowed.1 solutions Answer 428531 by stanbon(57984)   on 2012-12-18 09:13:12 (Show Source): You can put this solution on YOUR website!Determine the number of ways to form 4-digit numbers by using the digits 1,2,3,4,5,6, and 7 if repetitions of digits are allowed. --- Ans: 7*7*7*7 = 7^4 = 2401 numbers ============ Cheers, Stan H.