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Trigonometry-basics/281579: a stone is thrown vertically upwards at a speed of 24 m/s. its height h meters after t seconds is given approximately by the formula h=24t-5t squared. Use this formula to find when the stone is 27 meters up, and explain the double answer. apply thr quadratic formula could someone please help? 1 solutions Answer 204556 by solver91311(16897)   on 2010-03-16 15:42:04 (Show Source): You can put this solution on YOUR website! The solution to the general quadratic equation, is the quadratic formula: For your equation, , , and , so: The discriminant, that is the portion of the formula under the radical, can readily be seen to be less than zero. That means that the roots are a conjugate pair of complex numbers: John

Finance/281581: Write the formula for the slope of the line passing through the points (x₁ ,y₁ ) and (x₂,y₂ ):____________ 1 solutions Answer 204549 by solver91311(16897)   on 2010-03-16 15:34:16 (Show Source): You can put this solution on YOUR website! John

Numbers_Word_Problems/281577: Half of the first plus twice the second of two consectutive intergers equals 22 1 solutions Answer 204547 by solver91311(16897)   on 2010-03-16 15:33:07 (Show Source): You can put this solution on YOUR website! I don't know what an "interger" is, but I can do this problem if I consider two consecutive integers. Let represent the first of two consecutive integers. Then must represent the second. Half of the first: Twice the second: So: Just solve for John

Permutations/281485: You flip a coin 10 times.What is the P(8H)?What is the P(>8H)? Please answer this question. 1 solutions Answer 204488 by solver91311(16897)   on 2010-03-16 11:49:42 (Show Source): You can put this solution on YOUR website! The probability of successes out of trials where is the probability of success on any given trial is given by: Where is the number of ways to select things out of things and is equal to . So for the first part of your question, you need to calculate: Because you want the probability of 8 heads in 10 flips where the probability of getting heads is The probability of more than successes out of trials where is the probability of success on any given trial is given by: So, you need to calculate: Use MS Excel to check your work. Pick any cell on a blank worksheet and type in: for the first part and for the second part. John

Rate-of-work-word-problems/281487: one pipe can fill a bathtub in 6 minutes and a second pipe can fill it in 12 minutes.If the tub is empty how long will it take to fill the tub if both pipes were to fill it? 1 solutions Answer 204480 by solver91311(16897)   on 2010-03-16 11:18:17 (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

real-numbers/280205: write all names that apply to each number -3.2 1 solutions Answer 203661 by solver91311(16897)   on 2010-03-12 17:38:42 (Show Source): You can put this solution on YOUR website! Hard for me to answer this because I don't know what set of names you have from which to select. But here goes anyway: It is complex, or at least the real part of a complex number with an zero imaginary part. It is real It is rational, that is it can be expressed as I suspect that last one is what you are looking for It is negative. John

Quadratic_Equations/280211: Evaluate h(x) = x2 – 4x + 5 h(4) = h(–4) = h(0) = 1 solutions Answer 203659 by solver91311(16897)   on 2010-03-12 17:29:54 (Show Source): You can put this solution on YOUR website! If Then So and Congratulations, you get to do your very own arithmetic. John

Quadratic_Equations/280216: Solve by any method (x – 3)(2x + 2) = -15 1 solutions Answer 203657 by solver91311(16897)   on 2010-03-12 17:25:43 (Show Source): You can put this solution on YOUR website! I just finished answering this one. Check for problems already solved before you post. Question Number 280190

Quadratic_Equations/280190: Solve by any method (x – 3)(2x + 2) = -15 1 solutions Answer 203653 by solver91311(16897)   on 2010-03-12 17:16:55 (Show Source): You can put this solution on YOUR website! Use FOIL to multiply the two binomials on the left: Add 15 to both sides: Check the discriminant: The roots are a conjugate pair of complex numbers. Using the rest of the quadratic formula: Graphical validity check: The graph of does not intersect the -axis so there are no real number roots. John

Miscellaneous_Word_Problems/280182: 112. Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s) = s^3 -13s^2 + 54s- 72. a) Find V(10). b) If the new width is s - 6 centimeters, then what are the new length and height? c) Find the volume when s = 10 by multiplying the length, width, and height. 1 solutions Answer 203644 by solver91311(16897)   on 2010-03-12 16:51:20 (Show Source): You can put this solution on YOUR website! The given function doesn't make any sense. If you start with a cube that measures cm on an edge, and you decrease each edge by a whole number , then each edge would measure and the volume of the reduced cube would be: In order for your given function to make sense in the stated context, then there must be a positive integer that simultaneously satisfies: Each of these equations has a different solution and none of them are integers. Therefore the given function cannot represent the situation where the measure of the edges are reduced by a whole number amount. You can determine the first part simply by substitution and a little arithmetic: The second part is trivial. If the width is some value, the length and height must be the identical value so long as the shape remains a cube. But the last part is nonsensical. Since there is no solution for the integer value of the reduction amount, you cannot compute the actual measure of the edge of the cube based on knowing the original dimension. And by the way, the problem statement is incorrectly worded because the linear dimensions of a cube are edges. Sides as related to a cube are actually faces which area is measured in square units. ************************************************************ There is another possibility that just occurred to me. If you re-word the question: Decreasing cube. Each of the three dimensions of a cube with edges of length s centimeters is decreased by a different whole number of centimeters forming a rectangular prism. The new volume in cubic centimeters is given by The answer to the first part doesn't change. The answer to the second part is significantly different. If the width is and we know that the volume is the product of width, length, and height, if we divide the volume function by the width, we will get a quotient that is an expression equal to the area of one face of the cube bounded by the length and the height. You can use polynomial long division or synthetic division, but you should get a quotient of: Which is an expression for the length times the height Factored: Hence one of those is the length and the other the height. Your choice. Now if , the three dimensions are 4, 7, and 6] And the volume is: And that should come out to the same value as the first part of the question -- given precisely performed arithmetic. John

Numeric_Fractions/280177: how do I build up fractions like 5/7 = ?/98 do not understand how to do this please explain 1 solutions Answer 203625 by solver91311(16897)   on 2010-03-12 15:57:58 (Show Source): You can put this solution on YOUR website! There are a couple of ways to look at this. First is you can consider having multiplied by 1 in the form of , like this: to obtain some number over 98. That means that must equal 98. And that means you can determine the value of by dividing 98 by 7. Once you have the value of you can multiply that by 5 to get the numerator you don't know. The other way is to look a this like a proportion: Cross-multiply: and then just solve for which is your missing numerator. John

Miscellaneous_Word_Problems/280174: Fax paper cost $17 per case and copier paper $11 per case.If an order is received for a total of 250 cases for $3,650, what is the exact number of cases of copier paper? 1 solutions Answer 203619 by solver91311(16897)   on 2010-03-12 15:49:56 (Show Source): You can put this solution on YOUR website! Let represent the number of cases of FAX paper. Let represent the number of cases of copier paper. Then: Just solve the system. Hint: Multiply the first equation by -11 then add the two equations to eliminate the -variable. John

Geometry_Word_Problems/280165: Julia Stone designed a rectangular patio that is 25 feet by 40 feet. This patio is surrounded by a terraced strip of uniform width planted with small tress and shrubs. If the area A of this terraced strip is 504 feet squared, find the width x of the strip. I drew a picture and labeled it and came up with: (2x+25)(2x+40)=504 but I must be doing something wrong because everytime I work it out and simplify, I get a negative number. 1 solutions Answer 203611 by solver91311(16897)   on 2010-03-12 15:25:55 (Show Source): You can put this solution on YOUR website! and are the outer dimensions of the ENTIRE patio PLUS the strip around the outside. 504 square feet is the area of JUST the strip. Try solving: And see if that doesn't give you a more reasonable answer. Write if you are still having difficulty. John

Proofs/277579: The outside of an unpainted 3cm by 4cm by 5cm cuboid is painted blue. It is then cut into 1cm cubes. How many of the 1cm cubes have no paint on them? Establish a rule for a cube a cm by b cm by c cm. 1 solutions Answer 203609 by solver91311(16897)   on 2010-03-12 15:18:38 (Show Source): You can put this solution on YOUR website! If you have a dimension , then one cube on each end will be painted and therefore will remain unpainted. The general rule is then: John

test/280149: x + y = 47 y + z = 62 x + z = 51 these are in one big braket together. solve it please i'm in algebra 1 working on linear combinations and substituions. 1 solutions Answer 203606 by solver91311(16897)   on 2010-03-12 14:51:18 (Show Source): You can put this solution on YOUR website! Start with the equation that shows the relationship between and . Solve it for in terms of . Add to both sides: Now, do the same thing with to get Now that we have an expression in that is equal to and another expression in that is equal to , we can substitute these expressions into the equation that shows the relationship between and , thus: Now all you need to do is solve for . Knowing , it will be a simple subtraction to calculate either or . By the way, the proper way to express your answer is an ordered triple of the form John

Angles/280150: Two angles are complementary. Their difference is 34 degrees. what are their angles? 1 solutions Answer 203604 by solver91311(16897)   on 2010-03-12 14:41:57 (Show Source): You can put this solution on YOUR website! Solve the system. John

Rectangles/280074: I have two right triangle which are exactly equal and that make a rectangle, if we know three xy coordinates of the the one triangle and all angles how can find unknown xy coordinate of the rectangle 1 solutions Answer 203603 by solver91311(16897)   on 2010-03-12 14:35:05 (Show Source): You can put this solution on YOUR website! Read everything before you start doing anything Let be the right angle vertex of the given triangle. Let and be the other two vertices of the given triangle. Finally, let be the unknown point. Use the slope formula to calculate the slope of the line containing the segment AB: Opposite sides of a rectangle are parallel. Parallel lines have equal slopes. Using the point-slope form of the equation of a line write an equation of the line parallel to AB that passes through C. Call that result Equation 1. Now repeat the entire process, this time computing the slope of the line containing AC and deriving an equation for its parallel through B. And call that Equation 2. Finally, solve the system of equations consisting of Equation 1 and Equation 2. The solution set will be . The above is the General solution If you happen to have a situation where the two legs of your given triangle are parallel to the axes, then the solution is much simpler. Take the -coordinate of the given point that is on a vertical line above (or below) the unknown point as the -coordinate of the unknown point. Take the -coordinate of the given point that is on a horizontal line to the right or left of the unknown point as the -coordinate of the unknown point. Done. John

Probability-and-statistics/280014: From a standard deck of 52playing cards a single card is drawn, recorded and then put back in the deck. Find the probability of each of the following events. P(a "face" card aka. Jack, Queen, King) P ( a "4") P(a red "15") 1 solutions Answer 203475 by solver91311(16897)   on 2010-03-12 00:18:29 (Show Source): You can put this solution on YOUR website! Basically, probability is a simple fraction: The total number of ways that something could happen in the denominator and the number of ways that are considered a success in the numerator. Sometimes it gets a little tricky to count the ways something could happen, but fortunately these three problems are pretty straightforward For all three of these problems, the denominator is the same. There are 52 cards in the deck, so there are 52 different things that could happen when you draw one card. There are 3 face cards in each of 4 suits, so there are 12 cards any one of which would be considered a successful outcome if you wanted to draw a face card. Hence, the probability is: There are 4 of any given number 2 through 10, so the probability of drawing a 4 is: There are no cards numbered 15, so the probability of drawing a 15 of either color, much less a red one is: John

Probability-and-statistics/279849: A committee of two is selected at random from a set consisting of three Democrats, four Republicans and one Independent. (a) What is the probability that the committee consists of no Republicans? (b) What is the probability that the committee consists of all Republicans? 1 solutions Answer 203397 by solver91311(16897)   on 2010-03-11 17:38:54 (Show Source): You can put this solution on YOUR website! There are 4 ways out of 8 to select other than a Republican for the first position on the committee. Once the first position has been filled and it is known that it is not a Republican, then there remain 3 ways out of 7 to select other than a Republican, hence the Probability of no Republicans is: The other part of this problem is left as an exercise for the student. Super Double Plus Extra Credit: What is the probability of exactly 1 Republican? Remember, sometimes it is easier to find the probability of anything else happening and then subtract from 1. John

Linear-equations/279804: (-3,0) 2y=x-1 don't inder stand how to do it show me how and the answere is in slope-intercept form. 1 solutions Answer 203386 by solver91311(16897)   on 2010-03-11 16:42:31 (Show Source): You can put this solution on YOUR website! JBarnum is right -- you have to tell us what you want. Put in the entire question. Having said that, I'm going to go out on a limb here and guess that you want the equation, in slope-intercept form, that is either parallel or perpendicular to the graph represented by and that passes through the point . First step is to find the slope of the given line. The easiest way to do that is to solve the equation for in terms of everything else and then examine the coefficient on Multiply both sides of the equation by : The coefficient on is , so the slope of the given line is . Now you need to determine the slope of the desired line. If you are looking for a line parallel to the given line, then parallel lines have identical slopes. In other words: That means the slope of the line you are trying to find is . On the other hand if you want a line that is perpendicular to the given line then the slope of the desired line is the negative reciprocal of the slope of the given line, thus: That would mean that the slope of the desired line is Next you need to use the point-slope form of the equation of a line: where are the coordinates of the given point and is the slope of the desired line. In this case, those values are: and either or Just substitute the values: or Finally, do the algebra required to put your equation into slope-intercept form which is or John

Finance/279801: Alicia opens her piggy bank to find only nickles and dimes inside. She counts the coins and finds that there are 38 coins totaling $3.20. How many nickles were in the piggy bank, and how many dimes where in the piggy bank? 1 solutions Answer 203383 by solver91311(16897)   on 2010-03-11 16:22:23 (Show Source): You can put this solution on YOUR website! Let represent the number of nickels. Let represent the number of dimes. Each nickel is worth 5 cents, so the value of the nickels in cents is . Likewise, the value of the dimes is cents. Finally, the total amount of money is $3.20 which is the same as 320 cents. Putting it all together you have: If you solve the first equation for in terms of you get: giving you an expression involving that is equal to and that can be substituted in place of in the other equation. Now solve for . So there are 26 dimes and therefore there must be nickels. Check: 26 dimes are worth $2.60, and 12 nickels are worth $0.60. $2.60 plus $0.60 is $3.20. Checks. Super Double Plus Extra Credit: Solve the system using either the Elimination Method or Cramer's Rule. John

Exponents/279573: Please help me solve this equation 1 solutions Answer 203225 by solver91311(16897)   on 2010-03-10 22:26:34 (Show Source): You can put this solution on YOUR website! What equation? I see a rational expression, but I don't see an equals sign anywhere. Not having an equals sign, you can't "solve" anything. The best I can do is help you simplify the expression. Remember , so: , so: Again, apply , so: Now apply: , so: Finally divide 8 into 216: John

Expressions-with-variables/279490: The sum of the digits of a two- digit number is 12. If 36 is added to the number, then the number obtained is the original with its digits interchanged. Find the original number. 1 solutions Answer 203165 by solver91311(16897)   on 2010-03-10 20:07:50 (Show Source): You can put this solution on YOUR website! Let represent the 10s digit. Let represent the 1s digit. The sum of the digits is 12 so: The value of the original number must be: Adding 36 The value of the number with the digits reversed must be: So: Which is to say: Or Add that last equation to the first equation: That means must be 12 - 4 = 8 and that makes the original number be 48. Check 48 plus 36 is 84 which is 48 with the digits reversed. John

Expressions-with-variables/279488: The Denominator of a fraction is 5 more than the numerator. If 1 is subtracted from the numerator, the resulting fraction is equal to 1/3. Find the Original fraction. 1 solutions Answer 203158 by solver91311(16897)   on 2010-03-10 19:56:37 (Show Source): You can put this solution on YOUR website! Let represent the numerator of the original fraction. Let represent the denominator of the original fraction. Subtracting 1 from the numerator and setting it equal to results in: Cross-multiply and solve: Original fraction is then: Check: John

Probability-and-statistics/278989: What is the probability of getting at least one correct answer on a 20-question test with 4 possible answers per question? 1 solutions Answer 202937 by solver91311(16897)   on 2010-03-09 19:04:53 (Show Source): You can put this solution on YOUR website! The hard way to do this is to compute the probability of getting exactly 1 right, , then the probability of getting exactly 2 right, , then 3, then 4, and so on up to 20, and finally adding all of these probabilities together. All of that being a big pain in the sit-down because each of the calculations involves the following formula: Where is the number of trials, is the number of successes, is the probability of success on an individual trial, is the probability of failure on an individual trial, and is the number of ways to choose things from a collection of things and is equal to . All of which means that you have 19 complex calculations plus a 19-term addition problem. Ah, but there truly is a better way. The opposite case of getting at least one right is getting none right. So the probability of getting at least one right plus the probability of getting none right is equal to 1. So, just calculate the probability of getting none of them right and subtract that from 1. So: Hint: Remember and Also: 0.75 "x^y" 20 = on your Windows built-in calculator in Scientific mode will give you The rest of the arithmetic is yours to do. John

Linear-equations/278990: Explain why the line y = -2 is a horizontal line. 1 solutions Answer 202921 by solver91311(16897)   on 2010-03-09 18:40:15 (Show Source): You can put this solution on YOUR website! The equation has a solution set that consist of every possible ordered pair where the -coordinate is -2. Since the value of the function is a fixed number, there is no variation in the vertical direction, either up or down -- hence it is horizontal. John

Polynomials-and-rational-expressions/278988: Height difference. A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is -16t^2 + 96t feet. The green ball is given an initial velocity of 80 feet per second, and its height t seconds after it is tossed is -16t2 + 80t feet. a) Find a polynomial D(t) that represents the difference in the heights of the two balls. b) How much higher is the red ball 2 seconds after the balls are tossed? c) In reality, when 1 solutions Answer 202918 by solver91311(16897)   on 2010-03-09 18:36:55 (Show Source): You can put this solution on YOUR website! After 2 seconds, they are: feet apart. John

Square-cubic-other-roots/278983: whats the closest cubed root to 4,000 1 solutions Answer 202914 by solver91311(16897)   on 2010-03-09 18:32:12 (Show Source): You can put this solution on YOUR website! What do you mean by the closest? Do you mean the closest integer to the cube root of 4000? John

Square-cubic-other-roots/278985: whats the closest cubed square root to 950 1 solutions Answer 202913 by solver91311(16897)   on 2010-03-09 18:30:52 (Show Source): You can put this solution on YOUR website! Do you mean to solve for where and ? Or are you asking something else entirely? John

Polygons/278950: If you have the measure of a vertex angle like 140 degrees how do you determine how many sides a regular polygon has? 1 solutions Answer 202910 by solver91311(16897)   on 2010-03-09 18:26:16 (Show Source): You can put this solution on YOUR website! The measure of an interior angle of a regular -gon is given by: So, set this expression equal to your given interior angle measure and then solve for John

Miscellaneous_Word_Problems/278955: A student gets 9 questions incorrect out of 38 questions what is the percent of right questions 1 solutions Answer 202895 by solver91311(16897)   on 2010-03-09 17:17:48 (Show Source): You can put this solution on YOUR website! Just do the arithmetic and add a % sign to your ansewer John