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 Triangles/333575: the flower garden has the shape of a right triangle. 5 ft of a perrineal border forms the hypotenuse of the triangle and one leg is 1 ft longer than the other legs, find the lengths of the legs Can you please help me thank you1 solutions Answer 239064 by jrfrunner(365)   on 2010-08-21 16:41:55 (Show Source): You can put this solution on YOUR website!When you are dealing with a right triangle and you are trying to find lenght of the sides, you will most likely end up using the pythagorean theorem which states: where c is the side opposite the right angle, and is called the hypotenuse. -- Given in your problem: c=5, a=x and b=x+1 so by the pythagorean theorem of a right triangle: --- (expanding the squared term) (combining terms) (putting the quadratic equation in standard form}}} (divide the whole thing by 2, to simplify the equation) 0=(x+4)*(x-3) (factor the expression on the right) x=-4, x=3, since we are dealing with lengths, the negative value x= -4 is extraneous and can be trown out -- so, one side is a=x=3 and the other is b=x+1=4 -- what you have is a special type of right triangle where the sides are in a ratio 3:4:5
 Travel_Word_Problems/333545: Jason and Kim were at the park. If they both left at the same time, and Jason was driving at 30 mph, and kim was driving at 40 mph in the opposite direction, how long will it be before they are 210 miles apart?1 solutions Answer 239061 by jrfrunner(365)   on 2010-08-21 16:27:35 (Show Source): You can put this solution on YOUR website!You need to understand the relationship: d=r*t (distance = rate*time) ---- Kim's distance after t hours: Jason's distance after t hours: -- They are travelling in opposite directions and you need to know the time when they are 210 miles apart, so add their distances -- 210/70 =t === t = 3 hours
 Quadratic-relations-and-conic-sections/333593: What is the vertex of the parabola y = 2(x - 1)2 - 5? 1 solutions Answer 239059 by jrfrunner(365)   on 2010-08-21 16:18:50 (Show Source): You can put this solution on YOUR website!when you have the parabola in the form you provide the vertex is straight forward, vertex =(h,k) -- So in your problem: h=1, k=-5, so the vertex = (1,-5)
 Miscellaneous_Word_Problems/333627: Bill swims at a speed of 6.7 mph in still water. The river he's in flows at a at speed of 3.6 mph. How long will it take Bill to swim 1.3 mi upstream?Round your answer to the nearest tenth of an hour, if necessary. 1 solutions Answer 239058 by jrfrunner(365)   on 2010-08-21 16:06:41 (Show Source): You can put this solution on YOUR website!Bill swims at a speed of 6.7 mph in still water. The river he's in flows at a at speed of 3.6 mph. How long will it take Bill to swim 1.3 mi upstream? --- You need to understand the relationship: d=r*t (distance = rate*time) --- Since you need to find time,rework this formula to find time (t=d/r) -- you are given the distance d = 1.3 miles The speed is the "net speed" he travels during this distance. Since he is swimming upstream, he is fighting the river flow Therefore, his net speed is his speed in still water minus the river flow -- net speed: (Bill's speed - river flow)==> r = 6.7mph - 3.6 mph = 3.1 mph -- time to swim 1.3 miles: t = d/r =1.3 miles /3.1 mph = 0.419 hours or 0.4 hour rounded to nearest tenth of an hour
 Exponents/333459: A school has a telephone system for letting parents know about emergency school closing. The system is a pyramid with five layers. Three parents are on top layer of the pyramid. Each parent in each layer calls three different parents. How many parents are in the chain? 1 solutions Answer 238971 by jrfrunner(365)   on 2010-08-20 22:52:06 (Show Source): You can put this solution on YOUR website!at layer k there are 3^k parents, where k=1 to 5 -- total = k=1 to 5 total = === note: In general total = k=1 to n total =
 logarithm/333471: solve 1n(e^3)1 solutions Answer 238970 by jrfrunner(365)   on 2010-08-20 22:40:07 (Show Source): You can put this solution on YOUR website!solve 1n(e^3) ---
 Problems-with-consecutive-odd-even-integers/333482: The product of two consecutive integers is 4 less than four times their sum. Find the integers.I had tried to solve it but it made me just get more confused with the whole question. 1 solutions Answer 238959 by jrfrunner(365)   on 2010-08-20 20:35:46 (Show Source): You can put this solution on YOUR website!A. two consecutive integers : x and x+1 B. The product of two consecutive integers x*(x+1) C. 4 less than four times their sum: 4[x+(x+1)]-4 D. x*(x+1)=4[x+(x+1)]-4 (equate the sides) E. x^2+x=4(2x+1)-4 (simplify the equation) F. x^2 +x=8x+4-4=8x (simplify the equation) G. x^2=-x+8x=7x (subtract x from both sides) H. x=7 (divide both sides by x) === check solution by substituting x=7 back in original equation -- x*(x+1)=4[x+(x+1)]-4 7*(7+1)=4*(7+(7+1))-4 7*8=4*(15)-4 56=60-4=56
 Probability-and-statistics/333313: 2. A scientist wants to compare two delicate weighing instruments by repeated weighing of the same object. The first scale is used 30 times and the weights have a standard deviation of 72 milligrams. The second scale is used 41 times and the weights have a standard deviation of 98 milligrams. At the 0.05 significance level, test the claim that the second scale produces greater variance.1 solutions Answer 238930 by jrfrunner(365)   on 2010-08-20 16:17:47 (Show Source): You can put this solution on YOUR website!To test the hypothesis of two variances use the F distribution and a test statistic F= --- Ho: Ha: at -- critical value: test statistic -- reject Ho if test statistic > critical value since test statistic = 1.853 > critical value=1.806 then reject Ho -- conclusion: at the level, the evidence suggest that
 Miscellaneous_Word_Problems/333406: Give an example of something having these distribution shapes: (a) bimodal, (b) approximately rectangular, and (c) positively skewed1 solutions Answer 238929 by jrfrunner(365)   on 2010-08-20 16:03:00 (Show Source): You can put this solution on YOUR website!(a) bimodal This is usually a mixture of two different distribution, such as heigths of people, there is the distribution for men and for women, so if we dont separate the genders, there will tend to be a bimodal effect --- (b) approximately rectangular This is the uniform distribution, where all events have equal probability of occuring. Such as tossing a die, the probability of 1 or 2, 3 etc each has 1/6 chance of occuring -- c) positively skewed Many distributions are positively skewed (have long tails to the right) examples are wealth distributons (a few people have the largest amounts of money) population by country, some countries have most of the populations country sizxe, a few countries have the biggest square aress,
 Probability-and-statistics/333394: Consider the following statements: A. The salary of an employee at the hotel is a nominal variable. B. The distance travelled by motor on a freeway is an interval variable. C. The outcome of a soccer match is an ordinal variable. D. Degree obtained at a university is a nominal variable. Which of the following statements is / are correct? 1. Only A 2. A and C 3. Only C 4. B and D 5. Only D1 solutions Answer 238928 by jrfrunner(365)   on 2010-08-20 15:52:12 (Show Source): You can put this solution on YOUR website!Nomimal means a label or category that has no order Ordinal means a ranking, rating, its not measured on a continuous scale but has order Interval means it can be measured in a continous scale --- B & D would b e the logical answers
 Permutations/333411: find the number of ways in which an arrangement of of 4 letters can be made from the word MATHEMATICS a)1680 b)756 c)18 d)24541 solutions Answer 238927 by jrfrunner(365)   on 2010-08-20 15:46:51 (Show Source): You can put this solution on YOUR website!while the word MATHEMATICS has 11 words, there are really only 8 unique words M, A and T are duplicated. --- So, your problem becomes number of arrangements of 4 letters from a word of 8 unique letters --- there are 8 choices for the first word there are then 7 choices for the second word after that there are 6 choices for the third word and finally there are 5 choices for the fourth word 8*7*6*5=1680
 Triangles/333416: if i have the measurements of a video screen that is 17.5 ft diagonally, how can i figure out the height and width of this video screen?1 solutions Answer 238925 by jrfrunner(365)   on 2010-08-20 15:40:56 (Show Source): You can put this solution on YOUR website!unless the video screen is a square, there is not enough information to figure out the length and width. You need to provide either a ratio of L to W or the angle that the diagonal makes to one of the sides.
 Miscellaneous_Word_Problems/333428: The mass of Mercury is about 3.302x10^20 metric tons. The mass of the sun is about 1.998x10^27 metric tons. About how many times the mass of Mercury is the mass of the sun? Give answer in scientific notation.1 solutions Answer 238915 by jrfrunner(365)   on 2010-08-20 15:10:35 (Show Source): You can put this solution on YOUR website!mass of Sun relative to Mercury: == (Mass of the sun) /(mass of Mercury) = or 6.021 million times
 Probability-and-statistics/333315: 35 employees who completed two years college were asked to take basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8 respectively. In a random sample of 50 employees who only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6 respectively. Estimate with 90% confidence the difference in mean scores between the two groups of employees.1 solutions Answer 238909 by jrfrunner(365)   on 2010-08-20 13:28:32 (Show Source): You can put this solution on YOUR website!Many people will make lots of assumptions to simplify a problem like this and in many cases you will get answers close enough, but you should be aware of the proper way to do things --- 1. You are dealing with a test of two independent samples, with unknown population variances. 2. You did not state the underlying distribution that these samples came from, but as long as you are analyzing averages and the samples are larger than 30, you can rely on the Central limit theorem for license to utilize Normal approximations to whatever underlying distributions you started with. --- Now just because you can rely on normal approximations does not mean you can just jump into the Z normal distribution, there is the t normal distribution. -- Since the population variances are not known, this indicates that you should use a "t" distribution. Althought, the samples sufficiently large, both the t distribution and Z distribution will merge and become indistinguishable. but...... most people believe that this happens at samples even close to 30. In fact, the two distributions do not merge close enough until the samples are in the magnitude of approximately 200 each. --- So in your case you really should stick with the t distribution. -- To do things correctly, there are two basic types of t distribution. One for when the "unknown" population variances can be assummed equal and one where the variances cannot be assumed equal. (There is a F statistic for testing this, and I carried it out and determined that the population variances can be deemed to be equal, but I am not going to cover that here) --- So the particular t test that you use is the one where you can pool the sample standard deviations (since the population variances are deemed to be equal) -- Confidence interval for population mean differences -/+ and =pooled_variance = t = critical t value with 0.05 tail probability and 50+35-2 =83 degrees of freedom = 1.663, NOTE: for 90% confidence you will have 5% at the tails -- plugging in your information = -/+ 3.0 -/+ 5.09 (-2.09, 8.09)is the 90% confidence interval for the population mean differences
 Probability-and-statistics/333376: Numbers 1,2,3,4,5,6,7,8,9 are written on seperate cards. The cards are shuffled and the top one turned over. Let A = to an even number. B = to a number greater than 6. Which one of the following statements is incorrect? 1. The sample space is S = {1,2,3,4,5,6,7,8,9} 2. P(A) = 4/9 3. P(B) = 1/3 4. P(A and B) = 1/9 5. P(A or B) = 7/91 solutions Answer 238887 by jrfrunner(365)   on 2010-08-20 10:58:34 (Show Source): You can put this solution on YOUR website!1 thru 4 are correct #5 is wrong P(A or B) =P(A) + P(B)-P(A and B) = 4/9+1/3-1/9 = 6/9 or 2/3
 Probability-and-statistics/333373: Five horses compete in a race. How many selections are there of the first two horses to past the finishing line?1 solutions Answer 238885 by jrfrunner(365)   on 2010-08-20 10:55:27 (Show Source): You can put this solution on YOUR website!this was answered already see 333044
 Permutations/333367: In how many ways can the word SUNDAY be arranged. How many arrangements begin with S and do not end with Y?1 solutions Answer 238880 by jrfrunner(365)   on 2010-08-20 10:50:53 (Show Source): You can put this solution on YOUR website!assuming there are no duplicated letters, there are n! different ways of ordering a word with n letters ---- the word SUNDAY be arranged in 6!=6*5*4*3*2=720 ways --- The are 5! ways of ordering the word SUNDAY if the first letter is rstricted to S, because only the 5 remaining ones are allowed to change. There are 4! ways of ordering the word SUNDAY if the first letter is restricted to S "and" the last letter is restricted to Y -- Therefore, there are 5!-4! ways that the word SUNDAY can be arranged such that the first letter is S and the last letter "is not" Y 5!-4! = 120-24 =96
 Probability-and-statistics/333318: After sampling from two binomial populations, we found the following: p = 0.48 n1 = 100 p2 = 0.052 n2 =100 if we estimate with 90% confidence the difference in population proportions, what would be the outome? 1 solutions Answer 238879 by jrfrunner(365)   on 2010-08-20 10:41:19 (Show Source): You can put this solution on YOUR website!you can apply the binomial method directly which can be tedious and difficult or "if" the assumptions are met, can apply a normal approximation to the binomial. -- The enable the use of the normal approximation, the following need to be met 1. and and and -- you provided p1 = 0.48 n1 = 100 p2 = 0.052 n2 =100 NOTE: not sure if your p2 is correct. Nevertheless, it looks like the requirements above are met. --- 90% confidence interval for difference in the population proportions yields Z=1.645 --- Upper confidence interval value: Lower confidence interval value: --- confidence interval = to -- you can do the math
 Probability-and-statistics/333361: when you throw a fair dice ,what is the probability of obtaining a number which is odd ?1 solutions Answer 238875 by jrfrunner(365)   on 2010-08-20 09:53:05 (Show Source): You can put this solution on YOUR website!Fundamentally, probability is straight foward --- Probability = (Number of a certain type of events)/(total number of events) The difficult part is sometimes enumarating the number in each part of that fraction. --- In your case is not bad at all to enumarate the events. probability of obtaining a number which is odd on a fair die, there are a total of 6 events {1,2,3,4,5,6} and there are 3 odd events {1,3,5} -- so P(a number which is odd)=Number of odd events/total events = 3/6=1/2