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# Recent problems solved by 'robertb'

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, >>Next

 Probability-and-statistics/367001: 1. A 99% confidence interval estimate for a population mean was computed to be (29.2, 46.6). Determine the mean of the sample, which was used to determine the interval estimate (show all work). 2. A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 170 was taken, and the mean amount spent was \$248.72. Assuming a standard deviation equal to \$48.31, find the 90% confidence interval for m, the mean for all such families (show all work).1 solutions Answer 261637 by robertb(4012)   on 2010-11-06 22:56:17 (Show Source): You can put this solution on YOUR website!1. (29.2 + 46.6)/2 = 37.9, the sample mean. 2. 248.72 +-(1.645)*(48.31)/= 248.72+-6.095, so the 90% C.I. is (242.625, 254.815).
 Equations/366877: solve for x and show all the steps: 7(x+4)-10=3x+20+4x-2 Then, show all the steps to CHECK YOUR SOLUTION! You will find something "odd" here that has to do with "infinity". What is it? What does it mean when "x" can be an "infinite" number of values? 1 solutions Answer 261630 by robertb(4012)   on 2010-11-06 22:37:49 (Show Source): You can put this solution on YOUR website!7(x+4)-10=3x+20+4x-2 7x+28-10 = 7x+18 7x + 18 = 7x+18, ultimately 0 = 0. What does this mean, my dear STUDENT? Obviously 0 = 0 is an irrefutably true statement (unless your number system is different from ours, hehe.) It means whatever real value you put in for x will always lead you to 0 = 0, which means the solution set is the set of ALL real numbers, which, you know, has infinitely many elements.
 Inequalities/366837: How do you solve for this inequality algebraically. (x+1)(x-2)(2^x) > 0 1 solutions Answer 261629 by robertb(4012)   on 2010-11-06 22:27:53 (Show Source): You can put this solution on YOUR website!. The factor for all real values of x, and so we can just eliminate it from the inequality by dividing both sides by it. Hence we're actually solving . The critical numbers are -1 and 2. Choosing test numbers x = -2, 0 and 3, we find out that the solution set is (, -1)U(2, ).
 Numeric_Fractions/366994: 9 4/5 x 7 4/10 + 5 12/15 =?1 solutions Answer 261628 by robertb(4012)   on 2010-11-06 22:22:02 (Show Source):
 Probability-and-statistics/366909: Assume that the mean score on a certain aptitude test across the nation is 100, and that the standard deviation is 20 points. Find the probability that the mean aptitude test score for a randomly selected group of 150 8th graders is 1001 solutions Answer 261625 by robertb(4012)   on 2010-11-06 22:13:17 (Show Source): You can put this solution on YOUR website!Without the help of further information we assume that scores on aptitude tests are normally distributed. Since the normal distribution is a CONTINUOUS distribution, P(X = 100) = 0. We can only talk about the CUMULATIVE DISTRIBUTION for a continuous distribution. Thus we can only talk about or , which in either case is equal to 0.50.
 Quadratic_Equations/366939: Prove if the diagonals of a paarallelogram are congruent, then the parallelogram is a rectangle.1 solutions Answer 261624 by robertb(4012)   on 2010-11-06 22:06:11 (Show Source): You can put this solution on YOUR website!The relationship between the sides of a parallelogram L,L,W,W and its diagonals A and B:. If the diagonals are congruent, then A = B, hence . Dividing both sides by 2 we get , which is a statement of the Pythagorean Theorem. By the converse of the Pythagorean Theorem the sides L, W, and A form a right triangle, hence the parallelogram is a rectangle.
 Mixture_Word_Problems/366940: A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution below: Price 10 12.50 15. Probability 0.2 0.3 0.5 How much should the lab budget for the next year's rat orders assuming this distribution does not change. Find the expected price.1 solutions Answer 261620 by robertb(4012)   on 2010-11-06 21:53:40 (Show Source): You can put this solution on YOUR website!The expected price is equal to 10*0.2 + 12.50*0.3 + 15*0.5 = 13.25, this is the expected price for the weekly shipment of rats.
 Quadratic_Equations/366982: determine what type of number the solutions are and how many solutions exist 1 solutions Answer 261619 by robertb(4012)   on 2010-11-06 21:49:19 (Show Source): You can put this solution on YOUR website!Evaluate the discriminant , hence the roots are two distinct real numbers. Also note that
 logarithm/366984: Condense the expression to the loga rithm of a single quantity. ln(x + 5) + 5 ln(x – 5) + 2 ln(x)1 solutions Answer 261615 by robertb(4012)   on 2010-11-06 21:45:05 (Show Source):
 Probability-and-statistics/366972: In San Francisco, 30% of workers take public transportation daily (USA Today, December 21,2005). a.In a sample of 8 workers, what is the probability that exactly three workers take public transportation daily (to 4 decimals)? b.In a sample of 8 workers, what is the probability that at least three workers take public transportation daily (to 4 decimals)? 1 solutions Answer 261613 by robertb(4012)   on 2010-11-06 21:36:56 (Show Source): You can put this solution on YOUR website!a. b.
 Probability-and-statistics/366980: Hello Tutors, Glad you are here to help. a sample of 4 different calculators is randomly selected from a group containging 18 that are defective. and 35 with no defects. What is the probability that at least 1 calculator is defective. I started with adding all calculators together to get a total of 53. Then I divided 1/52 since we are looking for at least 1 defect out of 4. the answer I got was .0189. Is this correct? If not, please solve and show your work. Thank you kindly 1 solutions Answer 261608 by robertb(4012)   on 2010-11-06 21:21:16 (Show Source): You can put this solution on YOUR website!. How? The event that at least 1 calculator is defective is complementary with the event that no calculator is defective. Hence P(at least 1 calculator is defective) = 1 - P(no calculator is defective). But P(no calculator is defective) = , and hence the answer above. (Note: This is an example of a hypergeometric probability distribution.)
 Linear-systems/366973: Solve this equation by the substitution method. Help {2y=x+2 {6x-12y=01 solutions Answer 261605 by robertb(4012)   on 2010-11-06 21:08:23 (Show Source): You can put this solution on YOUR website!From the top equation, x = 2y-2. Substitute this into the bottom equation:6(2y-2)-12y = 0. 12y-12-12y = 0. -12 = 0. This obviously a false statement. Thus the system has no solution set, it is inconsistent.
 Mixture_Word_Problems/366701: a store mixes kenyan coffee worth1 solutions Answer 261446 by robertb(4012)   on 2010-11-06 07:19:39 (Show Source): You can put this solution on YOUR website!Must be good coffee, :D
 Travel_Word_Problems/366787: how long does it take for a car that is going at a speed of 90 km/h to cover up a total distant of 70 kilometerts1 solutions Answer 261445 by robertb(4012)   on 2010-11-06 06:44:25 (Show Source): You can put this solution on YOUR website!70 km/90 km/hr = 7/9 hr, or around 47 minutes.
 Rational-functions/366755: Simplify x/x+y + x/x-y1 solutions Answer 261440 by robertb(4012)   on 2010-11-06 03:53:08 (Show Source):
 Exponential-and-logarithmic-functions/366764: Simplify 16^3/21 solutions Answer 261438 by robertb(4012)   on 2010-11-06 03:50:00 (Show Source):
 Exponential-and-logarithmic-functions/366765: Simplify (-64)^-2/31 solutions Answer 261437 by robertb(4012)   on 2010-11-06 03:49:17 (Show Source):
 Exponential-and-logarithmic-functions/366766: Simplify 8^1/31 solutions Answer 261436 by robertb(4012)   on 2010-11-06 03:48:01 (Show Source):
 Exponential-and-logarithmic-functions/366767: Simplify (-27)^2/31 solutions Answer 261435 by robertb(4012)   on 2010-11-06 03:47:21 (Show Source):
 Quadratic_Equations/366775: The Quotient Rule for Exponents states if m,n, and x are real number x does not equal 0, then x^m/x^n=1 solutions Answer 261433 by robertb(4012)   on 2010-11-06 03:46:26 (Show Source):
 Exponential-and-logarithmic-functions/366768: Simplify 64^4/31 solutions Answer 261432 by robertb(4012)   on 2010-11-06 03:45:21 (Show Source):
 Polynomials-and-rational-expressions/366774: what is the answer to the problem. Simplify the expression below. 9c + 5 - 3c + 21 solutions Answer 261430 by robertb(4012)   on 2010-11-06 03:44:26 (Show Source): You can put this solution on YOUR website!9c - 3c + 5 + 2 = 6c + 7
 Exponential-and-logarithmic-functions/366762: Simplify 1000^4/31 solutions Answer 261429 by robertb(4012)   on 2010-11-06 03:43:33 (Show Source):
 Trigonometry-basics/366690: A wheel is rotating at an angular velocity of 1.2pi radians/s, while a point on the circumefence of the wheel travels 9.6pi m in 10s what is the radius of the wheel1 solutions Answer 261398 by robertb(4012)   on 2010-11-05 23:35:01 (Show Source): You can put this solution on YOUR website!From the formula v = r*a, where v is the linear velocity, r = radius, and a = angular velocity, we get r = v/a. Now m/s, and rad/s. Then meters.
 Quadratic-relations-and-conic-sections/366728: Which of the following options causes this line to shift up 2 units on the axes? f(x)=-4-11 solutions Answer 261396 by robertb(4012)   on 2010-11-05 23:27:20 (Show Source): You can put this solution on YOUR website!where are the options?
 Mixture_Word_Problems/366705: at the begining of a walk roberto1 solutions Answer 261395 by robertb(4012)   on 2010-11-05 23:26:33 (Show Source): You can put this solution on YOUR website!Where's he going? :)
 Linear_Equations_And_Systems_Word_Problems/366665: Give the equation of the line in functional notation tht is perpendicular to the graph of 3X-2y=5 and contains (-4,5).1 solutions Answer 261393 by robertb(4012)   on 2010-11-05 23:20:41 (Show Source): You can put this solution on YOUR website!The equation would have the form 2x+3y = c, where c is a an unknown constant. To solve for c, let x = -4 and y = 5. Then 2*-4 + 3*5 = -8 + 15 = 7. Then the equation is 2x + 3y = 7.
 Travel_Word_Problems/366627: A plane averaged 500 mph on a trip going east, but only 350 mph on the return trip. The total flying time in both directions was 8.5 hours. What was the one way distance?1 solutions Answer 261389 by robertb(4012)   on 2010-11-05 23:16:22 (Show Source): You can put this solution on YOUR website!, d = 1750 miles, after solving the equation above.
 Money_Word_Problems/366729: The sales price of a photography book is 20 percent off the list price. If the sales price is \$10 what is the list price ? 1 solutions Answer 261385 by robertb(4012)   on 2010-11-05 23:12:43 (Show Source): You can put this solution on YOUR website!let L = list price. Then 0.80L = 10, or L = 12.50.
 Trigonometry-basics/366624: Find a numerical value of one trigonometric function of x if 2tan(x)sin(x)+2cos(x)=csc(x).1 solutions Answer 261345 by robertb(4012)   on 2010-11-05 21:26:45 (Show Source): You can put this solution on YOUR website!After some algebraic manipulation, the equation reduces to . Just use your scientific calculator to evaluate
 Probability-and-statistics/366535: What is the relationship between the Confidence Level and Type I Error?1 solutions Answer 261342 by robertb(4012)   on 2010-11-05 21:21:34 (Show Source): You can put this solution on YOUR website!Probability of Type I error = 1 - Confidence Level. For example, assigning a confidence level of 95% means you're only giving yourself 1 - 0.95 =0.05, or 5% chance of making a type I error, that is, a 5% window of making the mistake of rejecting the null hypothesis (status quo) when it is actually true.