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# Recent problems solved by 'richard1234'

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 Geometry_Word_Problems/608200: how many yards in a meter?1 solutions Answer 383099 by richard1234(5390)   on 2012-05-07 17:01:58 (Show Source): You can put this solution on YOUR website!1 meter is about 1.094 yards.
 Probability-and-statistics/607540: 3.Determine whether the distribution below represents a probability distribution. If not, identify the requirement that is not satisfied. X 1 2 3 4 5 p(x) 1.2 1.2 1.4 1.1 1.11 solutions Answer 383095 by richard1234(5390)   on 2012-05-07 16:44:53 (Show Source): You can put this solution on YOUR website!No; probabilities of certain events are greater than 1.
 Proofs/607887: Determine by showing work and using any method whether argument is valid The number 91 is prime just in case it is not composite. The number 91 is not both prime and divisible by 2. The number 91 is divisible by 2. Therefore the number 91 is composite. 1 solutions Answer 383094 by richard1234(5390)   on 2012-05-07 16:43:20 (Show Source): You can put this solution on YOUR website!"91 is composite" is correct but not for the right reason. 91 = 7*13, cannot be both prime and divisible by two other factors. Therefore 91 is composite.
 Exponential-and-logarithmic-functions/607865: how do you graph the logarithmic equation y= 1/3^(x-1) ?1 solutions Answer 383093 by richard1234(5390)   on 2012-05-07 16:41:53 (Show Source): You can put this solution on YOUR website!That is exponential, not logarithmic. If you know how to graph y = 3^x, this one is easy. The graph of (1/3)^x is simply an inverted y = 3^x (since 3^x = (1/3)^(-x)). Basically, reflect y = 3^x across the y-axis. However, the exponent is x-1, not x, so just shift the function one unit to the right. Final result should look something like this: http://www.wolframalpha.com/input/?i=y+%3D+%281%2F3%29%5E%28x-1%29
 Functions/608154: Given the function f(x) = 9x - 9 a. Find the rate of change between the two stated values for x: 8 to 9. b. Find the equation of a secant line containing the given points: (8,f(8)) and (9,f(9)) I could use the answer as soon as you can.1 solutions Answer 383090 by richard1234(5390)   on 2012-05-07 16:37:29 (Show Source): You can put this solution on YOUR website!a. Rate of change is 9 (slope is constant) b. f(x) = 9x - 9. If it were any other function, e.g. f(x) = x^2, we would have to find the slope between the two points, find y-intercept, etc. but here, we don't have to do that.
 Polynomials-and-rational-expressions/608182: Solve the system of equations below by graphing them with a pencil and paper. Enter your answer as an ordered pair. y = x + 5 y = -2x - 11 solutions Answer 383089 by richard1234(5390)   on 2012-05-07 16:35:53 (Show Source): You can put this solution on YOUR website!http://www.wolframalpha.com/input/?i=y+%3D+x%2B5+and+y+%3D+-2x+-+1 They intersect at (-2,3).
 Probability-and-statistics/607983: A random sample of size 2 is taken from the digits 3, 8, 10, 11 The range of each sample is calculated. What is the probability that the range is 1?1 solutions Answer 382989 by richard1234(5390)   on 2012-05-07 09:33:37 (Show Source): You can put this solution on YOUR website!Range is 1 if and only if 10 and 11 are chosen. The probability this occurs is 1/(4C2) = 1/6.
 Rectangles/607917: Determine the equation of a line through the point (3,-4) that is perpendicular to the line y=3x+7. Show work.1 solutions Answer 382954 by richard1234(5390)   on 2012-05-07 00:06:46 (Show Source): You can put this solution on YOUR website!Slope of the desired line is -1/3 Since we know the slope and a point on the line (3,-4), we can use point-slope form. y + 4 = (-1/3)(x - 3)
 Probability-and-statistics/607768: Ok this is the question as it is written, I have worked on it so long and messed it up so now Im totally confused...When 15 different second year medical students at Fletcher Allen Hospital measured the systolic blood pressure of the same person, they obtained the results listed below (in mmHg). Assuming that the population standard deviation is known to be 10mmHg, use a .05 significance level to test the claim that the mean blood pressure level is less than 140mmHg. Hypertension is defined to be a blood pressure level that is too high (140 mmHg or greater). Based on the hypothesis test results, can it be safely concluded that the person does not have hypertension? 142 133 139 143 125 128 130 134 133 148 146 144 133 150 142 1 solutions Answer 382952 by richard1234(5390)   on 2012-05-07 00:04:06 (Show Source): You can put this solution on YOUR website!Use a one-sample z-test with We know that , and . Input the data values into your calculator (carefully) and run a z-test.
 Matrices-and-determiminant/607697: Evaluate the determinant: Please show me the steps. {{8,1,3},{2,-1,4},{1,-1,2}}1 solutions Answer 382951 by richard1234(5390)   on 2012-05-06 23:58:41 (Show Source): You can put this solution on YOUR website!Look up the following website: http://en.wikipedia.org/wiki/Determinant Basically the determinant is 8*det(A) - 1*det(B) + 3*det(C) where A,B,C are the matrices determined by truncating every entry in the same column or row as 8, 1, 3. In other words, A = {{-1,4}{-1,2}} B = {{2,-4}{1,2}} C = {{2,-1}{1,-1}} Finding the determinant of a 2x2 matrix should be easy.
 Probability-and-statistics/607534: what is the probability of rolling a single die four times and rolling exactly two fives?1 solutions Answer 382950 by richard1234(5390)   on 2012-05-06 23:54:12 (Show Source): You can put this solution on YOUR website!This is a binomial distribution. The probability of rolling exactly two 5's is
 Geometry_proofs/607766: 47. In quadrilateral PQRS, ∠P ≅ ∠Q ≅ ∠R ≅ ∠S. What type of quadrilateral is PQRS? trapezoid parallelogram rectangle rhombus 1 solutions Answer 382949 by richard1234(5390)   on 2012-05-06 23:49:16 (Show Source): You can put this solution on YOUR website!Rectangle, since P ≅ ∠Q ≅ ∠R ≅ ∠S = 90 degrees.
 logarithm/606592: Hello iam currently taking a college algebra class and my professor gave me this bonus problem y=log9(log 8(log 7(log 6(log 5(x)))))) and find the domain of dy/dx. i have no idea where or how to begin this problem any help is appreciated.1 solutions Answer 382697 by richard1234(5390)   on 2012-05-05 20:30:18 (Show Source): You can put this solution on YOUR website! First, we should find where x is defined. Note that the domain of any log function is always the positive real numbers (unless we are dealing with complex logarithms -- which we are not). Hence, (see the pattern?) Therefore any value of x such that is in the domain. Since log x is a differentiable function, log(log(x)) is differentiable, and so on. The domain of dy/dx is the same as the domain of y.
 Linear_Algebra/606873: < does this mean you shade above or under the line ? And what does this one mean too ? >1 solutions Answer 382694 by richard1234(5390)   on 2012-05-05 20:19:36 (Show Source): You can put this solution on YOUR website!< is "less than," > is "greater than" So if you have an inequality y < 4x, you would graph y = 4x and shade everything under the line y = 4x. Vice versa for y > 4x.
 Exponential-and-logarithmic-functions/607259: Solve the equation for x. ROUND your answer to TWO DECIMAL places, and do not include "x=" in your answer 3*ln x=151 solutions Answer 382693 by richard1234(5390)   on 2012-05-05 20:17:21 (Show Source): You can put this solution on YOUR website!ln x = 5 x = e^5 = 148.41 Why am I not supposed to include "x = ?"
 Linear-equations/607343: 1.If f(x) = 4x2 - 3x + 2, evaluate f(-1). 2.State the domain of the function f(x) = (x+3)/(x-1). 3.Write the equation of the line that passes through the points (1, 1) and (2, Write your answer in slope-intercept form. 4.Write the equation of the line with a slope of 2/3 and y-intercept of 1. Write your answer in slope-intercept form. 5.Solve the equation: (4x+1)(2x-7) =0. 6.If f(x) = 4x + 3, evaluate f(x+h). 7.If g(x) = x², evaluate g(x+h). 8.If f(x) = -x + 1, evaluate f(x+h). 9.If f(x) = -x + 1, evaluate f(x-h). 10.Use the quadratic formula to solve the equation: x² - x - 1 = 0. 1 solutions Answer 382692 by richard1234(5390)   on 2012-05-05 20:15:57 (Show Source): You can put this solution on YOUR website!1, 6, 7, 8, 9: Substitute the given expression into the function, simplify. 2: The domain is all real numbers except those where the function is undefined. 3. Incomplete. 4. y = mx + b where m is the slope and b is the y-intercept. 5. zero-property rule. 10. Use quadratic formula, substitute in numbers. Like the other tutor said, no one's going to do all ten problems for you. The instructions for posting say, one problem per post, limit five posts per day.
 Trigonometry-basics/607319: Verify that sec theta/sin theta * cot theta/csc theta = csc theta is an identity, help? I got csc theta as my answer, but I'm not sure how to prove that it is an identity.1 solutions Answer 382610 by richard1234(5390)   on 2012-05-05 12:00:05 (Show Source): You can put this solution on YOUR website!That means it's an identity. It works for all values of theta given that both sides of the equation are defined.
 Permutations/606545: At a local college, of the male students are smokers and are non-smokers. Of the female students, are smokers and are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are non-smokers? Do not round your answer. Thanks for your help!!1 solutions Answer 382517 by richard1234(5390)   on 2012-05-04 19:57:50 (Show Source): You can put this solution on YOUR website!You didn't provide any numbers...
 Trigonometry-basics/607009: which of the following statements is true about the graph y= cosӨ1 solutions Answer 382342 by richard1234(5390)   on 2012-05-04 00:42:41 (Show Source): You can put this solution on YOUR website!What are "the following statements?"
 Proportions/607042: 3 1/3 divided by 1 5/91 solutions Answer 382341 by richard1234(5390)   on 2012-05-04 00:41:18 (Show Source): You can put this solution on YOUR website!Convert to improper fraction, i.e. 10/3 divided by 14/9. To divide, we invert the divisor (14/9) and multiply. (10/3)(9/14) = 90/42 = 15/7.
 Trigonometry-basics/607037: Can someone please help me with this problem? Even after using the equation correctly, the results aren't right. If sin(x)=(7/8), x in quadrant I, then find (without finding x) sin(2x)= cos(2x)= tan(2x)= Thank you!1 solutions Answer 382340 by richard1234(5390)   on 2012-05-04 00:40:15 (Show Source): You can put this solution on YOUR website!Use the double-angle formulas. Here you need to find cos x. Since sin x = 7/8 and then (note that cos x > 0) Plug everything in to obtain Finding cos x is fairly simple. Use the identity and replace sin x with 7/8. Finding tan x is even simpler. Since tan x = (sin x)/(cos x), use the results you found in the previous two parts to find tan x.
 Linear_Equations_And_Systems_Word_Problems/607034: Find the rule of the linear function f that gives the number of hours in x days. 1 solutions Answer 382339 by richard1234(5390)   on 2012-05-04 00:27:24 (Show Source): You can put this solution on YOUR website!24 hours in 1 day f(x) = 24x
 Probability-and-statistics/606772: four cards are selected, one at a time from a standard deck of 52 cards. Let x represent the number of aces drawn in a set of 4 cards. a) if this experiment is completed without replacement, explain why x is not a binomial random variable. b) if this experiment is completed with replacement explain why x is a binomal random variable1 solutions Answer 382286 by richard1234(5390)   on 2012-05-03 18:07:19 (Show Source): You can put this solution on YOUR website!By definition, a binomial random variable includes independent trials. Since keeping the card alters the probability of drawing an ace in future trials, the experiment in a) is not a binomial variable.
 Functions/606718: how to show X^2+4x+5 is not one -one?1 solutions Answer 382282 by richard1234(5390)   on 2012-05-03 17:48:14 (Show Source): You can put this solution on YOUR website!If it were one-to-one, every x would map to exactly one output (or y-value) and vice versa. Since x = 0 and x = 4 yield the same value, 5, the function f(x) = x^2 + 4x + 5 is not one-to-one. You can also show it by graphing the function.
 Rectangles/606865: A rectangle's length is seven centimeters more than its width. The rectangle's area is 78 square centimeters. What is its length? 1 solutions Answer 382280 by richard1234(5390)   on 2012-05-03 17:45:16 (Show Source): You can put this solution on YOUR website!For some of these area problems it helps to try factoring 78 before doing anything else. Since 78 = 6*13, and 13 = 6+7, we know right away this works. Therefore the length is 13 cm. Or you can let L be the length, then L-7 is the width (since the length is 7 cm longer). Then L(L-7) = 78. Solve for L.
 Numbers_Word_Problems/606856: I am a 4 digit number greater than 9,000. My hundreds digit is twice my ones digit. My ones digit is greater than my tens digit. The sum of my digits is 20. What number am I?1 solutions Answer 382279 by richard1234(5390)   on 2012-05-03 17:41:38 (Show Source): You can put this solution on YOUR website!Suppose the number is 9abc We know that a = 2c, c > b. Also, 9+a+b+c = 20, so a+b+c = 11. We can assume c = 0, c = 1, c = 2, etc. and find all the possible triples (a,b,c): c = 0 --> a = 0, b = 11 c = 1 --> a = 2, b = 8 c = 2 --> a = 4, b = 5 c = 3 --> a = 6, b = 2 The first three cases don't work, because b > 9, or b is greater than c. The third case does work, so (a,b,c) = (6,2,3) and the number is 9623.
 Probability-and-statistics/606543: A student in your algebra class is selected at random. One of the remaining students is selected at random. Is it dependent or independent?1 solutions Answer 382115 by richard1234(5390)   on 2012-05-03 00:52:18 (Show Source): You can put this solution on YOUR website!Dependent, the first selection influences the second selection.
 Polynomials-and-rational-expressions/606587: classify the expresion as monmial,binomial,trinomial,or not a polynomial -3a2b4c1 solutions Answer 382114 by richard1234(5390)   on 2012-05-03 00:50:26 (Show Source): You can put this solution on YOUR website! is a monomial.
 Numbers_Word_Problems/606481: 1 rectangular swimming pool has an area of 24 sq. yds. Another rectangular swimming pool has an area of 90 sq. yds. What is the largest possible integer dimension common to both pools? 1 solutions Answer 382097 by richard1234(5390)   on 2012-05-02 21:41:17 (Show Source): You can put this solution on YOUR website!GCF(24,90) = 6, so the answer is 6 yd. To check, note that 24 = 6*4 and 90 = 6*15. 4 and 15 do not have any common factors.
 Numeric_Fractions/606530: How to solve 500 as a fraction with algebra?1 solutions Answer 382095 by richard1234(5390)   on 2012-05-02 21:39:39 (Show Source): You can put this solution on YOUR website!What do you mean "solve 500 as a fraction with algebra?"
 Probability-and-statistics/606332: Find the probability of getting a prime number in the case that a number is chosen randomly from the set {1,2,3,4,...12} So my thoughts were the prime numbers are 1,2,3,5,7,11 and there are 12 possibilities so the answer should be 1/2. But the answer given to me is 5/12. What am I missing? 1 solutions Answer 382068 by richard1234(5390)   on 2012-05-02 19:19:08 (Show Source): You can put this solution on YOUR website!1 is not a prime number. If it were prime, then any "prime number" such as 3 could be expressed as the product of two or more primes (3*1, 3*1*1, etc.) and therefore wouldn't be prime. Therefore the probability is 5/12.