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Probability-and-statistics/325274: You are given 12 to 1 odds against tossing 3 tails in 3 tosses of a fair coin. This means that you win $12 if you succeed and you lose $1 if you fail. Find the expected value(to you) of the game. Round to the nearest cent. 1 solutions Answer 232946 by solver91311(16885)   on 2010-07-24 20:18:58 (Show Source): You can put this solution on YOUR website! The probability of successes in trials where the probability of success on any given trial is is given by: where is the number of combinations of things taken at a time and is computed using For this problem, given a fair coin, the probability of success on any given trial is , and you want 3 successes out of 3 trials, hence: You can calculate this for yourself. Hint: and anything to the zero power is 1. That gives you the probability of winning. The probability of losing is . The expected outcome is the amount you lose whenever you lose times the probability of losing plus the amount you win whenever you win times the probability of winning. John

Probability-and-statistics/325275: When two balanced dice are rolled,there are 36 possible outcomes. Find the probability that the sum is a multiple of 3 or greater than 8. 1 solutions Answer 232940 by solver91311(16885)   on 2010-07-24 19:27:17 (Show Source): You can put this solution on YOUR website! Successful outcomes are 3, 6, 9, 10, 11, 12. 2, 4, 5, 7, and 8 don't count because none of them are either multiples of 3 or greater than 8. (8 is just 8, NOT greater than 8). To make a 3 you need 1 & 2 or 2 & 1, so 2 ways. To make a 6 you need 1 & 5, 2 & 4, 3 & 3, 4 & 2, or 5 & 1, so 5 ways. You get to figure out the number of ways to make each of 9, 10, 11, and 12. Once you have determined the number of ways to make each of the allowable combinations, add them all up to make the numerator of your probability fraction. You already have the denominator, i.e. the number of possible outcomes. John

Finance/325273: Find the slope, if it exists x=-5 m= use integer or a simplfied fraction Type N if the slope is undefined. 1 solutions Answer 232939 by solver91311(16885)   on 2010-07-24 19:18:36 (Show Source): You can put this solution on YOUR website! The equation describes the set of all ordered pairs such that nobody cares what is, so long as . Therefore, and represent two elements of such a set. Given two points on a line, you can compute the slope of the line: . That is a rational expression with a zero denominator. What do you know about expressions with a zero denominator? John

Polynomials-and-rational-expressions/324714: The polynomial 0.041h-0.018a-2.69 can be used to estimate the lung capacity in liters of a female with height h in centimetersand age a in years. Find the lng capacity of a 20 year old woman who is 170 centimenters tall? I think it is 3.92 liters am I right? 1 solutions Answer 232473 by solver91311(16885)   on 2010-07-22 14:24:08 (Show Source): You can put this solution on YOUR website! Spot on. John

Probability-and-statistics/324753: A home security system is designed to be triggered in 97% of attempted burglaries. If 10 homes equipped with such a system experience an attempted burglary, find the probability that at least 9 alarms are triggered. Round your answer to four decimal places 1 solutions Answer 232471 by solver91311(16885)   on 2010-07-22 14:17:19 (Show Source): You can put this solution on YOUR website! The probability of successes in trials where is the probability of success on any given trial is given by: Where is the number of combinations of things taken at a time and is calculated by You want: Hint: The rest of the arithmetic is yours to do. John

Quadratic_Equations/324727: f(x)= -x^2 - 2x + 7 1 solutions Answer 232470 by solver91311(16885)   on 2010-07-22 14:08:23 (Show Source): You can put this solution on YOUR website! That's a handsome little quadratic function. What did you want to do with it? John

Quadratic_Equations/324734: Glenn cuts half a rectangular lawn, 40m by 30m, by mowing strips of equal width around the perimeter. Brad cuts the small rectangular left. How wide a strip does Glenn cut so that they share the work equally? I need to solve using the quadratic formula. 1 solutions Answer 232468 by solver91311(16885)   on 2010-07-22 14:04:37 (Show Source): You can put this solution on YOUR website! Since Glenn cuts a strip meters wide all the way around, each of the dimensions of the rectangle left for Brad is the original dimension reduced by . The entire lawn area is 30 times 40 meters or 1200 square meters. That means we need to choose so that Brad's piece which measures by is half of that area or 600 square meters. Expand the binomials, put the equation in standard form, and then solve the resulting quadratic for . John

Geometry_proofs/324750: given trapezoid abcd with diagonals ac and bd intercept at point e prove triangle dec is congruent to triangle bea 1 solutions Answer 232466 by solver91311(16885)   on 2010-07-22 13:59:47 (Show Source): You can put this solution on YOUR website! This can't be done in general. The two triangles described are NOT congruent in a general trapezoid. If the trapezoid is isosceles, meaning the base angles are of equal measure, then the diagonals are of equal measure and the congruence of the two described triangles follows easily. John

Travel_Word_Problems/324748: Can someone please help me work through this word problem? A flare is fired directly upward into the air from a boat that is experiencing engine problems. The height of the flare (in feet) above the water, t seconds after being fired, is given by the formula h = -16t2 + 128t + 15. If the flare is designed to explode when it reaches its highest point, at what height will this occur? Thank you, Alberto beto@san.rr.com 1 solutions Answer 232463 by solver91311(16885)   on 2010-07-22 13:53:12 (Show Source): You can put this solution on YOUR website! Note that the graph of is a parabola. It opens downward because the lead coefficient is negative, hence the vertex is a maximum. The value of the -coordinate of the vertex of a parabola which equation is in standard form is given by: for this problem: hence the maximum height is reached 4 seconds after the flare is fired. The maximum height reached is therefore . You can do your own arithmetic. John

Numbers_Word_Problems/324747: Five more than the square of a number is two more than four times the number. Find al such numbers. 1 solutions Answer 232460 by solver91311(16885)   on 2010-07-22 13:44:48 (Show Source): You can put this solution on YOUR website! Let represent the number. The square of the number is . Five more than that is . Four times the number is . Two more than that is . Finally "is" means equals, so: Just factor and solve. Remember to check both answers in the original equation. John

logarithm/324723: log5x = 2-logx5 1 solutions Answer 232448 by solver91311(16885)   on 2010-07-22 12:55:56 (Show Source): You can put this solution on YOUR website! I'm presuming you mean: And that you want to solve the equation for To the extent that is all true, please remember the following things for the next time you post. 1. The proper way to render on the standard keyboard is log_b(x). 2. Take the time to tell us what it is you want. Just putting in a problem and not saying anything else sends a very strong message, to wit: "Here chump, go do my homework for me. I've got more important things to occupy my time, like video games or hanging out at the mall." That sort of thing is not very conducive to getting someone to help you. =================================== First, convert the base of the log function in the RHS to the same base as the log function in the LHS: Use the log base conversion formula: So: But since we now have: Put everything into the LHS: Multiply both sides by Let and substitute: Factor: Hence: Substitute back: Use the definition of the log function: Hence: Which is to say: Check: Checks! John

Quadratic_Equations/324721: How do i put 2x^2+3x=(3x-1)^2-x^2 into the quadtric formula? 1 solutions Answer 232440 by solver91311(16885)   on 2010-07-22 12:22:00 (Show Source): You can put this solution on YOUR website! You can't, at least not in the form it is in. In order to use the quadratic formula, the equation must be in standard form, namely: Expand the binomial and then collect like terms. Put everything into the LHS. Then you can identify , , and and use the formula. John

Linear-systems/324718: y = x +7, y= -x +2, determine whether the lines are parallel, perpendicular, neither 1 solutions Answer 232439 by solver91311(16885)   on 2010-07-22 12:16:53 (Show Source): You can put this solution on YOUR website! Parallel lines have identical slopes, that is to say: Perpendicular lines have slopes that are negative reciprocals, that is to say: Both of your equations are in slope-intercept form, hence the slopes are the coefficients on the terms. John

test/324717: If for all x and y, 2x-b-y=0, then b=? 1 solutions Answer 232437 by solver91311(16885)   on 2010-07-22 12:07:42 (Show Source): You can put this solution on YOUR website! Add to both sides: John

Linear-equations/324711: How do I create a linear table of values? 1 solutions Answer 232435 by solver91311(16885)   on 2010-07-22 12:04:57 (Show Source): You can put this solution on YOUR website! Make two columns, one labeled and the other labeled (or whatever two variables your equation uses). Pick a value for . Write that value in the column. Substitute that value into the equation in place of and then do the arithmetic to determine the resulting value of . Write this result in the column. Repeat as often as you like, although for a linear equation, you really only need to do it twice for any given equation. That is because two points uniquely determine a line (remember geometry?) Hint: Save yourself from inconvenient (read error-prone) arithmetic. When picking values for , small integers generally work the best. If the coefficient on is a fraction, pick the denominator or an integer multiple of it as a replacement for . John

Functions/324697: I need help with two questions please. 1. Find the inverse of the one-to-one function f)x) = (x - 2)^3. 2. The function f(x) = (x + 1)/(2x - 1) is a one-to-one function. What is the range of f^1(x)? 1 solutions Answer 232430 by solver91311(16885)   on 2010-07-22 11:55:04 (Show Source): You can put this solution on YOUR website! Next time, one question per post. Why should I do two problems and only get credit for one? 1. Replace with Solve for in terms of Swap the positions of the variables and replace with Can also be expressed: Done. 2. Use the procedure above to determine that the inverse of the given function is: Zero of the denominator is . When from the left, , but when from the right, . Since the numerator and denominator polynomials are of the same degree, the rational function is asymptotic to the ratio of the lead coefficients, namely in this case. Hence, is excluded from the range. Range, in interval notation: Range, in set builder notation: John

Geometry_Word_Problems/324696: If a floor has a perimeter of 288 feet and the length is two times the width how do you find the width and length? 1 solutions Answer 232424 by solver91311(16885)   on 2010-07-22 11:20:09 (Show Source): You can put this solution on YOUR website! Let represent the width. Then represents the length. The perimeter is given by: Hence Solve for for the width, then double it to get the length. John

Matrices-and-determiminant/324567: find the determinant and inverse of the following matrices: use the Gauss Jordan Method for the inverse. 1 2 3 0 1 4 0 0 8 I got the determinant, it should be 8. i would like to know if im correct. thank you. 1 solutions Answer 232309 by solver91311(16885)   on 2010-07-21 22:57:56 (Show Source): You can put this solution on YOUR website! Yes, the Determinant is 8. Write back and I'll send you a document that shows you the Gauss-Jordan Inverse. John

Functions/324516: Find a polynomial equation with integral coefficients that has the roots: -2, 2, -3 1 solutions Answer 232293 by solver91311(16885)   on 2010-07-21 22:26:39 (Show Source): You can put this solution on YOUR website! A polynomial function has a zero if and only if is a factor of the polynomial. Hence: Just multiply it out to get your polynomial. John

Length-and-distance/324563: a store space in a shopping mall is ofter rented by the square foot. What is the area if a rectangular jewelry store that is 12 feet wide and 18 feet long? 1 solutions Answer 232289 by solver91311(16885)   on 2010-07-21 22:21:10 (Show Source): You can put this solution on YOUR website! Multiply 12 times 18 John

Functions/324531: For the following function, find the value of f(2). The x+2 is absolute value but didn't know how to represent that with keystrokes so I used the backslash key. And I did <- for less than equal to and >- for greater than equal to. f(x)= {/x+2/ if -4 <- x <1 { 4 if 1 <- x <3 {-x+5 if x >- 3 1 solutions Answer 232287 by solver91311(16885)   on 2010-07-21 22:20:20 (Show Source): You can put this solution on YOUR website! I think you mean: Since 2 is between 1 and 3, John

logarithm/324536: How do you solve log25(x-1)+log25(x+3)=1/2 1 solutions Answer 232257 by solver91311(16885)   on 2010-07-21 20:25:10 (Show Source): You can put this solution on YOUR website! First use: The sum of the logs is the log of the product, that is: Then use the definition of a logarithm: Which factors tidily. You will, as is usual with a quadratic equation, get 2 roots. However, in this case, and any time you are solving problems where you start out with functions, such as logarithms, that have restricted domains, you MUST check BOTH answers. It is possible that the original equation will have 2, 1, or 0 valid answers. Remember that the argument of the logarithm function, regardless of the base, must be strictly greater than zero. John

test/324529: You drop a penny from a 70-foot high bridge. What is the velocity of the penny when it hits the water below? Neglect the effect of air resistance and round your answer to the nearest unit. 1 solutions Answer 232255 by solver91311(16885)   on 2010-07-21 20:09:05 (Show Source): You can put this solution on YOUR website! The height of an object in vertical motion near the earth's surface at time is given by: Where is the initial velocity (assumed to be zero for this problem since the penny was dropped, not thrown) and is the initial height, 70 feet in this case. We want to know the time when We are ignoring the negative square root since it is unlikely that we will be able to make time go backwards. The instantaneous velocity of a falling object at time is given by: Clever calculus students will recognize this function as the first derivative of the height function. All that is required is to calculate the velocity at the time calculated above, recalling that : You can push buttons on a calculator as well as I can. "But wait," you say, "why is the velocity negative?" Easy, the penny is going downward. John

Quadratic_Equations/324449: What is the square root of m squared + 30m + 225 1 solutions Answer 232214 by solver91311(16885)   on 2010-07-21 15:36:15 (Show Source): You can put this solution on YOUR website! John

Volume/324451: -What is the largest possible volume of a cone that lies entirely within a cylinder of volume 30mcubed? -Ahmed is making his bed with a bed sheet measuring 250 cm by 200 cm. When he is done, he notices that exactly 5 cm of the bed sheet is tucked in under each of the four sides of the mattress. If the mattress is 20 cm thick, then what is the area of the top (the sleeping area) of the bed? 1 solutions Answer 232213 by solver91311(16885)   on 2010-07-21 15:32:51 (Show Source): You can put this solution on YOUR website! The volume of a cone is one-third the volume of a cylinder with the same base and height. Subtract from each of the dimensions of the sheet. Multiply the two remaining dimensions. John

Graphs/324450: i am to write the equation oof a line shown on a graph 1 solutions Answer 232212 by solver91311(16885)   on 2010-07-21 15:29:04 (Show Source): You can put this solution on YOUR website! Figure out two of the ordered pairs that are on the line. Then use the two-point form of an equation of a line: where and are the coordinates of the given points. John

Polynomials-and-rational-expressions/324442: i need your help on this problem by factoring this polynomial 1 solutions Answer 232211 by solver91311(16885)   on 2010-07-21 15:27:09 (Show Source): You can put this solution on YOUR website! First take out a 3: Hint: , , and John

Money_Word_Problems/324444: Suppose I agree to pay you 8 cents for every problem in this class that you solve correctly and fine you 5 cents for every problem done incorrectly. If at the end of 26 problems we do not owe each other any money, how many problems did you solve correctly? 1 solutions Answer 232210 by solver91311(16885)   on 2010-07-21 15:20:41 (Show Source): You can put this solution on YOUR website! Let represent the number of correct answers. Let represent the number of incorrect answers. The sum is 26 The value (to the student) of correct answers is . The value (to the student) of incorrect answer is . The sum is zero. Solve the system. John

Radicals/324447: Solve for the r in the equation w=Cr^-2. To is the negative power the equation is raised to. then if an object is 100 pnds at sea level. find the value of C that makes the equation true. Sea level is 3,963 miles from the center of the Earth. Use the value of C to answer a place at 282 feet below sea level. and one at 20,320 above sea level. Please show me how to find these answers. 1 solutions Answer 232208 by solver91311(16885)   on 2010-07-21 15:13:38 (Show Source): You can put this solution on YOUR website! Part a: "Solve for (something)" means to do whatever is legal to get that something all by itself on one side of the equal sign (typically the left because we read left to right) and everything else on the other side. Remember that , so the equation becomes: Multiply both sides by And divide both sides by w And finally take the square root of both sides. We only need the positive square root because we are interested in a radius which is a distance. And that's all there is to that. Part b: Here you need to solve the equation for C and then plug in the values of 100 for weight and 3963 for r at sea level. We could start over from the original equation, but let's take the easy way and go back to an intermediate result that we obtained doing part a: , which can be written: Part c: Here's where you need to be careful with your units. Death Valley is 282 FEET below sea level, but the earth's radius is given in miles. Now we could either convert 282 feet to miles, or 3963 miles to feet. The first way, the numbers are going to be a horror, but the second way, they will be sublimely ridiculous, so let's go with the lesser of two evils. (approximately, and plenty close enough) That means that the radius in Death Valley has to be So, using the original formula: So if something weighs 100 lbs at sea level, it will gain three thousanths of a pound if you take it to Death Valley. The Mt. McKinley part is done the same way, just different numbers: (close enough) So the radius becomes and I'll let you do the calculator work from here. John

Linear-equations/324446: Can some tell me if I did this right? I suppose to use the elimination method to solve two linear equations. Thanks 7x+3y=15 8x-4y=12 28x+12y=60 24x-12y=48 52x=108 13/27 1 solutions Answer 232207 by solver91311(16885)   on 2010-07-21 15:11:28 (Show Source): You can put this solution on YOUR website! Missed it by thatttttt much, he said holding his thumb and forefinger very close together. 3 times 12 is 36, not 48. Besides that, you have your fraction upside-down, 108 divided by 52 is greater than one. And so is 96 divided by 52, hence: Now substitute back: I'll let you do that arithmetic. Let me know what you discover about the value of . John

Angles/324427: The measure of the complement to a 35° angle is ? 1 solutions Answer 232205 by solver91311(16885)   on 2010-07-21 14:59:20 (Show Source): You can put this solution on YOUR website! The sum of the measure of an angle and the measure of its complement is John