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# Recent problems solved by 'ewatrrr'

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 Probability-and-statistics/635420: Twenty-six small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 44.5 cases per year. (a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit = upper limit = margin of error = (b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit = upper limit = margin of error = (c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.) lower limit = upper limit = margin of error = 1 solutions Answer 400318 by ewatrrr(10682)   on 2012-08-07 11:00:43 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: z-values for various confidence levels 90% z = 1.645 95% z = 1.96 98% z = 2.33 99% z = 2.576 a) ME = 1.645(44.5/sqrt(10000)= .732 138.5 - ME < < 138.5 + ME b)ME = 1.96(44.5/sqrt(10000)= .873 138.5 - ME < < 138.5 + ME c)ME = 2.576(44.5/sqrt(10000)= 1.146 138.5 - ME < < 138.5 + ME ```
 Radicals/635403: Solve for x and y (x)/(y+1) = 3/2 ; (x+y)/(x-y) = 7/21 solutions Answer 400316 by ewatrrr(10682)   on 2012-08-07 10:17:50 (Show Source): You can put this solution on YOUR website! ``` Hi, || Cross Multiply 2x = 3(y+1) x = and y = || Cross Multiply 2(x+y) = 7(x-y) 2x + 2y = 7x - 7y 9y = 5x and ```
 Radicals/635366: 2 times the square root of x+4 minus 1 =x1 solutions Answer 400312 by ewatrrr(10682)   on 2012-08-07 09:24:26 (Show Source): You can put this solution on YOUR website! ``` Hi, The idea is... to isolate the radical term on one side of the EQ and then square both sides of the EQuation 4(x+4) = x^2 + 2x + 1 4x + 4 = x^2 + 2x + 1 x^2 - 2x -3 = 0 (x-3)(x+1) = 0 x = 3 0r x = -1 ```
 Exponents-negative-and-fractional/635399: solve the following; (-1/64)^-1/3 (16/81)^-3/4 (1/Radical32)^-2/5 -(1/25)^-4/3 (9/4)^-1/21 solutions Answer 400310 by ewatrrr(10682)   on 2012-08-07 09:14:01 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: and Will let you finish it up ```
 Equations/635243: how do i solve the equation 1/6-x/2=x-5 ____ 31 solutions Answer 400302 by ewatrrr(10682)   on 2012-08-07 08:31:10 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: Goal is to isolate the variable on one side of the Equation That gives a plan of action! ||Multiplying thru by 6 so as all denominators = 1 1 - 3x =2( x-5) |Distribute the 2 to remove the parenthesis 1 - 3x = 2x - 10 |Adding 3x to both sides 1 = 5x - 10 |Adding 10 to both sides 11 = 5x ```
 Equations/635402: 3z+5+2z=12+3z1 solutions Answer 400300 by ewatrrr(10682)   on 2012-08-07 08:21:30 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: Goal is to isolate the variable on one side of the Equation That gives a plan of action! 3z+5+2z=12+3z |Subtracting 3z from both sides 5+2z = 12 |Subtracting 5 from both sides 2z = 7 z = 7/2 0r 0r 3.5 ```
 Quadratic-relations-and-conic-sections/635404: Write the equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola . x2 + 4y2 + 2x - 24y + 33 = 01 solutions Answer 400298 by ewatrrr(10682)   on 2012-08-07 08:12:59 (Show Source): You can put this solution on YOUR website! ``` Hi, x2 + 4y2 + 2x - 24y + 33 = 0 (x+1)^2 + 4(y-3)^2 - 1 - 36 + 33 = 0 (x+1)^2 + 4(y-3)^2 = 4 Ellipse: C(-1,3) Standard Form of an Equation of an Ellipse is where Pt(h,k) is the center. (a variable positioned to correspond with major axis) a and b are the respective vertices distances from center and ±are the foci distances from center: a > b ```
 Reduction-of-unit-multipliers/635378: (4sqrt5+5)^2= it says to simplify? thanks for your help!!1 solutions Answer 400297 by ewatrrr(10682)   on 2012-08-07 08:06:02 (Show Source): You can put this solution on YOUR website! ``` Hi, = F First terms 80 O Outside terms 20 I Inside terms 20 L Last terms 25 ```
 Reduction-of-unit-multipliers/635375: (sqrt t -sqrt 17)(sqrt t+ sqrt 17) simplify each expression. thanks for your help:)1 solutions Answer 400296 by ewatrrr(10682)   on 2012-08-07 08:01:07 (Show Source): You can put this solution on YOUR website! ``` Hi, = F First terms t O Outside terms ||Note: I Inside terms - L Last terms -17 ```
 Quadratic_Equations/635380: (sqrt x + sqrt 7)^21 solutions Answer 400295 by ewatrrr(10682)   on 2012-08-07 07:58:31 (Show Source): You can put this solution on YOUR website! ``` Hi, = F First terms x O Outside terms ||Note: I Inside terms L Last terms 7 ```
 Quadratic_Equations/635381: (6+5sqrt3)(1- sqrt3)= ? simplify thanks for your help1 solutions Answer 400294 by ewatrrr(10682)   on 2012-08-07 07:52:45 (Show Source): You can put this solution on YOUR website! ``` Hi, = F First terms 6 O Outside terms -6 I Inside terms 5 L Last terms -5·3 ```
 Radicals/635382: (8-sqrt10)(5-sqrt10)=?? it says to simplify? thanks for your help1 solutions Answer 400293 by ewatrrr(10682)   on 2012-08-07 07:47:15 (Show Source): You can put this solution on YOUR website! ``` Hi, = F First terms 40 O Outside terms -8 I Inside terms -5 L Last terms 10 ```
 Human-and-algebraic-language/635395: Suppose you work in a lab. You need a 15% acid solution for a certain test, but your supplier only ships a 10% solution and a 30% solution. Rather than pay the hefty surcharge to have the supplier make a 15% solution, you decide to mix 10% solution with 30% solution, to make your own 15% solution. You need 10 liters of the 15% acid solution. How many liters of 10% solution and 30% solution should you use?1 solutions Answer 400289 by ewatrrr(10682)   on 2012-08-07 07:24:50 (Show Source): You can put this solution on YOUR website! ``` Hi, needing 10 liters of the 15% acid solution... How many liters of 10% solution and 30% solution should you use? Note: y = 10L - x .30x + .10(10-x) = .15·10 |May multiply thru by 100 first, if one wishes .20x = .5 x = 2.5L of the 30% and 7.5L of the 10% and... ```
 Triangles/635240: Please help me. The perimeter of a triangle is 90 cm The lengths of the sides of the triangle are in the ratios 3 : 5 : 7 Work out the length of the longest side of the triangle.1 solutions Answer 400177 by ewatrrr(10682)   on 2012-08-06 16:47:33 (Show Source): You can put this solution on YOUR website! ``` Hi, The perimeter of a triangle is 90 cm The lengths of the sides of the triangle are in the ratios 3 : 5 : 7 3k + 5k + 7k = 90cm | Letting k be the constant of the proportion 15k = 90cm k = 6cm , the longest side and... ```
 Age_Word_Problems/635227: Mary's mother is 3 times as old as Mary, 4 years ago Mary was 1/4 her mothers age. How old is Mary now? 1 solutions Answer 400174 by ewatrrr(10682)   on 2012-08-06 16:31:47 (Show Source): You can put this solution on YOUR website! ``` Hi, Mary's mother is 3 times as old as Mary's age y = 3x is mary's mother's age Question states*** 4 yrs ago... x-4 = (1/4)(y-4) x - 4 = (1/4)(3x-4) (1/4)x = 3 x = 12, Mary's age. Mother is 36. and... 4 yrs ago ```
 Polynomials-and-rational-expressions/635232: A cubic polynomial equation with real coefficients has two zeros, 5 and 6 + 2i. Which of the following is the polynomial equation? Which answer is it? a. -x^3 - 17x^2 + 100x + 200 = 0 b. x^3 + 17x^2 + 100x + 200 = 0 c. x^3 - 17x^2 + 100x - 200 = 0 d. x^3 - 17x^2 - 100x - 200 = 01 solutions Answer 400172 by ewatrrr(10682)   on 2012-08-06 16:24:38 (Show Source): You can put this solution on YOUR website! ``` Hi, A cubic polynomial equation with real coefficients has two zeros, 5 and 6 + 2i. x^3 - 17x^2 + 100x - 200 = 125 - 425 + 500-200 = 0 5 1 -17 100 -200 6 -60 200 1 -12 40 0 (x^2 - 12x + 40) ```
 Quadratic_Equations/635228: A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the equation P = -25x^2 + 450x. What number of clerks will maximize the profit?1 solutions Answer 400171 by ewatrrr(10682)   on 2012-08-06 16:04:23 (Show Source): You can put this solution on YOUR website! ``` Hi, y = ax^2 + bx + c ⇒ y = a(x -(-b/2a)^2) - a(-b/2a)^2 + c P = -25x^2 + 450x. | Note: -450/(2*-25) = 9 P= -25(x-9)^2 + 2025 9 cleks will maximize the daily profit at \$2025 ```
 Inequalities/635221: Alex has twice as much money as Jennifer. Jennifer has \$6 less than Shannon. Together they have \$54. How much money does each have?1 solutions Answer 400170 by ewatrrr(10682)   on 2012-08-06 15:57:06 (Show Source): You can put this solution on YOUR website! ``` Hi, Alex has twice as much money as Jennifer. Jennifer has \$6 less than Shannon's Shannon x Jennifer (x-6) Alex 2(x-6) Question states*** x + (x-\$6) + 2(x-\$6) = \$54 4x = \$72 x = \$18, shannon's amount. Jennifer \$12 and Alex \$24 and.. ```
 Linear-equations/635218: -2+y+5=3y+91 solutions Answer 400168 by ewatrrr(10682)   on 2012-08-06 15:50:50 (Show Source): You can put this solution on YOUR website! ``` Hi, In general, combine like terms and isolate variable on one side of the EQ -2+y+5=3y+9 y + 3 = 3y + 9 ||subtracting y and 9 from both sides of EQ -6 = 2y -3 = y ```
 Radicals/635225: what is 2 to the power -3? 1 solutions Answer 400167 by ewatrrr(10682)   on 2012-08-06 15:47:52 (Show Source): You can put this solution on YOUR website! ``` Hi, what is 2 to the power -3? | In general: ```
 Exponents/635186: simplify,write in simplest form.(12xy)^0(x^2y^4)^5 I've tried... (12xy)^0 (x^2y^4)^5 (12xy)^0 x^10y^20 12x^11y^211 solutions Answer 400166 by ewatrrr(10682)   on 2012-08-06 15:46:01 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: n^0 = 1 | you solved for (12xy)^1 ```
 Graphs/635219: Sketch the graph of the parabola. y=x(squared)+51 solutions Answer 400163 by ewatrrr(10682)   on 2012-08-06 15:41:04 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: the vertex form of a Parabola opening up(a>0) or down(a<0), where(h,k) is the vertex and x = h is the Line of Symmetry Parabola opens Upward, V(0,5) , y-axis the line of symmetry (x=0) (2,9) &(-2,9)are Pts on this parabola Always good idea to sketch any curve ```
 Triangles/635207: find the area of a triangle that has a base of 2 1/4 yards and height of 4/5 yard.1 solutions Answer 400161 by ewatrrr(10682)   on 2012-08-06 15:33:14 (Show Source): You can put this solution on YOUR website! ``` Hi, triangle that has a base of 2 1/4 yards and height of 4/5 yard. A = ```
 Quadratic_Equations/635204: An arrow is shot into the air and its path is modeled by the function h(x) = -4.9t2 + 34.3t - 49 where "h" is the height of the arrow (given in meters) at any given time t (given in seconds). Find the number of seconds necessary for the arrow to reach its maximum height. Thanks, it means a lot! :)1 solutions Answer 400160 by ewatrrr(10682)   on 2012-08-06 15:30:27 (Show Source): You can put this solution on YOUR website! ``` Hi, h(x) = -4.9t2 + 34.3t - 49 || Note: h(x)= -4.9(x-3.5)^2 + 60.025 - 49 V(3.5,11.025) Takes 3.5 sec to reach maximum height 0f 11.025m ```
 Sequences-and-series/635192: find a[20] when a[1]=9 and d=21 solutions Answer 400158 by ewatrrr(10682)   on 2012-08-06 15:23:32 (Show Source): You can put this solution on YOUR website! ``` Hi, find a[20] when a[1]=9 and d=2 Arithmetic Sequence ```
 percentage/635205: The value of a property declines every year by 5%. presently it's value is \$350,000. What will be its value 4 years from now?1 solutions Answer 400148 by ewatrrr(10682)   on 2012-08-06 14:35:39 (Show Source): You can put this solution on YOUR website! ``` Hi, The value of a property declines every year by 5%. (each year ...worth 95% of previous year's value) presently it's value is \$350,000. = \$297,271.30 ```
 Circles/635189: The circumference of a circle is 42 pi inches. What is the area of the circle to the nearest tenth of an inch? Which answer is it? a. 66.0 in.^2 b. 131.4 in.^2 c. 1185.4 in.^2 d. 1385.4 in.^21 solutions Answer 400141 by ewatrrr(10682)   on 2012-08-06 14:26:51 (Show Source): You can put this solution on YOUR website! ``` Hi, The circumference of a circle is 42 pi inches. r = 21 A = = 1385.4 in^2 ```
 Probability-and-statistics/635146: A company has three divisions and three conference rooms for meetings. To keep track of the use of their facilities, for each meeting held in the company, the division holding the meeting is recorded, the room for the meeting is recorded, and the length of time of the meeting is recorded. Which of the variables is quantitative? A. the division holding the meeting B. the conference room for the meeting C. the length of time for the meeting D. all of the above 1 solutions Answer 400124 by ewatrrr(10682)   on 2012-08-06 12:37:27 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: Quantitative variables are numerical. They represent a measurable quantity A. the division holding the meeting B. the conference room for the meeting C. the length of time for the meeting **** D. all of the above ```
 Probability-and-statistics/635149: A description of different houses on the market includes the following three variables. Which of the variables is quantitative? A. the square footage of the house B. the monthly gas bill C. the monthly electric bill D. all of the above 1 solutions Answer 400123 by ewatrrr(10682)   on 2012-08-06 12:35:40 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: Quantitative variables are numerical. They represent a measurable quantity. A. the square footage of the house B. the monthly gas bill C. the monthly electric bill D. all of the above **** ```
 Probability-and-statistics/635168: A shop offers 17 varieties of bagels, 28 flavors of cream cheese, and 24 flavors of coffee. How many different orders for a bagel, cream cheese, and a coffee can a customer place? thank you so much.1 solutions Answer 400120 by ewatrrr(10682)   on 2012-08-06 11:59:55 (Show Source): You can put this solution on YOUR website! ``` Hi, A shop offers 17 varieties of bagels, 28 flavors of cream cheese, and 24 flavors of coffee. is the number of different types of orders that can be made ```
 Probability-and-statistics/635161: A surgical technique is performed on eight patients. You are told that there is an 80% chance of success. a) Construct a binomial distribution. b) Find the mean, variance, and standard deviation of the probability distribution. c) Find the probability that the surgury is successful for exactly six patients. d) Find the probability that the surgury is successful for fewer than six patients1 solutions Answer 400119 by ewatrrr(10682)   on 2012-08-06 11:52:45 (Show Source): You can put this solution on YOUR website! ``` Hi, A surgical technique is performed on eight patients. You are told that there is an 80% chance of success. a) Construct a binomial distribution. P = nCx* p= .8 and q = .2 and n = 8 b) Find the mean = np = variance = npq = standard deviation of the probability distribution. c) P(x = 6) = = .2936 or 29.36% d) P(x < 6) = 1 - P(x = 8) - P(x = 7) - P(x = 6) = 1 - .1678 - .3355 - .2936 = .2031 or 20.31% ```