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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/281450: I am having trouble with this question can some one please help me I opened up a savings account today at Carthage Federal Savings and Loan with \$800.00. If the yearly interest rate of 4% is compounded each month, how much interest will I earn in six months? Thank you for your help in advance. 1 solutions Answer 204442 by stanbon(57282)   on 2010-03-16 08:58:17 (Show Source): You can put this solution on YOUR website!I opened up a savings account today at Carthage Federal Savings and Loan with \$800.00. If the yearly interest rate of 4% is compounded each month, how much interest will I earn in six months? ------------------ A(t) = P(1+(r/n))^(nt) A(1/2) = 800(1+(0.04/12)^(12*(1/2)) A(1/2) = 800(1+0.0033)^6 A(1/2) = 800*1.02017 A(1/2) = \$816.13 --------------------- Interest is \$16.13 ======================== Cheers, Stan H.
 Finance/280586: The hypotenuse of a given right triangle is 6 cm longer than the shorter leg. The length of the shorter leg is 2 cm less than that of the longer leg. 1 solutions Answer 204441 by stanbon(57282)   on 2010-03-16 08:50:12 (Show Source): You can put this solution on YOUR website!The hypotenuse of a given right triangle is 6 cm longer than the shorter leg. The length of the shorter leg is 2 cm less than that of the longer leg. --- Let shorter leg be "x". Other leg is "x+2" Hypotenuse = "x+6" --------------------- Use Pythagoras to solve for "x" and the length of each side. (x+6)^2 = x^2 + (x+2)^2 x^2 + 12x + 36 = 2x^2 + 4x+4 x^2 - 8x - 32 = 0 --- Quadratic Formula: x = [8 +- sqrt(64-4*-32)]/2 --- x = [8 +- sqrt(192)]/2 --- Positive solution: x = (8 + sqrt(192))/2 x = 10.93 cm (shorter leg) x+2 = 12.93 cm (other leg) x+6 = 16.93 cm (hypotenuse) =============================== Cheers, Stan H.
 Probability-and-statistics/281358: A.The diameters of bolts produced by a certain machine are normally distributed with a mean of U=0.30 inches and a standard deviation, r=0.042, inches. What percentage of bolts will have a diameter greater than 0.320 inches? B.If 11 bolts are selected, what percentage of bolts will have a mean diameter greater than 0.32 inches?1 solutions Answer 204382 by stanbon(57282)   on 2010-03-15 22:51:38 (Show Source): You can put this solution on YOUR website!A.The diameters of bolts produced by a certain machine are normally distributed with a mean of U=0.30 inches and a standard deviation, r=0.042, inches. What percentage of bolts will have a diameter greater than 0.320 inches? ------------------ z(0.320) = (0.320-0.300)/0.42 = 0.0476 P(x > 0.32) = P(z > 0.0476) = 0.4812 = 42.12% --------------------------------------------------- B.If 11 bolts are selected, what percentage of bolts will have a mean diameter greater than 0.32 inches? z(0.32) = (-.320-0.300)/[0.42/sqrt(11)] = 0.1579 P(xbar > 0.32) = P(z > 0.1579) = 0.4373 = 43.73% =================================================== Cheers, Stan H.
 Permutations/281343: how many 4 card hand can you make out of a deck of card1 solutions Answer 204358 by stanbon(57282)   on 2010-03-15 21:55:09 (Show Source): You can put this solution on YOUR website!how many 4 card hand can you make out of a deck of card ----- 52C4 = 270,725 ================= Cheers, Stan H.
 Proportions/281342: Judy, Mark and Helen receive funds from a settlement in the ratio 7:10:14. Helen receives \$100,000 more than Mark. How much did Judy receive?1 solutions Answer 204356 by stanbon(57282)   on 2010-03-15 21:52:55 (Show Source): You can put this solution on YOUR website!Judy, Mark and Helen receive funds from a settlement in the ratio 7:10:14. Helen receives \$100,000 more than Mark. How much did Judy receive? --------------------------- Equation: 7x + 10x + 14x = 100,000 31x = 100,000 x = 3225.81 ---------------- 7x = 22,580.65 10x = 32,258.10 14x = 45161.34 ====================== Cheers, Stan H.
 Complex_Numbers/281341: Solve in the complex number system: x2 = 1.1 solutions Answer 204352 by stanbon(57282)   on 2010-03-15 21:49:05 (Show Source): You can put this solution on YOUR website!Solve in the complex number system: x^2 = 1. ------------- x^2-1 = 0 (x-1)(x+1) = 0 x = 1 or x = -1 ==================== Cheers, Stan H.
 Permutations/281338: There is a class of 20 with 13 boys and 7 girls. A) how many ways are there to form a committee of 3 boys and 3 girls? B) A committee will be formed by randomly selecting 6 persons. what is the probability that the committee will have 3 boys and 3 girls1 solutions Answer 204349 by stanbon(57282)   on 2010-03-15 21:47:21 (Show Source): You can put this solution on YOUR website!There is a class of 20 with 13 boys and 7 girls. A) how many ways are there to form a committee of 3 boys and 3 girls? Picking 3 boys: 13C3 Picking 3 girls: 7C3 --- # of ways to form the committee: Multiply the two numbers to get: 10,010 ------------------------------------------------- B) A committee will be formed by randomly selecting 6 persons. what is the probability that the committee will have 3 boys and 3 girls --- # of possible 6-member committees: 20C6 = 38,760 P(3 boys and 3 girls) = 10,010/38,760 = 0.2583 ================================================= Cheers, Stan H.
 Length-and-distance/281331: A farmer has 3000 feet of fencing available to enclose a rectangular field. What is the maximum area? 1 solutions Answer 204345 by stanbon(57282)   on 2010-03-15 21:39:56 (Show Source): You can put this solution on YOUR website!A farmer has 3000 feet of fencing available to enclose a rectangular field. What is the maximum area? ---------------------- Perimeter = 2(L+W) 3000 = 2(L+W) 1500 = L+W L = W-1500 --------------------- Area = W*L A = W(W-1500) A = W^2-1500W --- Quadratic equation with a = 1, b = -1500 -------------------------------------------- Maximum occurs when W = -b/2a = 1500/2 = 750 ft. --- Since L+W = 1500 L = 1500-750 L = 750ft ====== Final Answer: length and width need both be 750' =================================================== Cheers, Stan H.
 Angles/281329: How many cubic centimeters can a cigar box hold if its dimensions are 3 centimeters by 16 centimeters by 12 centimeters? Include correct units with your solution. 1 solutions Answer 204341 by stanbon(57282)   on 2010-03-15 21:33:58 (Show Source): You can put this solution on YOUR website!How many cubic centimeters can a cigar box hold if its dimensions are 3 centimeters by 16 centimeters by 12 centimeters? Include correct units with your solution. -------------------- Volume = 3*16*12 = 576 cm^3 =============================== Cheers, Stan H.
 Evaluation_Word_Problems/281325: A representative tells you that floor plan one (x) sells for \$175,000 and floor plan two (y) sells for \$200,000. She also mentions that all the available houses combined are worth \$7,200,000. Write an equation that illustrates this situation. Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer.1 solutions Answer 204340 by stanbon(57282)   on 2010-03-15 21:31:27 (Show Source): You can put this solution on YOUR website!A representative tells you that floor plan one (x) sells for \$175,000 and floor plan two (y) sells for \$200,000. She also mentions that all the available houses combined are worth \$7,200,000. Write an equation that illustrates this situation. ---------------------- Value Eq:::: 175000x + 200000y = 7200000 Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer. ----------- You would need information to form a 2nd equation so you could eliminate one of the variable. =========================================== Cheers, Stan H.
 Parallelograms/281309: Trying to help my duaghter with the folowing problem. one side will be 5x+y = 7 the other side is 3x-4y=18 We need to slove for x and y. Thanks for any help.1 solutions Answer 204329 by stanbon(57282)   on 2010-03-15 21:09:22 (Show Source): You can put this solution on YOUR website!Trying to help my duaghter with the folowing problem. one side will be 5x+y = 7 the other side is 3x-4y=18 We need to solve for x and y. -------------------------------- 5x+y = 7 3x-4y = 18 ----------------- Two popular methods for solvin "systems" of equations are substitution and elimination. ----- I'll show you both ways since your daughter may not have been introduced to one or the other. ------------------------------------------------------------------------- Substitution: 5x+y = 7 3x-4y = 18 --------------- Solve the 1st equation for "y": y = -5x+7 ------ Substitute for "y" in the 2nd equation: 3x - 4(-5x+7) = 18 3x + 20x - 28 = 18 23x - 28 = 18 23x = 46 x = 2 ---------------------- Subtitute for x in the equation y = -5x+7 y = -5(2)+7 y = -10+7 y = -3 ---------------------- Final Answer: (2,-3) ================================================================= Elimination: 5x+y = 7 3x-4y = 18 ------------------- Multiply both sides of the 1st equation by 4 to get: 20x + 4y = 28 3x - 4y = 18 -------------- Add to get: 23x = 46 x = 2 ----------------------- Substitute that value of "x" into either of the original equations and solve for "y": 5x+y = 7 5*2+y = 7 10+y = 7 y = -3 ------------------------ Final Answer: (2,-3) ======================================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/281308: i dont know how to do: The Rocket Coaster has 15 cars, some that hold 4 people and some that hold 6 people. There is room for 72 people altogether. How many 4-passenger cars are there? How many 6-passenger cars are there?1 solutions Answer 204320 by stanbon(57282)   on 2010-03-15 20:54:15 (Show Source): You can put this solution on YOUR website!The Rocket Coaster has 15 cars, some that hold 4 people and some that hold 6 people. There is room for 72 people altogether. How many 4-passenger cars are there? How many 6-passenger cars are there? ---------------------------- Equations: Car Eq:::::::: f + s = 15 cars People Eq:::::4f +6s = 72 people --------------------------------- Multiply thru the Car Equation by 4 to get: 4f + 4s = 60 --- Subtract that from the People Eq and solve for "s": 2s = 12 s = 6 (3 of six-passenger cars) ==================================== Cheers, Stan H.
 Probability-and-statistics/281293: The equation y = -1777x + 27,153 can be used to predict the number of gun deaths in the U.S. x years after 2000, that is, x=0 corresponds to 2000, x=3 corresponds to 2003, x=6 corresponds to 2006, and so on. Predict the number of gun deaths in 2006 and 2007. In what year will the number of gun deaths be 12,937? The predicted gun deaths in 2006 will be ___ The predicted gun deaths in 2007 will be ___ The predicted number of gun deaths will be 12,937 in the year___ 1 solutions Answer 204317 by stanbon(57282)   on 2010-03-15 20:50:03 (Show Source): You can put this solution on YOUR website!The equation y = -1777x + 27,153 can be used to predict the number of gun deaths in the U.S. x years after 2000, that is, x=0 corresponds to 2000, x=3 corresponds to 2003, x=6 corresponds to 2006, and so on. Predict the number of gun deaths in 2006 and 2007. In what year will the number of gun deaths be 12,937? The predicted gun deaths in 2006 will be -1777*6+27,153 = 16491 The predicted gun deaths in 2007 will be -1777*7+27,153 = 14714 The predicted number of gun deaths will be 12,937 in the year___ Solve -1777x+27,153 = 12,937 for "x": -1777x = -14216 x = 8 --- Year: 2008 ==================== Cheers, Stan H.
 Linear-equations/281294: i want to find the equation of a line given that in slope intercept form: slope=-8, y-intercept is (0,-9)1 solutions Answer 204308 by stanbon(57282)   on 2010-03-15 20:18:34 (Show Source): You can put this solution on YOUR website!i want to find the equation of a line given that in slope intercept form: slope=-8, y-intercept is (0,-9) -------------------------------------- y = mx + b -9 = -8*0 + b b = -9 ================= Equation: y = -8x - 9 =================== Cheers, Stan H.
 Linear-equations/281291: Find the domain of the function. g(x)= 5/8-5x Choose the correct domain below. a) {xIx is a real number and x ≥ 8/5} b) {xIx is a real number and x ≠ 0} c) {xIx is a real number and x ≠ 8/5} b) {xIx is a real number and x ≠ 5} 1 solutions Answer 204307 by stanbon(57282)   on 2010-03-15 20:15:40 (Show Source): You can put this solution on YOUR website!Find the domain of the function. g(x)= 5/(8-5x) The denominator cannot zero. Solve 8-5x = 0 5x = 8 x = 8/5 ------------------------------------------------- Ans: c -------- Cheers, Stan H. ================================================= Choose the correct domain below. a) {xIx is a real number and x ≥ 8/5} b) {xIx is a real number and x ≠ 0} c) {xIx is a real number and x ≠ 8/5} b) {xIx is a real number and x ≠ 5}
 Inverses/275381: Let f(x)=e^x sketch the graph g(x)=-f(x-2)+3,identify any intercepts and asymptotes give domain and range of g(x)1 solutions Answer 204306 by stanbon(57282)   on 2010-03-15 20:09:51 (Show Source): You can put this solution on YOUR website!): Let f(x)=e^x sketch the graph g(x)=-f(x-2)+3,identify any intercepts and asymptotes give domain and range of g(x) ----------------------- Start with the graph of y = e^x ------------------------------------------ Shift 2 to the right because of the x-2 Reflect in the x axis because of the "negative" Apply a positive vertical shift because of the "3". ---------------------------------------------- ---------------------------------------------- Cheers, Stan H.
 Probability-and-statistics/281279: Three cards are drawn from an ordinary deck of cards one by one without replacement. Find the probability of the following: a) Getting all Jacks b) Getting an Ace, a King and a Queen in order c) Getting an club-a spade and a heart in order d) Getting three clubs.1 solutions Answer 204305 by stanbon(57282)   on 2010-03-15 20:03:54 (Show Source): You can put this solution on YOUR website!Three cards are drawn from an ordinary deck of cards one by one without replacement. Find the probability of the following: a) P(Getting all Jacks) = 4C3/52C3 ------------------------------------------- b) P(Getting an Ace) = 1-P(no aces) = 1-[48C3/52C3] ------------------------------------------- a) P(King and a Queen in order) = (4/52)(4/51) ------------------------------------------- c) P(Getting an club-a spade and a heart in order) = (13/52)(13/39)(13/26) ------------------------------------------- d) P(Getting three clubs) = 13C3/52C3 ---------------------------------------------- Cheers, Stan H.
 Probability-and-statistics/281268: In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles? Crash1 Crash Damage (\$) Goliath Varmint Weasel 1,600 1,290 1,090 760 1,400 2,100 880 1,390 1,830 1,950 1,850 1,250 1,220 950 1,920 1 solutions Answer 204301 by stanbon(57282)   on 2010-03-15 19:41:37 (Show Source): You can put this solution on YOUR website!Five test vehicles of each type were crashed, with the results shown below. Research questions: (a) Are the mean crash damages the same or significantly different among these three vehicles? (b) Are there any significant differences between pairs of groups? What test did you use? Explain. Crash Damage in Dollars Goliath 1100 750 970 1000 850 Varmint 1290 1400 1390 1850 1100 Weasel 1100 1500 1000 1250 1920 --------------------------- Ho: the means are all equal Ha: at least one of the means is different ----------------- I ran an ANOVA test against the three lists of data and go the following results: test statistic : F = 4.3638 p-value : 0.0377 ------------------------- Conclusion: Fail to reject Ho if alpha is 5% but reject Ho if alpha=1%. ------------------------- Further testing could reveal which mean(s) is higher or lower if you reject Ho. ==================================== Cheers, Stan H.
 Equations/281226: 8k+3.8=231 solutions Answer 204287 by stanbon(57282)   on 2010-03-15 18:25:08 (Show Source): You can put this solution on YOUR website!8k+3.8=23 Subtract 3.8 from both sides: 8k = 19.2 Divide both sides by 8 k = 2.4 ============== Cheers, Stan H.
 Functions/281224: Can you help solved the domain of (1)/(sqrt(19x+16)) Thank You1 solutions Answer 204285 by stanbon(57282)   on 2010-03-15 18:22:07 (Show Source): You can put this solution on YOUR website!Can you help solved the domain of (1)/(sqrt(19x+16)) --------------------------- The denominator cannot be zero. The radicand cannot be negative. --------------------------- Solve 19x+16 > 0 19x > -16 x > -16/19 ------------------ Domain: All Real Numbers greater than -16/19 ============================================== Cheers, Stan H.
 Quadratic_Equations/281216: How do I write x^2-16x+56=0 in vertex form? And, how do I identify the vertex?1 solutions Answer 204284 by stanbon(57282)   on 2010-03-15 18:16:01 (Show Source): You can put this solution on YOUR website!How do I write x^2-16x+56 = y in vertex form? And, how do I identify the vertex? ----------------------------------- x^2-16x + ? = y -56 + ? ----------------------------------- x^2-16x + 64 = y-56+64 (x-8)^2 = y+8 -------------------- Vertex at (8,-8) ======================== Another Method: y = x^2-16x+56 a = 1 ; b = -16 The vertex occurs where x = -b/2a = 16/-1 = 8 f(8) = 8^2 -16*8 + 56 = -8 ================================= Notice the answers are the same. ================================= Cheers, Stan H.
 Geometry_Word_Problems/281213: Definition: if x≠0, then x⁰=?1 solutions Answer 204282 by stanbon(57282)   on 2010-03-15 18:07:07 (Show Source): You can put this solution on YOUR website!Definition: if x≠0, then x⁰=? ------------------- x^0 = 1 for all x not equal to 0 ==================================== Cheers, Stan H.
 Polynomials-and-rational-expressions/281195: 6v^2-24/9v^2-36 answer is a fraction: 1 solutions Answer 204281 by stanbon(57282)   on 2010-03-15 18:03:55 (Show Source): You can put this solution on YOUR website!6v^2-24/9v^2-36 answer is a fraction: --- Factor: [6(v^2-4)]/[9(v^2-4)] ----- Cancel the v^2 -4 factors ----- = 6/9 = 2/3 =========== Cheers, Stan H.
 Linear-equations/281182: Imagine you want to add a sprinkler system and the location of one section of the sprinkler line can be described by the equation y=-1/2x-4 Complete the table for this equation. x y (x,y) ___ -1 -2 ___ ___ -4 2 ___ 8 ___ 1 solutions Answer 204278 by stanbon(57282)   on 2010-03-15 17:48:28 (Show Source): You can put this solution on YOUR website!Imagine you want to add a sprinkler system and the location of one section of the sprinkler line can be described by the equation y=-1/2x-4 Complete the table for this equation. x y (x,y) ___ -1 y = (-1/2)x - 4 --- -1 = (-1/2)x - 4 3 = (-1/2)x x = -6 -------------------------------- y=(-1/2)x-4 -2 ___ y = (-1/2)(-2) - 4 y = 1-4 y = -3 --------------------------------- y=(-1/2)x-4 ___ -4 -4 = (-1/2)x -4 0 = (-1/2)x x = 0 --------------------------------- y=-1/2x-4 2 ___ y = (-1/2)2 -4 y = -1-4 y = -5 --------------------------------- y=(-1/2)x-4 8 ___ y = (-1/2)8-4 y = -8 ==================================== Cheers, Stan H.
 Systems-of-equations/281144: If using the elimination method what is the answer to 5x+2y=24 and 4x+3y=291 solutions Answer 204237 by stanbon(57282)   on 2010-03-15 16:15:51 (Show Source): You can put this solution on YOUR website!If using the elimination method what is the answer to 5x+2y=24 4x+3y=29 ------------------- Let's say you want to eliminate the "y" terms: Multiply thru the 1st Eq. by 3 Multiply thru the 2nd Eq. by 2 ------------------- 15x + 6y = 48 8x + 6y = 58 ------------------ Subtract -7x = 10 x = -10/7 ---------------- Substitute into the 1st Equation and solve for "y": 5(-10/7) + 2y = 24 (-50/7) + 2y = (168/7) 2y = 218/7 y = 109/7 =================== Cheers, Stan H.
 Probability-and-statistics/281134: In a binomial distribution, n=25 and p=0.432 A.Show your work to find a save the mean and standard deviation of this binomial distribution. B.Find the probability that x<=14.1 solutions Answer 204231 by stanbon(57282)   on 2010-03-15 16:07:45 (Show Source): You can put this solution on YOUR website!In a binomial distribution, n=25 and p=0.432 A.Show your work to find a save the mean and standard deviation of this binomial distribution. --- mean = np = 25*0.432 = 10.8 std = sqrt(npq) = sqrt(10.8*0.568) = 2.4768 --------------------------------------------------- B.Find the probability that x<=14. Note: If this is binomial x should be a whole number. What is the meaning of your "x"? --------------------------------------------------- Cheers, Stan H.
 Rectangles/281135: The perimeter of a rectangular backyard is 6x + 6 yards. If the width is x yards, find a binomial that represents the length. I know that the perimeter of a rectangle is p=2L + 2W but I am not sure how to work out this problem.1 solutions Answer 204226 by stanbon(57282)   on 2010-03-15 16:01:35 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangular backyard is 6x + 6 yards. If the width is x yards, find a binomial that represents the length. ---- Perimeter = 2(W + L) --- 6x+6 = 2(x + L) Divide both sides by 2 to get: 3x+3 = x+L --- Length = 2x+3 ================== Cheers, Stan H. ==================
 Probability-and-statistics/281097: A Researcher would like to test the effectiveness of a newly developed growth hormone. The Researcher knows that under normal circumstances laboratory rats reach an average weight of μ = 950 Grams at 10 Weeks of age. The Distribution of weights is normal with σ = 30. A random sample of n = 25 Newborn rats is obtained, and the hormone is given to each rat. When The rats in the sample reach 10 Weeks old, each rat is weighed. The Mean weight for this sample is M = 974. a. Identify the independent and the dependent variables for this study. b. Assuming a two-­‐tailed test, state the null hypothesis in a sentence that includes the independent variable and the dependent variable. c. Using symbols, state the hypotheses (H0 And H1) For the two tailed test. d. Sketch the appropriate distributions, and locate the critical region for α =.05. e. Calculate the test statistic (z-­‐score) For the sample. f. What decision should be made about the null hypothesis, and what decision should be made about the effect of the hormone? 1 solutions Answer 204219 by stanbon(57282)   on 2010-03-15 15:41:17 (Show Source): You can put this solution on YOUR website!A Researcher would like to test the effectiveness of a newly developed growth hormone. The Researcher knows that under normal circumstances laboratory rats reach an average weight of μ = 950 Grams at 10 Weeks of age. The Distribution of weights is normal with σ = 30. A random sample of n = 25 Newborn rats is obtained, and the hormone is given to each rat. When The rats in the sample reach 10 Weeks old, each rat is weighed. The Mean weight for this sample is M = 974. ------------------------------------------ a. Identify the independent and the dependent variables for this study. Independent: amt of hormone dependent: weight of the rats ------------------------------------------ b. Assuming a two-­‐tailed test, state the null hypothesis in a sentence that includes the independent variable and the dependent variable. Hormones do or do not make a difference in rat weights. ------------------------------- c. Using symbols, state the hypotheses (H0 And H1) For the two tailed test. Ho: u(no hor)-u(hor) = 0 Ha: u(no hor)-u(hor) is not equal to 0 ------------------------------- d. Sketch the appropriate distributions, and locate the critical region for α =.05. +-invT(0.975 with df=24) = +-2.0639 ------------------------------- e. Calculate the test statistic (z-­score) For the sample. t(950-974)= -24/(standard deviation) Note: No standard deviation for the sample was posted. ------------------------------- f. What decision should be made about the null hypothesis, and what decision should be made about the effect of the hormone? Note: No decision because test statistic cannot be calculated. ===================================== Cheers, Stan H.
 Geometric_formulas/281092: A line segment has endpoints (X1,Y1) and (X2,Y2). Find the expressions in terms of X1,X2,Y1,Y2 for the coordinates of the points that divides the segment into four equal parts. Thanks, in advance1 solutions Answer 204208 by stanbon(57282)   on 2010-03-15 14:27:05 (Show Source): You can put this solution on YOUR website!A line segment has endpoints (X1,Y1) and (X2,Y2). Find the expressions in terms of X1,X2,Y1,Y2 for the coordinates of the points that divides the segment into four equal parts. ----------------- mid-point: [(x1+x2)/2 , (y1+y2)/2] ------ mid-point of the mid-point between (x1,y1) and [(x1+x2)/2 , (y1+y2)/2] = [(3x1+x2))/4),(3y1+y2)/4] ------------- mid-point of the mid-point between [(x1+x2)/2 , (y1+y2)/2] and (x2,y2) = [(x1 + 3x2)/4 , (y1 + 3y2)/4] ===================================== cheers, Stan H.
 Trigonometry-basics/281086: (toughness- 6.5/10) Question: Suppose " 0 < X < pi/2 " and " sin X = 5/11 ". Evaluate "cos X" . Express your answer as a fraction.1 solutions Answer 204207 by stanbon(57282)   on 2010-03-15 14:18:06 (Show Source): You can put this solution on YOUR website!Suppose " 0 < X < pi/2 " and " sin X = 5/11 ". Evaluate "cos X" . Express your answer as a fraction. --------------------- If sin(x) = 5/11, y = 5 and r = 11 --- Solve 11^2 = 5^2 + k^2 where cos(x) = k/11 k^2 = 121-25 k = sqrt(96) = 9.8 ---------------------- Then cos(x) = 9.8/11 = 0.8907 ================================== Cheers, Stan H.