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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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 Probability-and-statistics/598992: On a certain day the chance of rain is 80% in San Fran and 30% in Sydney. Assume that chances are independent in the two cities. What is the probability that it will not rain in either city?1 solutions Answer 378765 by stanbon(57399)   on 2012-04-15 07:25:04 (Show Source): You can put this solution on YOUR website!On a certain day the chance of rain is 80% in San Fran and 30% in Sydney. Assume that chances are independent in the two cities. What is the probability that it will not rain in either city? -- Ans: 0.20*0.70 = 0.14 ========================= Cheers, Stan H.
 Probability-and-statistics/598999: A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 25 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 26.5 minutes and the standard deviation was found to be 4 minutes. Is there evidence to reject the manager’s claim at alpha =.05? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. 1 solutions Answer 378764 by stanbon(57399)   on 2012-04-15 07:23:25 (Show Source): You can put this solution on YOUR website!A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 25 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 26.5 minutes and the standard deviation was found to be 4 minutes. Is there evidence to reject the manager’s claim at alpha =.05? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results. ----------------------------------- Ho: u <= 25 Ha: u > 25 (claim) -------------- z(26.5) = (26.5-25)/4 = 0.3750 --- p-value = P(z > 0.3750 = 0.3538 ---- Since the p-value is greater than 5%, fail to reject Ho. Conclusion: The test results do not support the claim. ============ Cheers, Stan H.
 Age_Word_Problems/599004: Alex is 4 years older than mark. Mark's age is 4/5 Alex's age. What are their ages?1 solutions Answer 378763 by stanbon(57399)   on 2012-04-15 07:17:02 (Show Source): You can put this solution on YOUR website!Alex is 4 years older than mark. Mark's age is 4/5 Alex's age. What are their ages? ------ Equations: a = m + 4 m = (4/5)a ---- Substitute for "m" and solve for "a": a = (4/5)a + 4 (1/5)a = 4 a = 20 yrs (Alex's age) ---- Solve for "m": m = (4/5)a = (4/5)20 = 16 yrs (Mark's age) ===================== Cheers, Stan H.
 Travel_Word_Problems/599014: An aeroplane was flying at a height of 1600m.From the time it started to land, it made a change of 70m in every minute. How many minutes will it take to descend to a height of 200m? 1 solutions Answer 378762 by stanbon(57399)   on 2012-04-15 07:10:57 (Show Source): You can put this solution on YOUR website! An aeroplane was flying at a height of 1600m.From the time it started to land, it made a change of 70m in every minute. How many minutes will it take to descend to a height of 200m? ---- Decent distance: 1600m-200m = 1400m --- Decent time: 1400/70 = 20 minutes ==================== cheers, Stan H.
 Trigonometry-basics/599013: If 2sin^2θ – cos^2θ = 2, then find the value of θ.1 solutions Answer 378761 by stanbon(57399)   on 2012-04-15 07:07:05 (Show Source): You can put this solution on YOUR website!If 2sin^2θ – cos^2θ = 2 ---- 2sin^2 - (1-sin^2) = 2 ---- 3sin^2 = 3 sin^2 = 1 sin^2-1 = 0 (sin-1)(sin+1) = 0 sin(theta) = 1 or sin(theta) = -1 theta = pi/2 or -pi/2 ============================ Cheers, Stan H.
 Probability-and-statistics/598971: A standardized test has a mean of 600 and a standard deviation of 75. If 1000 students took the test and their scores approximate a normal curve, how many scored between 600 and 750?1 solutions Answer 378748 by stanbon(57399)   on 2012-04-14 22:49:47 (Show Source): You can put this solution on YOUR website!A standardized test has a mean of 600 and a standard deviation of 75. If 1000 students took the test and their scores approximate a normal curve, how many scored between 600 and 750? ---- z(600) = (600-600)/75 = 0 z(750) = (750-600) = 150/75 = 2 ---- P(600< x <750) = P(0< z <2) = 0.4772 ---- # of scores = 0.4772*1000 ~ 477 ==================================== Cheers, Stan H.
 Functions/598961: use the graph y=-x^2-3x+4 to help solve the inequality -x^2-3x+4>0 ? 1 solutions Answer 378747 by stanbon(57399)   on 2012-04-14 22:41:55 (Show Source): You can put this solution on YOUR website!y=-x^2-3x+4 to help solve the inequality -x^2-3x+4>0 ? ---- ----------- Find the x-intercepts: -x^2-3x+4 = 0 x^2+3x-4 = 0 (x+4)(x-1) = 0 x = 1 or x = -4 ---------------- The "greater than zero" interval is -4< x <1 ================================ Cheers, Stan H.
 Polynomials-and-rational-expressions/598965: Can anyone help me with this problem? Thanks so much! Subtract (0.04x^3 -0.04x2 + 0.04x) - (0.03x^3 + 0.09x^2 -2)1 solutions Answer 378746 by stanbon(57399)   on 2012-04-14 22:33:11 (Show Source): You can put this solution on YOUR website!(0.04x^3 -0.04x2 + 0.04x) - (0.03x^3 + 0.09x^2 -2) ----- = 0.01x^3 -0.013x^2 + 0.04x - 2 ====================================== Cheers, Stan H.
 real-numbers/598962: "What are the real solutions of 2x3+5=3x2-2x" 1 solutions Answer 378745 by stanbon(57399)   on 2012-04-14 22:28:49 (Show Source): You can put this solution on YOUR website!What are the real solutions of 2x3+5=3x2-2x 2x^3-3x^2+2x+5 = 0 --- I graphed it and found a Real zero at x = -0.8415764... ; the other two zeroes are complex. ============== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/598963: What is the max value of the function y=-4(x-6)^2=8?1 solutions Answer 378743 by stanbon(57399)   on 2012-04-14 22:18:51 (Show Source): You can put this solution on YOUR website!What is the max value of the function y=-4(x-6)^2+8? --- Vertex is (6,8) The parabola opens downward So the maximum value is 8. ================================================ Cheers, Stan H.
 Probability-and-statistics/598865: There are 16 members on a board of directors. If they must elect a chairperson, a parliamentarian, a secretary, and a treasurer, how many different slates of candidates are possible?1 solutions Answer 378729 by stanbon(57399)   on 2012-04-14 19:32:36 (Show Source): You can put this solution on YOUR website!There are 16 members on a board of directors. If they must elect a chairperson, a parliamentarian, a secretary, and a treasurer, how many different slates of candidates are possible? ---- 16*15*14*13 = 16P4 = 43,680 ============================== Cheers, Stan H. ===========
 Probability-and-statistics/598854: 2 vases 1st vase red flwr(3), white flwr.(3), pink flwr. (3), 2nd Vase red flwr,(5),white flwr.(4), pink flwr. (3), What are chances of picking same color flw. if one picks 1 flw. from each vase blindfolded. Please tell me how you do this ? TIA1 solutions Answer 378728 by stanbon(57399)   on 2012-04-14 19:30:01 (Show Source): You can put this solution on YOUR website!2 vases 1st vase red flwr(3), white flwr.(3), pink flwr. (3), 2nd Vase red flwr,(5),white flwr.(4), pink flwr. (3), What are chances of picking same color flw. if one picks 1 flw. from each vase blindfolded. --- Ways to succeed: 2red or 2white or 2 pink # of ways to get 2red: 3*5 = 15 # of ways to get 2 white: 3*4 = 12 # of ways to get 2pink: 3*5 = 15 -- Total # of ways to succeed: 42 ---- # of random pairs: 9*12 = 108 --- P(2 of same color) = 42/108 = 21/54 = 7/18 ========================= Cheers, Stan H.
 Probability-and-statistics/598850: drawing cards three cards are drwn from a deck without replacement.find the probabilities. a. all are jacks. b.all are clubs. c. all are red cards1 solutions Answer 378727 by stanbon(57399)   on 2012-04-14 19:24:06 (Show Source): You can put this solution on YOUR website!drawing cards three cards are drwn from a deck without replacement.find the probabilities. a. all are jacks. # of ways to succeed: 4C3 = 4 # of random results: 52C3 -- P(3 jacks) = 4/(52C3) ------------------------------- b.all are clubs. Ans: (13C3)/52C3) ------------------------ c. all are red cards Ans: (26C3)/52C3) =========================== Cheers, Stan H.
 Probability-and-statistics/598869: Suppose the National Hurricane Center forecasts that hurricanes will hit the strike area with a .95 probablity. Answer the following questions: 1. What probability distribution does this follow? 2. What is the probability that 10 hurricanes reach landfall in the strkie area? 3. What is the probability at least one of 10 hurricanes reaches land outside the strike area?1 solutions Answer 378725 by stanbon(57399)   on 2012-04-14 19:21:08 (Show Source): You can put this solution on YOUR website!Suppose the National Hurricane Center forecasts that hurricanes will hit the strike area with a .95 probablity. Answer the following questions: 1. What probability distribution does this follow? Ans: binomial with n = 10 and P(hit) = 0.95 ; P(hit elsewhere) = 0.05 ------ 2. What is the probability that 10 hurricanes reach landfall in the strkie area? Ans: 0.95^10 = 0.5987 ----------------- 3. What is the probability at least one of 10 hurricanes reaches land outside the strike area? Ans: 0.05^10 = 9.76x10^-14 ==================================== Cheers, Stan H.
 Rate-of-work-word-problems/598909: A swimming pool is filling at the rate of 40 gallons every 2 minutes. If the pool continues to fill at the same rate, how many gallons will be in the pool after 3 hours?1 solutions Answer 378721 by stanbon(57399)   on 2012-04-14 18:39:10 (Show Source): You can put this solution on YOUR website!A swimming pool is filling at the rate of 40 gallons every 2 minutes. If the pool continues to fill at the same rate, how many gallons will be in the pool after 3 hours? ---- 3 hrs = 180 minutes --- Proportion: gallons/time = gallons/time ------------- x/180 = 40/2 --- x = 3600 gallons ==================== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/598910: trying to graph the following, but I've never seen something like this before: (x-2)^2+(y-3)^2/64=1 help please1 solutions Answer 378720 by stanbon(57399)   on 2012-04-14 18:35:17 (Show Source): You can put this solution on YOUR website!trying to graph the following, but I've never seen something like this before: (x-2)^2+(y-3)^2/64=1 ---- Draw an ellipse with center at (2,3) horizontal axis has length = 2 vertical axis has length = 16 =============================== Cheers, Stan H. =========================
 Mixture_Word_Problems/598912: a worker needs to form 12 gallons of 70% ammonia solution to strip wax from some floors. He has one solution of 30% ammonia and another solution of 90% ammonia. How many gallons of the 90% solution should he use in the mixture?1 solutions Answer 378718 by stanbon(57399)   on 2012-04-14 18:29:40 (Show Source): You can put this solution on YOUR website!a worker needs to form 12 gallons of 70% ammonia solution to strip wax from some floors. He has one solution of 30% ammonia and another solution of 90% ammonia. How many gallons of the 90% solution should he use in the mixture? ------- Equation: ammonia + ammonia = ammonia 0.30x + 0.90(12-x) = 0.70*12 ---------- 30x + 90*12 - 90x = 70*12 -60x = -20*12 x = 4 gallons (amt. of 30% solution needed) ----- 12-x = 8 gallons (amt. of 90% solution needed) ================================================================ Cheers, Stan H.
 Quadratic-relations-and-conic-sections/598692: y=-1/9(x-6)^2+14 How do I find the endpoints for this equation, and what is the domain and range? How would I graph this problem?1 solutions Answer 378680 by stanbon(57399)   on 2012-04-13 21:24:03 (Show Source): You can put this solution on YOUR website!y=-1/9(x-6)^2+14 How do I find the endpoints for this equation, and what is the domain and range? How would I graph this problem? -------------------------------- --- Domain: All Real Numbers Range: All Real number <= 14 Cheers, Stan H.
 Quadratic-relations-and-conic-sections/598696: Write the equation of an ellipse with vertices (0, 12) and (0, -12) and co-vertices (2, 0) and (-2, 0). 1 solutions Answer 378678 by stanbon(57399)   on 2012-04-13 20:56:23 (Show Source): You can put this solution on YOUR website!Write the equation of an ellipse with vertices (0, 12) and (0, -12) and co-vertices (2, 0) and (-2, 0). ----------------- x^2/4 + y^2/144 = 1 ============================================== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/598697: Write the equation of an ellipse with vertices (10, 0) and (-10, 0) and co-vertices (0, 2) and (0, -2). 1 solutions Answer 378677 by stanbon(57399)   on 2012-04-13 20:51:53 (Show Source): You can put this solution on YOUR website!Write the equation of an ellipse with vertices (10, 0) and (-10, 0) and co-vertices (0, 2) and (0, -2). ------- x^2/100 + y^2/4 = 1 ========================= Cheers, Stan H.
 Polynomials-and-rational-expressions/598686: Please check my answer: Short Answer. Find the following product: 7z(-7z^3 + 4z^2 - 9) -49z^4 + 17z^3 - 63z1 solutions Answer 378676 by stanbon(57399)   on 2012-04-13 20:28:00 (Show Source): You can put this solution on YOUR website!7z(-7z^3 + 4z^2 - 9) ----- = -49z^4 + 28z^3 - 63z ======================== Cheers, Stan H.
 Quadratic_Equations/598679: Solve using the square root property, assuming 2 is an exponent: (x - 7 ) 2 = 161 solutions Answer 378674 by stanbon(57399)   on 2012-04-13 20:18:51 (Show Source): You can put this solution on YOUR website!Solve using the square root property, assuming 2 is an exponent: (x - 7)^2 = 16 ---- (x-7)^2-4^2 = 0 -------- Factor: (x-7-4)(x-7+4) = 0 ---- (x-11)(x-3) = 0 x = 11 or x = 3 =========================== Cheers, Stan H.
 Exponential-and-logarithmic-functions/598645: Iodine-131 is used to find leaks in water pipes. It has a half life of 8.14 days. Write the exponential decay function for a 200 mg sample. Find the amount of Iodine 131 remaining after 72 days. 1 solutions Answer 378670 by stanbon(57399)   on 2012-04-13 20:08:13 (Show Source): You can put this solution on YOUR website!Iodine-131 is used to find leaks in water pipes. It has a half life of 8.14 days. Write the exponential decay function for a 200 mg sample. --------- A(t) = 200*(1/2)^(t/8.14) ----- Find the amount of Iodine 131 remaining after 72 days. ----------- A(72) = 200(1/2)^(72/8.14) --- = 200*0.0022 ========== = 0.4349 mg ========================= Cheers, Stan H. =========================
 Linear-systems/598672: I'm trying to help my son but I need a little help also, anything would be appreciated, shown in a way I can understand Please. Solve the system of two linear inequalities graphically. 2y is less than -5x-10 5y is equal to or greater than 4x + 20 step one# graph the first inequality: 2y is less than -5x -10 step two# graph the second inequality: 5y is equal to or greater than 4x + 20 step 3# indicate the region that satisfies both inequalities. 1 solutions Answer 378667 by stanbon(57399)   on 2012-04-13 19:54:36 (Show Source): You can put this solution on YOUR website!Solve the system of two linear inequalities graphically. 2y is less than -5x-10 5y is equal to or greater than 4x + 20 step one# graph the first inequality: 2y is less than -5x -10 2y < -5x-10 y < (-5/2)x - 5 ---- 1st: Graph the boundary as a dashed line: Use points (0,-5) and (2,-10) Draw a dashed line thru them 2nd: Shade the half-plane BELOW the boundary line. --------------------------------------------------------- step two# graph the second inequality: 5y is equal to or greater than 4x + 20 5y >= 4x+20 y >= (4/5)x + 4 1st: Graph the boundary as a solid line: Use points (0,4) and (5,8) Draw a solid line thru them. 2nd: Shade the half-plane ABOVE the boundary line ---- step 3# indicate the region that satisfies both inequalities. The solution is ALL of the points that are in both graphs. ======================================== ======================= Cheers, Stan H.
 Probability-and-statistics/598649: Find the area under the normal distribution curve to the right of z=3.24.1 solutions Answer 378666 by stanbon(57399)   on 2012-04-13 19:43:39 (Show Source): You can put this solution on YOUR website!Find the area under the normal distribution curve to the right of z=3.24. ---- Ans: normalcdf(3.24,100) = 0.0005977 ==================== Cheers, Stan H.
 Mixture_Word_Problems/598654: How many liters of each of a 25% acid solution and a 85% acid solution must be used to to produce 70 liters of a 55% acid solution? ( round to two decimal places if necessary.)1 solutions Answer 378663 by stanbon(57399)   on 2012-04-13 18:53:14 (Show Source): You can put this solution on YOUR website!How many liters of each of a 25% acid solution and a 85% acid solution must be used to to produce 70 liters of a 55% acid solution? ----------------------- Equation: acid + acid = acid 0.25x + 0.85(70-x) = 0.55*70 ----- 25x + 85*70 - 85x = 55*70 -60x = -30*70 x = 35 liters (amt. of 25% solution needed) ------ 70-x = 35 liters (amt. of 85% solution needed) =============================================== Cheers, Stan H. ============
 Trigonometry-basics/598647: the population of silver city was 347 when silver was discovered.ten years later the population was 6780 assuming exponential growth what was the population five years after the discovery of silver (y=ae^kx)1 solutions Answer 378661 by stanbon(57399)   on 2012-04-13 18:43:28 (Show Source): You can put this solution on YOUR website!the population of silver city was 347 when silver was discovered.ten years later the population was 6780 assuming exponential growth what was the population five years after the discovery of silver (y=ae^kx) ----------- y = ab^x --- 347 = ab^0 6780 = ab^10 ------------------- From the 1st equation a = 347 Divide and solve for "b": 19.54 = b^10 b = 19.54^(1/10) ---- Equation: f(x) = 347*10.54^(x/10) ---- What was the population five years after the discovery of silver? f(5) = 347*19.54^(5/10) f(5) = 347*sqrt(19.54) = 1534 ================================= cheers, Stan H.
 Length-and-distance/598640: Find the coordinates of the point that lies three fourths of the way from (10, -8) to (6, 0) a) (8, -4) b) (9, -2) c) (7, -2) d) (9, -6)1 solutions Answer 378658 by stanbon(57399)   on 2012-04-13 18:21:35 (Show Source): You can put this solution on YOUR website!Find the coordinates of the point that lies three fourths of the way from (10, -8) to (6, 0) a) (8, -4) b) (9, -2) c) (7, -2) d) (9, -6) ----------------------------------------------------- Let (x,y) be that point: x = 10 + (3/4)(6-10) = 10 + (3/4)(-4) = 10-3 = 7 --- y = -8 + (3/4)(0-(-8)) = -8 + (3/4)(8) = -8+6 = -2 --- Ans: (7.-2) ================= Cheers, Stan H. =================
 Permutations/598636: Find the number of distinguishable permutations formed by using each of the letters ``AABCD'' once and only once1 solutions Answer 378653 by stanbon(57399)   on 2012-04-13 18:03:51 (Show Source): You can put this solution on YOUR website!Find the number of distinguishable permutations formed by using each of the letters ``AABCD'' once and only once --------------- Ans: 5!/2! = 5*4*3 = 60 permutations ========================= Cheers, Stan H. =========================
 Finance/598641: annual profit in thousands of dollars is given by the function, P(x)= sqrt x-5+3000, where x is the number of items sold in thousands, x.5. will this profit function have a maximum, if so what is it? 1 solutions Answer 378651 by stanbon(57399)   on 2012-04-13 17:56:07 (Show Source): You can put this solution on YOUR website!annual profit in thousands of dollars is given by the function, P(x)= sqrt x-5+3000, where x is the number of items sold in thousands, x.5. will this profit function have a maximum, if so what is it? --- P(x) = sqrt(x-5)+3000 --- sqrt(x) has no maximum. So sqrt(x-5) has no maximum And raising all the points 3000 still provides jo maximum. ============================ Cheers, Stan H. ============================
 Linear-equations/598638: Graph 1st degree inequality in 2 unknowns y>2x-21 solutions Answer 378650 by stanbon(57399)   on 2012-04-13 17:48:02 (Show Source): You can put this solution on YOUR website!Graph 1st degree inequality in 2 unknowns y>2x-2 ------- 1st: Graph the boundary as a dashed line y = 2x-2 If x = 0, y = -2 If x = 1, y = 0 Plot (0,-2) and (1,0) and draw a dashed line thru them. --- 2ns: Shade the half-plane ABOVE the boundary beacause you want y to GREATER THAN 2x-2. ===================== The half-plane is the graph of the inequality. =================================================== ================== Cheers, Stan H. ==================