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Probability-and-statistics/322522: question: an executive committee consisted of ten members: four women and six men. Three members were selected at random to be sent to a metting in Hawaii. A blindfolded woman drew three of the ten names from a hat. All three names drawn were's women's. What was the probability of such luck? 1 solutions Answer 230896 by solver91311(16897)   on 2010-07-14 20:19:42 (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 Here you need 3 successes in 3 trials where the probability of success is 0.4 (4 out of 10 names were women) The arithmetic is yours to do. Hint: and John

Polynomials-and-rational-expressions/322524: which numbers can not be used in place of the variable in the rational expression? 2y+1/y^2-y-6 1 solutions Answer 230893 by solver91311(16897)   on 2010-07-14 20:05:05 (Show Source): You can put this solution on YOUR website! Set the denominator polynomial equal to zero and solve the resulting quadratic equation. The zeros of the denominator polynomial are the values that must be excluded from the domain of the rational function. John

Trigonometry-basics/322528: find the quadrant containing theta if given the following conditions are true: cos theta>0 and sin theta<0 1 solutions Answer 230892 by solver91311(16897)   on 2010-07-14 20:03:38 (Show Source): You can put this solution on YOUR website! is negative in QIII and QIV. is positive in QI and QIV. John

Expressions-with-variables/322530: reduce the expression to lowest terms -2x-8 ------- x^+2x-8 1 solutions Answer 230891 by solver91311(16897)   on 2010-07-14 20:00:58 (Show Source): You can put this solution on YOUR website! Factor a out of the numerator binomial and factor the quadratic denominator. Eliminate factors common to both numerator and denominator: And that should be sufficient. However if the minus sign in the numerator is aesthetically unpleasing, multiply by John

Length-and-distance/322525: Can anyone help me with this problem? Given 2 similar figures, explain how to tell if there is a size transformation that transforms one of the figures onto the other? Would you use an algorithm to model a change for stretching? Any help would be appreciated! 1 solutions Answer 230888 by solver91311(16897)   on 2010-07-14 19:53:41 (Show Source): You can put this solution on YOUR website! It depends on what you mean by "similar." If you mean similar in the common vernacular, meaning "sorta, kinda the same," then there is no way to tell. On the other hand if you mean similar in the Euclidian Geometry sense, then the figures are similar if and only if there is a size transformation. And the algorithm would be to multiply the measurements of one by the proportion of similar parts of the two figures. John

logarithm/322486: log3 x = 4.3 1 solutions Answer 230863 by solver91311(16897)   on 2010-07-14 17:24:21 (Show Source): You can put this solution on YOUR website! Use the definition of logarithms. My calculator said it, I believe it, that settles it. John

Probability-and-statistics/322463: A card is dealt from a deck of 52 playing cards (no jokers). Assuming Ace is high, find the probability of each of the following: a. Above a queen. b. Below a seven c. Both below a queen and above a seven. d. Above a queen or below a seven. 1 solutions Answer 230862 by solver91311(16897)   on 2010-07-14 17:20:57 (Show Source): You can put this solution on YOUR website! The probability of anything is the number of ways that something could happen that you consider to be a success divided by the total number of ways that it could happen. For all parts of this question, there are 52 cards, so there are 52 ways that one card can be drawn from the deck. Hence, 52 is the denominator of the probability fraction for all four parts of this question. For part a, draw one card above a queen. You can't count queens because a queen is not above a queen, it is the same size. Since Ace is high, there are two denominations higher than queen, namely king and ace. A standard deck of cards has 4 of each denomination, so there are 4 kings and 4 aces, making a total of 8 ways to be successful where success means drawing a card above a queen. You should be able to figure the rest of them -- just count the number of cards that fit the given criteria. John

Exponential-and-logarithmic-functions/322488: Explain how to solve a logarithmic equation such as Logx = 1 1 solutions Answer 230861 by solver91311(16897)   on 2010-07-14 17:09:05 (Show Source): You can put this solution on YOUR website! Use the definition of logarithms. Since you did not specify a base, I have to presume it is base 10. Therefore: Note that John

Volume/322478: if a cylinder is 57 inches tall and holds 10 gallons how wide is it? 1 solutions Answer 230855 by solver91311(16897)   on 2010-07-14 16:51:54 (Show Source): You can put this solution on YOUR website! 10 of what sort of gallons? A US liquid gallon is 231 cubic inches. A US dry gallon is 268.8025 cubic inches. Let represent the number of cubic inches per gallon. Since the volume of the cylinder is given by the area of the base times the height, the volume divided by the height must equal the area of the base: Solve for And the diameter is then twice that: Once you figure out what number you want to use for , plug it in and do the arithmetic. John

Quadratic_Equations/322477: I am still struggling with this topic. How would I create a quadratic equation with given solutions 9 and 16? 1 solutions Answer 230854 by solver91311(16897)   on 2010-07-14 16:37:31 (Show Source): You can put this solution on YOUR website! If is a zero of a polynomial function, , then must be a factor of the polynomial. Hence, if your zeros are 9 and 16, your quadratic polynomial must be comprised of the factors , , and a real number constant . John

Linear-systems/322469: Hello there. I need help on a problem. It says Use elimination to solve each system of equations. Heres the question. x+y= 14 x-y= 20 I did this x-y=14 x+y=20 I just basically got y=6 but it says its the wrong answer and i really dont know how to get the answer. If you know can you please show me step by step so i can better understand Algebra. Iv been taking this course for 2yrs and i failed it. This is my third atempt. Thank you. 1 solutions Answer 230850 by solver91311(16897)   on 2010-07-14 16:22:07 (Show Source): You can put this solution on YOUR website! The idea of solving a linear system by elimination is to multiply one or more of the given equations by a constant or constants so that the coefficients on one of the variables are additive inverses in two of the equations. For the example problem, this first step is unnecessary because you already have the coefficients on as additive inverses, namely 1 and -1. Now you need to add the equations, term by term: , , and , hence: Now that you know the value of , substitute it back into either of the original equations: And there you have it. The solution set is the ordered pair John

Numbers_Word_Problems/322468: The sum of two consecutive odd numbers is 80. Find both numbers. 1 solutions Answer 230845 by solver91311(16897)   on 2010-07-14 15:53:33 (Show Source): You can put this solution on YOUR website! Let represent the first odd integer. Then has to be the next consecutive odd integer. Adding these two numbers gives you: Solve for John

Problems-with-consecutive-odd-even-integers/322464: 3 consecutive odd integers with the sum of 237. 1 solutions Answer 230844 by solver91311(16897)   on 2010-07-14 15:51:50 (Show Source): You can put this solution on YOUR website! Let represent the first odd integer. Then has to be the next consecutive odd integer, and has to be the third one. Adding these three numbers gives you: Solve for John

Circles/322450: What is the diameter of a cirlce that has a 3" square inside? 1 solutions Answer 230835 by solver91311(16897)   on 2010-07-14 14:54:55 (Show Source): You can put this solution on YOUR website! If the circle is circumscribed on the square, meaning that the vertices of the square all lie on the circle, then the diameter of the circle is equal to the length of the diagonal of the square. Use Pythagoras on an isosceles right triangle with legs of 3 inches. If the square is simply inside of the circle such that one or more of the square's vertices do not lie on the circle, then all you can say is that the diameter of the circle is greater than the diagonal of the square. John

Functions/322390: Imagine you are at a gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation C(g)=3.50(g) Please help don't understand!!!! What does the number 3.50 represent in this problem? 1 solutions Answer 230833 by solver91311(16897)   on 2010-07-14 14:50:55 (Show Source): You can put this solution on YOUR website! Think about this for just a minute. You go to a store to buy something. You buy some number of this one thing -- like 3 loaves of bread or 5 t-shirts or 6 gallons of gasoline. How much money did you spend? The number of things times the price for one, right? So if the total cost at the gas station is and represents the number of gallons of gas you bought, what must the 3.50 represent? John

Probability-and-statistics/322420: The student number at a University consists of 2 letters, followed by 4 digits, followed by 2 letters. How many different student numbers are possible if: a. Letters and digits cannot be repeated. b. Letters can be repeated, but digits cannot. 1 solutions Answer 230817 by solver91311(16897)   on 2010-07-14 13:32:53 (Show Source): You can put this solution on YOUR website! a. There are 26 ways to select the first letter, then 25 ways to select the 2nd letter, then 24 ways to select the 3rd letter and 23 ways to select the 4th letter. There are 10 ways to select the first digit, 9 ways to select the second digit...and so on. b. Since you can repeat letters, the calculation changes to: You get to do your own arithmetic. John

test/322416: Write the equation of the line passing through the points (-6,1) and (-4,2). 1 solutions Answer 230816 by solver91311(16897)   on 2010-07-14 13:26:43 (Show Source): You can put this solution on YOUR website! Use the two-point form of an equation of a line: where and are the coordinates of the given points. However, be aware that you cannot write the equation of a line. Since there are infinite representations of any given line, the best you can do is write an equation of a line. John

test/322419: Write the equation of the line passing through the points (0, -4) and (-2, 2). 1 solutions Answer 230815 by solver91311(16897)   on 2010-07-14 13:25:38 (Show Source): You can put this solution on YOUR website! Use the two-point form of an equation of a line: where and are the coordinates of the given points. However, be aware that you cannot write the equation of a line. Since there are infinite representations of any given line, the best you can do is write an equation of a line. John

Equations/322394: How Do I simplify the following equation: 4 - 4[5 - (3x + 2)] 1 solutions Answer 230813 by solver91311(16897)   on 2010-07-14 13:21:18 (Show Source): You can put this solution on YOUR website! What equation? Equations have equal signs in them -- that's where they get the name "equation" To simplify the expression , proceed as follows: Distribute the -1 over the inside parentheses: Combine like terms: Distribute the -4 across the remaining parentheses: Collect like terms: Done. John

Linear-systems/322404: It costs us $900 dollars a day to make 15 batches of slice pepperoni. This includes labor costs and materials. If we have 3 people working on the line making $15 an hour working an 8 hour shift. What is our bill of Materials cost for 15 batches? 1 solutions Answer 230812 by solver91311(16897)   on 2010-07-14 13:00:37 (Show Source): You can put this solution on YOUR website! John

Polynomials-and-rational-expressions/322409: What is 8 divided by x-9 + 5 divided by x + 8 divided by x-9 + 5 divided by x. The question is the length of a rectangle is 8 divided by x-9 while it width is 5 divided by x. Find the perimeter. I have tried everything and can't find the LCD, 1 solutions Answer 230811 by solver91311(16897)   on 2010-07-14 12:58:36 (Show Source): You can put this solution on YOUR website! First simplify things by multiplying each of the length and width expressions by 2 and then you only have to add two fractions. Your denominators are coprime, which is to say that they have no factors in common, therefore the LCD is simply the product of the two denominators, to wit . (It may be necessary, or simply aesthetic to multiply this out later on, but for now is a perfectly good representation of your LCD. Multiply the entire sum by 1 in the form of the LCD divided by the LCD: Which can also be expressed as: If you think that is prettier. John

Polynomials-and-rational-expressions/322408: What is 1-3/x divided by x-9/x This problem deals with simplifying complex fractions. I am in college and taking an algebra 2 class 1 solutions Answer 230804 by solver91311(16897)   on 2010-07-14 12:39:51 (Show Source): You can put this solution on YOUR website! I'm going to presume you mean: Use plenty of parentheses next time so that your meaning is clear. To divide one fraction by the other, use the same procedure they taught you in elementary school; invert and multiply: Apply the LCD of to the expression on the left: Multiply numerator times numerator and denominator times denominator: Eliminate factors common to both numerator and denominator: And that's all you can do with this one. John

Travel_Word_Problems/322396: Bird A travels 6 times faster than bird B. Together they travel @224 mph. what's the speed of each bird? I think bird B is traveling at about 37.34 mph but I dont know how to get bird A. 1 solutions Answer 230802 by solver91311(16897)   on 2010-07-14 12:37:04 (Show Source): You can put this solution on YOUR website! Let represent the speed of the slower bird. Then represents the speed of the faster bird. The sum is 224, so Which, of course is a big load of buffalo excrement because: Fastest Flying Bird "The peregrine falcon (Falco peregrinus) is the fastest living creature, reaching speeds of at least 124 mph and possibly as much as 168 mph when swooping from great heights during territorial displays or while catching pry birds in midair." http://www.victorialodging.com/recreation/birding/small-big-fast-slow Tell your instructor that if they are going to make up a "real world" problem, make up one that actually models the real world. This one was just silliness because you could have illustrated the same principle by having one bird go 3 times faster than the other and the total be 128. (The answers to this one are left as an exercise for the student -- double extra credit if you don't use paper and pencil, just do it in your head). John

Expressions-with-variables/322398: Find all the numbers for which the rational expression is undefined. Use comma to separate answers. n^3 - 7n / n^2 - 9 Thank you!! 1 solutions Answer 230800 by solver91311(16897)   on 2010-07-14 12:21:27 (Show Source): You can put this solution on YOUR website! Set the denominator polynomial equal to zero and solve the resulting quadratic equation. The zeros of the denominator polynomial are the values that must be excluded from the domain of the rational function. John

Rate-of-work-word-problems/322403: two brothers are digging a drainage ditch for a french drain around there home. the ditch is to be 2 feet deep,1 foot wide and 40 feet long. the older brother can dig the ditch in 14 hours. the younger brother can dig the ditch in 17 hours. how long will the two brothers take if they both work together take to dig the ditch? 1 solutions Answer 230799 by solver91311(16897)   on 2010-07-14 12:19:57 (Show Source): You can put this solution on YOUR website! If A can do a job in x time periods, then A can do of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do of the job in 1 time period. So, working together, they can do of the job in 1 time period. Therefore, they can do the whole job in: time periods. John

Functions/322400: find the domain of the following function for the range given below. f(x)=-4x+1 range = (0,1,2,3) 1 solutions Answer 230798 by solver91311(16897)   on 2010-07-14 12:17:48 (Show Source): You can put this solution on YOUR website! Set the function equal to each of the given range values and then solve the resulting single variable linear equation for . The set of 4 values obtained will be the desired domain. is your first domain value. Just repeat the process three more times. John

Linear-equations/322399: use the given conditions to write an equation in the point-slope form and the slope-intercept form. Slope = 8, passing through (4, –1) 1 solutions Answer 230797 by solver91311(16897)   on 2010-07-14 12:12:41 (Show Source): You can put this solution on YOUR website! The point-slope form of the equation of a line is: where are the coordinates of the given point and is the given slope. Once you have substituted the given values, solve the equation for to put the equation into slope-intercept form: John

Expressions-with-variables/322401: Solve, unless there is no solution? c^2 + 3c - 28 = 0 Thank you!! 1 solutions Answer 230796 by solver91311(16897)   on 2010-07-14 12:08:35 (Show Source): You can put this solution on YOUR website! Hint: John

Travel_Word_Problems/322397: To deliver a package, a messenger must travel at a speed of 60 miles per hour on land and then use a motorboat whose speed is 20 miles per hour in still water. The messenger goes by land to a dock and then travels on a river against a current of 4 miles per hour. He reaches his destination in 4.5 hours and then returns to the starting point in 3.5 hours. How far did the messenger travel by land and how far by water? 1 solutions Answer 230795 by solver91311(16897)   on 2010-07-14 12:06:15 (Show Source): You can put this solution on YOUR website! Everything in this problem is based on the distance equals rate times time formula. Let represent the distance traveled on land. Let represent the distance traveled on the water. Let represent the elapsed time traveling on land. We know the rate of speed on land because that is given as 60 mph. The rate of speed for the outbound trip on water is the rate in still water MINUS the rate of the current (because he was traveling AGAINST the current), so 20 mph minus 4 mph is 16 mph. Likewise, the rate of speed for the return trip on water is 24 mph. If the total outbound trip took 4.5 hours and the land part of the trip took hours, then the water part of the outbound trip must have taken hours. Similarly, the water part of the return trip must have taken hours. Let's put some of this together. We can describe the outbound trip over water by the relationship: And we can describe the return trip over water as: Having two things both equal to , we can set them equal to each other: From which we can solve for hours, the travel time on land. (Verification of this result is left as an exercise for the student). Then, knowing that , we can say that Further, says that the travel time for the outbound trip on water is , hence the distance over water for the outbound trip is miles. As a check, the distance over water for the return trip better be the same as for the outbound trip: And our answer checks. John

Inequalities/322257: A truck can be rented from Basic Rental for $50 per day. In addition, you have to pay $0.20 per mile. Continental charges $20 per day in addition to $0.50 per mile to rent out the same truck. How many miles must you drive in a day to make the rental cost for Basic Rental a better deal than that for Continental? Please show all the steps. 1 solutions Answer 230706 by solver91311(16897)   on 2010-07-13 23:58:52 (Show Source): You can put this solution on YOUR website! Solve for x. Anything larger than x is a better deal with Basic. John

Quadratic_Equations/322271: how to do punt and square? 1 solutions Answer 230703 by solver91311(16897)   on 2010-07-13 23:54:06 (Show Source): You can put this solution on YOUR website! What? John