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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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

 Quadratic_Equations/193591: on a scatter plot of data,a trend line passes through the points (-6,7) and (-2,10). describe the correlation.1 solutions Answer 145306 by stanbon(57286)   on 2009-04-28 17:54:55 (Show Source): You can put this solution on YOUR website!on a scatter plot of data,a trend line passes through the points (-6,7) and (-2,10). describe the correlation. -------------- slope = (10-7)/(2--6) = 3/8 --------------------------------- Form: y = mx + b You have x,y,and m ; solve for "b": 10 = (3/8)*2 + b 10 = (3/4) + b b = 37/4 ------------------- Equation: y = (3/8)x + (37/40) ====================================== Cheers, Stan H.
 Quadratic_Equations/193592: which equation describes a horizontal line that passes through the point(7,1)?1 solutions Answer 145302 by stanbon(57286)   on 2009-04-28 17:46:19 (Show Source): You can put this solution on YOUR website!y=1 ============= Cheers, Stan H.
 Quadratic_Equations/193575: I'm sorry. I know this problem is very similar to the example, but I get a very crazy answer when I've tried to do this like the example many times. I must be doing something wrong. Please help. One leg of a right triangle is 96 inches. Find the hypotenuse and teh other leg if the length of the hypotenuse exceeds 2 and 1/2 times teh other leg by 4 inches. 1 solutions Answer 145299 by stanbon(57286)   on 2009-04-28 17:35:13 (Show Source): You can put this solution on YOUR website!One leg of a right triangle is 96 inches. Find the hypotenuse and the other leg if the length of the hypotenuse exceeds 2 and 1/2 times teh other leg by 4 inches. -------------------- One leg is 96 in Let the "other leg" be "x" inches. hypotenuse = (5/2)x + 4 ---------------------------- Equation: h^2 = leg^2 + "otherleg"^2 [(5/2)x + 4]^2 = 96^2 + x^2 [(5x+ 8)/2^2 = 96^2 + x^2 (5x+8)^2 = 4*96^2 + 4x^2 25x^2 + 90x + 91 = 36864 + 4x^2 21x^2 + 90x - 36773 = 0 ----- Positive solution: x = 39.76 hypotenuse = (5/2)x+4 = 103.4 ==================================== Cheers, Stan H.
 Quadratic_Equations/193573: Please check my work: Form each of the following: A linear equation in one variable: X + 3 = -5 A linear equation in two variables: y = 5x - 3 A quadratic equation: 3x2 + x - 2 = 0 A polynomial of three terms: 7x2y3 + 4x − 9 An exponential function: 32 = 9 A logarithmic function: log39 = 2 1 solutions Answer 145295 by stanbon(57286)   on 2009-04-28 16:21:40 (Show Source): You can put this solution on YOUR website!Please check my work: Form each of the following: A linear equation in one variable: Y + 3 = -5 A linear equation in two variables: y = 5x - 3 A quadratic equation: 3x2 + x - 2 = Y A polynomial of three terms: 7x^2 + 4x − 9 = y An exponential function: y = 3^x +2 A logarithmic function: y = 3 + log(x-2) ============================================= Cheers, Stan H.
 Probability-and-statistics/193546: Determining null and alternative hypotheses A presidential candidate claims that the proportion of college students who are registered to vote in the upcoming election is at least 63%. Suppose that we want to sample a number of college students and carry out a hypothesis test to see if this claim may be refuted. State the null hypothesis Ho and the alternative hypothesis H1 that we would use for this test. Ho: H1: 1 solutions Answer 145290 by stanbon(57286)   on 2009-04-28 15:52:43 (Show Source): You can put this solution on YOUR website!Determining null and alternative hypotheses A presidential candidate claims that the proportion of college students who are registered to vote in the upcoming election is at least 63%. Suppose that we want to sample a number of college students and carry out a hypothesis test to see if this claim may be refuted. State the null hypothesis Ho and the alternative hypothesis H1 that we would use for this test. --------------------------------------------------------- Ho: p >= 0.63 H1: p < 0.63 ------------------ Cheers, Stan H.
 Functions/193570: Can you please help me with the following problem: Find the domain of f(g(x)). F(x)= 4/(x-2) and g(x)=3/(x-5) I know that the domain of f(x) is (-infinity,2)U (2,infinity) and g(x) is (-infinity,5)U (5,infinity) I know that f(x) has got to be set to the number that the domain cannot use in g(x) So that would be 5=4/(x-2) Then multiply each side by (x-2). (x-2)(5)=(4/(x-2))(x-2) this cancel out the denominator. Then the problem would be 5x-10=4, subtract 10 from each side to isolate the variable. 5x-10+10=4+10 => 5x=14. Then to isolate x, x would have to be divided by 5. 5x/5=14/5 => x=14/5 So would the domain be (-infinity,2)U(2,(14/5))U((14/5),5)U(5,infinity)? please let me know if any mistakes were made thanks! 1 solutions Answer 145289 by stanbon(57286)   on 2009-04-28 15:48:07 (Show Source): You can put this solution on YOUR website!Find the domain of f(g(x)). F(x)= 4/(x-2) and g(x)=3/(x-5) f[g(x)] = f[3/(x-5)] = 5/[3/(x-5) -2] = 5/[(3-2x+10)/(x-5)] = 5/[13-2x/(x-5)/ = [5(x-5)]/[13-2x] ----------------------- Domain: All Real numbers except x = 13/2 ============================================== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/193559: This question is from textbook algebra and trigonometry structure and method book 2 ``Find the vertex, focus, directrix, and axis of symmetry of each parabola. x^2+8y+4x-4=0 We have been using the formulas y-k=a(x-h)^2 and x-h=a(y-k)^2 I don't understand which to use here, even after completing the square and its confusing because I don't know which is which. please explain and be specific. thank you. We also use the fact that the focus is F(h,k+c) when a=1/4c. Please explain in these terms so that I can understand. thank you1 solutions Answer 145288 by stanbon(57286)   on 2009-04-28 15:42:54 (Show Source): You can put this solution on YOUR website!Find the vertex, focus, directrix, and axis of symmetry of each parabola. x^2+8y+4x-4=0 We have been using the formulas y-k=a(x-h)^2 and x-h=a(y-k)^2 I don't understand which to use here, even after completing the square and its confusing because I don't know which is which. please explain and be specific. thank you. We also use the fact that the focus is F(h,k+c) when a=1/4c. Please explain in these terms so that I can understand. thank you ------------- x^2+8y+4x-4=0 ----------------- Complete the square on the x-terms x^2 + 4x + ? = -8y+4 + ? x^2 + 4x + 4 = -8y + 4+4 (x+2)^2 = -8(y-1) ------------------------ Rearrange: (x-1) = (-1/8)(y+2)^2 h = 1, k= -2, a = -1/8 = (1/4)c c = -1/2 ---------------------- Find the vertex, focus, directrix, and axis of symmetry of each parabola. Vertex = (h,k) = (1,-2) Focus = (h+c, k) because this parabola is opening to the left. Focus = (1-(1/2),-2) = ((1/2),-2) Directrix: x = h - c = 1+1/2 = 3/2 Axis of symmetry: Horizontal line passing thru the vertex: y = -2 ================================================================= Cheers, Stan H.
 Geometry_Word_Problems/193565: This question is from textbook Explain how you would find the volume of an irregular shape.1 solutions Answer 145286 by stanbon(57286)   on 2009-04-28 15:26:12 (Show Source): You can put this solution on YOUR website!Explain how you would find the volume of an irregular shape. You would have to chop it up (actually or through measurements) into regular 3 dimensional shapes; then measure the volume of each and add. ------------------- You could also put the ship in a "regular" container (cube or cylinder) and measure how much the water rises. =================================================== Cheers, Stan H.
 Exponential-and-logarithmic-functions/193557: Could you please provide a detailed explanation of how to solve the following... 5^3log3(2)1 solutions Answer 145285 by stanbon(57286)   on 2009-04-28 15:18:46 (Show Source): You can put this solution on YOUR website!provide a detailed explanation of how to solve the following... 5^3log3(2) Let x = 5^3log2 (2) -------------- log means "exponent" log2 (2) is the exponent of 2 that gives you 2. So, log2 (2) = 1 ---------------------- x = 5^3*1 x = 5^3 x = 125 Therefore 5^(3log2 ( 2)) = 125 =============== Cheers, Stan H.
 Miscellaneous_Word_Problems/193547: A Coast Gaurd Ship is rushing to the aid of a sailboat. A rescue helicopter is already hovering above the sailboat at an altitude of 125 feet. The angle of elevation from the deck of the Coast Gaurd Ship and the helicopter is 24 degrees. How far is the Coast Gaurd Ship from the sail boat?1 solutions Answer 145283 by stanbon(57286)   on 2009-04-28 15:13:46 (Show Source): You can put this solution on YOUR website!A Coast Gaurd Ship is rushing to the aid of a sailboat. A rescue helicopter is already hovering above the sailboat at an altitude of 125 feet. The angle of elevation from the deck of the Coast Gaurd Ship and the helicopter is 24 degrees. How far is the Coast Gaurd Ship from the sail boat? ----------------------------------- Draw the right triangle picture. Put the sailboat at the ri. angle vertex ; the helicopter is 125ft above it. The 24 degree angle is opposite the 125 leg -------------------------------------------------- Find the length of the base. tan(24) = 125/base base = 125/tan(24) = 280.75 ft ===================================== Cheers, Stan H.
 Exponential-and-logarithmic-functions/193541: Could you please provide me with a detailed explanation on how to solve the following... log2 (5) - log2 (15) + log2 (24)1 solutions Answer 145282 by stanbon(57286)   on 2009-04-28 15:08:29 (Show Source): You can put this solution on YOUR website!log2 (5) - log2 (15) + log2 (24) ----------------- logs are exponents. When you subtract exponents you are dividing some numbers When you add exponents you are multiplying some numbers ---------------------- Your problem involves subtracting (divide) and adding (multiply): = logc [5*24/15] = log2 [8] = 3 ================ Cheers, Stan H. Ask, if you do not understand. ===================
 Probability-and-statistics/193471: 2)In a group of 20 adults, 4 out of 7 women and 2out of 13 men wear glasses. What is the probability that a person chosen at random from the group is a women or someone who wear glasses. 3) A firm of charted accountants has two vacancies for trainee students. In the past , 40% of the students who were offered the training contract have not reported to join.If two students are offered training contract, what is the probability that one will join?1 solutions Answer 145247 by stanbon(57286)   on 2009-04-28 10:43:03 (Show Source): You can put this solution on YOUR website!In a group of 20 adults, 4 out of 7 women and 2 out of 13 men wear glasses. What is the probability that a person chosen at random from the group is a women or someone who wear glasses. --- P(w or g) = P(w) + P(g) - P(w and g) = 7/20 + 6/20 - 4/20 = 9/20 ============================= 3) A firm of charted accountants has two vacancies for trainee students. In the past , 40% of the students who were offered the training contract have not reported to join.If two students are offered training contract, what is the probability that one will join? P(one will join) = 1 - (P(0 join) + P(both join)) = 1 - (0.6)^2 + (0.4)^2) = 1 - 0.36 - 0.14 = 1 - 0.5 = 0.5 ==================================== Cheers, Stan H.
 Inequalities/193460: How do I solve the inequality x^3-x^2-6x>0?1 solutions Answer 145242 by stanbon(57286)   on 2009-04-28 08:35:05 (Show Source): You can put this solution on YOUR website!solve the inequality x^3-x^2-6x > 0 --------- Factor to find values that x cannot have: x(x^2-x-6) > 0 x(x-3)(x+2) > 0 x cannot be 0, 3 or -2 ------------------------------- Draw a number line and plot x = -2, 0, and 3 --------------------------------- Test a value in each of the four resulting intervals to see where solutions are for the inequality: Test x = -5, you get (-5)^3-(-5)^2-6(-5) > 0 which is false Test x = -1, you get (-1)^3-(-1)^2-8(-1) > 0 which is true Test x = 1, you get 1 -1 - 6 > 0 which is false Test x = 5, you get (5)^3 - (5)^2 -6(5) > 0 which is true ---------------------------------- Solutions are in -2 < x < 0 and 3 < x < +inf ========================================================= Cheers, Stan H.
 Numeric_Fractions/193432: i dont now how to resolve algebra fractions x4-6 _____ 5Y_71 solutions Answer 145241 by stanbon(57286)   on 2009-04-28 08:19:30 (Show Source): You can put this solution on YOUR website!x4-6 _____ 5Y_7 -------------------------- [x^4/5y] - [6/7] least common divisor = 35y --- Rewrite each fraction with the lcd as its denominator: = [7x^4/lcd] - [5y*7/lcd] --- Combine the numerators over the lcd: = [x^4 - 35y]/lcd = [x^4- 35y]/35y ===================== Cheers, Stan H.
 Polynomials-and-rational-expressions/193469: Add -5 to both sides of the inequality 7 > 1. Then divide both sides of the inequality -25 > -30 by -6. Explain what happens in both examples and when the direction of the inequality symbol is reversed. 1 solutions Answer 145239 by stanbon(57286)   on 2009-04-28 07:44:23 (Show Source): You can put this solution on YOUR website!Add -5 to both sides of the inequality 7 > 1. You get 2 > -4 which is true Notice that the order of the inequality has not been affected. -------------------------------------- Then divide both sides of the inequality -25 > -30 by -6. You get 25/6 < 5 if you do it correctly Notice that when you divide an inequality by a negative the order of the inequality is reversed. ------------------------------------------------ Explain what happens in both examples and when the direction of the inequality symbol is reversed. ============================== Cheers, Stan H.
 Probability-and-statistics/193470: 1) A Class contains 10 men and 20 women of which half of the men and half of the women have brown eyes. Find the probability that a person chosen at random is a man or has brown eyes.1 solutions Answer 145238 by stanbon(57286)   on 2009-04-28 07:38:11 (Show Source): You can put this solution on YOUR website!A Class contains 10 men and 20 women of which half of the men and half of the women have brown eyes. Find the probability that a person chosen at random is a man or has brown eyes. -------- P(A or B) = P(A) + P(B) - P(A and B) -------------- P(man or brown eyes) = P(man) + P(brown eyes) - P(man and brown eyes) P(m or be) = (10/20) + (10/20) - (5/30) = 1- (5/30) = 25/30 = 5/6 ============================== Cheers, Stan H.
 Average/193466: if f(x) = 4/(x+6)` (a) State the vertical asymptote(s). Should be -6 right? (b) State the horizontal asymptote. 0? (c) Find the inverse function of f. f(x)=4/(x+6) y=4/(x+6) x= 4/(y+6) x=4(y+6) x=4y+24 are a, b and c correct? 1 solutions Answer 145237 by stanbon(57286)   on 2009-04-28 07:33:24 (Show Source): You can put this solution on YOUR website!if f(x) = 4/(x+6)` (a) State the vertical asymptote(s). Should be -6 right? (b) State the horizontal asymptote. 0? (c) Find the inverse function of f. f(x)=4/(x+6) y=4/(x+6) x= 4/(y+6) y+6 = 4/x y = (4/x)-6 ------------------ are a, b and c correct? --------------- a and b are correct I have corrected "c". ============================ Cheers, Stan H.
 Proportions/193439: This question is from textbook Mathematics 1/4=5kilometers while 2 inches= what?1 solutions Answer 145218 by stanbon(57286)   on 2009-04-27 21:03:54 (Show Source): You can put this solution on YOUR website!1/4=5kilometers while 2 inches= what? ------ x/2inches = 5 km/(1/4)in x = 10/(1/4) = 40 km -------- 2 inches represents 40 km =============================== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/193437: what do they mean by find the exact solutions of each system of equations: x^2+y^2=100 and y=2-x?1 solutions Answer 145217 by stanbon(57286)   on 2009-04-27 20:57:59 (Show Source): You can put this solution on YOUR website!what do they mean by find the exact solutions of each system of equations: x^2+y^2=100 and y=2-x? ---------------------------- They mean for you to find x/y pairs that make both equations true. ---------------------------- Substitute y = 2-x in the other equation to solve for "x": x^2 + (2-x)^2 = 100 x^2 + 4 -4x + x^2 = 100 2x^2-4x-96 = 0 x^2 -2x-48 = 0 (x-8)(x+6) = 0 x = 8 or x = -6 ------------------ If x = 8, y = 2-x = 6 giving you point (8,6) If x = -6, y = 2-x = 9 giving you point (-6,8) ==================================================== Cheers, Stan H.
 Rational-functions/193433: FIND ALL ROOTS List all possible rational zeroes of the function--- 5x^7-7x^3+12x-4 I don't know where to start. 1 solutions Answer 145216 by stanbon(57286)   on 2009-04-27 20:32:13 (Show Source): You can put this solution on YOUR website!FIND ALL ROOTS List all possible rational zeroes of the function--- 5x^7-7x^3+12x-4 -------------------------------------------------------------------- If p/q is a rational root of the polynomial, p is a factor of -4 such as +/-1, +/-2, +/-4 and q is a factor of 5 such as +/-1, +/-5 ------------------------------------------------- So check out +/-1. +/-2, +/-4, +/-1/5, +/-2/5, +/-4/5 -------------------- If none of these is a root, there are no rational roots. ------------------------------- I do not find any rational roots. I do find a root around x = 0.36028589.... =============================== Cheers, Stan H.
 Linear-equations/193431: This question is from textbook You must state your answer in words. You must set up a system of two equations in two variables. You must state what the variables represent. You must show all the steps in solving the system of equations. Heather made an extra \$12,000 last year from a part-time job. She invested part of the money at 7% and the rest at 9%. She made a total of \$970 in interest. How much was invested at 7%? Thank You!1 solutions Answer 145215 by stanbon(57286)   on 2009-04-27 20:11:42 (Show Source): You can put this solution on YOUR website!Heather made an extra \$12,000 last year from a part-time job. She invested part of the money at 7% and the rest at 9%. She made a total of \$970 in interest. How much was invested at 7%? ----- Equations: Quantity Eq: S + N = 12000 Interest Eq:0.07S + 0.09N = 970 ---------------------- Multiply thru the 1st equation by 0.07 0.07S + 0.07N = 0.07*12000 0.07S + 0.09N = 970 ---------------------------- Subtract to solve for "N": 0.02N = 970 - 0.07*12000 N = \$6500 ---- S = 12000 - 6500 = \$5500 (amt. invested at 7% ================================================ Cheers, Stan H.
 Equations/193416: Anna's recipe for apple fritters makes eighteen fritters using two-thirds cup of milk. Anna wants to make six fritters how much milk will she need?1 solutions Answer 145211 by stanbon(57286)   on 2009-04-27 19:42:42 (Show Source): You can put this solution on YOUR website!Anna's recipe for apple fritters makes eighteen fritters using two-thirds cup of milk. Anna wants to make six fritters how much milk will she need? -------------------------------- x/6 = (2/3)/18 x = 4/18 x = 2-9th cup of milk ========================== Cheers, Stan H.
 Sequences-and-series/193422: This question is from textbook Algebra and Trignometry the problem that i need help on states: Sebastian has a test that has 20 questions on it. The first question is worth one point, and each question after the first is worth four points more than the question before it. What is the maximum score Sebastian can obtain? Please help asap!1 solutions Answer 145208 by stanbon(57286)   on 2009-04-27 19:22:00 (Show Source): You can put this solution on YOUR website!Sebastian has a test that has 20 questions on it. The first question is worth one point, and each question after the first is worth four points more than the question before it. What is the maximum score ------------------ It is an arithmetic series: Formulas S(n) = (n/2)(a+l) ; a is the 1st term and l is the last a(n) = a(1) + (n-1)d a(20) = 1 + 19*4 = 77 ------------- S(20) = (20/2)(1 + 77) = 10*78 = 780 ------------ Cheers, Stan H.
 Equations/193406: I am having a problem solving the following equation in terms of logarithms. Could someone please help? Problem : 2^2x-4= 3^x-21 1 solutions Answer 145206 by stanbon(57286)   on 2009-04-27 19:07:25 (Show Source): You can put this solution on YOUR website!I am having a problem solving the following equation in terms of logarithms. Could someone please help? Problem : 2^(2x-4) = 3^(x-21) Take the log of both sides: (2x-4)log2 = (x-21)log3 2xlog2 - 4log2 = xlog3 - 21*log3 ---- (2log2-log3)x = 4log(2) - 21*log(3) 0.12494x = -8.81543 x = -70.557281 Cheers, Stan H.
 Probability-and-statistics/192692: The mean weight of adult mountain lions is 150lbs with a standard deviation of 8 lbs. A random sample of 50 mountain lions is selected. a) What is the probability that the mean weight of the sample is less that 150 lbs? b) What is the probability that the mean weight of the sample is between 149 and 151 lbs? c) What is the probability that the mean weight of the sample is more than 153lbs? What is the standard deviation of the sampling distribution?1 solutions Answer 145167 by stanbon(57286)   on 2009-04-27 15:41:25 (Show Source): You can put this solution on YOUR website!The mean weight of adult mountain lions is 150lbs with a standard deviation of 8 lbs. A random sample of 50 mountain lions is selected. a) What is the probability that the mean weight of the sample is less that 150 lbs? Ans: 0.5000 ---------------------------- b) What is the probability that the mean weight of the sample is between 149 and 151 lbs? Ans: 0.09948... ------------------------------------------- c) What is the probability that the mean weight of the sample is more than 153lbs? 0.35393.. ------------------------------------------- What is the standard deviation of the sampling distribution? Ans: 8/sqrt(50) = 1.13137.. ================================ Cheers, Stan H.