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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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 Equations/190587: #13 i have tired ti figure this out but I do not know where to start The questions asked A discount store sold plastic cups for 3.50 and each ceramic cups for 4 dollars each. If 400 cups were sold for a total of \$1,458, how many cups of each type were sold ? what is the dollar value of each type of cup sold 1 solutions Answer 143054 by stanbon(57347)   on 2009-04-11 12:23:40 (Show Source): You can put this solution on YOUR website!A discount store sold plastic cups for 3.50 and each ceramic cups for 4 dollars each. If 400 cups were sold for a total of \$1,458, how many cups of each type were sold ? what is the dollar value of each type of cup sold ------------------------------------------- Equations: Quantity: p + c = 400 Value: 3.5p +4c = 1458 ---------------------------- Multiply thru the 1st equation by 4 to set up the system for elimination: 4p + 4c = 1600 3.5p+4c = 1458 -------------------- Subtract 2nd Eq. from 1st to get: 0.5p= 142 p = 284 (# of plastic cups sold) dollar value = 3.5*284 = \$994.00 -------------------- Substitute into p+c=400 to solve for "c": 284 + c = 400 c = 116 (# of ceramic cups sold) dollar value = \$464 ===================== Cheers, Stan H.
 Angles/190588: How do you find the angle's measure is 70 more than that of it's complement? I know the answer is 80, but how do you find the answer?1 solutions Answer 143053 by stanbon(57347)   on 2009-04-11 12:16:00 (Show Source): You can put this solution on YOUR website!How do you find the angle's measure is 70 more than that of it's complement? I know the answer is 80, but how do you find the answer? -------- Let the angle be "x". Then its complement is "90-x" ------------------------------ EQUALITY: angle - complement = 70 x - (90-x) = 70 2x - 90 = 70 2x = 160 x = 80 ============= Cheers, Stan H.
 Probability-and-statistics/190466: A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the children in other group were fed a standard baby formula without any iron supplements. Here are summary results on blood hemoglobin levels at 12 months of age. Group n Mean s Breast-fed 23 13.3 1.7 Formula 19 12.4 1.8 a. Is there significant evidence that the mean hemoglobin level is higher among breastfed babies? State null hypothesis and alternate hypothesis and conduct a t-test. b. Give a 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants.1 solutions Answer 143052 by stanbon(57347)   on 2009-04-11 12:12:37 (Show Source): You can put this solution on YOUR website!A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the children in other group were fed a standard baby formula without any iron supplements. Here are summary results on blood hemoglobin levels at 12 months of age. Group...... n Mean s Breast-fed 23 13.3 1.7 Formula... 19 12.4 1.8 a. Is there significant evidence that the mean hemoglobin level is higher among breastfed babies? State null hypothesis and alternate hypothesis and conduct a t-test. Ho: u(breastfed)-u(formula) = 0 Ha: u(breastfed)-u(formula > 0 ----------------- I ran a 2-sample T-test on a TI caluclator and got the following: test statistic: t= 1.6537 p-value.......: P(t.1.6537 with df=37.6) = 0.05325 --- Conclusion: Since the p-value is greater than 5%, fail to reject Ho. Note: The p-value is so close to 5% more testing should be done. ======================================================================= b. Give a 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants. I ran a 2-Sample T-interval on a TI caluculator and got the folowing 95% C.I.:::: ( -0.2021 , 2.0021) Conclusion: Since zero is in the 95% C.I., fail to reject Ho. ======================================================================= Cheers, Stan H.
 Graphs/190566: This question is from textbook saxon algebra 2 Graph the following equation. Identify the values of a, b, c, as well as the major and minor axes. Calculate the eccentricity e. x^2/5^2 + y^2/3^2=1 I worked it out to: c=4 eccentricity is c/a=4/5 Question: How do I identify the major and minor axes? Also, am I correct thus far?1 solutions Answer 143020 by stanbon(57347)   on 2009-04-10 23:50:50 (Show Source): You can put this solution on YOUR website!Graph the following equation. Identify the values of a, b, c, as well as the major and minor axes. Calculate the eccentricity e. x^2/5^2 + y^2/3^2=1 I worked it out to: c=4 eccentricity is c/a=4/5 Question: How do I identify the major and minor axes? Also, am I correct thus far? ----------------------------------------- a = 5; b = 3; c = 4 ---- The center is at the origin. The major axis is the horizontal distance from x=-5 to x=+5 ---------------------------------------- The minor axis is the vertical distance from y= -3 to y=+3 ---------------------------------------- e = c/a = 4/5 ========================================== You are correct so far. ========================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/190567: This question is from textbook saxon algebra 2 Determine whether the polynomial P(x) has a zero remainder when divided by (x-3). Determine Q(x). P(x)=x^5-5x^4-2x^3+18x^2+24x-18 Determine Q(x) is throwing me off. I need help please.1 solutions Answer 143019 by stanbon(57347)   on 2009-04-10 23:43:29 (Show Source): You can put this solution on YOUR website!Determine whether the polynomial P(x) has a zero remainder when divided by (x-3). Determine Q(x). P(x)=x^5-5x^4-2x^3+18x^2+24x-18 Determine Q(x) is throwing me off. I need help please. -------------------- Q(x) is the quotient when you divide by x-3. ---- Using synthetic division you get: 3)....1....-5....-2....18....24....-18 .......1.....-2....-8....-6....6....|..0 ============== Quotient: x^4 -2x^3 -8x^2 -6x + 6 Remainder: 0 ================================================ Cheers, Stan H.
 Polynomials-and-rational-expressions/190563: This question is from textbook beginning algebra I am trying to solve the problem 4m/7 + m =11 and am getting no where with my answer. thanks1 solutions Answer 143018 by stanbon(57347)   on 2009-04-10 23:36:42 (Show Source): You can put this solution on YOUR website! solve the problem 4m/7 + m =11 ------------ (4m/7) + m = 11 --- Multiply thru by 7 to get: 4m + 7m = 77 11m = 77 m = 7 ====================== Cheers, Stan H.
 Inequalities/190565: This question is from textbook saxon algebra 2 Solve x-9/x+7 is greater than 0 by finding the sign of the numerator and the denominator of the rational expression. I worked it out to: x is less than -7 or x is greater than 9 Am I correct?1 solutions Answer 143015 by stanbon(57347)   on 2009-04-10 23:31:42 (Show Source): You can put this solution on YOUR website!Solve x-9/x+7 is greater than 0 by finding the sign of the numerator and the denominator of the rational expression. I worked it out to: x is less than -7 or x is greater than 9 Am I correct? ------------------------- (x-9)/(x+7) > 0 ---- x cannot be -7 and x cannot be 9 ------ Draw a number line and mark x = -7 and 9 ------------ Check a value in each of the resulting intervals to see there the solutions are. Check x = -10: you get -/- > 0 ; true, so solutions in (-inf,-7) Check x = 0; you get -/+ > 0 ; false Check x = 10; you get +/+ > 0 ; so solutions in (9,+inf) ========================================================== Solution: (-inf,7) U (9,+inf) ========================================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/190564: Find the restricted values of x. -9x^2 + 11 __________ 23x1 solutions Answer 143014 by stanbon(57347)   on 2009-04-10 23:19:42 (Show Source): You can put this solution on YOUR website!Find the restricted values of x. -9x^2 + 11 __________ 23x ------------------------ x cannot be zero ================================= Cheers, Stan H.
 Permutations/190561: How many different 5 digit zip codes are possible if digits are allowed to repeat?1 solutions Answer 143013 by stanbon(57347)   on 2009-04-10 23:17:08 (Show Source): You can put this solution on YOUR website!How many different 5 digit zip codes are possible if digits are allowed to repeat? -------------------------- If 00000 is allowed there are 10^5 = 100,000 ===================================== Cheers, Stan H.
 Quadratic_Equations/190555: I have a world problem, not sure if I solved it correctly. Could I have some help, thank you. A picture frame is 14cm by 18cm. There are 192cm2 of the picture showing. Find the width of the frame. I have 2cm. Is this correct. Thank you.1 solutions Answer 143011 by stanbon(57347)   on 2009-04-10 22:37:02 (Show Source): You can put this solution on YOUR website!A picture frame is 14cm by 18cm. There are 192cm2 of the picture showing. Find the width of the frame. I have 2cm. ---------------------- Draw a rectangle inside a rectangle. --------------------------------------------- Let the uniform frame width be "x". (18-2x)(14-2x) = 192 252-28x-36x+4x^2 = 192 4x^2-64x+60 = 0 x^2-16x+15) = 0 (x-15)(x-1)=0 Realistic solution: x = 1 cm --------------- Cheers, Stan H.
 Miscellaneous_Word_Problems/190556: The width of a rectangle is fixed at 17cm. What lenghts will make the perimeter greater than 90cm? The length must be graeter than ?? cm.1 solutions Answer 143004 by stanbon(57347)   on 2009-04-10 22:20:16 (Show Source): You can put this solution on YOUR website!The width of a rectangle is fixed at 17cm. What lengths will make the perimeter greater than 90cm? The length must be greater than ?? cm. ---------------------------- Perimeter = 2(L + W) --------- 2(L + 17) > 90 L+17 > 45 L > 28 cm ============== Cheers, Stan H.
 Miscellaneous_Word_Problems/190558: The function described by H (x) = 2.75x+ 71.48 can be used to predict the height, in centimeters, of a woman whose humerous (the bone from the elbow to the shoulder)is x cm long. Predict the height of a woman whose humerous is 36 cm long.1 solutions Answer 143003 by stanbon(57347)   on 2009-04-10 22:14:39 (Show Source): You can put this solution on YOUR website!H (x) = 2.75x+ 71.48 ----- H(36) = 2.75*36 + 71.48 H(36) = 170.48 ---------------- Cheers, Stan H.
 Graphs/190534: When examining the graphs of logarithmic functions, for what value(s) x is it not possible to determine log(x)? Explain your reasoning.1 solutions Answer 142987 by stanbon(57347)   on 2009-04-10 16:49:45 (Show Source): You can put this solution on YOUR website!When examining the graphs of logarithmic functions, for what value(s) x is it not possible to determine log(x)? Explain your reasoning. --------------------------------------------------------------- The log function is undefined for all x < 0. The log is an exponent of a base used to express positive numbers. Powers of a positive base connot express negative numbers, so logs are not defined for negative numbers. The exponent (log) can be negative but the antilog cannot be negative. ========================================================================== Cheers, Stan H.
 Word_Problems_With_Coins/190528: Bill has 4 times as many quarters as dimes in all he has is 2 dollars and twenty cents how many coins each of type does he have? I cant figure out how to solve this. We have to make some type of chart with it too, and work it out with a certain eqaution. But I have no idea what to do.1 solutions Answer 142986 by stanbon(57347)   on 2009-04-10 16:29:25 (Show Source): You can put this solution on YOUR website!Bill has 4 times as many quarters as dimes in all he has is 2 dollars and twenty cents how many coins each of type does he have? ----------------------- Let # of dimes be "x" ; value is 10x cents Then # of quarters is "4x"; value is 25*4x = 100x cents --------------------------- Value Equation: value + value = value 10x+100x =220 cents 110x = 220 x = 2 (# of dimes) 4x = 8 (# of quarters) =========================== Cheers, Stan H.
 Rectangles/190530: find the length and width of a rectangle lot with a perimeter of 70 meters if the length is 5 meters more than the width. i know the length is 20 and the width is 15 but I need the formula or the steps of how to get the answer1 solutions Answer 142985 by stanbon(57347)   on 2009-04-10 16:18:05 (Show Source): You can put this solution on YOUR website!find the length and width of a rectangle lot with a perimeter of 70 meters if the length is 5 meters more than the width. ------------------------ Let the width = "x", then thelength = "x+5" ------------------------------ Perimeter = 2(length + width) 70 = 2(x+5 + x) 35 = 2x+5 2x = 30 x = 15 meters(this is the width) x+5 = 20 meters (this is the length) ======================================= Cheers, Stan H.
 Polynomials-and-rational-expressions/190477: Multiply -7x(x-2) 1 solutions Answer 142982 by stanbon(57347)   on 2009-04-10 16:08:01 (Show Source): You can put this solution on YOUR website!Multiply -7x(x-2) = -7x^2+14x ============ Cheers, Stan H.
 Equations/190475: This question is from textbook If P = 2y – 6xy – 3x and Q = 4 – 5y, find 2P – 3Q and simplify the answer. I am sooo Lost! Thank You.1 solutions Answer 142940 by stanbon(57347)   on 2009-04-10 11:01:14 (Show Source): You can put this solution on YOUR website!If P = 2y – 6xy – 3x then 2P = 4y-12xy-6x ----------------------------- and Q = 4 – 5y so 3Q = 12 - 15y ------------------------------ find 2P – 3Q and simplify the answer. 3P - 3Q = (4y-12xy-6x)-(12-15y) = 4y+15y -12xy -6x -12 = 19y -12xy - 6x - 12 =========================================================== Cheers, Stan H.
 Equations/190476: This question is from textbook Sandy has \$3.25 in change. She has five more dimes than quarters but twice as many nickels as dimes. Express the given information as an algebraic equation and simplify each side of the equation. [You are not required to solve the problem.] You must name the variable used in the equation. Thank You!1 solutions Answer 142939 by stanbon(57347)   on 2009-04-10 10:56:30 (Show Source): You can put this solution on YOUR website!Sandy has \$3.25 in change. She has five more dimes than quarters but twice as many nickels as dimes. Express the given information as an algebraic equation and simplify each side of the equation. [You are not required to solve the problem.] You must name the variable used in the equation. -------------- Let the number of dimes be "x" worth 10x cents. Then # of quarters is "x-5" worth 25(x-5) cents And # of nickels = "2x" worth 5(2x) cents -------------------------------- Value Equation: 10x + 25(x-5) + 5(2x) = 325 cents ====================================== Cheers, Stan H.
 Probability-and-statistics/190443: In this question, answer to at least 3 decimal places accuracy. Data shows that 86% of all people are right handed. In a group of 10 people, what would be the expected value for the number of right handed people in the group? 8.6 What is the probability that exactly 8 of the people in the group are right handed? What is the probability that at least 8 of the people in the group are right handed? thanks bunches1 solutions Answer 142928 by stanbon(57347)   on 2009-04-09 22:09:22 (Show Source): You can put this solution on YOUR website!In this question, answer to at least 3 decimal places accuracy. Data shows that 86% of all people are right handed. In a group of 10 people, what would be the expected value for the number of right handed people in the group? 8.6 ------------------------------------------------- What is the probability that exactly 8 of the people in the group are right handed? n=10 ; p = 0.86 ; x = 8 P(x=8) = 10C8*(0.86)^8*(0.14)^2 = 45*0.29922*0.1960 = 0.2639 -------------------------------------------------------------------- What is the probability that at least 8 of the people in the group are right handed? P(x = 8,or 9,or,10) = 0.2639 + 10C9(0.86)^9(0.14)^1 + (0.86)^10 = 0.84547.. ---------------------- Cheers, Stan H.
 Proportions/190412: The ratio of two numbers is 3:4. Their sum is to the sum of their squares as 7 is to 50. Find the numbers. (Thanks for your help.)1 solutions Answer 142921 by stanbon(57347)   on 2009-04-09 20:54:01 (Show Source): You can put this solution on YOUR website!The ratio of two numbers is 3:4. Let the numbers be 3x and 4x -------------------------------------- Their sum is to the sum of their squares as 7 is to 50. Find the numbers. Equation: (3x+4x)/((3x)^2+(4x)^2) = 7/50 7x/25x^2 = 7/50 x/25x^2 = 1/50 1/25x = 1/50 x = 2 ---------- One number is 3x = 6 The other is 4x = 8 ======================== Cheers, Stan H.
 Linear-systems/190428: I need some help with solving direct and indirect variations. The problem I have is how to set them up. The problem is: The volume of gas at a constant temperature varies inversely as the pressure. Find the volume of a gas under pressure of 24 pound per cubic centimeter if the gas occupies a volume of 123 cubic centimeters under a pressure of 20 pounds per cubic centimeter. I know i need to use the formula Q=k/m but I am not quite sure what goes where. Thanks in advance for any help.1 solutions Answer 142919 by stanbon(57347)   on 2009-04-09 20:41:33 (Show Source): You can put this solution on YOUR website!The volume of gas at a constant temperature varies inversely as the pressure. Find the volume of a gas under pressure of 24 pound per cubic centimeter if the gas occupies a volume of 123 cubic centimeters under a pressure of 20 pounds per cubic centimeter. I know i need to use the formula Q=k/m but I am not quite sure what goes where. ------------------------------------- Volume = k/pressure --- 1st: solve for "k": 123 = k/20 k = 2460 ------------ So the equation is Vol = 2460/pressure ------------------------------------------ Find the volume of a gas under pressure of 24 pound per cubic centimeter Vol = 2460/24 Volume = 102.5 cc ======================== Cheers, Stan H.
 Equations/190421: Ok, I am having problems finding the y-intercept in the following problem: For the function y= (x-5)(x+3)(8x-2), its y-intercept is y= ? its x-intercepts are x= 5,-3,and (1/4) Could someone help me and explain how to find the y-intercept? 1 solutions Answer 142917 by stanbon(57347)   on 2009-04-09 20:13:04 (Show Source): You can put this solution on YOUR website!For the function y= (x-5)(x+3)(8x-2), its y-intercept is y= ? its x-intercepts are x= 5,-3,and (1/4) ---------------------------------------- To find ANY y-intercept, let x=0. You get: y = (-5)(3)(-2) = 30 ============================= Cheers, Stan H.
 Exponential-and-logarithmic-functions/190415: Ok I have this really complicated problem that i don't know howto Solve can you please help me: Use composition of functions to prove that it does matter what order you use these discounts at the store to get the greatest toal discount. The coupons are for \$25 and 40% discount on your total purchase price.1 solutions Answer 142916 by stanbon(57347)   on 2009-04-09 20:03:24 (Show Source): You can put this solution on YOUR website!Use composition of functions to prove that it does matter what order you use these discounts at the store to get the greatest toal discount. The coupons are for \$25 and 40% discount on your total purchase price. ------------------ Let f(x) = x-25 Let g(x) = 0.75x ======================= f[g(x)] = f[0.75x] = 0.75x-25 g[f(x)] = g[x-25] = = 0.75(x-25) = 0.75x-18.75 ---------------------------------------------------- Evaluate if x = \$100 f[g(100)] = 0.75*100-25 = \$50 g[f(100)] = 0.75*100-18.75 = \$56.25 ==================================================== Cheers, Stan H.
 Finance/190419: If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? 1 solutions Answer 142911 by stanbon(57347)   on 2009-04-09 19:49:33 (Show Source): You can put this solution on YOUR website!If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? -------------------------------- Sally DATA: time = 4 hrs/job ; rate = 1/4 job/hr -------------------------------------- John DATA: time = 6 hrs/job ; rate = 1/6 job/hr ------------------------------------- Together DATA: time = x hrs/job ; rate = 1/x job/hr ========================================= Equation: rate + rate = together rate 1/4 + 1/6 = 1/x 3x + 2x = 12 x = 12/5 = 2.4 hrs (time for them to do the job together) ========================================================= Cheers, Stan H. ---------------------
 Polynomials-and-rational-expressions/190417: How do you evaluate (3*10^4)(3*10^5)1 solutions Answer 142908 by stanbon(57347)   on 2009-04-09 19:28:05 (Show Source): You can put this solution on YOUR website!How do you evaluate (3*10^4)(3*10^5) -------------------------------------- = 3*3*10^4*10^5 --- = 9*10^9 = 9,000,000,000 =============== Cheers, Stan H.
 Exponential-and-logarithmic-functions/190411: Can you please help me with this problem: simplify: 3(5x^2)^(1/3) I tried to to distribute the (1/3) first and got 3(5^(1/3)*x^(2/3)) then I tried to distribute in the 3 and got 15^(1/3)*x^(2/3) but then I do not know what to do1 solutions Answer 142905 by stanbon(57347)   on 2009-04-09 19:22:43 (Show Source): You can put this solution on YOUR website!simplify: 3(5x^2)^(1/3) ---- There is no way to simplify what you have posted. Cheers, Stan H. --------------------
 Miscellaneous_Word_Problems/190229: Worker efficiency. In a study of worker efficiency at Wong Laboratories it was found that the number of components assembled per hour by the average worker t hours after starting work could be modeled by the formula N(t)=3t^3+ 23^t2 + 8t. a) Rewrite the formula by factoring the right-hand side completely. b) Use the factored version of the formula to find N(3). 1 solutions Answer 142904 by stanbon(57347)   on 2009-04-09 19:09:18 (Show Source): You can put this solution on YOUR website!N(t)=3t^3 + 23^t2 - 8t. N(t) = t(3t^2 + 23t - 8) N(t) = t(3t^2 +24t-t-8) N(t) = t(3t(t+8) - (t+8)) N(t) = t(t+8)(3t-1) ================================ a) Rewrite the formula by factoring the right-hand side completely. b) Use the factored version of the formula to find N(3). N(3) = 3*11*8 = 264 ========================= Cheers, Stan H.
 Probability-and-statistics/190337: stanbon 21772 having trouble to figure out how you solved the question about the baseball player hits a homerun on the average of once every 12 times at bat= would you mind letting me what to due thanks 1 solutions Answer 142893 by stanbon(57347)   on 2009-04-09 17:52:48 (Show Source): You can put this solution on YOUR website!Hope the additional explanation is helpful. Let me know if there are statements you do not understand. --------------------------- A baseball player hits a homerun on the average of once every 12 times at bat. Use the idea of independent trials to answer the following questions. --- If he bats 5 times in a game, what is the probability he will hit exactly one home run? It's binomial with n=5, p = 1/12, x = 1 If you use a TI calculator you get binompdf(5,12^-1,1) = 0.2942 -------- If you do not have a TI: P(x=1) = 5C1(1/12)^1(11/12)^4 = 5*(1/12)(0.70607) = 0.2942 ------------------------------------------ If he comes to bat 5 times, what is the probability he will hit at least one home run? P(at least one) = 1 - P(no home runs) = 1-binompdf(5,12^-1,0) = 0.3528 OR P(at least one) = 1-P(no home runs) = 1 - 5C0(1/12)^0(11/12)^5 = 1 - 1*1* = 1-0.6472 = 0.3528 ------------------------------------------ If he comes to bat 5 times in a game, what is the expected value for the number of home runs he will hit? E(x) = np = 5(1/12) = 5/12 ============================================== Cheers, Stan H.
 Equations/190302: hi. i need some help in performing this indicated operation and simplifying it: a^2 - a - 20/a^2 - 16 divided by a-5 thanks!1 solutions Answer 142839 by stanbon(57347)   on 2009-04-09 09:08:03 (Show Source): You can put this solution on YOUR website!a^2 - a - 20/a^2 - 16 divided by a-5 ------------- Factor where you can to get: = [(a-5)(a+4)]/[(a-4)(a+4)]/(a-5) Invert the denominator and multiply to get: = [(a-5)(a+4)]/[(a-4)(a+4)] Cancel factors that are common to a numerator and a denominator such as (a+4), (a-5) = [1/(a-4)] =============== Cheers, Stan H.
 Quadratic_Equations/190316: Prove the identity : sin theta tan theta + cos theta= sec theta1 solutions Answer 142838 by stanbon(57347)   on 2009-04-09 09:02:12 (Show Source): You can put this solution on YOUR website!Prove the identity : sin theta tan theta + cos theta= sec theta ----------- sin(sin/cos) + cos = sec Multiply thru by cos to get: sin^2 + cos^2 = 1 1 = 1 ============== Cheers, Stan H.
 Linear_Algebra/190317: This question is from textbook algebra and trigonometry structure and method book 2 The stretch on a wire under a given tension varies directly as the length of the wire and inversely as the square of its diameter. A wire having length 2m and diameter 1.5mm stretches 1.2 mm. If a second wire of the same material(and under the same tension) has length 3m and diameter 2.0mm, find the amount of stretch. Please help as i keep on messing the decimals up and can't seem to get the right answer. Please explain also. thank you!1 solutions Answer 142837 by stanbon(57347)   on 2009-04-09 08:58:17 (Show Source): You can put this solution on YOUR website!The stretch on a wire under a given tension varies directly as the length of the wire and inversely as the square of its diameter. stretch = k[L/d^2] ------------------------------ A wire having length 2m and diameter 1.5mm stretches 1.2 mm. 1.2 = k[2/1.5^2] 1.2 = k[8/9] k = (9/8)1.2 k = 27/20 So the equation for your problem is stretch = (27/20)[L/d^2] --------- If a second wire of the same material(and under the same tension) has length 3m and diameter 2.0mm, find the amount of stretch. stretch = (27/20)[3/2^2] = 1.0125 ===================================== Cheers, Stan H. -----------------------